Risks and Opportunities of Reactive Power Compensators in Environ-ments with HarmonicsStefan FassbinderDKI German Copper InstituteAm Bonneshof 5D-40474 DüsseldorfTel.: +49 / 211 / 4796-323Fax: +49 / 211 / 4796-310sfassbinder@kupferinstitut.dewww.kupferinstitut.de

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Everybody knows reactive power

But what do we really mean by it?

But what do we really mean by it?

Generation of leading reactive power = Absorption of lagging reactive powerGeneration of lagging reactive power = Absorption of leading reactive power

But what do we really mean by it?

Reactive power is the share of the power which does notcontribute to the transmission of energy (work)

So what then is reactive energy?

If the voltage is sinusoidal, the current is sinusoidal too – right?

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Sine voltageL current with sine voltageC current with sine voltage

L = 55 mHC = 175 µFf = 50 Hz

t)sin(*û)( ω=tu t)cos(*î)( ω−=tiL

t)cos(*î)( ω=tiC

And what about other voltage-current profiles?

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Sine voltageL current with sine voltageC current with sine voltage

L = 55 mHC = 175 µFf = 50 Hz

t)sin(*û)( ω=tu t)cos(*î)( ω−=tiL

t)cos(*î)( ω=tiC

E. g. when a square-wave voltage with small conductive angle is applied to an inductor?

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i L Rectangular

voltage

L current withrectangularvoltage

Conductive angle = 30 %Peak value = 100 V

L = 3 mHf = 50 Hz

Or when a triangular voltage with a small conductive angle is applied to a capacitor?

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Triangularvoltage

C current withtriangularvoltage

Conductive angle = 30 %Peak value = 100 V

C = 1500 µFf = 50 Hz

Or when a triangular current profile with a small conductive angle is driven through a capacitor?

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u C Triangular current

C voltage with triangular current

Conductive angle = 75 %Peak value = 100 V

C = 3750 µFf = 50 Hz

But fortunately:

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Every periodic waveform can be written as the finite sum of sinusoidal waves whose frequencies are integer multiples of the fundamental frequency

Harmonic reactive power

Currents are no longer sinusoidal Voltages are no longer sinusoidal Voltages and currents contain higher-frequency constituents

Risk that capacitors will overload

Capacitors can help to eliminate this high

frequency contamination

Static var compensators in such an environment – a threat and an opportunity!

fLX L π2=

fCXC π2

1=

2222 )( CLCuSCu XXRXRZ −+=+=

fCfLXXX CLS π

π2

12 −=−=

The real-life behaviour

Why detune?To prevent the occurrence oftransformer resonances, for example.

Why detune?To prevent the occurrence oftransformer resonances, for example.

Why detune?To prevent the occurrence oftransformer resonances, for example.

Why detune?To prevent the occurrence oftransformer resonances, for example.

So it’s quite natural to ask:What is harmonic reactive power?Well, it all depends on how you see things and how you measure them...

Detuned Static VAR Compensator (SVC)

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f

Z

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Reactor reactanceCapacitor reactanceSerial impedancePhase angle

R Cu = 1 Ω

L = 8 mH

C = 50 µF

Detuned Static VAR Compensator (SVC)

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f

Z

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φ

Reactor reactanceCapacitor reactanceSerial impedancePhase angle

R Cu = 1 Ω

L = 4 mH

C = 100 µF

Parallel resonant bandpass filter(‘rejection circuit’)

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Z

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φ

Reactor reactanceCapacitor reactanceParallel impedace Phase angle

R Cu = 1 Ω

L = 8 mH

C = 50 µF

Parallel resonant bandpass filter(‘rejection circuit’)

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Reactor reactanceCapacitor reactanceParallel impedace Phase angle

R Cu = 1 Ω

L = 4 mH

C = 100 µF

Parallel resonant bandpass filter(‘rejection circuit’)

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Reactor reactanceCapacitor reactanceParallel impedace Phase angle

R Cu = 0.25 Ω

L = 8.00 mH

C = 50.00 µF

Trying to save money byTrying to save money byskimping on skimping on coppercopperusually turns out to be a costlymistake. And in the case of power factor cor-rection circuits, you can end up paying twice!According to the experts at ElectroniconKondensatoren GmbH in Gera:‘Most customers aren’t even aware that by focusing solely on cutting costs, the money they saved through reactive power com-pensation measures is lost via active power losses in the compensation circuit.’

VArWWVAPSQ 146)858()160( 2222 ≈+−=−=

VAAVS 16067,0*230 ==

Example: a 58-W tube with a low-loss ballast Example: an 11-W tube with a

conventional magnetic ballast

Fluorescent lamps with magnetic ballasts:A classic source of reactive power that

requires compensation

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Systems voltageLamp voltageCurrent

or in the so-called ‘duo’or lead-lag configuration

either in a conventional

parallel configuration

Compensation is best done right at the source – as is in fact often the case in fluorescent lamps –

Two 58W lamps with two ballasts and one capacitor

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f

Z

X(L)

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Z(ser)

Correctlydimensioned

RCu =13.8 ΩL =878 mHC = 5.7 µF

22RLC )

212(Z CuRfC

fL +−=π

π

fCπ21XC =

Fπ2XL =

Two 58W lamps with two ballasts and one capacitor

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X(L)

X(C)

Z(ser)

RCu =13.8 ΩL =878 mHC = 6.8 µF

Dimensioning is 20% in error: Reactance is 32% in

error!

fCπ21XC =

fLπ2XL =

22RLC )

212(Z CuRfC

fL +−=π

π

58W lamp with a class B1 magnetic ballast

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I(L)

Two 58W lamps, one in series with a 5.3 µF capacitor

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U

I(L)

I(C=5.3µF)

Two 58W lamps, one in series with a 5.3 µF capacitor

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i

UI(L)I(C=5.3µF)I(C+L)

Two 58W lamps, one with reduced 4.6µF capacitor

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i

UI(L)I(C=4.6µF)I(tot)(C=4.6µF)

Possible overloading of capacitors attached directly to the mains due tohigher frequenciespresent in thesupply system

Dealing with side effectsof the first kind:

Filter capacitor current into a PC power supply

while switched of

Risk with parallel compensation:

Higher frequencies cause capacitor to overload, as shown here for an 11W fluorescent lamp with magnetic ballast

A reliable concept:Conventional power factorcompensation system detunedto draw off the strongest harmonics

Dealing with side effectsof the second kind:

Rejection circuits ensure that ripple-control signals don’t get lost

Cleaning effect of a 250Hz filterrecorded in a residential areain Germany, June 30, 2002, 14:30

The advantageous dual passive filtercan reduce e. g. the harmoniccontent of a dimmer current substantially

Well, this was just a model

Here come three real-life examplesof detuned static var compensators withthree different ratings, actually built and sold by a specialized companyReactive

power rating

Detuning factor

Reactor losses per

phase

I(in delta wiring)

X C

50 HzX L

50 HzC L R Cu

kVAr % W A Ω Ω µF mH mΩ10.0 7% 15.7 8.33 51.360 3.360 62.0 10.695 225.622.5 7% 24.3 18.75 22.827 1.493 139.4 4.753 69.267.4 7% 52.3 56.17 7.620 0.499 417.7 1.587 16.6

The values are convincing, losses areminimal!

Dimensioning a twin filter made of 2 acceptor circuits operating in parallel – input valuesHarmonics in the mains voltage: Ratings of your system and the filters:

No. f U f U 240.000 V Rated TRMS mains voltage1 50Hz 239.49V f 50.000 Hz Rated mains frequency2 100Hz 0.00V R 5 16.600 mΩ Ohmic winding resistance of lower frequency reactor (usually tuned to or near the 5th harmonic)3 150Hz 12.00V L 5 1.587 mH Inductance of lower frequency reactor (usually tuned to or near the 5th harmonic)4 200Hz 0.00V C 5 417.700 µF Capacitance of lower frequency reactor (usually tuned to or near the 5th harmonic)5 250Hz 8.00V R 7 16.600 mΩ Ohmic winding resistance of higher frequency reactor (usually tuned to or near the 7th harmonic)6 300Hz 0.00V L 7 0.810 mH Inductance of higher frequency reactor (usually tuned to or near the 7th harmonic)7 350Hz 4.00V C 7 213.112 µF Capacitance of higher frequency reactor (usually tuned to or near the 7th harmonic)8 400Hz 0.00V f 0(5) 195.479 Hz Resonance frequency of the 5th order filter9 450Hz 3.00V f 0(7) 383.138 Hz Resonance frequency of the 7th order filter

10 500Hz 0.00V11 550Hz 2.50V12 600Hz 0.00V13 650Hz 2.00V14 700Hz 0.00V15 750Hz 1.50V16 800Hz 0.00V17 850Hz 1.00V18 900Hz 0.00V19 950Hz 0.50V20 1000Hz 0.00V21 1050Hz 0.00V22 1100Hz 0.00V23 1150Hz 0.00V24 1200Hz 0.00V25 1250Hz 0.00V26 1300Hz 0.00V27 1350Hz 0.00V

X L-X

C

RCu

Z

C5

L5 U

RCu5

C7

L7

RCu7

A calculation template is available at:

www.leonardo-energy.org/drupal/dimensioning-passive-filter-tool

Behaviour of said dual filter

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5Ω

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Z

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φ

Z5Z7Ztotφ5φ7φtot

Complementary behaviourCCCurrent is proportional to the rate of change of voltage.

LLVoltage is proportional to the rate of change of current.

Reactance decreases with increasing frequency.

Energy content proportional to the square of the voltage.

Large current spikes when switching on, unless switching occurs when voltage is passing through zero.

Reactance increases with increasing frequency.

Energy content proportional to the square of the current.

Large voltage spikes when switching off, unless switching occurs when current is passing through zero.

Series LC resonant circuit (‘acceptor circuit’)

Parallel LCresonant circuit (‘rejector circuit’)

Switch on anytime(soft switching)

Zero-current switch-off (otherwise: hard switching generates voltage transients)

Zero-voltage switch-on (otherwise: hard switching generates current transients)Switch off anytime(soft switching)

Complementary behaviour

gave a total of 3 million Euros from within the frameworkgave a total of 3 million Euros from within the frameworkof their LEONARDO of their LEONARDO programmeprogramme to establish to establish thethe European website European website dealing with dealing with allall aspects of power quality with the help of adequate aspects of power quality with the help of adequate partners! Just go topartners! Just go towww.lpqi.orgwww.lpqi.orgfrom time to time and watch the from time to time and watch the Leonardo Power Quality InitiativeLeonardo Power Quality Initiativegrowing! We want to develop and provide vocational training mategrowing! We want to develop and provide vocational training material on rial on the mitigation of power quality problems inthe mitigation of power quality problems in 11 languages!11 languages!We address all electrical experts working in the field: EngineerWe address all electrical experts working in the field: Engineers, s, handicraftsmen, building maintenance technicians, architectural handicraftsmen, building maintenance technicians, architectural and and planning consultants as well as trainers and trainees.planning consultants as well as trainers and trainees.So long, we are 86 partners from Europe, North and South AmericaSo long, we are 86 partners from Europe, North and South America, , among them commercial companies, institutes, universities and 5 among them commercial companies, institutes, universities and 5 national national copper copper centrescentres. Participation and contributions of further partners from . Participation and contributions of further partners from industry and academics is possible at any time and even desired industry and academics is possible at any time and even desired by the by the existing project partners.existing project partners.Just give us a click!Just give us a click!

www.lpqi.org

The European Union

The European Union

3 projects out of about 4000 awarded – one of them was:

gave a total of 3 million Euros from within the frameworkgave a total of 3 million Euros from within the frameworkof their LEONARDO of their LEONARDO programmeprogramme to establish to establish thethe European website European website dealing with dealing with allall aspects of power quality with the help of adequate aspects of power quality with the help of adequate partners! Just go topartners! Just go towww.lpqi.orgwww.lpqi.orgfrom time to time and watch the from time to time and watch the Leonardo Power Quality InitiativeLeonardo Power Quality Initiativegrowing! We want to develop and provide vocational training mategrowing! We want to develop and provide vocational training material on rial on the mitigation of power quality problems inthe mitigation of power quality problems in 11 languages!11 languages!We address all electrical experts working in the field: EngineerWe address all electrical experts working in the field: Engineers, s, handicraftsmen, building maintenance technicians, architectural handicraftsmen, building maintenance technicians, architectural and and planning consultants as well as trainers and trainees.planning consultants as well as trainers and trainees.So long, we are 86 partners from Europe, North and South AmericaSo long, we are 86 partners from Europe, North and South America, , among them commercial companies, institutes, universities and 5 among them commercial companies, institutes, universities and 5 national national copper copper centrescentres. Participation and contributions of further partners from . Participation and contributions of further partners from industry and academics is possible at any time and even desired industry and academics is possible at any time and even desired by the by the existing project partners.existing project partners.Just give us a click!Just give us a click!

www.lpqi.org

The European Union