Harmonic

n 152harmonics inindustrialnetworks

E/CT 152 first issued october 1994

Nol Quillon

After joining Merlin Gerin's LowVoltage Equipment Department in1968, he subsequently took part inthe development of LV circuit brea-kers within the testing laboratory.A graduate engineer from the INPG,he worked in the "Network Studied"department of the Central R&Dorganisation for eight years where hestudied electrical network pheno-mena and their behaviour in order toestablish guidelines to control thesephenomena. In 1985, he joined theTraining Department. After being incharge of the electrotechnical trai-ning programme, he is presently thetraining correspondent for the UPSdivision.

Pierre Roccia

Obtained an Electrical Engineeringdegree from the INPG (National Poly-technic Institute of Grenoble) in 1969.Worked as project manager in theindustrial equipment and high vol-tage public distribution sector, beforebeing put in charge of extending theMerlin Gerin range of protectionrelays and developing a technicalapproach for the protection of highvoltage industrial networks usingdevices associated with circuitbreakers.After three years as a traininginstructor, he is presently working asan engineer in the "Network Studies"department of the Central R&Dorganisation.

Cahier Technique Merlin Gerin n 152 / p.2

glossary

Symbols:C capacitance or, more generally, the capacitors themselvesD harmonic distortion loss angle of a capacitorf1 fundamental frequencyfar anti-resonance frequencyfn frequency of the nth harmonic componentfr resonance frequencyn phase angle of the nth harmonic component when t = 0In rms current of the nth harmonic componentj complex operator equal to the square root of 1L inductance or, more generally, the reactors, producing the inductanceLsc short-circuit inductance of a network, seen from a given point, as defined by Thevenin's theoremn the order of a harmonic component (also referred to as the harmonic number)nar the order of anti-resonance, i.e. the radio of the anti-resonance frequency to the fundamental frequencynr the order of resonance, i.e. the radio of the resonance frequency to the fundamental frequencyk a positive integerp number of rectifier arms (also referred to as the pulse number)p1 filter losses due only to the fundamental currentpn filter losses due only to the nth harmonic currentP (W) active powerPB pass-band of a resonant shunt filterq quality factor of a reactorQ quality factor of a filterQ (var) reactive powerr resistanceR resistance (or the real part of the impedance)spectrum the distribution, at a given point, of the amplitudes of the various harmonic components expressed relative to the

fundamentalSsc short-circuit power of a network at a given pointT period of an alternating quantityU phase-to-phase rms voltageVn rms voltage of the nth harmonic componentX reactanceX0 characteristic inductance or impedance of a filterXsc short-circuit reactance of a network, seen from a given point, as defined by Thevenin's theoremY0 amplitude of the DC componentYn rms value of the nth harmonic componentZ impedanceAbbreviations:CIGRE Confrence Internationale des Grands Rseaux Electriques (International Conference on Large Electrical

Networks)IEC International Electrotechnical Commission


harmonics in industrial networks

summary

1. Introduction: harmonic distortion is a problem that must often be p. 4dealt with in industrial power distribution networks2. Harmonic quantities p. 43. Principal disturbances caused by Instantaneous effects p. 6

Long-term effects p. 64. Acceptable limits, recommendations Typical limits for distribution p. 7and standards networks

Typical limits for industrial p. 7networks

5. Harmonics generators Static converters on 3-phase p. 8networksArc furnaces p. 8Lighting p. 9Saturated reactors p. 9Rotating machines p. 9Calculation model p. 9

6. Can capacitors cause a problem on In the absence of capacitor banks p. 10In the presence of a capacitor p. 10bank

7. Anti-harmonic reactors p. 138. Filters Resonant shunt filters p. 14

Damped filters p. 159. Measurement relays required for the Basic protection against device p. 17

failuresBasic protection against abnormal p. 17stresses on the devices

10. Example of the analysis of a Capacitor bank alone p. 18Reactor-connected capacitor bank p. 18Resonant shunt filter tuned to the p. 195th harmonic and a damped filtertuned to the 7th harmonic

11. Conclusion p. 2112. Bibliography p. 22

harmonic currents and voltages

networks comprising disturbingequipment

protection of reactor-connectedcapacitors and filters

simplified network


1. introduction

harmonic distortion is aproblem that must often bedealt with in industrialpower distributionnetworksElectricity is generally distributed asthree voltage waves forming a 3-phase

sinusoidal system. One of thecharacteristics of such a system is itswaveform, which must always remainas close as possible to that of a puresine wave.If distorted beyond certain limits, as isoften the case on networks comprisingsources of harmonic currents and

voltages such as arc furnaces, staticpower converters, lighting systems,etc., the waveform must be corrected.The aim of the present document is toprovide a better understanding of theseharmonics problems, including theircauses and the most commonly usedsolutions.

2. harmonic quantities

To help the reader follow thediscussion, we will first review thedefinitions of a number of terms relatedto harmonics phenomena. Readersalready familiar with the basicterminology may proceed directly to thenext chapter.On AC industrial power supplynetworks, the variation of current andvoltage with time is considerablydifferent from that of a pure sine wave(see fig. 1). The actual waveform iscomposed of a number of sine wavesof different frequencies, including oneat the power frequency, referred to asthe fundamental component or simplythe fundamental.Harmonic componentThe term harmonic component, orsimply harmonic, refers to any one ofthe above-mentioned sinusoidalcomponents, the frequency of which isa multiple of that of the fundamental.The amplitude of a harmonic isgenerally a few percent of that of thefundamental.Harmonic orderThe harmonic order, also referred to asthe harmonic number, is the ratio of thefrequency fn of a harmonic to that of thefundamental (generally the powerfrequency, i.e. 50 or 60 Hz):

n = fnf1

.

By definition, the harmonic order of thefundamental f1 is equal to 1. Note thatthe harmonic of order n is often referredto simply as the nth harmonic.SpectrumThe spectrum is the distribution of theamplitudes of the various harmonics asa function of their harmonic number,often illustrated in the form of ahistogram (see fig. 2).

Expression of the distorted waveAny periodic phenomenon can be re-presented by a Fourier series as follows:

y(t) = Y0 +n = 1

n = Yn 2 sin (nt n )

where:n Y0 = the amplitude of the DCcomponent, which is generally zero inelectrical power distribution;

fig.1: shape of a distorted wave.

harmonic

t

fundamental

distorted wave

I phase


n Yn = the rms value of thenth harmonic component,n n = phase angle of the nth harmoniccomponent when t = 0.Harmonics with an order above 23 areoften negligible.Rms value of a distorted waveHarmonic quantities are generallyexpressed in terms of their rms valuesince the heating effect depends on thisvalue of the distorted waveform.For a sinusoidal quantity, the rms valueis the maximum value divided by thesquare root of 2.For a distorted quantity, under steady-state conditions, the energy dissipatedby the Joule effect is the sum of theenergies dissipated by each of theharmonic components:

R I2 t = R I12 t + R I2

2 t + ... + R In2 t

where:

I2 = I12 + I2

2 + ... + I

n2

i.e. where:

I = In2

n = 1

n =

if the resistance can be considered tobe constant.The rms value of a distorted waveformcan be measured either directly byinstruments designed to measure the

true rms value, by thermal means or byspectrum analysers.Individual harmonic ratio and totalharmonic distortionThe industrial harmonic ratios and thetotal harmonic distortion quantify theharmonic disturbances present in apower supply network.n individual harmonic ratio (or harmonicpercentage)The harmonic ratio expresses themagnitude of each harmonic withrespect to the fundamental (see fig. 2).The nth harmonic ratio is the ratio of therms value of the nth harmonic to that ofthe fundamental.For example, the harmonic ratio of In isIn/I1 or 100 (In/I1) if expressed as apercentage (note that here In is not thenominal or rated current);n total harmonic distortion (alsoreferred to as THD, the total harmonicfactor or simply as distortion D).The total harmonic distortion quantifiesthe thermal effect of all the harmonics.It is the ratio of the rms value of all theharmonics to that of one of the twofollowing quantities (depending on thedefinition adopted): the fundamental (CIGRE), which cangive a very high value:

D = Yn

2

n = 2

n =

Y1

the measured rms quantity(IEC 555-1), in which case 0 < D < 1:

D = Yn

2

n = 2

n =

Yn2

n = 1

n =

Unless otherwise indicated, we will usethe definition adopted by CIGRE (seethe glossary) which corresponds to theratio of the rms value of the harmoniccontent to the undistorted current atpower frequency.

fig. 2: the amplitude of a harmonic is oftenexpressed with respect to that of thefundamental.

100 %

1 5 7 n


3. principal disturbances caused byharmonic currents and voltages

Harmonic currents and voltages super-imposed on the fundamental have com-bined effects on equipment and devicesconnected to the power supply network.The detrimental effects of theseharmonics depend on the type of loadencountered, and include:n instantaneous effects;n long-term effects due to heating.

instantaneous effectsHarmonic voltages can disturbcontrollers used in electronic systems.They can, for example, affect thyristorswitching conditions by displacing thezero-crossing of the voltage wave (seeIEC 146-2 and Merlin Gerin CahierTechnique n 141).Harmonics can cause additional errors ininduction-disk electricity meters. Forexample, the error of a class 2 meter willbe increased by 0.3 % by a 5th harmonicratio of 5 % in current and voltage.Ripple control receivers, such as therelays used by electrical utilities forcentralised remote control, can bedisturbed by voltage harmonics withfrequencies in the neighbourhood of thecontrol frequency. Other sources ofdisturbances affecting these relays,related to the harmonic impedance ofthe network, will be discussed further on.Vibrations and noiseThe electrodynamic forces produced bythe instantaneous currents associatedwith harmonic currents cause vibrationsand acoustical noise, especially inelectromagnetic devices (transformers,reactors, etc.).Pulsating mechanical torque, due toharmonic rotating fields, can producevibrations in rotating machines.Interference on communication andcontrol circuits (telephone, controland monitoring)Disturbances are observed whencommunication or control circuits arerun along side power distributioncircuits carrying distorted currents.Parameters that must be taken intoaccount include the length of parallel

running, the distance between the twocircuits and the harmonic frequencies(coupling increases with frequency).

long-term effectsOver and above mechanical fatiguedue to vibrations, the main long-termeffect of harmonics is heating.Capacitor heatingThe losses causing heating are due totwo phenomena: conduction anddielectricc hysteresis.As a first approximation, they areproportional to the square of the appliedvoltage for conduction and to thefrequency for hysteresis.Capacitors are therefore sensitive tooverloads, whether due to anexcessively high fundamental or to thepresence of voltage harmonics.These losses are defined by the lossangle of the capacitor, which is theangle whose tangent is the ratio of thelosses to the reactive power produced(see fig. 3). Values of around 10-4 maybe cited for tan . The heat producedcan lead to dielectric breakdown.Heating due to additional losses inmachines and transformersn additional losses in the stators (copperand iron) and principally in the rotors(damping windings, magnetic circuits) ofmachines caused by the considerabledifferences in speed between theharmonic inducing rotating fields and therotor. Note that rotor measurements(temperature, induced currents) aredifficult if not impossible.n supplementary losses in transformersdue to the skin effect (increase in theresistance of copper with frequency),hysteresis and eddy currents (in themagnetic circuit).Heating of cables and equipmentLosses are increased in cables carryingharmonic currents, resulting intemperature rise. The causes of theadditional losses include:n an increase in the apparentresistance of the core with frequency,due to the skin effect;

n an increase in dielectric losses in theinsulation with frequency, if the cable issubjected to non-negligible voltagedistortion;n phenomena related to the proximityof conductors with respect to metalcladding and shielding earthed at bothends of the cable, etc.Calculations can be carried out asdescribed in IEC 287.Generally speaking, all electricalequipment (electrical switchboards)subjected to voltage harmonics orthrough which harmonic currents flow,exhibit increased energy losses andshould be derated if necessary.For example, a capacitor feeder cubicleshould be designed for a current equalto 1.3 times the reactive compensationcurrent. This safety factor does nothowever take into account theincreased heating due to the skin effectin the conductors.Harmonic distortion of currents andvoltages is measured using spectrumanalysers, providing the amplitude ofeach component.The rms value of the distorted current(or voltage) may be assessed in any ofthree ways:n measurement using a devicedesigned to give the true rms value,n reconstitution on the basis of thespectrum provided by spectral analysis,n estimation from an oscilloscopedisplay.

fig. 3: triangle relating to the capacitorpowers, (active (P), reactive (Q),apparent (R)).

Q

p

tan = pQ


4. acceptable limits, recommendations and standards

General limitsn synchronous machines: permissiblestator current distortion = 1.3 to 1.4 %;n asynchronous machines: permissiblestator current distortion = 1.5 to 3.5 %;n cables: permissible core-shieldingvoltage distortion = 10 %;n power capacitors: currentdistortion = 83 %, corresponding to anoverload of 30 % (1.3 times the ratedcurrent); overvoltages can reach up to10 % (see IEC 871-1, 931-1 andHD 525.1S1);n sensitive electronics: 5 % voltagedistortion with a maximum individualharmonic percentage of 3 % dependingon the equipment.

typical limits fordistribution networksThe French electrical utility, EDF,considers that voltage distortion will notexceed 5 % at the supply terminals aslong as each individual subscriber doesnot exceed the following limits:n 1.6 % voltage distortion;n individual harmonic percentages of: 0.6 % for even voltage harmonics, 1 % for odd voltage harmonics.The table in figure 4 lists typicalpercentages observed for the variousvoltage harmonics where:n low value = value likely to be found inthe vicinity of large disturbing loads andassociated with a low probability ofhaving disturbing effects;n high value = value rarely exceeded inthe network, and with a higherprobability of having disturbing effects.

typical limits for industrialnetworksIt is generally accepted that industrialnetwork without any sensitiveequipment such as regulators,

programmable controllers, etc. canaccept up to 5 % voltage distortion.This limit and the limits for theindividual harmonic ratios may bedifferent if sensitive equipment isconnected to the installation.

fig. 4: individual voltage harmonic percentages measured in high voltage distribution networks.

harmonic low highorder value (%) value (%)2 1 1.53 1.5 2.54 0.5 15 5 66 0.2 0.57 4 58 < 0.29 0.8 1.510 < 0.211 2.5 3.512 < 0.213 2 314 < 0.215 < 0.316 < 0.217 1 218 < 0.219 0.8 1.520 < 0.221 < 0.222 < 0.223 0.5 1


5. harmonics generators

In industrial applications, the maintypes equipment that generateharmonics are:n static converters;n arc furnaces;n lighting;n saturated reactors;n other equipment, such as rotatingmachines which generate slotharmonics (often negligible).

static converters on3-phase networksRectifier bridges and, more generally,static converters (made up of diodesand thyristors) generate harmonics.A Graetz bridge, for instance, requiresa rectangular pulsed AC current (seefig. 5) to deliver a perfect DC current. Inspite of their different waveforms, thecurrents upstream and downstreamfrom the delta-star connectedtransformer have the samecharacteristic harmonic components.The characteristic harmoniccomponents of the current pulsessupplying rectifiers have the followingharmonic numbers n, with n = kp 1,where:n k = 1, 2, 3, 4, 5...n p = number of rectifier arms, forexample: Graetz bridge p = 6, 6-pulse bridge p = 6, 12-pulse bridge p = 12.Applying the formula, the p = 6rectifiers cited above generateharmonics 5, 7, 11, 13, 17, 19, 23 and25, and the p = 12 rectifiers generateharmonics 11, 13, 23 and 25.The characteristic harmonics are allodd-numbered and have, as a firstapproximation, an amplitude of In = I1/nwhere I1 is the amplitude of thefundamental.This means that I5 and I7 will have thegreatest amplitudes. Note that they canbe eliminated by using a 12-pulsebridge (p = 12).In practice, the current spectrum isslightly different. New even and oddharmonics, referred to as non-

fig. 5: alternating current upstream from a Graetz bridge rectifier delivering a perfect directcurrent.

characteristic harmonics, of lowamplitudes, are created and theamplitudes of the characteristicharmonics are modified by severalfactors including:n asymmetry;n inaccuracy in thyristor opening times;n switching times;n imperfect filtering.For thyristor bridges, a displacement ofthe harmonics as a function of thethyristor phase angle may also beobserved.Mixed thyristor-diode bridges generateeven harmonics. They are used only atlow ratings because the 2nd harmonicproduces serious disturbances and isvery difficult to eliminate.Other power converters such as cyclo-converters, dimmers, etc. have richerand more variable spectra thanrectifiers. Note that they areincreasingly replaced by convertersusing the PWM (Pulse WidthModulation) technique. These devices

operate at high chopping frequencies(20 to 50 kHz) and are generallydesigned to generate only low levels ofharmonics.The harmonic currents of severalconverters combine vectorially at thecommon supply busbars. Their phasesare generally unknown except for thecase of diode rectifiers. It is thereforepossible to attenuate the 5 th and 7 thcurrent harmonics using two equallyloaded 6-pulse diode bridges, if thecouplings of the two power supplytransformers are carefully chosen(see fig. 6).

arc furnacesArc furnaces used in the steel industrymay be of the AC (see fig. 7) orDC type.AC arc furnaces(see fig. 7)The arc is non-linear, asymmetric andunstable. It generates a spectrum

load

phase current upstream from a delta-starconnected transformer supplying the rectifier

rectifier supply phase current

T/6

IT

t

T/6 T/3

IT

t


1 3 5 7 9 rang

0.1

1

10

100

43.2

1.3

0.5

continuous spectrum

in %

100

including odd and even harmonics aswas well as a continuous component(background noise at all frequencies).The spectrum depends on the type offurnace, its power rating and theoperation considered (e.g. melting,refining). Measurements are thereforerequired to determine the exactspectrum (see fig. 8).DC arc furnaces(see fig. 9)The arc is supplied via a rectifier and ismore stable than the arc in AC furnaces.The current drawn can be broken downinto:n a spectrum similar to that of arectifier;n a continuous spectrum lower thanthat of an AC arc furnace.

lightingLighting systems made up of dischargelamps or fluorescent lamps aregenerators of harmonic currents.A 3rd harmonic ratio of 25 % isobserved in certain cases. The neutralconductor then carries the sum of the3rd harmonic currents of the threephases, and may consequently besubjected to dangerous overheating ifnot adequately sized.

saturated reactorsThe impedance of a saturable reactor isvarying with the current flowingthrough it, resulting in considerablecurrent distortion. This is, for instance,the case for transformers at no load,subjected to a continuous overvoltage.

rotating machinesRotating machines generate high orderslot harmonics, often of negligibleamplitude. However small synchronousmachines generate 3rd order voltageharmonics than can have the followingdetrimental effects:n continuous heating (without faults) ofearthing resistors of generator neutrals;n malfunctioning of current relaysdesigned to protect against insulationfaults.

calculation modelWhen calculating disturbances, staticconverters and arc furnaces areconsidered to be harmonic currentgenerators.

To a large extent, the harmoniccurrents drawn by the disturbingequipment are independent of the otherloads and the overall networkimpedance. These currents cantherefore be considered to be injectedinto the network by the disturbingequipment. It is simply necessary toarbitrarily change the sign so that, forcalculation purposes, the disturbingequipment can be considered ascurrent sources (see fig. 10).The approximation is somewhat lessaccurate for arc furnaces. In this case,the current source model must becorrected by adding a carefully selectedparallel impedance.

fig. 6: attenuation circuit for I5 and I7.

fig. 7: arc furnace supplied by AC power.

fig. 8: current spectrum for an arc furnacesupplied by AC power.

fig. 10: harmonic current generators aremodelled as current sources.

InI1

fig. 9: arc furnace supplied by DC power.

load load

I5 and I7 attenuated

Dy 11

6-pulsediodebridge

Yy 0

6-pulsediodebridge

equal loads

I5 and I7I5 and I7

furnace

cable

transformer

HV

cable

rectifier

IZ

furnace

cable

transformer

HV


6. can capacitors cause a problem on networkscomprising disturbing equipment?

We will consider the two followingcases:n networks without power capacitors;n networks with power capacitors.

in the absence of capacitorbanks, harmonicdisturbances are limitedand proportional to thecurrents of the disturbingequipment.In principle, in so far as are concernedharmonics, the network remainsinductive.Its reactance is proportional to thefrequency and, as a first estimate, theeffects of loads and resistance arenegligible. The impedance of thenetwork, seen from a network node, istherefore limited to the short-circuitreactance Xsc at the node considered.The level of harmonic voltages can beestimated from the power of thedisturbing equipment and the short-circuit power at the node (busbars) towhich the disturbing equipment isconnected, the short-circuit reactanceconsidered to be proportional to thefrequency (see fig. 11).In figure 11:Lsc = the short-circuit inductance of thenetwork, seen from the busbars towhich the disturbing equipment isconnected,In = currents of the disturbingequipment,Xscn = Lsc n = Lsc n (2pi f1)thereforeVn = Xscn In = Lsc n (2pi f1) In.The harmonic disturbances generallyremain acceptable as long as thedisturbing equipment does not exceeda certain power level. However, thismust be considered with caution asresonance (see the next section) maybe present, caused by a nearbynetwork possessing capacitors andcoupled via a transformer.

Note: In reality, the harmonicinductance of network X, withoutcapacitors (essentially a distributionnetwork), represented by Lsc, can onlybe considered to be proportional to thefrequency in a rough approximation.For this reason, the network short-circuit impedance is generallymultiplied by a factor of 2 or 3 for thecalculations.Therefore: Xn = k n X1 with k = 2 or 3.The harmonic impedance of a networkis made up of different constituentssuch as the short circuit impedance ofthe distribution system as well as theimpedance of the cables, lines,transformers, distant capacitors,machines and other loads (lighting,heating, etc.).

in the presence of acapacitor bank parallelresonance can result indangerous harmonicdisturbancesResonance exists between thecapacitor bank and the reactance ofthe network seen from the bankterminals.The result is the amplification, with avarying degree of damping, of theharmonic currents and voltages if theorder of the resonance is the same asthat of one of the harmonic currentsinjected by the disturbing equipment.This amplified disturbance can bedangerous to the equipment.This is a serious problem and will bedealt with in below.This phenomenon is referred to asparallel resonance.What is this parallel resonance andhow can it cause dangerousharmonic disturbances?In so far as harmonic frequencies areconcerned, and for a firstapproximation, the network may berepresented as in figure 12.

fig. 12: equivalent diagrams for a circuitsubject to harmonic currents and including acapacitor bank.

fig. 11: the harmonic voltage Vn isproportional to the current In injected by thedisturbing equipment.

In

VnXsc I

node A (busbar)

node A (busbars)

Lsc C

0

InVnload

E

Lsc

50 Hz source

C load disturbing equipment

a: harmonic electricalrepresentation of a phase.

b: single-line diagram.

I


In this diagram: Lsc = the short-circuit inductance ofthe network seen from the busbars towhich the capacitor bank and thedisturbing equipment are connected, C = capacitors, In = currents of the disturbingequipment, load = loads (Joule effect,transmission of mechanical energy).In principle, we consider the short-circuit harmonic reactance seen fromthe busbars, i.e. the node (A) to whichthe capacitors, the loads and thedisturbing equipment are connected,giving Vn = ZAO In.The impedance versus frequencycurves (see fig.13) show that:n for the resonance frequency far, theinductive effect is compensated forexactly by the capacitive effect;n the reactance of the rejecter circuit: is inductive for low frequencies,including the fundamental frequency, increases with frequency, becomingvery high and suddenly capacitive atthe resonance frequency far;n the maximum impedance valuereached is roughly R = U2/P where Prepresents the sum of the active powervalues of the loaded motors, other thanthose supplied by a static converter.If a harmonic current In of order n , withthe same frequency as the parallelresonance frequency far, is injected bythe disturbing equipment, thecorresponding harmonic voltage can beestimated as Vn = R Inwith n = n ar = f ar/f1.Estimation of narThe order nar of parallel resonance isthe ratio of the resonance frequency farto the fundamental frequency f1 (powerfrequency).Consider the most elementary industrialnetwork, shown in the equivalentdiagram in figure 14, including acapacitor bank C supplied by atransformer with a short-circuitinductance LT, where Lsc representsthe short-circuit inductance of thedistribution network seen from theupstream terminals of the transformer,

far = 1

2pi (Lsc + LT ) C.

The order of the parallel resonance isroughly the same whether the network

impedance is seen from point A orpoint B (e.g. the supply terminals).In general, given the short-circuit powerat the capacitor bank terminals,

nar = SscQ

where:Ssc = short-circuit power at thecapacitor bank terminals,Q = capacitor bank power at theapplied voltage.Generally S is expressed in MVA andQ in Mvar.Practical consequences:n if the order of a harmonic currentinjected by disturbing equipmentcorresponds to the parallel resonanceorder, there is a risk of harmonicovervoltages, especially when thenetwork is operating at low loads. Theharmonic currents then becomeintensively high in network constituents

and undoubtedly present a danger tothe capacitors.n if the parallel resonance ordercorresponds to the frequency of thecarrier-current control equipment of thepower distribution utility, there is a riskof disturbing this equipment.To prevent resonance frombecoming dangerous, it must beforced outside the injected spectrumand/or damped.The short-circuit impedance of thenetwork is seldom accurately knownand, in addition, it can vary to a largeextent, thereby resulting in largevariations of the parallel resonancefrequency.It is therefore necessary to stabilise thisfrequency at a value that does notcorrespond to the frequencies of theinjected harmonic currents. This isachieved by connecting a reactor inseries with the capacitor bank.

fig. 14: the capacitor, together with the sum of the upstream impedances, forms a resonantcircuit.

distributorLsc

B ALT

lopp

loadC

0

I

fig. 13: curves showing the impedance due to the loads and due to the resistance of theconductors.

f (Hz)

inductive

capacitive

0

far

without capacitorsX = Lsc 2pi f

Xwithout capacitorsIZI = Lsc 2pi f

f (Hz)far

0

IZI ~R


n a minimum resistive value r(resistance of the inductance coil) forthe resonance frequency fr;n a capacitive reactance below theresonance frequency fr;n an inductive reactance above theresonance frequency fr, where

fr = 1

2pi L C.

The curves in figure 17 show the shapeof the network inductance, including theshort-circuit impedance and that of theLC branch, seen from busbars A.The choice of far depends on Lsc, Land C, while that of fr depends only onL and C; far and fr therefore becomecloser as Lsc becomes small with

The rejecter circuit thus created is thenrepresented by the diagram in figure 15where Vn = ZAO In.A series resonance, between L and C,appears. As opposed to this resonance,which gives a minimum impedance, theparallel resonance is often referred toan anti-resonance.The equation giving the frequency ofthe anti-resonance is:

far = 1

2pi (Lsc + L) CLsc generally being small compared toL, the equation shows that thepresence of reactor L, connected inseries with the capacitors, renders thefrequency far less sensitive to thevariations of the short-circuit inductanceLsc (from the connections points =busbars A).Series resonanceThe branch made up of reactor L andcapacitor C (see fig. 16), form a seriesresonance system of impedanceZ = r + j(L - 1/C) with:

respect to L. The level of reactivepower compensation, and the voltageapplied to the capacitors, depend partlyon L and C.The reactor L can be added in twodifferent manners, depending on theposition of the series resonance withrespect to the spectrum. The two formsof equipment are:n anti-harmonic reactors (for seriesresonance outside the spectrum lines);n filters (for series resonance on aspectrum line).

fig. 15: the reactor, connected in series withthe capacitor, forms a rejecter circuit. fig. 16: impedance of the rejecter circuit. fig. 17: network impedance at point A.

busbar node, point A

Lsc

C

0

InVnL

I

f (Hz)

X

0

f (Hz)0r

ph1

neutral

fr

inductive

capacitive

fr

IZI

C

L

r

f (Hz)0

f (Hz)

X

inductive

capacitivefr

far

farfr

0

IZI

~ r


7. anti-harmonic reactors

An anti-harmonic reactor can be usedto protect a capacitor bank againstharmonic overloads. Such solutions areoften referred to as reactor-connectedcapacitor installations.The reference diagram is once againfigure 15.In this assembly, the choice of L is suchthat the LC branch (where L is thereactor and C the reactive powercompensation capacitors) behavesinductively for the harmonicfrequencies, over the spectrum.As a result, the resonance frequency frof this branch will be below thespectrum of the disturbing equipment.The LC branch and the network (Lsc)are then both inductive over thespectrum and the harmonic currentsinjected by the disturbing equipmentare divided in a manner inverselyproportional to the impedance.Harmonic currents are therefore greatlyrestricted in the LC branch, protectingthe capacitors, and the major part ofthe harmonic currents flow in the rest ofthe network, especially in the short-circuit impedance.The shape of the network impedance,seen from the busbars to which the LCbranch is connected, is shown infigure 18.There is no anti-resonance inside thecurrent spectrum. The use of an anti-harmonic reactor therefore offers twoadvantages;

n it eliminates the danger of highharmonic currents in the capacitors;n it correlatively eliminates the highdistortions of the network voltage,without however lowering them to aspecified low value.Certain precautions are necessary:n no other capacitor banks must bepresent that could induce, through anti-resonance, a capacitive behaviour inthe initial network inside the spectrum;n care must be taken not to introducean anti-resonance with a frequencyused by the distribution utility for

carrier-current control, since this wouldplace an increased load on the highfrequency generators (175 Hz, 188 Hz).The anti-harmonic reactor is tuned toan order of 4.5 to 4.8, giving a valueof fr between 225 to 240 Hz for a50 Hz network, which is very near theripple control frequency used on manydistribution networks;n due to the continuous spectrum, theuse of anti-harmonic reactors on arcfurnaces requires certain precautionswhich can only be defined after carryingout special studies.

fig. 18: the capacitors are protected when fr is well below the harmonic spectrum.

IzI

f1 fr

theoretical impedance withoutthe LC branch

far

f (Hz)harmonic currentspectrum


r

ffr

f (Hz)

IZI

8. filters

Filters are used when it is necessary tolimit harmonic voltages present on anetwork to a specified low value. Twotypes of filters may be used to reduceharmonic voltages:n resonant shunt filters,n damped filters.

resonant shunt filtersThe resonant shunt filter (see fig. 16) ismade up of an LC branch with afrequency of

fr = 1

2pi L Ctuned to the frequency of the voltageharmonic to be eliminated.This approach is thereforefundamentally different than that ofreactor-connected capacitorsalready described. At fr, the resonantshunt presents a low minimumimpedance with respect to theresistance r of the reactor. It thereforeabsorbs nearly all the harmoniccurrents of frequency fr injected, withlow harmonic voltage distortion (sinceproportional to the product of theresistance r and the current flowing inthe filter) at this frequency.In principle, a resonant shunt isinstalled for each harmonic to belimited. They are connected to thebusbars for which harmonic voltagereduction is specified. Together theyform a filter bank.Figure 19 shows the harmonicimpedance of a network equipped witha set of four filters tuned to the 5th, 7th,11th and 13th harmonics. Note that

there are as many anti-resonances asthere are filters. These anti-resonancesmust be tuned to frequencies betweenthe spectrum lines. A careful study musttherefore be carried out if it is judgednecessary to segment the filter bank.Main characteristics of a resonantshuntThe characteristics depend onn r = fr/f1 the order of the filter tuningfrequency, with:n fr = tuning frequency;n f1 = fundamental frequency (generallythe power frequency, e.g. 50 Hz).These characteristics are:n the reactive power for compensation:Qvar.The resonant shunt, behavingcapacitively below its tuning frequency,contributes to the compensation ofreactive power at the power frequency.The reactive power produced by theshunt at the connection busbars, for anoperating voltage U1, is given by thefollowing equation:

Qvar = nr

2

n1 n2 U1

2 C 2pi f1

(note that the subscript 1 refers to thefundamental).C is the phase-to-neutral capacitanceof one of the 3 branches of the filterbank represented as a star.At first glance, the presence of areactor would not be expected toincrease the reactive power supplied.The reason is the increase in voltage atpower frequency f1 caused by theinductance at the capacitor terminals;

n characteristic impedance:

X0 = LC

;

n the quality factor:q = X0/r.An effective filter must have a reactorwith a large quality factor q, therefore:r


0

f (Hz)

fr

X

inductive

capacitive

neutral

r

C

L

phase

R

with: Qvar = reactive power forcompensation produced by the filter, p1 = filter losses at power frequencyin W;n the losses due to the harmoniccurrents cannot be expressed by simpleequations; they are greater than:

pn = Unr

2

r

in which Unr is the phase-to-phaseharmonic voltage of order nr on thebusbars after filtering.In practice, the performance ofresonant shunt filters is reduced bymis-tuning and special solutions arerequired as follows:n adjustment possibilities on thereactors for correction of manufacturingtolerances;n a suitable compromise between the qfactor and filter performance to reducethe sensitivity to mis-tuning, therebyaccepting fluctuations of f1 (networkfrequency) and fr (caused by thetemperature dependence of thecapacitance of the capacitors).

damped filters2nd order damped filterOn arc furnaces, the resonant shuntmust be damped. This is because thecontinuous spectrum of an arc furnaceincreases the probability of an injectedcurrent with a frequency equal to theanti-resonance frequency. In this case, itis no longer sufficient to reduce thecharacteristic harmonic voltages. Theanti-resonance must also be diminishedby damping.Moreover, the installation of a largenumber of resonant shunts is oftencostly, and it is therefore better to use awide-band filter possessing the followingproperties:n anti-resonance damping;n reduced harmonic voltages forfrequencies greater than or equal to itstuning frequency, leading to the namedamped high-pass filter;n fast damping of transients producedwhen the filter is energised. The 2ndorder damped filter is made up of aresonant shunt with a dampingresistor R added at the reactor

terminals. Figure 21 shows one of thethree phases of the filter.The 2nd order damped filter has zeroreactance for a frequency fr higher thanthe frequency f where:

f = 12pi L C

and

fr = 1 + Q q

2pi q (Q2 1) L C.

The filter is designed so that frcoincides with the first characteristicline of the spectrum to be filtered. Thisline is generally the largest.When Q (or R) take on high values, frtends towards f, which means that theresonant shunt is a limiting case of the2nd order damped filter.It is important not to confuse Q, thequality factor, with Qvar, the reactivepower of the filter for compensation.The 2nd order damped filter operatesas follows:n below fr: the damping resistorcontributes to the reduction of thenetwork impedance at anti-resonance,thereby reducing any harmonicvoltages;n at fr: the reduction of the harmonicvoltage to a specified value is possiblesince, at this frequency, no resonancecan occur between the network and thefilter, the latter presenting animpedance of a purely resistivecharacter.However, this impedance being higherthan the resistance r of the reactor, the

filtering performance is less than for aresonant shunt;n above fr: the filter presents aninductive reactance of the same type asthe network (inductive), which lets itadsorb, to a certain extent, thespectrum lines greater than fr, and inparticular any continuous spectrum thatmay be present. However, anti-resonance, if present in the impedanceof the network without the filter, due tothe existing capacitor banks, reducesthe filtering performance. For thisreason, existing capacitor banks mustbe taken into account in the design ofthe network and, in some cases, mustbe adapted.The main electrical characteristics of a2nd order damped filter depend onn r = fr/f1 , the order of the filter tuningfrequency, with:n fr = tuning frequency;n f1 = fundamental frequency (generallythe power frequency, e.g. 50 Hz).These characteristics are:n the reactive power for compensation:For a 2nd order damped filter atoperating voltage U1 (the subscript 1referring to the fundamental), thereactive power is roughly the same asfor a resonant shunt with the sameinductance and capacitance, i.e. inpractice:

Qvar = nr

2

nr 12 U1

2 C 2pi f1

C is the phase-to-neutral capacitance ofone of the 3 branches of the filter bankrepresented as a star.

fig. 21: 2nd order damped filter.

f = 12pi L C


n characteristic impedance:

X0 = LC

;

n the quality factor of the reactor:q = X0/rwhere r is the resistance of the reactor,dependent on the skin effect anddefined at frequency fr;n the quality factor of the filter:Q = R/X0.The quality factors Q used aregenerally between 2 and 10;n the losses due to the fundamentalcompensation current and to theharmonic currents; these are higherthan for a resonant shunt and can onlybe determined through networkanalysis.The damped filter is used alone or in abank including two filters. It may alsobe used together with a resonant shunt,with the resonant shunt tuned to thelowest lines of the spectrum.Figure 22 compares the impedance ofa network with a 2nd order dampedfilter to that of a network with aresonant shunt.Other types of damped filtersAlthough more rarely used, otherdamped filters have been derived fromthe 2nd order filter:n 3rd order damped filter (see fig. 23)Of a more complex design than the 2ndorder filter, the 3rd order filter isintended particularly for highcompensation powers.The 3rd order filter is derived from a 2ndorder filter by adding another capacitorbank C2 in series with the resistor R,thereby reducing the losses due to thefundamental.C2 can be chosen to improve thebehaviour of the filter below the tuningfrequency as well, which favours thereduction of anti-resonance.The 3rd order filter should be tuned tothe lowest frequencies of the spectrum.Given the complexity of the 3rd orderfilter, and the resulting high cost, a 2ndorder filter is often preferred forindustrial applications;n type C damped filter (see fig. 24)In this filter, the additional capacitorbank C2 is connected in series with thereactor. This filter offers characteristicsroughly the same as those of the 3rdorder filter;

Znetwork

f (Hz)

with resonant shunt

with 2nd order damped filter

IZIr

C

neutral

L

phase

R

fig. 22: the impedance, seen from point A, of a network equipped with either a 2nd orderdamped filter or a resonant shunt.

Rr

C

neutral

L

phase

C2

R

r

C

neutral

L

phase

C2

n damped double filter (see fig. 25)Made up of two resonant shuntsconnected by a resistor R, this filter isspecially suited to the damping of theanti-resonance between the two tuningfrequencies;n low q resonant shuntThis filter, which behaves like adamped wide-band filter, is designedespecially for very small installationsnot requiring reactive powercompensation.The reactor, with a very highresistance (often due to the addition ofa series resistor) results in losseswhich are prohibitive for industrialapplications.

fig. 23: 3rd order damped filter. fig. 24: type C damped filter.

fig. 25: damped double filter.

ra

La

rb

Lb

Ca

neutral

Cb

neutral

phase

R


9. measurement relays required for the protection ofreactor-connected capacitors and filters

An anti-harmonic reactor mustwithstand the 3-phase short-circuitcurrent at the common reactor-capacitor terminals.Furthermore, both anti-harmonicreactors and filters must continuouslywithstand fundamental and harmoniccurrents, fundamental and harmonicvoltages, switching surges anddielectric stresses.In this chapter, anti-harmonic reactor-connected capacitor assemblies andfilters will be referred to collectively asdevices.

basic protection againstdevice failuresAll the elements of these devices canbe subject to insulation faults and short-circuits, while the capacitor banks aremainly the source of unbalance faultscaused by the failure of capacitorelements.n protection of these devices againstinsulation faults can be provided byresidual current relays (or zero phasesequence relays).Note: the neutral is generally not distributedon such devices; for higher sensing accuracy, it isbetter to use a toroidal typetransformer, encircling all the liveconductors of the feeder, rather thanthree step-down current transformers;n protection against short-circuits canbe provided by overcurrent relaysinstalled on the filter feeder.This protection must detect 2-phaseshort-circuits at the common reactor-capacitor terminals, while lettingthrough inrush transients;n detection of unbalance currents in theconnections between the neutrals of

the double star connected capacitorbanks (see fig. 26).In addition to the damage that can becaused by the resulting unbalancedstresses, the failure of a small numberof capacitor elements is detrimental tofilter performance.This protection is therefore designed todetect, depending on its sensitivity, thefailure of a small number of capacitorelements. Of the single-pole type, thisprotection must be: insensitive to the harmonics, set to above the natural unbalancecurrent of the double star connectedcapacitor bank (this unbalance dependson the accuracy of the capacitors), set to below the unbalance currentdue to the failure of a single capacitorelement,

operate on a major fault causing anunbalance.The fluctuation of the supply voltagemust be taken into account in thecalculation of all these currents.

basic protection againstabnormal stresses on thedevicesThese abnormal stresses areessentially due to overloads. To protectagainst them, it is necessary to monitorthe rms value of the distorted current(fundamental and harmonics) flowing inthe filter.It is also necessary to monitor thefundamental voltage of the powersupply using an overvoltage relay.

fig. 26: unbalance detection for a double star connected capacitor bank.

C/2

phase 1 phase 2 phase 3

current relayC/2 C/2 C/2 C/2 C/2

r

L

r

L

r

L


10. example of the analysis of a simplified network

The diagram in figure 27 represents asimplified network comprising a2,000 kVA six-pulse rectifier, injecting aharmonic current spectrum, and thefollowing equipment which will beconsidered consecutively in threedifferent calculations:n a single 1,000 kvar capacitor bank;n anti-harmonic reactor-connectedcapacitor equipment rated 1000 kvar;n a set of two filters comprising aresonant shunt tuned to the 5thharmonic and a 2nd order damped filtertuned to the 7th harmonic. Thecapacitor bank implemented in thismanner is rated 1,000 kvar.Note that:n the 1,000 kvar compensation poweris required to bring the power factor toa conventional value;n the harmonic voltages alreadypresent on the 20 kV distributionnetwork have been neglected for thesake of simplicity.This example will be used to comparethe performance of the three solutions,however the results can obviously notbe applied directly to other cases.

capacitor bank aloneThe network harmonic impedancecurve (see fig. 28), seen from the nodewhere the harmonic currents areinjected, exhibits a maximum (anti-resonance) in the vicinity of the7th current harmonic. This results in anunacceptable individual harmonicvoltage distortion of 11 % for the 7thharmonic (see fig. 29).The following characteristics are alsounacceptable:n a total harmonic voltage distortion of12.8 % for the 5.5 kV network,compared to the maximum permissiblevalue of 5 % (without considering therequirements of special equipment);n a total capacitor load of 1.34 timesthe rms current rating, exceeding thepermissible maximum of 1.3(see fig. 30).The solution with capacitors alone istherefore unacceptable.

reactor-connectedcapacitor bankThis equipment is arbitrarily tuned to4.8 f1.Harmonic impedance(see fig. 31)

The network harmonic impedancecurve, seen from the node where theharmonic currents are injected, exhibitsa maximum of 16 ohms (anti-resonance) in the vicinity ofharmonic order 4.25. This unfortunatelyfavours the presence of 4th voltage

fig. 28: harmonic impedance seen from thenode where the harmonic currents areinjected in a network equipped with acapacitor bank alone.

fig. 29: harmonic voltage spectrum of a5.5 kV network equipped with a capacitorbank alone.

motor

network20 kVIsc 12.5 kA20/5.5 kV5,000 kVAUsc 7.5 %Pcu 40 kW

5.5/0.4 kV1,000 kVAUsc 5 %Pcu 12 kW

560 kW500 kVA at cos = 0.9

2,000 kVAdisturbing equipment

capa.

reactor+capa.

resonant shuntand2nd order damped filterload

fig. 27: installation with disturbing equipment, capacitors and filters.

H7.75

38.2

Z ()

3 5 7 9 H8 10 11 13

350 11 %

V (V)


harmonic. However, the lowimpedance, of an inductive character,of the 5th harmonic favours the filteringof the 5th harmonic quantities.Voltage distortion(see fig. 32)For the 5.5 kV network, the individualharmonic voltage ratios of 1.58 %(7th harmonic), 1.5 % (11th harmonic)and 1.4 % (13th harmonic) may be toohigh for certain loads. However in manycases the total harmonic voltagedistortion of 2.63 % is acceptable.

For the 20 kV network, the totalharmonic distortion is only 0.35 %, anacceptable value for the distributionutility.Capacitor current load(see fig. 33)The total rms current load of thecapacitors, including the harmoniccurrents, is 1.06 times the current rating,i.e. less than the maximum of 1.3.This is the major advantage of reactor-connected capacitors compared to thefirst solution (capacitors alone).

resonant shunt filter tunedto the 5th harmonic and adamped filter tuned to the7th harmonicIn this example, the distribution of thereactive power between the two filtersis such that the filtered 5th and 7thvoltage harmonics have roughly thesame value. In reality, this is notrequired.Harmonic impedance(see fig. 34)The network harmonic impedancecurve, seen from the node where theharmonic currents are injected, exhibitsa maximum of 9.5 ohms (anti-resonance) in the vicinity ofharmonic 4.7.For the 5th harmonic, this impedance isreduced to the reactor resistance,favouring the filtering of the 5thharmonic quantities.For the 7th harmonic, the low, purelyresistive impedance of the dampedfilter also reduces the individualharmonic voltage.For harmonics higher than the tuningfrequency, the damped filter impedancecurve reduces the correspondingharmonic voltages.This equipment therefore offers animprovement over the second solution(reactor-connected capacitors).

3 5 7 9 H8 10 11 13

- 82

I (A)

fig. 30: spectrum of the harmonic currentsflowing in the capacitors for a networkequipped with a capacitor bank alone.

fig. 32: harmonic voltage spectrum of a5.5 kV network equipped with reactor-connected capacitors.

fig. 31: harmonic impedance seen from thenode where the harmonic currents areinjected in a network equipped with reactor-connected capacitors.

fig. 33: spectrum of the harmonic currentsflowing in the capacitors for a networkequipped with reactor-connectedcapacitors.

fig. 34: harmonic impedance seen fromthe node where the harmonic currentsare injected in a network equipped with aresonant shunt filter tuned to the5th harmonic and a damped filtertuned to the 7th harmonic.

Z ()

H4.7

9.5

75

5 7 H11 13

3424 %

I (A)Z ()

H~ 4.25

15.6

4.8

3 5 7 9 H84 11 13

50 1.55 %

V (V)

19 0.6 %

48 1.5 % 45

1.4 %


Voltage distortion(see fig. 35)For the 5.5 kV network, the individualharmonic voltage ratios of 0.96 %,0.92 %, 1.05 % and 1 % for the 5th,7th, 11th and 13th harmonicsrespectively are acceptable for mostsensitive loads. The total harmonicvoltage distortion is 1.96 %.For the 20 kV network, the totalharmonic distortion is only 0.26 %, anacceptable value for the distributionutility.Capacitor current loadThe total rms current load of theresonant shunt filter capacitors(see fig. 36) is greater than 1.3 time thecurrent rating. The capacitance musttherefore be increased, which willimprove the filtering performance,

reducing the 5th harmonic ratio to lessthan 1 %.The result is of course an increase inthe reactive power compensationcapacity.To avoid overcompensating, a compro-mise must be found for the size ofthese capacitors. The calculation istherefore repeated with this new data.For the damped filter tuned to the 7thharmonic, the total rms current load ofthe capacitors (see fig. 37) is within thetolerance of 1.3 times their currentrating.This example demonstrates an initialapproach to the problem. However inpractice, over and above thecalculations relative to the circuitelements (L, r, C and R), othercalculations are required before

proceeding with the implementation ofany solution:n the spectra of the currents flowing inthe reactors connected to thecapacitors;n the total voltage distortion at thecapacitor terminals;n reactor manufacturing tolerances andmeans for adjustment if necessary;n the spectra of the currents flowing inthe resistors of the damped filters andtheir total rms value;n voltage and energy transientsaffecting the filter elements duringenergisation.These more difficult calculations,requiring a solid understanding of boththe network and the equipment, areused to determine all the electro-technical information required for thefilter manufacturing specifications.

fig. 35: harmonic voltage spectrum of a5.5 kV network equipped with aresonant shunt filter tuned to the 5thharmonic and a damped filter tuned tothe 7th harmonic.

fig. 36: spectrum of the harmonic currentsflowing in the capacitors of a resonant shuntfilter tuned to the 5th harmonic on a networkequipped with a damped filter tuned to the7th harmonic.

fig. 37: spectrum of the harmonic currentsflowing in the capacitors of a damped filtertuned to the 7th harmonic on a networkequipped with a resonant shunt filter tunedto the 5th harmonic.

5 H

I (A)

39

5 7 H11 13

22 23 %

10 10 %

I (A)

5 7 H11 13

0.91 %

V (V)

0.96 %1.05 %

1 %


11. conclusion

Static power converters areincreasingly used in industrialdistribution. The same is true for arcfurnaces in the growing electric-powered steel industry. All these loadsproduce harmonic disturbances andrequire compensation of the reactivepower they consume, leading to theinstallation of capacitor banks.Unfortunately these capacitors, inconjunction with the inductances in thenetwork, can cause high frequency

oscillations that amplify harmonicdisturbances. Installers and operatorsof industrial networks are thus oftenconfronted with a complex electricalproblem.The main types of harmonicdisturbances and the technical meansavailable to limit their extent have beenpresented in this document. Withoutoffering an exhaustive study of thephenomena involved or relating all

acquired experience, this documentshould provide the necessarybackground to, if not solve theproblems, at least facilitate discussionswith specialists.For further information or assistance,feel free to contact the Network Studiesdepartment of the Central R&D organi-sation of Merlin Gerin, a group ofspecialised engineers with more thantwenty years of experience in this field.


Standardsn IEC 146: Semi-conductor converters.n IEC 287: Calculation of thecontinuous current rating of cables.n IEC 555-1: Disturbances in supplysystems caused by householdappliances and similar electricalequipment - Definitions.n IEC 871-1 and HD 525.1-S-T:Shunt capacitors for AC power systemshaving a rated voltage above 660 V.n NF C 54-100.n HN 53 R01 (May 1981): EDF generalorientation report. Particular aspectsconcerning the supply of electricalpower to sensitive electronic equipmentand computers.Merlin Gerin's Cahier Techniquen Residual current devicesCahier Technique n 114R. CALVASn Les perturbations lectriques en BTCahier Technique n 141R. CALVASOther publicationsn Direct current transmission, volume 1E. W. KIMBARKpublished by: J. WILEY and SONS.n Le cyclo-convertisseur et sesinfluences sur les rseauxd'alimentation (The cyclo-converter andits effects on power supply networksT. SALZAM and W. SCHULTZ - AIMLige CIRED 75.n Perturbations rciproques desquipements lectroniques depuissance et des rseaux - Quelquesaspects de la pollution des rseaux parles distorsions harmoniques de laclientle (Mutual disturbances betweenpower electronics equipment andnetworks - Several aspects concerningnetwork pollution by harmonic distortionproduced by subscribers).Michel LEMOINE - DER EDFRGE T 85 n 3 03/76.

n Perturbations des rseaux industrielset de distribution. Compensation parprocds statistiques.Rsonances en prsence desharmoniques crs par lesconvertisseurs de puissance et lesfours arc associs des dispositifsde compensation.(Disturbances on industrial anddistribution networks. Compensation bystatistical processes.Resonance in the presence ofharmonics created by power convertersand arc furnaces associated withcompensation equipment.)Michel LEMOINE - DER EDFRGE T 87 n 12 12/78.n Perturbations des rseaux industrielset de distribution. Compensation parprocds statistiques.Perturbations de tension affectant lefonctionnement des rseaux -fluctuations brusques, flicker,dsquilibres et harmoniques.(Disturbances on industrial anddistribution networks. Compensation bystatistical processes.Voltage disturbances affecting networkoperation - fluctuations, flicker,unbalances and harmonics.M. CHANAS - SER-DER EDFRGE T 87 n 12 12/78.n Pollution de la tension(Voltage disturbances).P. MEYNAUD - SER-DER EDFRGE T 89 n 9 09/80.n Harmonics, characteristicparameters, methods of study,estimates of existing values in thenetwork.(ELECTRA) CIGRE 07/81.n Courants harmoniques dans lesredresseurs triphass commutationforce.(Harmonic currents in forcedcommutation 3-phase rectifiers)W. WARBOWSKICIRED 81.

n Origine et nature des perturbationsdans les rseaux industriels et dedistribution.(Origin and nature of disturbances inindustrial and distribution networks).Guy BONNARD - SER-DER-EDFRGE 1/82.n Problmes particuliers poss parltude du phnomne de distorsionharmonique dans les rseaux.(Particular problems posed by the studyof harmonic distortion phenomena innetworks).P. REYMONDCIGRE Study Committee 36 09/82.n Rduction des perturbationslectriques sur le rseau avec le four arc en courant continu (Reduction ofelectrical network disturbances by DCarc furnaces).G. MAURET, J. DAVENEIRSID SEE LYON 05/83.n Line harmonics of converters with DCmotor loads.A. DAVID GRAHAM and EMIL T.SCHONHOLZER.IEEE transactions on industryapplications.Volume IA 19 n 1 02/83.n Filtrage dharmoniques etcompensation de puissance ractive -Optimisation des installations decompensation en prsenced'harmoniques.(Harmonic filtering and reactive powercompensation - Optimisingcompensation installations in thepresence of harmonics).P. SGARZI and S. THEOLERE,SEE Seminar RGE n 6 06/88.

12. bibliography

Cahier Technique Merlin Gerin n 152 / p.24Ral. : Illustration Technique Lyon -DTE - 10/94 - 2500 - Imprimeur :

Documents

Harmonic