外文翻译-无源滤波器拓扑结构的选择方法研究

英文原文ResearchonSelectionMethodofPassivePowerFilterTopologiesJunpengJi,GuangZeng,HaiwaLiu,LeiLuo,JinggangZhangDepartmentofElectricalEngineeringXianUniversityofTechnology,XUTXian,ChinaAbstractPassivePowerFilter(PPF)iswidelyusedinpowersystembecauseofitsadvantagesinperformance-priceratio.ForPPF,thereareseveraltopologies,eachofwhichhasdifferentfrequencycharacteristic.Inpowersystem,inordertoachievethecertainfilteringeffect,itisnecessarytocombinedifferentfiltertopologies.Currently,theselectionofPPFtopologiesisbasedontheengineeringpracticalexperienceofPPFdesigner.However,thereisalackinsystematicdesignmethodandscientificdesignbasis.Forthisreason,thispaper,takingthefilteringeffectandfilterscostasthedesignindices,deeplyinvestigatestheselectionproblemofPPFtopologies,andproposesaselectionmethodofPPFtopologies.Theresearchresultsshowthatthemostreasonablecombinationofdifferentfiltertopologiescanbeobtainedbythismethodfordifferentsituationneededtomitigateharmonicandcompensatereactivepower.Keywords-harmonicmitigation;PassivePowerFilter(PPF);selectionoftopologiesI.INTRODUCTIONWiththeincreaseoftherectifiers,frequencycontroldevices,electricarcfurnaces,electricrailwayandamountofpowerelectronicdevicesinpowergrid,thepowergridispollutedseriously.Forimprovingpowerqualitiesandpowerenvironment,thetechnologiesofharmonicsuppressionandreactivecompensationarewidelyapplied.ItismainsolutionusingActivePowerFilter(APF)andPassivePowerFilter(PPF)tomitigatetheharmonic.BecauseofPPFadvantagesinperformance-priceratio,PPFisstillabetterchoiceforlarge-scaleusers.CurrentlythemoststudiesofPPFistheparameteroptimization,thereisalackfortheselectionmethodofPPFtopologies1.However,fortheselectionofPPFtopologies,thereisnotauniversalmethod.AndthecombinationofPPFisalwaysdesignedaccordingtotheexperiencesoffilterdesigner.TakingtechnicalandeconomicindicestoevaluatetherationalityoftheselectedPPFtopologiescombination,thispaperpresentsaselectionmethodofPPFtopologies.II.THETOPOLOGIESANDFREQUENCYCHARACTERISTICSOFPPFA.TheTopologiesofPPFUsuallytherearesixtopologiesforafilterdesigner.Thesetopologiescanbedividedintotwocategories:tunedfiltersandhigh-passfilters2.ThetopologiesoftunedfiltersareshowninFig.1,includingsingle-tunedfilteranddouble-tunedfilter.Thesingle-tunedfiltercontainsacapacitorinserieswithaninductor.Thesingle-tunedfilterseeFig.1(a)provideslowimpedanceatacertaintunedfrequency,itcanbypassthisharmonic.Thedouble-tunedfilterseeFig.1(b)provideslowimpedanceattwocertaintunedfrequencies,itcanbypassthesetwodifferentharmonic.Forthetunedfilters,thesingle-tunedfilterisusedwidely3.(a)Single-tunedfilter(b)Double-tunedfilterFig.1.Thetopologyoftunedfilters(a)first-order(b)second-order(c)third-order(d)CtypeFig.2.Thetopologyofhigh-passfiltersThetopologiesofhigh-passfiltersareshowninFig.2,includingthefirst-orderhigh-passfilter,second-orderhigh-passfilter,thethird-orderhigh-passfilterandC-typehigh-passfilter.High-passfiltersareabletotrapawiderangeofharmonicsbyprovidingalowimpedancepathathighfrequencies.Thefirst-orderhigh-passfilterseeFig.2(a)providessmallimpedanceathighfrequenciesbecausethecapacitorcharacteristics.Thesecond-orderhigh-passfilterseeFig.2(b)consistsofacapacitorinserieswithaparallelinductorandresistor.Thethird-orderhigh-passfilterseeFig.2(c)isaddedacapacitoratparallelresistorbranchbasedonthesecond-orderhigh-passfilter.TheC-typehigh-passfilterseeFig.2(d)isaddedacapacitoratparallelinductorbranchbasedonthesecond-orderhigh-passfilter.Forthehigh-passfilters,thesecond-orderhigh-passfilterisusedwidely3.B.TheFrequencyCharacteristicsofPPFForthesingle-tunedfilter,theseriesresonantbetweeninductorsandcapacitorsatacertainharmonicfrequencymakestheimpedanceofthefilterverysmall.Sotheharmoniccanbefilteredbythesingle-tunedfilter.However,theimpedanceofdouble-tunedfilterissmallattwodifferentharmonicfrequencies.Thereforetherearetwodifferentharmoniccurrentcanbefilteredbythedouble-tunedfilter.ThefrequencycharacteristicsoftunedfilterareshowedbyFig.34.(a)Thefrequencycharacteristicofsingle-tunedfilter(b)Thefrequencycharacteristicofdouble-tunedfilterFig.3.ThefrequencycharacteristicsoftunedfilterHigh-passfiltersareabletotrapawiderangeofharmonicsbyprovidingalowimpedancepathathighfrequencies.Takesecond-orderhigh-passfilterforexample,thefrequencycharacteristicisshowinFig.44.Fig.4.TheFrequencyCharacteristicofSecond-orderHigh-passFilterIII.THEDESIGNREQUIREMENTSANDEVALUATIONINDICEEveryPPFcomposedofdifferenttopologiesshouldsatisfycertaindesignrequirements,alsoneedtomeetcertaindesignindexeswhichissuedbythecountry.A.TheFilteringEffectThemainroleofPPFistofiltertheharmoniccurrentinthepowersystem.Itisnecessarytomakesurethattheharmonicvalueofpowergridislowerthanthenationalstandardlimits.InChina,thestattechnologicalsupervisionbureauissuednationalstandardGB/T14549-93“QualityofelectricenergysupplyHarmonicsinpublicsupply”in19935.Forvoltage,GB/T14549-93stipulatesthelimitsofthetotalharmonicvoltagedistortion(THDu)andtheh-orderharmonicvoltageratio(HRUh)indifferentbusvoltagebenchmark.THDuandHRUhcanbecalculatedbyformulas(1)and(2).%10102UTHDhu(1)1RUh(2)Where,UhandU1aretheh-orderharmonicvoltagevalueandthefundamentalvoltagevalue.Forcurrent,GB/T14549-93stipulatesthelimitsofeveryorderharmoniccurrentcomponentsfrom2to25,thelimitsarebasedondifferentclassicvoltageandbenchmarkshort-circuitcapacity.Forexample,thelimitof25thharmoniccurrentis4.1Abasedonthe10kVvoltageand100MVAshort-circuitcapacity5.B.ThePowerFactorInadditiontofilteringtheharmonic,PPFprovidethereactivepowerwhichthesystemneed.So,thesizeofcapacitorofthedesignedfiltershouldbebasedonthesizeofthereactivepowercompensationrequiredbythepowersystem.Generally,afterthereactivepowercompensation,thepowerfactorshouldbebiggerthan0.9andlessthan1.Butitcannotappearovercompensation,whichmeanstheallsystemdoesntshowcapacitivecharacter.AccordingtothepowerfactorswithoutPPFandwithPPF,thesizeofreactivepowercompensationcanbecalculated.Theamountofinjectedreactivepowerisapproximatelyproportionaltothesizeofmaincapacitoroffilter.ThesizeofreactivepowercompensationQccanbecalculatedbyformulas(3).21arostnarcostnpfpfPQc(3)Where,pf1andpf2arethepowerfactorwithoutPPFandwithPPF,Pistheactivepowerofthepowersystem.thepowerfactorwithoutPPFandwithPPF,Pistheactivepowerofthepowersystem.C.TheFrequencyResponseofPPFThisindexmeasuresthefilterperformanceaccordingtotheoverallfrequencyresponsesofPPF.Ateveryharmonic-order,systemharmonicimpedancecanbecalculatedbyfrequencyscanafterinstallingPPF.Thesmallerthevalueoffrequencyresponseis,thebettertheeffectofPPFis.Thevalueisgreatlyrelatedtotheimpedanceofsystem,theparametersofcapacitorsandinductors,theinstallationmode,theworkingenvironmentsetc6.D.TheIndexofCostTheinitialinvestmentofPPFshouldbetheminimum,forsimplicityignoringthesmalladditionalcost.TheinitialcostTheinitialcostF1ofPPFisexpressedbythefollowingequation.niiiiCkLRkF132(4)Where,k1,k2,k3arethepricefactorscorrespondingtotheresistance,inductorsancapacitorsofPPF(determinedbytheratedvoltageandcurrentvaluesofpassivefiltercomponents).Andnisthenumberoffilterstopologies.Thevalueofpricefactorsisobtainedbythemarketsurvey7.E.ThePowerLossesThepowerlossesaremainlygeneratedbytheresistorofPPF.Theselossesareundesirablelossandcancausethefinancialinefficiency.TheselossesmaycancauseexcessiveoverheatofPPFcomponent.ThereforewhendesigningPPF,thedesignerespeciallypayattentiontothisindex.However,thesizeofresistoriscloselyassociatedtoqualityfactorQ.SothisindexisusedtomeasurethefiltereffectofthePPFcausedbydifferentQ.Thequalityfactorofsingle-tunedfilterisexpressedbyformula(5),andthequalityfactorofhigh-passfilterisstatedbyformula(6)8.RCL(5)(6)IV.THEMETHODOFFILTERTOPOLOGIESSELECTIONA.TheAssumptiveConditionsForinvestigatingtheselectionmethodoffiltertopologies,themainstrategyistocomparetheperformancesofallpossiblefiltertopologiescombinations,therearetwoassumptiveconditions.Theseassumptionsarehighlightedandjustified.First,thenumberofPPFbranchesisobtainedbyPPFdesignersaccordingtodifferentharmonicvoltageandcurrent.Forthemostsituationencounteredbyindustry,threeorfourPPFbranchesarethebestsolutions.Butfourbranchesaremoreexpensivethanthreebranches.Second,thesizesofeveryPPFbranchesaresame.However,therehasthedifferencefordifferentbranchessizes,butthedifferenceisverysmallsothatitcanbeignored.Third,thedouble-tunedfilterisexcludedinthisinvestigation,becauseinstallationanddebuggingareverydifficult.Theoretically,thedouble-tunedfilterisveryeasy,butintheengineeringpractices,itisrarelyusedinPPF.B.TheProcedureofSelectionMethodofPPFTopologiesBecausedouble-tunedfilterisexcludedinthisinvestigation,therearefivePPFtopologiesforselection.ForaPPFwithkfilterbranches,therearePPFtopology5kcombinations.Inthispaper,thebasicstrategyofthisresearchisobtainingthebestPPFtopologycombinationusingeliminatingmethod.ThedetailedflowchartofthemethodproposedbythispaperisshowninFig.5.Thestepsareasfollows:Step1:Calculatetheminimumandmaximumcompensationcapacitybaseonthepowerfactorcompensationrequirement.Step2:Selectonetopologycombinationforinvestigating.Step3:Selecttheminimumcompensationcapacity.Step4:Calculatetheinductorvalue(L),thecapacitorvalue(C)andtheresistorvalue(R).Step5:Carryoutharmonicvoltageandcurrentanalysis.Step6:Checkwhetherthetotalharmonicvoltagedistortion()islessthanuTHDthelimitsofthenationstandard.Ifnot,eliminatethistopologycombination.Step7:Checkwhethertheh-orderharmonicvoltageratio()islessthanhHRUthelimitsofthenationstandard.Ifnot,eliminatethistopologycombination.Step8:Checkharmoniccurrentcomponentsarelessthanthelimitsofthenationstandard.Ifnot,eliminatethistopologycombination.Step9:Checkwhetherthecompensationcapacitywasalreadyuptothemaximum.Ifnot,increasethecompensationcapacityandreturntoStep4.Ifyes,gotoStep10.Step10:Checkifthereisothertopologycombinationtobeinvestigated.Ifyes,returntoStep2.Ifnot,gotoStep11.Step11:Carryoutfrequencyresponseanalysisintheinvestigatedsystemusingfrequencyscan.Step12:Verifythesystemimpedanceandeliminatecombinationswithhighimpedanceinfrequencyresponseanalysis.Step13:Carryoutlossesanalysis.Step14:Verifythelossesofselectedcombinationsandeliminatecombinationswithhighlosses.Step15:Verifythecostofselectedcombinationsandeliminateallcombinationswithhighcost.V.THEENGINEERINGCASEA.SystemDescriptionandAssociatedDataThenetworkstructureofatypicalengineeringcaseIselectedinthispaper,whichispresentedinFig.6.10Kvsystemisobtainedfrompowersystemsourceof110kVthrough63MVAmaintransformer.PPFcombinationsareinstalledbetweentransformerandharmonicsource.PowersystemsourceTransformerPPFcombinationHarmonicsourceThevoltageofpowersystemsourceis110kV,3-phaseshort-circuitcapacityis6000MVA,X/Rratiois6.Theturnratioofmaintransformeris110kV/10kV,thecapacityis100MVA.Theloadis3-phasebridgeconvertermadeupofdiodecluster,whichistheharmonicsourceofthissystem.Thecharacteristicharmonicsofloadmainlyare.Forcontrollingtheharmonicinthelimitsofthenationstandardon16nthe10kVbus,PPFcombinationsareinstalled.Fig.7showsthe10kVbusvoltageandcurrentwaveformsofinvestigatedsystemafterPTandCTbeforefiltering.TheuTHDis4.5%,themaximumoddharmonicvoltageratioHRUis3.3%,themaximumevenharmonicvoltageratioHRUis0.1%.TherelatedvaluesofvoltageharmonicandthelimitsofthenationstandardGB/T14549-93areshowninTABLEI.TherelatedvaluesofcurrentharmonicandthelimitsofthenationstandardGB/T14549-93areshowninTABLEII.Fig.7.The10kVbusvoltageandcurrentwaveformsbeforefilteringB.TheMethodofSimulationandAnalysisInthestudyofthisengineeringcase,theMATAB/SIMULINKcanbeusedtosimulatetheinvestigatedsystemandthefilteringeffectofPPF.Accordingtothefactosituationofvoltageandcurrentharmonic,itisthebestsolutiontoselectthreePPFbranches.AccordingtothestepsoftheinvestigatedmethodonselectionofPPFtopologyinsectionIV,forthisengineeringcase,thecombinationconstitutedbythreesingle-tunedfiltersisthebestPPFcombination.C.TheAnalysisofEngineeringCaseResultUsingthismethod,thebestPPFtopologycombinationcanbeobtained.Fig.8showsthe10kVbusvoltageandcurrentwaveformsofinvestigatedsystemafterPTandCTwiththebestPPFtopologycombination.WiththebestPPFtopologycombination,therelatedvaluesofvoltageharmonicareshowninTABLEI,therelatedvaluesofcurrentharmonicareshowninTABLEII.CanseefromFig.8,TABLEIandTABLEII,thefilteringeffectofbestPPFtopologycombinationisnotthebest,butinconjunctionwitheconomicindices,itisthebest.Fig.8.The10kVbusvoltageandcurrentwaveformswiththebestPPFTABLEI.THERELATEDVALUESOFVOLTAGEHARMONICTABLEII.THERELATEDVALUESOFCURRENTHARMONICVI.CONCLUSIONThepaperdeeplyresearchestheproblemofselectionofPPFtopologiesinpowersystem.Asystematicdesignmethodandscientificdesignbasisareproposed,itmakesupthelackinthePPFdesignprocess.Usingthismethod,thebestPPFtopologycombinationcanbeobtainedthrougheliminatingtheunsatisfiedPPFcombinations,thesecombinationscannotmeetthelimitsofnationalstandardGB/T14549-93ortheimpedanceoffrequencyresponseorcostindexofPPF.Forverifyingthevalidityandrationalityofthismethod,thepaperanalysesanengineeringcaseof10kVbussystemusingsimulationtechnology.VerifiedresultsshowthatthebestPPFcombinationcanbeobtainedusingthisselectionmethod.ACKNOWLEDGMENTThisresearchwassupportedbySpecialFoundationofkeydisciplineofShaanxiprovincialproject,andsupportedbyResearchPlanofXianUniversityofTechnology(105-211019).REFERENCES1EricOchlak,BabakForouraghi,“AParticleSwarmAlgorithmforMultiobjectiveDesignOptimization.”IEEEInternationalConferenceonToolswithArtificialIntelligence,2006.2JunpengJI,XuHAN,“TheDesignandPerformanceAnalysisforHybridActivePowerFilterofRectifierCircuit,”PowerandEnergyEngineeringConference2010(PEEC2010),September1112,2010inWuhan.3G.W.Chang,S.Y.Chu,andH.L.Wang,“Anewmethodofpassiveharmonicfilterplanningforcontrollingvoltagedistortioninapowersystem,”IEEETrans.PowerDel.,vol.21,no.1,pp.305312,Jan.20064JiJunpeng,“ThedesignandparameteroptimizationofSVCsystemfilter,”D.Xianuniversityoftechnology,mastersdegreepaper,2010.5Thestatetechnologicalsupervisionbureau.ThenationalstandardGB/T14549-93QualityofelectricenergysupplyHarmonicsinpublicsupplyS,1993.6C.J.Chou,C.W.Liu,andJ.Y.Lee,“Optimalplanningoflargepassive-harmonic-filterssetathighvoltagelevel,”IEEETrans.PowerSyst.,vol.15,no.1,pp.433441,Feb.2000.7D.Bohaichuk,C.Muskens,andW.Xu,“Mitigationofharmonicsinoilfieldelectricsystemsusingacentralizedmediumvoltagefilter,”inProc.9thIEEEICHQP,Oct.2000,pp.614618.8Y.P.ChangandC.J.Wu,“Optimalmultiobjectiveplanningoflarge-scalepassiveharmonicfiltersusinghybriddifferentialevolutionmethodconsideringparameterandloadinguncertainty,”IEEETrans.PowerDel.,vol.20,no.1,pp.408416,Jan.2005.中文译文无源滤波器拓扑结构的选择方法研究摘要由于其较高的性价比优势，无源滤波器在电力系统中广泛应用。对于无源滤波器而言，它有几种不同的拓扑结构，而且每种拓扑结构都有其不同的频率特性。在电力系统中，为了实现一定的滤波效果，将不同拓扑结构的滤波器结合使用是必不可少的。目前，无源滤波器拓扑结构的选择是基于无源滤波器设计师的工程实践经验基础上的。然而，这缺乏系统的设计方法和科学的设计依据。出于这个原因，本文以滤波效果和滤波器成本为设计指标，深入研究了无源滤波器拓扑结构的选择问题，同时提出了一种无源滤波器拓扑结构的选择方法。研究结果表明，可以通过该方法获得不同滤波器拓扑结构的最合理结合，并针对不同情况以减轻谐波并进行无功补偿。关键字：谐波缓解；无源滤波器（PPF）;结构选择一、简介在电网中，随着整流器、变频控制设备、电弧炉、电气化铁路和大量电力电子设备的增加，电网污染逐渐加重。为了改善电能质量和电能环境，谐波抑制和无功补偿得到广泛应用。采用有源电力滤波器(APF)和无源电力滤波器缓解谐波（PPF）是主要的解决方案。因为无源滤波器的较高性价比优势，对于大规模用户而言，无源滤波器仍然是一个更好的选择。目前对于无源滤波器的研究大多数局限在参数的优化方面，缺乏对于无源滤波器拓扑结构选择的研究。然而，无源滤波器拓扑结构的选择没有一个通用的方法，无源滤波器拓扑结构的选择往往依据设计者的经验来确定。这篇文章提出一种无源滤波器拓扑结构的选择方法，以综合技术和经济性为指标来评估其合理性。二、PPF的拓扑结构和频率特性A拓扑结构对滤波器设计者而言通常有六种拓扑结构，这些拓扑结构通常被分为两类：调谐滤波器和高通滤波器。调谐滤波器的结构如图(1)所示，包括单调谐滤波器和双调谐滤波器。单调谐滤波器包含一个串联的电容和电感，单调谐滤波器【图1（a）】在某个特定频率提供低阻抗，使该次谐波电流滤除；双调谐滤波器【图1（b）】在两个特定频率时提供低阻抗，使其滤除。在调谐滤波器中单调谐无源滤波器使用较为广泛。(a)单调谐滤波器（b）双调谐滤波器图（1）调谐滤波器的拓扑结构（a）一阶（b）二阶（c）三阶（d）c阶图（2）高通滤波器的拓扑结构高通滤波器的拓扑结构如图（2）所示，包括一阶高通滤波器、二阶高通滤波器、三阶高通滤波器、C阶高通滤波器。通过在高频率时提供一个低阻抗，高通滤波器可以滤除一系列的高次谐波。一阶高通滤波器【图2（a）】由于电容的特性在高频率时阻抗较低，二阶高通滤波器【图2（b）】包含一个电容和一个并联的电感和电阻串联。三阶高通滤波器【图2（c）】在二阶高通滤波器的基础上加入一个与与电阻支路并联的电容。C型高通滤波器在二阶高通滤波器的基础上，在并联的电感支路上加入一个电容。B无源滤波器的频率特性对于但调谐滤波器，在特定谐波频率上电容器和电感器的串联谐振使得滤波器的阻抗非常小，因此单调谐滤波器可滤除该次谐波。然而，双调谐滤波器的阻抗在两个不同的谐振频率时阻抗较小，因此双调谐滤波器可同时滤除两种不同的谐波。调谐滤波器的频率特性如图(3)所示。(a)单调谐滤波器的频率特性(b)双调谐滤波器的频率特性图（3）调谐滤波器的频率特性高通滤波器可通过在高频率时提供较小的阻抗从而滤除一些列的谐波。以二次阶高通滤波器为例，它的幅频特性如图（4）所示。图（4）二次高通滤波器的频率特性3、设计要求和评价标准每种不同拓扑结构的无源滤波器在满足特定要求的同时，还应当符合国家规定的设计标准。A.滤波效果在电力系统中，无源滤波器的主要作用是滤除谐波电流，必须确保电网的谐波幅值低于国家的标准限制。1993年中国国家技术监督局颁布了国标GB/T14549-93电能质量公用电网谐波。对于电压而言，GB/T14549-93规定了在不同基准电压母线上总的电压谐波失真和第H次谐波电压的比。THD和HRU可通过公式（1）、（2）计算得出。%10102UTDhHu(1)%10UHRh(2)其中Uh和U1为别为第H次谐波电压值和基准电压值。对于电流而言，GB/T14549-93规定了从第2-25次每次谐波电流的组成，这些范围是基于不同的额定电压和基本短路容量规定的。例如，基于10KV电压，100MVA短路容量的第25次谐波电流是4.1A。B功率因数除了滤除谐波，无源滤波器同时为系统提供无功补偿，因此，所设计滤波器的电容器的大小应根据电力系统所需的无功补偿量来确定。一般来说无功补偿后的功率因数应大于0.9且小于1。但是，不能够过度补偿，否则这意味着所有的系统不显示容性。根据安装无源滤波器前后的功率因数，即可计算出无功功率补偿的大小。注入的无功功率大致正比于滤波器主电容的大小。无功补偿量可以由公式（3）计算得出。21arcostnarcostnpfpfPQc(3)其中pf1和pf2是安装无源滤波器前后的功率因数。P为系统的有功功率。C无源滤波器的的频率响应该指数根据无源滤波器的整体频率响应测量滤波器的性能。在各阶次谐波，可以通过安装无源滤波器后的频率扫描频计算系统谐波阻抗，频率响应的值越小，无源滤波器的效果越好。该值与系统阻抗电容器和电感器的参数，安装模式，工作环境等，密切相关。D.成本指数无源滤波器的初期投资应该是最低的，因为为简单起见略了小的额外费用。无源滤波器的初始投资成本可有下列等式表示。niiiiCkLRkF132(4)其中，K1，K2，K3是对应无源滤波器（由无源滤波器元件的额定电压和电流值确定）的对应电阻、电感和电阻的价格系数。N为滤波器拓扑结构的数目。价格因数的确定应通过市场调查来确定。E.功率损耗无源滤波器的功率损耗主要由电阻产生，这些损失是人们所不希望的，同时可造成经济效益损失。这些损失可能会导致无源滤波器的组件过热，因此，在设计无源滤波器时，设计师尤其要注意该指数。然而，电阻器的大小与品质因数Q密切相关。因此，该指数被用于测量在品质因数不同时无源滤波器的滤波效果。单调谐滤波器的品质因数由公式（5）表示，高通滤波器的品质因数由公式式（6）表示。(5)RCLQ(6)四、无源滤波器拓扑结构的选择方法A.假设条件研究滤波器拓扑结构的选择方法，主要是将所有可能的滤波器拓扑结构组合的性能进行比较，有两个假设条件。这些假设条件是显著合理的。首先，PPF设计师根据不同的谐波电压和电流来确定无源滤波器的分支的数目。对于行业所遇到的大多数情况，使用三个或四个的PPF分支是最好的解决方案。但是四个分支要比三个的滤波器分支贵得多。第二，每一个无源滤波器分支的大小是相同的。然而，不同分支的尺寸是存在差异的，但这差异是非常小的，以至于可以被忽略。第三，因为安装和调试的困难，双调谐滤波器被排除在本调查中。从理论上讲，双调谐滤波器