外文翻译原文-谐波传播在电力配电系统设计中的影响

ORIGINALPAPERJ.A.GhijselenW.A.RyckaertJ.A.MelkebeekInfluenceofelectricpowerdistributionsystemdesignonharmonicpropagationReceived:5June2003/Accepted:11September2003/Publishedonline:14November2003C211Springer-Verlag2003AbstractTheimpactofthedesignparametersofelectricpowerdistributionsystemsonthepropagationofhar-monicdistortionisinvestigated.Thisconceptualstudyisbasedonsimulationsonageneralizeddistributionsys-temmodel,andleadstoanincreasedinsightinthemechanismsofthegenerationandpropagationofvolt-agedistortion.Moreover,analyticalexpressionsarepresentedthatpredicttheimpactofchangingdesignparametersonvoltagedistortion.KeywordsDistributionsystemsVoltagedistortionHarmonicsPowerqualityPowersystemimpedance1IntroductionBecauseoftheincreasingpenetrationofnon-linearloadsinelectricpowerdistributionsystems,utilitiesandequipmentmanufacturersareincreasinglyconcernedwithharmonicpollutionofthevoltagewaveform.Voltagedistortionisknowntoexhibitmanyadverseeects1,andespeciallyinareaswheretheelectricitytradeisbeingliberalized,itisfearedthatvoltagedis-tortionwillincreaseinthenearfuture2.Inmanypartsoftheworld,theactualvoltagedistortionlevelsaremaintainedwithinplanninglevelsbyimposingappro-priateemissionlimitstotheharmoniclinecurrentsofequipment3.Todetermineappropriateequipmentemissionlimits,bothmeasurementcampaigns4andsimulations5,6arerequiredtostudytheharmonicpropagationinanactualnetwork.Atfirstsight,itseemseasierandcheapertoconductsimulationsinsteadofmeasurements.How-ever,theparametersanddesignstrategiesmaybeverydierentfromonenetworktoanother7,makingalargenumberofsimulationsnecessary.Moreover,manyparametersareunknownandarethereforeestimatedorevenneglected,renderingresultsthatmaydierlargelyfrommeasureddata8.Finally,asharmonicpropaga-tionstudiesaremostlylimitedtoratherspecificcases(e.g.,5),fundamentalinsightinthemechanismsofharmonicpropagationandtheinfluenceofthedistri-butionsystemdesignisnotobtained.Inthispaper,theimpactofdierentdistributionsystemdesignparametersonharmonicpropagationisinvestigated.Thestudyisbasedontheanalysisofageneralizeddistributionfeedermodelofwhichtheparametersarevaried.Somepreliminaryandqualitativeresults,basedonsimulationsofaspecificcasestudy,arereportedin9.Inthepresentpaper,however,amorefundamentalapproachisadopted.Analyticalexpres-sionsandquantitativeresultsarepresentedthatapproximatelypredicttheimpactofchangingdesignparametersonthedistortionlevels.Thevalidityoftheanalyticalpredictionsisconfirmedbysimulations.Sub-sequently,theanalysisisextendedtoincludetheeectsofshuntcapacitance,whicharestronglyrelatedwithpowersystemresonances.2Basicpowersystemsetup2.1NetworktopologyInordertoinvestigatetheinfluenceofdierentdistri-butionsystemparametersonharmonicpropagation,asimplifiedmodelofatypicalmediumvoltage(MV)distributionsystemisadopted(Fig.1).Thehigh-to-mediumvoltage(HV/MV)transformer,whichisfeedingthepointofcommoncoupling(PCC),isrepresentedbyitsshort-circuitimpedanceZm.Severalparallelandidenticalradialfeeders,havingfivenodeseach,connecttotheloads.TheconductorsegmentsinterconnectingJ.A.Ghijselen(&)W.A.RyckaertJ.A.MelkebeekFacultyofEngineering,ElectricalEnergyLaboratory(EELAB),GhentUniversity,Sint-Pietersnieuwstraat41,9000Gent,BelgiumE-mail:jozef.ghijselenugent.beTel.:+32-9-2643442Fax:+32-9-2643582ElectricalEngineering(2004)86:181190DOI10.1007/s00202-003-0201-7thefeedernodesarerepresentedbytheirseriesimped-ancesZs,k.TheMV/LVtransformersmaybelocatedbetweentheMVbusandthefeeders(Zl,Fig.1a)orbetweenthefeedernodesandtheloads(Zc,Fig.1b).Theformerpracticecallsforextendedlowvoltage(LV)feeders,whichisthepracticeinlargepartsofEurope.ThelatterpracticecallsforextendedMVfeeders,whichisthepracticeinmanyNorthAmericanregions.Theloadsconnectedtothenodesaremodeledasidealcurrentsources;thisapproximationisallowedasformoderatevoltagedistortionlevels(totalharmonicdistortion(THD)45C14,theharmonicimpedanceforharmonicsh3isapproximatelyinductiveandequalto:Zm;l;chC25jhZm;l;cC12C12C12C12sinhZm;l;c1Consequently,theharmonictransformerimpedancedependsonboththemagnitudeandphaseangleofthefundamentaltransformerimpedance.Forinstance,itfollowsfrom(1)thatthesmallHV/MVandMV/LVtransformersexhibitanharmonicimpedancethatis1.39and3.48timessmaller,respectively,thantheharmonicimpedanceofthelargeHV/MVtransformer.2.3ConductorparametersBecauseoftheconsiderablelengthoftheconductorsinmanydistributionsystems,voltagedropisgenerallymoreimportantthanpowerloss.Themaximalallowablemagnitude|Zs|ofthe(fundamental)conductorimped-anceisdeterminedtolimitthe(fundamental)voltagedropDV=|VFl|)|VF5|to0.12pualongthefeeder,whilethevoltageatthebeginningofthefeederequals|VFl|=1.06pu.Thetotalfeederloadissupposedtoequal1puatapowerfactorofcos/=0.8,andisequallydividedamongthenodes.Thesevaluesaretypicalfordistributionsystemoperation.Theconductortype(overheadorcable)ofallcon-ductorsegmentsisconsideredequal,buttheconductorsectionmaybetapered.Forsimplicity,theimpedanceofthefeedersegmentsissupposedtoincreaselinearlytowardstheendofthefeeder.Mtdenotesthetaperingfactordeterminingtheimpedanceofthelastfeedersegment:Zs;4MtZs;12Anon-taperedlineisobtainedforMt=1.Thefol-lowingmaximalconductorimpedancevaluesarethenfoundandserveinthefollowingsectionstoobtaindif-ferentfeederarrangementswithequal(fundamental)voltagedropsDV:ZsjZsjejhZs0:04815pu55C14regularoverheadline;notaperingZsjZsjejhZs0:06089pu80C14widelyspacedoverheadline;notaperingZsjZsjejhZs0:04626pu30C14cable;notaperingZs;1jZs;1jejhZs;10:02898pu55C14regularoverheadline;Mt3Fig.1BasicMVdistributionsystemmodel:aMV/LVtransformerlocatedatthebeginningofthefeeder,bMV/LVtransformerslocatedinthefeedernodes182Zs;1jZs;1jejhZs;10:02070pu55C14regularoverheadline;Mt5ZsjZsjejhZs0:09300pu55C14regularoverheadline;notapering;expectedloadpowerfactorcos/1Thepuvaluesarereferredtotheratingofasinglefeeder.Aswiththetransformerimpedance,thecon-ductorimpedanceisconsideredtoberesistive-inductive.BecausehZs30C14,theharmonicimpedanceofthecon-ductorsisapproximatelyinductive:ZshC25jhZsjjsinhZs3Consequently,whentheregularoverheadlineisreplacedbythecableorthewidelyspacedoverheadline,themagnitudeoftheharmonicimpedance(3)decreaseswithafactor1.71orincreaseswithafactor1.52,respectively.Whenexpectedpowerfactorofthefeederloadisincreasedfrom0.8to1,theharmonicimpedanceoftheregularoverheadlineincreasesbyModelingpeakrectifierloadsInthispaper,peakrectifiersaresupposedtobethemostcommonnon-linearload.Becauseofthelimitednumberofnodesinasinglefeeder,alargenumberofloadsisaggregatedineverysinglenode.Arealisticloadcurrentspectrumshouldthereforeincludetheeectsofattenu-ationanddiversity11.AtypicalcurrentspectrumcomplyingwiththeserequirementsislistedinTable112.Itshouldberememberedthatthenumericalresultsofvoltagedistortioncalculationsdependontheactualloadcurrentspectrum.Someexamples,illustratinginmoredetailthespecificinfluenceofthezero-sequence(h=3,9,15,.)andhigher-order(h17)harmonicloadcur-rents,aregivenin9.3InfluenceofneutralconductorpracticeWhentheloadcurrentcontainsazero-sequencecom-ponent(e.g.,causedbyloadunbalanceortriplenhar-monics),theimpactoftheneutralconductorpracticeonthevoltagedistortionthroughoutthedistributionsys-tembecomesimportant.Boththearrangementsofthefeederconductorandtransformersinfluencetheneutralconductorpractice.3.1FeederconductorarrangementInthispaper,twotypicalfeederconductorarrangementsarestudied.Forasymmetricalthree-phase,four-wirearrangementwithequalconductorsections,theimped-anceforzero-sequencecurrentsequalsfourtimestheimpedanceforthepositive-andnegative-sequencecomponents.Insuchsystems,triplenharmonics(behavingaszero-sequencecurrentsinbalancedsys-tems)maycauseconsiderablevoltagedistortion13.Whenthethree-phaseconductorsaresplitintothreesingle-phase,two-wire,conductorsets,athree-phase,six-wirearrangementisformed,forwhichthezero-sequenceimpedanceoftheconductorsequalsthepositive-andnegative-sequenceimpedances.Therefore,zero-sequencecurrentscauseconsiderablylessvoltagedistortionthaninathree-phase,four-wirearrangement.Toassesstheinfluenceoftheconductorarrangement,thetotalharmonicvoltagedropDVhofasinglecon-ductorsegmentisdefinedastheRMSvalueoftheharmonicvoltagedrop:DVhX1h2Zshjj2Ihjj2s4withI(h)denotingtheharmoniccurrentcomponentsflowingintheconductor.Ifbalancedloadsareassumed,thereductionofthetotalharmonicvoltagedropDVhwhenchangingafour-wireforasix-wirearrangementdependsontheimportanceofthetriplenharmoniccomponentsoftheloadcurrentspectrumandcanbeapproximatedusing(4)and(3):DVh;4wDVh;6wC25Ph63=h1h2Ihjj2k2sPh3=h1h2Ihjj2Ph1h2Ihjj2vuuuut5whereksdenotestheratioofthezero-sequencetopositive-sequenceimpedancesoftheconductorsinthefour-wirearrangement.FortheloadcurrentspectrumofTable1andks=4(symmetricalfour-wirearrangement),thereductionfactor(5)equals2.62.Inpractice,theneutralconductorsectionisoftenchosensmallerthanthephaseconductorsections,causingks4andhenceresultinginanevengreaterreductionfactor.Inthesamemanner,thereductionfactorofthetotalharmonicvoltagedropofaconductorsegmentcanbeTable1Linecurrentspectrumoftheappliednon-linearloadh|I(h)/I(1)|11.00030.82050.53470.31690.166110.082130.015150.010170.0060190.0050210.0030230.0010250.0010270,h25183approximatedwhenthezero-sequencecurrentcompo-nentsareeliminatedbeforeenteringthefeederconduc-tors(e.g.,bymeansofanintermediateMV/LVtransformerconnectedinDY):DVh;neutralDVh;noneutralC25Ph63=h1h2Ihjj2k2sPh3=h1h2Ihjj2Ph63=h1h2Ihjj2vuuuuut6ForthelinecurrentspectrumofTable1,thereduc-tionfactor(6)equals1.28forks=1(six-wirearrange-ment)andbecomes3.36forks=4(symmetricalfour-wirearrangement).Inpractice,theremovalofthezero-sequencecurrentsfromsix-wirearrangementsisnotpracticalandisthereforeneverencountered;theassoci-atedreductionfactoristhereforeofpurelyacademicvalue.3.2TransformerarrangementsTheneutralconductormaybeinterruptedbytheMV/LVtransformer,e.g.,byconnectingitinDYarrange-ment,therebyreducingtheharmonicvoltagedropoftheHV/MVtransformerlocatedupstream(inthePCC).Using(1),andassumingbalancedloads,thereductionfactorofthevoltagedistortioninthePCCcanbecal-culated:THDVPCCneutralTHDVPCCnoneutralC25Ph63=h1h2Ihjj2k2mPh3=h1h2Ihjj2Ph63=h1h2Ihjj2vuuuuut7wherekmdenotestheratioofthezero-sequencetothepositive-sequenceimpedancesoftheHV/MVtrans-former.FortheloadcurrentspectrumofTable1andkm=1,thereductionofthevoltagedistortioninthePCCequals1.28.4BasicfactorsgoverningpowersystemharmonicpropagationToassesstheinfluenceofthepowersystemparameterspresentedintheprevioussections,simulationshavebeenperformedonthenetworkofFig.1.Inthissection,theimpedanceoftheMV/LVtransformersisneglected(i.e.,|Zc|=|Zl|=0).Non-zeroMV/LVtransformerimped-anceswillbeassumedinSect.5,whereacasestudyispresented.Inthissection,alsotheeectsofshuntcapacitanceareneglected;formoderatefeederconduc-torlengths(uptoseveralkilometersforcableconduc-tors,anduptoafewtensofkilometersforoverheadconductors)theshuntcapacitancebecomesimportantforhigherharmonicsonly,forwhichtheinjectedcurrentisusuallysmall.TheeectsofcapacitancearediscussedinSect.6.Thetotal(fundamental)loadofasinglefeederequals1puatcos/=1,andisbalancedandequallydividedamongthefeedernodes.Thevoltageinthefirstfeedernode(closesttothePCC)iscontrolledto|VFl|=1.06puforallsimulations.ThesourcevoltagefromtheHVbusisconsideredtobepurelysinusoidal.Thetotalamountofdistortingloads(withalinecurrentspectrumasinTable1)represents10%ofthetotalfundamentalload,whiletheremaining(linear)loadonlydrawsfunda-mentalcurrent.InaccordancewithIECregulations14,onlythefirst40harmonicsareconsideredwhencalculatingTHDvalues.Byanalogywith(4),thetotalharmonicvoltagedropDVFhofthefeederisdefinedas:DVFhX40h2VF1hC0VF5hjj2vuut8ThismeasureallowstoexplainthedierencebetweenthevoltagedistortioninthePCCandattheendofthefeeder.Indeed,exceptwhentheneutralconductorisinterrupted,theoperatingconditionsencounteredinthispaperallowforthefollowingapproximationifDVFhisexpressedinperunits:THDV5C25THDVPCCDVFh9Thisisconfirmedbythesimulationresults,whicharesummarizedinTable2andarediscussedinthefollow-ingsubsections.Simulationno.1isconsideredtobethebasecase,towhichtheeectsofallparametervariationsarecompared.4.1TransformerchoiceTheimpactofthetransformerparametersonvoltagedistortionisexplainedbycomparisonofsimulationnos.13fromTable2.Theresultsaregraphicallyrepre-sentedinFig.2a.FromSect.2.2,itfollowsthatforsimulationnos.2and3themagnitudeoftheharmonictransformerimpedanceis3.48and1.39timessmaller,respectively,thantheharmonicimpedanceforsimula-tionno.1(basecase).Asexpected,thiscausesthevoltageTHDinthePCCtodecreasewithaboutthesamefactor.Attheendofthefeeder,thevoltageTHDisseveraltimesgreaterthaninthePCCbecauseoftheharmonicvoltagedropofthefeederconductors.ThisresultisinaccordancewithrecentmeasurementsintheFrenchLVsystem13.BecausethetotalharmonicvoltagedropofthefeederconductorDVFhremainsconstantbetweensimulationnos.1,2,and3,thereductionofthevoltageTHDattheendofthefeederisrathersmallandisapproximatelyequaltothereductionofthevoltageTHDinthePCC.184Concluding,theimpactofthetransformerimpedanceonvoltagedistortionisquiteimportantinthePCC,butlessimportantattheendofthedistributionfeeder,wherethetotalharmonicvoltagedropofthefeederconductorsbecomesdominant.ItturnsoutthatthevoltagedistortioninthePCCincreaseswhenthe(fun-damental)transformerimpedanceincreasesorbecomesmoreinductive.4.2FeederconductortypeTheimpactofthefeederconductortypeonvoltagedis-tortionisexplainedbycomparingsimulationnos.46fromTable2.TheresultsaregraphicallyrepresentedinFig.2b.Forsimulationno.4,thephaseangleoftheconductorimpedanceisdecreasedfrom55C176to30C176,ascomparedwithsimulationno.1.AccordingtoSect.2.3,thiscausestheharmonicimpedanceofthefeedertore-ducewithafactor1.71.Asexpected,thetotalharmonicvoltagedropofthefeederDVFhisreducedbyaboutthesamefactoraswell.Inturn,thiscausesasignificantreductionofthevoltageTHDattheendofthefeeder.Similarresultsareobtainedwhencomparingsimulationnos.1and5,wheretheconductorimpedanceangleisincreasedfrom55C176to80C176(causingtheharmonicimped-anceofthefeedertoincreasebyabout1.52),andforsimulationno.6,wheretheexpecteddisplacementfactorisincreasedfrom0.8(inductive)to1.0(causingthehar-monicimpedanceofthefeedertoincreasebyabout1.93).Itistobenotedthattheincreaseoftheexpectedfun-damentaldisplacementfactor(simulationnos.1and6)hasmoreimpactthantheincreaseofthephaseangleoftheconductorimpedance(simulationnos.1and5).Table2VoltageTHDfordierentnetworkparametersSim.no.|Zm|(%pu)hZm(deg)|Zs,l|(%pu)hZs;1(deg)MlVoltageTHDDVFh(%pu)CommentsVPCC(%)V5(%)110.0804.8155514.1213.319.57TypicalHV/MVtransformerimpedancebasecase234.010.045454.8154.8155555111.213.0310.6312.349.579.57LowHV/MVtransformerimpedanceLowHV/MVtransformerimpedanceangle45610.010.010.08080804.6266.0899.3003080551114.223.984.1210.2816.9224.436.2713.8819.35CablefeederWidelyspacedoverheadfeederExpectedloadcosF=17810.010.080802.8982.0705555354.104.0913.2813.269.589.57ModeratetaperingfactorHightaperingfactor910111210.010.010.010.0808080804.8154.8154.8154.815555555551123.216.1611.007.926.572.819.573.623.62NeutralconductorinterruptedinnodesNeutralconductorinterruptedinPCC3-ph,6-w(or31-ph)feeders3-ph,6-w(or31-ph)feeders,neutralconductorinterruptedinPCCFig.2Influenceofdierentparameters:atransformerparameters,bfeederconductorparameters,ctapering185TheimpactonthevoltageTHDinthePCCisrathersmall.However,itisnoticedthatthevoltageTHDinthePCCisslightlyreduced,whentheconductorimpedanceangleisincreased.Thisiscausedbyphaseanglediversitybetweenthenodes11,andbecomesmoreimportantforincreasingharmonicordersandincreasinglyinductiveconductors.Thestrongerthehigherharmonicsoftheloadcurrent,themorethiseectbecomesnoticeable;anexampleisgivenin9.Concluding,theimpactofthefeederconductorimpedanceonvoltagedistortionisquiteimportantattheendofthefeeder,butverysmallinthePCC.Similaraswiththetransformerimpedance,itturnsoutthattheharmonicvoltagedropofthefeederincreaseswhenthe(fundamental)conductorimpedanceincreasesorbecomesmoreinductive.4.3FeederconductortaperingTheimpactoffeederconductortaperingonthevoltagedistortionisexplainedbycomparingsimulationnos.1,7,and8fromTable2.Theresultsaregraphicallyrep-resentedinFig.2c.Forsimulationnos.7and8,thetaperingfactorMtisincreasedfrom1to3and5,respectively,ascomparedwithsimulationno.1.TheimpactonthevoltageTHDinthePCCandattheendofthefeederisnegligible.ThisismainlyduetotheequalfundamentalvoltagedropcriterionforcalculatingtheconductorsegmentimpedancesZs,k(Sect.2.3).There-fore,feederconductortaperingwillnotbeexploredanyfurtherinthispaper.4.4Neutralconductorpractice4.4.1Four-wireconductorarrangementTheimpactofinterruptingtheneutralconductoronvoltagedistortionisexplainedbycomparingsimulationnos.1,9,and10fromTable2.Theresultsaregraphi-callyrepresentedinFig.3a.Insimulationno.9,theneutralconductorisinterruptedbetweenthefeederandloadnodesbyDYtransformerswithnegligibleimped-anceZc=0.ItfollowsthattheexpecteddecreaseofthevoltageTHDinthePCCbyabout1.28(Sect.3.2)matchesthesimulationsquitewell.Also,thereductionoftheharmonicvoltagedropofthefeeder(aboutthefactor3.36aspredictedinSect.3.1)causesaconsider-ablereductionofthevoltageTHDattheendofthefeeder.ThesameharmonicvoltagereductioninthePCCasaboveisfoundwhencomparingsimulationnos.1and10,where,inthelatter,theneutralconductorisinterruptedinthePCCbyaDYtransformerwithnegligibleimpedanceZl=0.However,theharmonicvoltagedropofthefeederconductorisnotinfluencedleadingtoonlyasmallreductionofvoltageTHDattheendofthefeeder.4.4.2Six-wireconductorarrangementInsimulationnos.11and12,asix-wireconductorarrangementisappliedinsteadofthefour-wirecon-ductorarrangementofsimulationno.1.TheresultsaregraphicallyrepresentedinFig.3b.Thesimulationresultsmatchwellthepredictedreductionofthetotalharmonicvoltagedropoftheconductor(withafactor2.62,Sect.3.1),againcausingaconsiderablere