Università degli Studi di Cassino e del Lazio Meridional ... · EN 50160:2010-07 Caratteristiche della tensione fornita dalle reti pubbliche di distribuzione ... prescrizioni nelle

1

Universitagrave degli Studi di Cassino

e del Lazio Meridional

Facoltagrave di Ingegneria

Associazione Nazionale

Gruppo Misure

Elettriche ed Elettroniche

Lezioni del Corso di

Misure Elettriche

AA 2012-2013

GG MM EE EE

Corso di Laurea Magistrale in Ingegneria Elettrica

Le Misure di Power Quality

2

La qualitagrave del servizio elettrico prende in considerazione

bull la continuitagrave dellrsquoalimentazione intesa come assenza di interruzioni

nella fornitura di energia elettrica

bull la qualitagrave della tensione intesa come qualitagrave della forma drsquoonda

(ampiezza frequenza variazioni ecc)

Esistono numerosi fattori che influiscono sulla qualitagrave dellrsquoenergia

elettrica ed in particolare

bull dipendenti dal Distributore (gestione ed esercizio della rete

manutenzione hellip)

bull dipendenti dal Cliente (guasti presso impianto del Cliente disturbi

emessi sulla rete hellip)

bull indipendenti (fattori ambientali eventi atmosferici danni prodotti da

Terzi hellip)

Universitagrave degli Studi di Cassino e del Lazio Meridionale

La Qualitagrave dellrsquoEnergia Elettrica (Power Quality ndash PQ)

3

Contesto Compatibilitagrave Elettromagnetica

Disturbi radiati Disturbi condotti

Disturbo elettromagnetico fenomeno elettromagnetico che puograve degradare la prestazione

di un dispositivo di unrsquoapparecchiatura o di un sistema



4

CIRCUITI NON LINEARI

Equivalent circuit of a non-linear load

Ih

Vh



5

Power quality

problems

Turn off the mixer love

the monitorrsquos flickering

again

are

usually of

terrestrial

origin



6



Dobbiamo separare gli eventi di power quality dagli altri

problemi

bullSe avete delle apparecchiature sensibili

bullDisservizi inaspettati e intermittentihellip

bullQualrsquoegrave la causa dei disservizi o guasti

Software bug Cattive connessioni

Errori delloperatore Temperatura

Screpolature nei materiali Umiditagrave

Bolle nellacqua di raffreddamento

ecc ecc

ndashOppure egrave un disturbo power quality

7

Universitagrave degli Studi di Cassino Corso di Fondamenti di Misure


Tensione costante e pari alla nominale

Frequenza costante e pari alla nominale

Tensioni e correnti sinusoidali

Continuitagrave del servizio

Le condizioni ideali

I ldquodisturbirdquo rappresentano lo scostamento

dei parametri elettrici dai valori ideali e la

non continuitagrave del servizio

La valutazione complessiva di questi

aspetti egrave denominata Power Quality

8

The good

old days bull

bull Ideal

three-phase

system

voltage

Three balanced

ohmic-inductive

single-phase loads

on the three phase

mains

-150A

-100A

-50A

0A

50A

100A

150A

0ms 5ms 10ms 15ms 20ms

t

i

i1 (L1)

i1 (L2)

i1 (L3)

-350V

-250V

-150V

-50V

50V

150V

250V

350V


t

u u1 (L1)

u1 (L2)

u1 (L3 )



9

Distorsione armonica

Interruzioni del servizio

Abbassamenti di tensione e sovratensioni

Buchi di tensione

Transitori

Frequenza nominale della tensione fornita

Flicker - variazioni rapide della tensione

Squilibrio delle tensioni



10

IEC 61000-2-22002 Electromagnetic compatibility (EMC) ndash Part 2-2 Environment ndash

Compatibility levels for low-frequency conducted disturbances and signalling in public

lowvoltage power supply systems


Compatibility levels in industrial plants for low-frequency conducted disturbances

IEC 61000-3-8 Electromagnetic compatibility (EMC) ndash Part 3 Limits ndash Section 8 Signalling

on low-voltage electrical installations ndash Emission levels frequency bands and electromagnetic

disturbance levels

IEC 61000-4-42004 Electromagnetic compatibility (EMC) ndash Part 4-4 Testing and

measurement techniques ndash Electrical fast transientburst immunity test


measurement techniques ndash General guide on harmonics and interharmonics measurements

and instrumentation for power supply systems and equipment connected thereto


measurement techniques ndash Power quality measurement methods

IEC 61000-4-15 Electromagnetic compatibility (EMC) ndash Part 4 Testing and measurement

techniques ndash Section 15 Flickermeter ndash Functional and design specifications

IEC 61180 (all parts) High-voltage test techniques for low voltage equipment

Normativa di riferimento



11

IEC 61000 - 4 ndash 30 Norm

Seri 61000 Electromagnetic Compatibility

International Electrotechnical Commission

Part 4 Test and Measurement Tecniques

Section 30 PQ measurement methods


Section 7 General guide on harmonics

and interharmonics measurements and

instrumentation for power supply

systems and equipment connected

thereto

Part 2 Environment ndashCompatibility levels


IEC International Electrotechnical Commission

Section xx details on the application sector

Part 3 Limits




12

EN 501602010-07 Caratteristiche della tensione fornita dalle reti pubbliche di distribuzione

dellrsquoenergia elettrica

Descrive e specifica le caratteristiche principali della tensione ai terminali di

alimentazione di un utente della rete pubblica in bassa media e alta tensione in corrente

alternata in normali condizioni di esercizio Essa descrive i limiti o valori entro i quali le

caratteristiche della tensione possono essere attesi ai punti di alimentazione da reti elettriche

pubbliche europee e non descrive la situazione media sperimentata da un singolo utente di rete

Le caratteristiche della tensione fornite nella presente Norma non sono utilizzabili ai fini dei

limiti di EMC o di disturbi condotti nella rete pubblica Esse non sono utilizzabili ai fini di

prescrizioni nelle norme di prodotto o nelle norme per impianti




13

Nel dettaglio la norma EN 50160 definisce i seguenti parametri

1 Frequenza nominale della tensione fornita

2 Ampiezza della tensione di alimentazione

3 Variazioni della tensione di alimentazione

4 Flicker - variazioni rapide della tensione

5 Buchi di tensione

6 Interruzioni della tensione di alimentazione

7 Squilibrio della tensione di alimentazione

8 Tensioni armoniche THD e fino al 25deg ordine



14

Si specifica che qualora lrsquoazienda distributrice installi un registratore

della qualitagrave delle caratteristiche della tensione diverse dalle

interruzioni senza preavviso lunghe brevi e transitorie lo strumento

deve essere conforme alla norma tecnica EN 61000-4-30

Richiami nella delibera 042004

dellAUTORITA PER LENERGIA ELETTRICA E IL GAS

Il 30 gennaio 2004 con delibera 404 lrsquoautoritagrave dellrsquoenergia ha indicato tra i vari

argomenti trattati i criteri di misura delle qualitagrave della tensione

Nellrsquoarticolo 39 (pagina 29) viene indicato nel punto 391 e 2 che per la

registrazione di interruzioni senza preavviso lunghe brevi e transitorie occorre

utilizzare un registratore conforme alla CEI EN 50160 In questo caso lo strumento

registratore dice quando e per quanto si ha unrsquointerruzione del servizio ma a tutti gli

effetti NON EFFETTUA UNrsquoOSSERVAZIONE QUALITATIVA dei parametri



15



16

17



CURVA DI TOLLERANZA AI DISTURBI

18

Caratteristiche dellrsquoalimentazione a bassa tensione



19


Frequenza nominale

La frequenza nominale della tensione fornita deve essere di 50 Hz In condizioni normali

di esercizio il valore medio misurato nellrsquointervallo di 10 secondi deve essere

Per i sistemi con collegamento sincrono ad un sistema interconnesso

1 50 Hz plusmn 1 durante il 95 di un anno

2 50 Hz +4 - 6 durante il 100 di un anno

Per i sistemi senza collegamento sincrono ad un sistema interconnesso





20




21




22

Variazioni della tensione di alimentazione (variazioni lente)

Le variazioni lente sono deviazioni ldquomedierdquo dal valore nominale dellrsquoampiezza della

tensione di consegna entro una fascia predefinita (per esempio del plusmn10) rispetto alla

tensione dichiarata

CAUSE variazione lenta dei carichi e dalla corrispondente azione di regolazione effettuata dai

variatori sotto carico dei trasformatori



23

Variazioni della tensione di alimentazione (variazioni rapide)

Le variazioni rapide sono abbassamenti (o aumenti) bruschi di qualche percento della

tensione preesistente generalmente seguiti se abbassamenti da un ritorno (a rampa o di

altra forma) ad un valore intermedio tra quello preesistente e tra il minimo raggiunto

CAUSE commutazione dei carichi (partenza motori in particolare) funzionamento di carichi

con ciclo operativo particolarmente variabile e in qualche caso da manovre in rete (linee

trasformatori condensatori ecc)



24

Flicker Il flicker egrave originato dalla fluttuazione della tensione Si definisce fluttuazione di tensione una

serie di variazioni rapide (uguali o diverse) della tensione

Fluttuazioni di tensione che presentano frequenze di modulazione del 50 Hz comprese tra 05 e

40 Hz danno origine al fenomeno del flicker (sfarfallio) ovvero della sensazione visiva

provocata dalle fluttuazioni dellrsquointensitagrave di illuminazione delle lampade

I suoi principali effetti sullrsquouomo possono essere mal di testa irritabilitagrave e fastidio agli occhi



25



26




27



28



29



30



31



32

Buchi di tensione Riduzione temporanea della tensione in un punto della rete elettrica sotto una determinata

soglia Se durante un buco la tensione scende sotto una soglia di interruzione lrsquoevento egrave

considerato essere sia un buco che unrsquointerruzione

CAUSE I buchi di tensione sono generalmente dovuti a guasti che sopravvengono negli

impianti utilizzatori o nel sistema di distribuzione pubblico Possono dipendere anche variazioni

di carico lungo la linea



33

Interruzioni della tensione di alimentazione Condizione in cui la tensione ad un terminale della rete egrave inferiore allrsquo1 della tensione

nominale per una durata fino a tre minuti (brevi) o maggiori di 3 minuti (lunghe)



34

Sovratensioni temporanee alla frequenza di rete fra fasi e terra Le sovratensioni sono sopraelevazioni della tensione conseguenti a modificazioni dello

stato elettrico della rete elettrica



35

Armoniche Le armoniche sono tensioni o correnti sinusoidali con frequenza pari ad un multiplo intero

(ordine) della frequenza fondamentale di funzionamento del sistema elettrico la cui

presenza determina una distorsione della forma drsquoonda della tensione di alimentazione

CAUSE In piccola parte dal sistema stesso (trasformatori etc) e per la maggior parte da

apparecchi utilizzatori carichi commutati elettronicamente raddrizzatori convertitori regolatori

in AC cicloconvertitori ecc carichi con caratteristiche non lineari apparecchiature a

saturazione magnetica lampade a scarica forni ad arco saldatrici ad arco trasformatori ecc

bull carichi inseriti e disinseriti da organi di manovra condensatori filtri e motori a induzione



36

Armoniche di tensione e corrente ndash Problemi

Vi sono diversi ambiti causati dalle armoniche

bull problemi causati da armoniche di corrente

1048707 sovraccarico del neutro

1048707 aumento delle perdite nei trasformatori

1048707 interventi intempestivi degli interruttori automatici

1048707 aumento dellrsquoeffetto pelle

bull problemi causati da armoniche di tensione

1048707 deformazione della tensione

1048707 disturbi nella coppia dei motori ad induzione

1048707 rumore al passaggio per lo zero

bull problemi causati quando le armoniche di corrente raggiungono lrsquoalimentazione



37

38



39

Strumentazione ldquohand heldrdquo con display



40




41

Strumentazione da registrazione



42

Schema di principio ndash 61000-4-30 copy IEC2008

The electrical quantity to be measured may be either directly accessible as is

generally the case in low-voltage systems or accessible via measurement

transducers

An instrument may include the whole measurement chain In this standard the

normative part does not consider the measurement transducers external to the

instrument and their associated uncertainty



43



Classi dei metodi di misura - 61000-4-30 copy IEC2008

For each class measurement methods and appropriate performance requirements

are included

Sono definite tre classi A S e B

Class A

This class is used where precise measurements are necessary for example for contractual

applications that may require resolving disputes verifying compliance with standards etc

Any measurements of a parameter carried out with two different instruments complying with

the requirements of Class A when measuring the same signals will produce matching results

within the specified uncertainty for that parameter

Class S

This class is used for statistical applications such as surveys or power quality assessment

possibly with a limited subset of parameters Although it uses equivalent intervals of

measurement as class A the class S processing requirements are lower

Class B

This class is defined in order to avoid making many existing instruments designs obsolete

NOTE Class B methods are not recommended for new designs Readers are advised that Class B may be removed in a

future Edition of this standard

44


Measurement aggregation over time intervals

CLASS A

The basic measurement time interval for parameter magnitudes (supply voltage harmonics

interharmonics and unbalance) shall be a 10-cycle time interval for a 50 Hz power system

or 12-cycle time interval for a 60 Hz power system

The 1012-cycle measurement shall be re-synchronized at every RTC 10 min tick

The 1012-cycle values are then aggregated over 3 additional intervals

ndash 150180-cycle interval (150 cycles for 50 Hz nominal or 180 cycles for 60 Hz nominal)

ndash 10 min interval

ndash 2 h interval

CLASS S

Same time intervals as Class A

CLASS B

The manufacturer shall specify the number and duration of aggregation time intervals



45



46



Class A

The 10-min aggregated value shall be tagged with the absolute time (for

example 01H1000) The time tag is the time at the conclusion of the 10-min

aggregation

The data for the 10-min time interval shall be aggregated from 1012-cycle time

intervals

Each 10-minute interval shall begin on a UTC 10-min tick The 10-min tick is

also used to re-synchronize the 1012-cycle intervals and the 150180-cycle

intervals

The final 1012-cycle interval(s) in a 10-min aggregation period will typically

overlap in time with the UTC 10-min clock tick Any overlapping 1012-cycle

interval (Overlap 1 in Figure 2) is included in the aggregation of the previous

10-min interval

47



48



49


Real time clock (RTC) uncertainty

Sono definite le specifiche per le 3 classi

Flagging concept

During a dip swell or interruption the measurement algorithm for other

parameters (for example frequency measurement) might produce an unreliable

value The flagging concept therefore avoids counting a single event more than

once in different parameters (for example counting a single dip as both a dip and a

frequency variation) and indicates that an aggregated value might be unreliable



50


Power quality parameters - INDICES

Per ogni parametro viene suggerito il metodo di misura per le tre classi e

(soprattutto) le caratteristiche di precisione Per alcuni parametri rimanda a

specifiche norme (ad esempio Flicker e Armonicheinterarmoniche)

Esempio - Power frequency Class A

The frequency reading shall be obtained every 10 s As power frequency may not be exactly 50 Hz or 60

Hz within the 10 s time clock interval the number of cycles may not be an integer number The

fundamental frequency output is the ratio of the number of integral cycles counted during the 10 s time

clock interval divided by the cumulative duration of the integer cycles Before each assessment

harmonics and interharmonics shall be attenuated to minimize the effects of multiple zero crossings

The measurement time intervals shall be non-overlapping Individual cycles that overlap the 10 s time

clock are discarded Each 10 s interval shall begin on an absolute 10 s time clock with uncertainty as

defined in 46

Other techniques that provide equivalent results such as convolution are acceptable

Class S Same as class A

Class B The manufacturer shall specify the process used for frequency measurement



51






Esempio - Power frequency

Measurement uncertainty and measuring range

ndash Class A

Under the conditions described in 61 the measurement uncertainty shall not exceed

plusmn10 mHz over the measuring ranges 425 Hz ~ 575 Hz 51 Hz ~ 69 Hz

ndash Class S



ndash Class B

The manufacturer shall specify the uncertainty over the measuring ranges 425 Hz ~

575 Hz 51 Hz ~ 69 Hz



52

Magnitude of the supply voltage

Measurement method

ndash Class A

The measurement shall be the rms value of the voltage magnitude over

a 10-cycle time interval for 50 Hz power system or 12-cycle time

interval for 60 Hz power system Every 1012-cycle interval shall be

contiguous and not overlapping with adjacent 1012-cycle intervals

except as shown as Overlap 1 in Figure 2

NOTE 1 This specific measurement method is used for quasi-stationary signals and is

not used for the detection and measurement of disturbances dips swells voltage

interruptions and transients

NOTE 2 The rms value includes by definition harmonics interharmonics mains

signalling etc

- Class S same as Class A



53



ndash Class A

Under the conditions described in Clause 6 the measurement uncertainty

shall not exceed plusmn01 of Udin over the range of 10 ~ 150 of Udin

ndash Class S





54

Supply voltage dips and swells

Measurement method

ndash Class A

The basic measurement Urms of a voltage dip and swell shall be the

Urms(frac12) on each measurement channel (see Clause 322)

The cycle duration for Urms(frac12) depends on the frequency The

frequency might be determined by the last non-flagged power frequency

measurement (see Clause 47 and Clause 51) or by any other method

that yields the uncertainty requirements of Clause 6

NOTE 1 The Urms(frac12) value includes by definition harmonics interharmonics mains

signalling voltage etc

NOTE 2 It is important to avoid loss of data when dips and swells occur in a rapid

sequence (for example three events in one second with up to one minute between

sequences may occur when a recloser operates into a sustained fault) If during a rapid

burst the dipswell event characteristics cannot be recorded then a count of events may

be useful



55


Detection and evaluation of a voltage dip

Voltage dip detection

The dip threshold is a percentage of either Udin or the sliding voltage

reference Usr (see 525 544) The user shall declare the reference

voltage in use

NOTE ndash On single-phase systems a voltage dip begins when the Urms voltage falls

below the dip threshold and ends when the Urms voltage is equal to or above the dip

threshold plus the hysteresis voltage

ndash On polyphase systems a dip begins when the Urms voltage of one or more channels is

below the dip threshold and ends when the Urms voltage on all measured channels is

equal to or above the dip threshold plus the hysteresis voltage

The dip threshold and the hysteresis voltage are both set by the user according to the

use



56

Calculation of a sliding reference voltage

The sliding reference voltage implementation is optional not mandatory

If a sliding reference is chosen for voltage dip or swell detection this

shall be calculated using a first-order filter with a 1-min time constant

This filter is given by

Usr(n) = 09967 times Usr(nndash1) + 00033 times U(1012)rms

where

Usr(n) is the present value of the sliding reference voltage

Usr(nndash1) is the previous value of the sliding reference voltage and

U(1012)rms is the most recent 1012-cycle rms value

When the measurement is started the initial value of the sliding reference voltage is set

to the declared input voltage The sliding reference voltage is updated every 1012-

cycles If a 1012-cycle value is flagged the sliding reference voltage is not updated

and the previous value is used



57


Voltage dip evaluation

A voltage dip is characterized by a pair of data either residual voltage

(Ures) or depth and duration

ndash the residual voltage of a voltage dip is the lowest Urms(frac12) value

measured on any channel during the dip

ndash the depth is the difference between the reference voltage (either Udin

or Usr) and the residual voltage It is generally expressed in percentage

of the reference voltage

NOTE 1 During the dip it may be useful to also record the lowest Urms(frac12) on each

channel in addition to the residual voltage of the dip The duration spent below the dip

threshold on each channel may also be useful



58



NOTE 2 If voltage waveforms are recorded before during and after a

dip useful information about phase angle changes may be available in

the recorded data

The start time of a dip shall be time stamped with the time of the start of

the Urms of the channel that initiated the event and the end time of the

dip shall be the time stamped with the time of the end of the Urms that

ended the event as defined by the threshold plus the hysteresis

The duration of a voltage dip is the time difference between the start

time and the end time of the voltage dip



59


Residual voltage and swell voltage magnitude measurement

uncertainty

ndash Class A

The measurement uncertainty shall not exceed plusmn02 of Udin

ndash Class S




60




61



62



63

Inter-Armoniche Le inter-armoniche sono tensioni o correnti sinusoidali con frequenza diversa da un

multiplo intero della fondamentale la cui presenza determina una distorsione

(modulazione) della forma donda della tensione di alimentazione

CAUSE dai carichi che assorbono correnti inter-armoniche

- carichi commutati elettronicamente convertitori cascata subsincrona cicloconvertitori regolatori con

controllo a pacchetti di cicli ecc

- carichi con caratteristiche non lineari eo non stazionarie forni ad arco saldatrici ad arco ecc



64



Un porsquo di esempi e

consigli praticihellip

65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today

bull Computed current and voltage profiles when a

230 V 58 W fluorescent lamp with an old-style

electronic ballast is driven on the phase wire of

a typical power distribution system

System voltage 230 V

System frequency 50 Hz

Source resistance 500 mW

Longitudinal induction 904 microH

System impedance 575 mW

Mean dc current 180 mA

Smoothing capacitance220 microF

66

And what about electronic ballasts that are rated over 25W

Introduce electronic power factor correction (PFC)

0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V

0deg 15deg 30deg 45deg

u

00A

03A

06A

09A

12A

i

67

Though todayrsquos ballasts are better if

rated gt25 W bull Only

the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68

This leads to a number of

previously unknown effects bull 1 Deformed voltage curves

bull 2 Huge inrush current peaks

bull 3 Instrument dependent measured parameters

bull 4 Increased loading of phase conductors

bull 5 Loading and overloading of the neutral conductor

bull 6 Overheating and start-up problems of induction motors

bull 7 Additional stray losses in transformers

bull 8 Repercussions of generators upon the mains

bull 9 Influence of capacitors repercussions upon the mains

and four additional complications in TN-C systems

10 Stray currents in equipotential bonding system magnetic fields

11 Contamination of data streams by stray currents

12 Stray currents in the earthing system corrosion damage

13 Lightning currents in devices and equipment

69

1 Deformed voltage curves

bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u

System voltage profile when driving

a single-phase load comprising

twenty 58 W energy-saver lamps in

parallel on a typical 230 V power

system

70

and in practice

bull An actual

current profile

bull

bull and

bull a voltage profile

bull

bull recorded in a large storage

dispatch and administrative

building

71

at home or in industrial environments

bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72

Every periodic waveform can be written

as the infinite sum of sinusoidal waves

-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

Synthesis of a triangular current profile 100mA

Content fundamental I = 99 mA Isup2 = 9855 mAsup2

Sum of squares Isup2 = 9855 mAsup2

Root of sum = RMS value I = 99 mA

-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3



Cont 3 rd harmonic I = -11 mA Isup2 = 122 mAsup2



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5




Cont 5 th harmonic I = 4 mA Isup2 = 16 mAsup2



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7





Cont 7 th harmonic I = -2 mA Isup2 = 4 mAsup2



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73

whose frequencies called harmonics are

integer multiples of the fundamental frequency

-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

Synthesis of a rectangular current profile 100mA




-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3



Cont 3 rd harmonic I = 30 mA Isup2 = 901 mAsup2



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74

Even far better simulations are

available free of charge at

bull wwwpowerstandardscomMcEachern

75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

Applying the Fourier

analysis to a real PC

current does not work

directly

bull

bull but it can be

modelled by a similar

triangular curve in

which not all of the

higher harmonics

have been included

Triangular current profile of

the same amplitude and a

pulse duty cycle of 17

Input current of a PC

with monitor

76

Analysis of the model triangular waveform

-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI

itot(t) L1 [A] i1(t) L1 [A]

i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important

bull Harmonics are created within the loads

themselves and can flow ldquoupstreamrdquo to

contaminate the power system

78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

Fundamental 502 mA 251986 mAsup2 the fundamental

3rd harmonic -479 mA 229000 mAsup2 229000 mAsup2

5th harmonic 434 mA 188595 mAsup2 188595 mAsup2

7th harmonic -374 mA 139903 mAsup2 139903 mAsup2






Sum of the squares 996362 mAsup2 744377 mAsup2

Root thereof 998 mAeff THD = 863 mA

What actually is THD Example shown here triangular current

profile with an rms current of 1000 mA

and a pulse duty cycle of 17

THDr (root mean square) = 863mA1000mA = 86

THDf (fundamental) = 863mA502mA = 172

79

Effect on phase-to-neutral

and phase-to-phase voltages

bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80

The triple-N harmonics drive

a circulating current in the

delta winding of a distribution

transformer

bull but the

bull voltage harmonics

propagate into the next

low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i

Switching on just as supply voltage passes through zero

0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i

Switching on just as supply voltage is at its peak

2 Huge inrush current peaks

ndash in theory

82

and in practice

bull Inrush current of a

compact energy-

saver lamp and its

effect on the system

voltage (recorded at

the Technical

University of

Budapest)

bull

83

enables us to infer what

happens when run by a

normal three-phase supply

The same fluorescent lamp

with a magnetic ballast

bull The behaviour measured

when connected to

a dc supply

bull

Behaviour of a 58 W fluorescent lamp connected to a dc

supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

MeasurementCalculation

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84

Warning ldquoCompensationrdquo is not

always what you think it is

bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85

5 (Over)loading the neutral conductor

bull Magnetic ballast Old-style electronic ballast

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150

0deg 30deg 60deg 90deg 120deg 150deg 180deg 210deg 240deg 270deg 300deg 330deg 360deg

L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87

Effect on a three-phase ac motor

appears almost identical

bull The same motor is being

driven

simultaneously in

these three modes

homopolar system

zero-sequence system

direct system

positive-sequence system

inverse system

negative-sequence system

88

The transformer

influences the load

89

but the load also effects

the transformer

Total transformer loss is

2

)()(

nom

nomCunomFeLossI

IPPP

While total transformer loss really is

2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90

6 ldquosupplementaryrdquo additional losses

in transformers

can be calculated rapidly

using the following two

simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu

Harmonics of an Osram Dulux 11W

CFL and a serial impedance of

R =291Ω amp X L=113Ω

U U sup2 I L I Lsup2 P aP Cu

n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91

Harmonics measurement on an

Osram Dulux 11W compact

fluorescent lamp

U U sup2 I L I Lsup2 P addP Cu

n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself

bull Always remember to

consider it

bull If the influence of the

transformer upon the load

did not exist then the

influence of the load upon

the transformer would be

nearly 9 times as high

7017

etc

etc

92

Rule of thumb Select transformers 35

larger than specification by apparent

power would require

bull This suffices to err

on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load

Efficiency of a 1 MVA transformer plotted against loading

985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h

Design with max Cu loss and min Fe loss

Design with min Cu loss and max Fe loss

1 MVA oil transformer according to HD 428

93

Measured response of an 11 W

fluorescent lamp operated with a

magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt

Effects 2 3 and 5 can be demonstrated

on DKIrsquos display panel

95

A conventional approximately resistive-

inductive load

mA

N L1 L2 L3

Two conventional approximately

resistive-inductive loads Three conventional approximately

resistive-inductive loads

96

A modern electronic load

mA

N

Two modern electronic loads Three modern electronic loads

L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98

The TN-C system that was perfectly

adequate some years ago is unable to meet

present-day requirements

-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland

In certain situations this affordable

filter can be of help

German

version ldquoTHXrdquo

100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle

Data and frequency response

of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use

bull In a nursery running sodium vapour lamps (500 kW)

In a typical office and administrative building

102

The EMC Transformer from Switzerland

7 The effects of stray magnetic fields

in TN-C systems

bull ldquoWhen we build transformers the first thing we focus on is complying with our customersrsquo

requirements and only then on complying with standards Why Because it is customer

needs and not standards that offer real scope for product innovationrdquo

103

8 In a TN-C system problems arise from data

streams and working currents mixing

bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts

consultants and many

others besides

104

9 Increased corrosive damage

bull This (once) galvanized steel strip ndash the earth

electrode of a TN-C-S system ndash was located close

to the transformer station

Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT

Working currents have no place

in earthing systems and

protective conductors

106

10 Lightning currents

107

Which bridge to

cross which bridge to

burn

Sometimes you just donlsquot

believe what you see

This one will soon

look rather charred

IEC 60364-5-54

54343 If from any point of the installation the neutral and protective

functions are provided by separate conductors it is not permitted to

connect the neutral conductor to any other earthed part of the

installation

108

Well then the rest is no longer a

miracle

109

110

111

Another means of (over)loading the

neutral conductor

bull dc currents

Original ldquoFakerdquo

112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr

No-load current in a

toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current

No-load current in a toroidal-core

transformer 200 VA when

running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113

The later models donlsquot do it any more

The EN 61000-3-2 has at least managed

to put an end to this approach

Domestic appliances Max 105 A of 2nd harmonic

114

An electrical engineering wonder

dc current generates ac voltage

115

Spicing things up with a pinch of HF

electronic halogen lamp transformers

116

Decorative HF reactors

117

Current and power loss as a function of voltage

00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]

Power loss capacitor voltage

and total voltage as a function of current

0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119

Half the solution has already been implemented

120

And if thatrsquos not enough

bull Passive filter circuits will do it

121

So what do we need to do

bull In low-voltage power distribution systems

Do not use cables in which the neutral or protective earth conductor has a

reduced cross-section

Use only 5-core cable Do not install TN-C- or TN-C-S systems

Be generous when dimensioning conductor cross-sections This helps to

reduce line voltage drops and thus reduces the effect of current distortions on

the voltage as well as lowering energy losses (see VDE 0298 Part 100)

Generously dimensioned conductors will have no problem coping with any

future increase in demand

Only use measuring instruments that display the true root mean square value

(TRMS meters)

In medium-voltage power distribution systems

Use a varied mix of distribution transformers with different vector groups

2

La qualitagrave del servizio elettrico prende in considerazione

bull la continuitagrave dellrsquoalimentazione intesa come assenza di interruzioni

nella fornitura di energia elettrica

bull la qualitagrave della tensione intesa come qualitagrave della forma drsquoonda

(ampiezza frequenza variazioni ecc)

Esistono numerosi fattori che influiscono sulla qualitagrave dellrsquoenergia

elettrica ed in particolare

bull dipendenti dal Distributore (gestione ed esercizio della rete

manutenzione hellip)

bull dipendenti dal Cliente (guasti presso impianto del Cliente disturbi

emessi sulla rete hellip)

bull indipendenti (fattori ambientali eventi atmosferici danni prodotti da

Terzi hellip)



3







4



Ih

Vh



5

Power quality

problems



again

are

usually of

terrestrial

origin



6




problemi








ecc ecc


7













8

The good

old days bull

bull Ideal

three-phase

system

voltage

Three balanced

ohmic-inductive

single-phase loads

on the three phase

mains

-150A

-100A

-50A

0A

50A

100A

150A


t

i

i1 (L1)

i1 (L2)

i1 (L3)

-350V

-250V

-150V

-50V

50V

150V

250V

350V


t

u u1 (L1)

u1 (L2)

u1 (L3 )



9




Buchi di tensione

Transitori






10








disturbance levels














11











thereto





Part 3 Limits




12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



3







4



Ih

Vh



5

Power quality

problems



again

are

usually of

terrestrial

origin



6




problemi








ecc ecc


7













8

The good

old days bull

bull Ideal

three-phase

system

voltage

Three balanced

ohmic-inductive

single-phase loads

on the three phase

mains

-150A

-100A

-50A

0A

50A

100A

150A


t

i

i1 (L1)

i1 (L2)

i1 (L3)

-350V

-250V

-150V

-50V

50V

150V

250V

350V


t

u u1 (L1)

u1 (L2)

u1 (L3 )



9




Buchi di tensione

Transitori






10








disturbance levels














11











thereto





Part 3 Limits




12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



4



Ih

Vh



5

Power quality

problems



again

are

usually of

terrestrial

origin



6




problemi








ecc ecc


7













8

The good

old days bull

bull Ideal

three-phase

system

voltage

Three balanced

ohmic-inductive

single-phase loads

on the three phase

mains

-150A

-100A

-50A

0A

50A

100A

150A


t

i

i1 (L1)

i1 (L2)

i1 (L3)

-350V

-250V

-150V

-50V

50V

150V

250V

350V


t

u u1 (L1)

u1 (L2)

u1 (L3 )



9




Buchi di tensione

Transitori






10








disturbance levels














11











thereto





Part 3 Limits




12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



5

Power quality

problems



again

are

usually of

terrestrial

origin



6




problemi








ecc ecc


7













8

The good

old days bull

bull Ideal

three-phase

system

voltage

Three balanced

ohmic-inductive

single-phase loads

on the three phase

mains

-150A

-100A

-50A

0A

50A

100A

150A


t

i

i1 (L1)

i1 (L2)

i1 (L3)

-350V

-250V

-150V

-50V

50V

150V

250V

350V


t

u u1 (L1)

u1 (L2)

u1 (L3 )



9




Buchi di tensione

Transitori






10








disturbance levels














11











thereto





Part 3 Limits




12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



6




problemi








ecc ecc


7













8

The good

old days bull

bull Ideal

three-phase

system

voltage

Three balanced

ohmic-inductive

single-phase loads

on the three phase

mains

-150A

-100A

-50A

0A

50A

100A

150A


t

i

i1 (L1)

i1 (L2)

i1 (L3)

-350V

-250V

-150V

-50V

50V

150V

250V

350V


t

u u1 (L1)

u1 (L2)

u1 (L3 )



9




Buchi di tensione

Transitori






10








disturbance levels














11











thereto





Part 3 Limits




12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



7













8

The good

old days bull

bull Ideal

three-phase

system

voltage

Three balanced

ohmic-inductive

single-phase loads

on the three phase

mains

-150A

-100A

-50A

0A

50A

100A

150A


t

i

i1 (L1)

i1 (L2)

i1 (L3)

-350V

-250V

-150V

-50V

50V

150V

250V

350V


t

u u1 (L1)

u1 (L2)

u1 (L3 )



9




Buchi di tensione

Transitori






10








disturbance levels














11











thereto





Part 3 Limits




12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



8

The good

old days bull

bull Ideal

three-phase

system

voltage

Three balanced

ohmic-inductive

single-phase loads

on the three phase

mains

-150A

-100A

-50A

0A

50A

100A

150A


t

i

i1 (L1)

i1 (L2)

i1 (L3)

-350V

-250V

-150V

-50V

50V

150V

250V

350V


t

u u1 (L1)

u1 (L2)

u1 (L3 )



9




Buchi di tensione

Transitori






10








disturbance levels














11











thereto





Part 3 Limits




12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



9




Buchi di tensione

Transitori






10








disturbance levels














11











thereto





Part 3 Limits




12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



10








disturbance levels














11











thereto





Part 3 Limits




12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



11











thereto





Part 3 Limits




12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



12














13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



13






5 Buchi di tensione






14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



14
















15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



15



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



16

17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



17




18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



18




19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



19


Frequenza nominale











20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



20




21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



21




22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



22




tensione dichiarata





23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



23










24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



24









25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



25



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



26




27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



27



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



28



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



29



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



30



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



31



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



32









33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



33





34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



34





35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



35











36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



36















37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



37

38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



38



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



39




40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



40




41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



41




42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



42




transducers






43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



43





are included


Class A






Class S




Class B




44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



44



CLASS A








ndash 2 h interval

CLASS S


CLASS B




45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



45



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



46



Class A



aggregation


intervals



intervals




10-min interval

47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



47



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



48



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



49




Flagging concept








50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



50














defined in 46






51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



51








ndash Class A



ndash Class S



ndash Class B


575 Hz 51 Hz ~ 69 Hz



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



52


Measurement method

ndash Class A










signalling etc




53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



53



ndash Class A



ndash Class S





54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



54


Measurement method

ndash Class A













be useful



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



55






voltage in use








use



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



56







where










57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



57















58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



58





the recorded data









59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



59



uncertainty

ndash Class A


ndash Class S




60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



60




61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



61



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



62



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



63










64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



64





65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



65

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

0V

50V

100V

150V

200V

250V

300V

350V


t

u

0A

1A

2A

3A

i

gleichgerichtete

Netzspannung

Kondensator-

spannung

gleichgerichteter

Netzstrom

The situation

today












66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



66



0V

20V

40V

60V

80V

100V

120V

140V

160V

180V

200V

220V


u

00A

03A

06A

09A

12A

i

67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



67



the

small

ones

continu

e to

pollute

just like

PCs

TV sets

do

68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



68
















69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



69


bull in theory

-350V

-300V

-250V

-200V

-150V

-100V

-50V

0V

50V

100V

150V

200V

250V

300V

350V

0 5 10 15 20

t ms

u





system

70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



70

and in practice

bull An actual

current profile

bull

bull and


bull



building

71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



71


bull

bull Television 40

W

bull 200 Vdiv 2

Adiv

bull 5 msdiv

Harmonic

spectrum

Frequency

converter

50 Adiv

Phase currents

I1=I2=I3=160 A

IN=295 A

5 msdiv

72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



72



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



73



-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1





-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3






-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5







-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot

i1

i3

i5

i7








-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9









-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11










-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13











-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15












-175

-150

-125

-100

-75

-50

-25

0

25

50

75

100

125

150

175

0 5 10 15 20

t ms

i

mA

itot i1

i3 i5

i7 i9

i11 i13

i15 i17













74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



74




75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



75

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A


t

i




directly

bull

bull but it can be


triangular curve in


higher harmonics

have been included





with monitor

76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



76


-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 5 10 15 20

t ms

iI


i3(t) L1 [A] i5(t) L1 [A]

i7(t) L1 [A] i9(t) L1 [A]

i11(t) L1 [A] i13(t) L1 [A]

i15(t) L1 [A] i17(t) L1 [A]

77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



77

M3

Harmonics

Energy

(active

power)

L1

L2

L3

N

PE

Important




78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



78

-6A

-5A

-4A

-3A

-2A

-1A

0A

1A

2A

3A

4A

5A

6A


t

i

Squared values

Without

















79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



79



bull Recorded

on June

30 2002

230 p

m

bull What

was the

matter

then

bull The

soccer

final

Germany

vs

Brazil

80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



80




transformer

bull but the



low-voltage power

distribution system

81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



81 0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i


0V

50V

100V

150V

200V

250V

300V

350V

400V

450V

500V

550V

0 10 20 30 40 50

t ms

u

0A

10A

20A

30A

40A

50A

60A

70A

80A

90A

100A

110A

120A

130A

140A

150A

i



ndash in theory

82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



82

and in practice


compact energy-

saver lamp and its



the Technical

University of

Budapest)

bull

83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



83







when connected to

a dc supply

bull


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V

Measurement


supply

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000 1200

i mA

u

V


-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Current

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

-10

-08

-06

-04

-02

00

02

04

06

08

10

i

A

Systems voltage

Lamp voltage

Current

84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



84



bull Distinguish

between

bull Reactive

power

compensatio

n

aka power

factor

correction

Remedial

measure

Parallel (or

sometimes series)

compensation

using capacitors

Filter circuits

tuned to the

individual harmonic

frequencies

Harmonic

compensation

85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



85



-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) N

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1 i(t) L2 i(t) L3

-25A

-20A

-15A

-10A

-05A

00A

05A

10A

15A

20A

25A

0 5 10 15 20

t ms

i

i(t) L1

i(t) L2

i(t) L3

86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



86

Adding the 3rd

harmonics

in the

neutral

wire

-150-100-50

050

100150


L1

-150-100-50

050

100150


L2

-150-100-50

050

100150


L3

-450-400-350-300-250-200-150-100-50

050

100150200250300350400450


f

iicirc

N

Physics dictates

that at any

moment in time

the phase and

neutral currents

must sum to zero

87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



87




driven

simultaneously in

these three modes

homopolar system


direct system


inverse system


88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



88

The transformer

influences the load

89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



89


the transformer


2

)()(

nom

nomCunomFeLossI

IPPP


2

)(

2

)(

2

)(

nomnom

nomad

nom

nomCu

nom

nomFeLossI

I

f

fP

I

IP

U

UPP

90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



90


in transformers



simple formulae 50

2

2

1

2

11

Nn

n

nqh

I

In

I

I

e

eK

50

1

2

1

1

50

1

2

Nn

n

nNn

n

nI

IIII

where

Oh well

perhaps a practical

example is clearer

1000 compact 11W

(15VA) energy-saver

lamps powered by a

15kVA transformer

uSC=4 Pa=01PCu





n V Vsup2 mA mAsup2

1 2302 529920 485 23523 56

3 83 689 371 13764 295

5 107 1145 203 4121 245

7 43 185 53 281 33

9 11 12 30 90 17

11 23 53 38 144 42

13 10 10 15 23 09

15 06 04 15 23 12

17 11 12 15 23 15

19 05 03 09 08 07

21 05 03 13 17 18

23 06 04 08 06 08

25 04 02 06 04 05

27 06 04 08 06 11

29 04 02 05 03 05

31 03 01 05 03 06

33 03 01 05 03 06

35 03 01 04 02 05

37 03 01 04 02 05

39 03 01 03 01 03

41 01 00 03 01 04

43 02 00 02 00 02

45 01 00 02 00 02

47 01 00 02 00 02

49 01 00 01 00 01

51 01 00 01 00 01

P aP Cu = 814814

etc

etc

91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



91



fluorescent lamp


n V Vsup2 mA mAsup2

1 2327 541493 489 23912 37

3 06 04 391 15288 215

5 44 194 264 6970 273

7 23 53 200 4000 307

9 01 00 192 3686 467

11 01 00 166 2756 522

13 01 00 127 1613 427

15 01 00 110 1210 426

17 01 00 102 1040 471

19 01 00 87 757 428

21 01 00 77 593 409

23 01 00 73 533 441

25 01 00 61 372 364

27 01 00 49 240 274

29 01 00 42 176 232

31 01 00 36 130 195

33 01 00 30 90 153

35 01 00 33 109 209

37 01 00 31 96 206

39 01 00 25 63 149

41 01 00 25 63 164

43 01 00 25 63 181

45 01 00 19 36 114

47 01 00 18 32 112

49 01 00 19 36 136

51 01 00 16 26 104

P aP Cu = 7017

To some extent

the transformer

protects itself


consider it







7017

etc

etc

92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



92



power would require


on the safe side

even in the worst

case and can

hardly ever be

wrong since

maximum

efficiency always

lies between 25

and 50 of rated

load


985

986

987

988

989

990

991

992

993

994

0 25 50 75 100 125

Relative load h




93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



93



magnetic ballast

94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



94

We are

dealing with

a complex

problem

bull These

effects

are not

isolated

but are

mutuall

y inter-

depende

nt



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



95


inductive load

mA

N L1 L2 L3




96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



96


mA

N


L1 L2 L3

97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



97

Discoveries on a

refurbished

junction box

System voltage

(as trigger

signal)

Current in the

earthing

conductor

between the

consumer unit

and the

bonding

busbar

98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



98




-6

-4

-2

0

2

4

6

0 5 10 15 20

t ms

i

A

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

0 5 10 15 20

t ms

u

V

99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



99

ldquoTHFrdquo

(third harmonic

filter) made in

Finland



German


100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



100

0Ω

5 Ω

1 0 Ω

1 5 Ω

2 0 Ω

2 5 Ω

3 0 Ω

3 5 Ω

4 0 Ω

0Hz 50Hz 100Hz 150Hz 200Hz 250Hz 300Hz

f

Z

-90deg

-75deg

-60deg

-45deg

-30deg

-15deg

0deg

15deg

30deg

45deg

60deg

75deg

90deg

φ

Reactorreactance

Capacitorreactance

Parallelimpedace

Phase angle


of the filter

bull 1320 microF

bull 875

14 mW microH

101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



101

The filter in use



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



102



in TN-C systems




103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



103



bull Others who

have drawn

attention to

this source of

data

transmission

errors include

engineering

and insurance

companies experts


others besides

104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



104





Side facing

transformer

station

Side facing

transformer

station

Side facing away

from transformer

station

Side facing away

from transformer

station

105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



105

bull WRONG RIGHT




106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



106


107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



107

Which bridge to


burn



This one will soon

look rather charred

IEC 60364-5-54




installation

108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



108


miracle

109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



109

110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



110

111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



111


neutral conductor

bull dc currents


112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



112

and their

effects U = 2285 V

I = 92 mA

P = 182 W

S = 209 VA

Q = 103 VAr

LF = 087

cos φ = 099

U = 2243 V

I = 126 A

P = 380 W

S = 2860 VA

Q = 2830 VAr


toroidal-core

transformer

200 VA

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 10 20 30 40

t ms

u

V

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

i

mA

Voltage

Current



running a 1500 W

hairdryer at

half-power

in parallel

-350-300

-250-200

-150-100

-500

50

100150

200250

300350

0 5 10 15 20 25 30 35 40

t ms

u

V

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

i

A

Voltage

Current

113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



113





114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



114



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



115



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



116


117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



117


00

02

04

06

08

10

12

14

16

18

0 40 80 120 160 200 240

U V

I

A

0

20

40

60

80

100

120

PV

W

I [A]

Pv [W]



0

50

100

150

200

250

300

350

400

450

000 025 050 075 100 125 150

I A

U

V

0

5

10

15

20

25

30

35

40

45

50

PV

W

Utot [V] Eff

UR [V] Eff

Pv [W]

The passive

harmonic filter

made of readily

available

components

bull is both

reliable

118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



118

and effective

bull befor

e

bull after

119


120



121












(TRMS meters)



119


120



121












(TRMS meters)



120



121












(TRMS meters)



121












(TRMS meters)



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