电力变压器的宽频带建模及阻抗分析

28120091AdvancedTechnologyofElectricalEngineeringandEnergyVol.28,No.1Jan.2009:2008209208:(50577034):(19822),,,,;(19462),,,P,,,,(,,100084):,,,,,,,20MHz:;;;;:TM13:A:100323076(2009)0120011205(GIS),,GIS(VFTO)[1,2],,,,,,,,,,[3],[427][8,9],,,,,,[426],,100kHz50MHz1,,1.2,()(1):9[u]9x=-[Lx]9[i]9t9[i]9x=-[Cx]9[u]9t(1),(),(2):9[u]9=-[L]9[i]9t9[i]9=-[C]9[u]9t(2),,2,2,(2),,(1),,(1)(2),,(2)r0(1),(1)(3)9[u]9x=-[L]9[i]9t-[R][i]9[i]9x=-[C]9[u]9t-[G][u](3)[u][i];[L][C][R][G],;;,(3):d[U]d=-(s[L]+[R])[I]d[i]d=-(s[C]+[G])[U](4)2,,,,11Y1Y2():Y1=Ptanhsl2W-11Fig.1typeequivalentcircuitfortransmissionlineY2=Psinh-1(sl)W-1(5)l,WP,LC,:W-1LCW=P-1CLP=20(6)0=P-1CW=W-1LP(7)WTP=PTW=0(8)0,,:ŽW-1L+RsC+GsŽW=‰P-1C+GsL+Rs‰P=2RsnL,GsnC,[10],,ŽWW,‰PP;:L+RsC+GsLC+1s(LG+RC)2=W-1L+RsC+GsWW-1LC+1sRC+1sLGW=20+1sW-1(RC+LG)W:21=W-1(RC+LG)W=W-1RP0+0P-1GW2=20+1s211sW-1(RC+LG)W,,,(5)Y2,Y1N,Y1Y2NN21283,1,Is,,:YnUn=(Is00)T(9)Nt,YnNtNt(9)Yn[L][C][R][G],1)A1A2A1A2NtN2)Yn,Yn:Yn=A1Y1AT1+A2Y1AT2+(A1-A2)Y2(A1-A2)T(10)Zn=Y-1n,(9):Un=ZnIs00=IsZn(1,1)Zn(2,1)Zn(n,1):Zin=Un(1)Is=Zn(1,1)(11)k:Un(k)=Zn(k,1)Zn(1,1)Un(1)(12)450--,68,353Agilen4395A,100kHz50MHz33,20MHz,,,,2Fig.2Modeloftransformerwinding,20MHz3Fig.3Comparisonofmeasuredimpedanceandcalculatedoneformodelcoil51220kV180,000kVA,,,,88,1012;21000kV1000,000kVA,,,,144,9114512:,Hz,(,100kHz45),100kHz,311,:,kHz20MHz;,(),41Fig.4Calculatedimpedanceoftransformer152Fig.5Calculatedimpedanceoftransformer220MHz,,,,GIS,GIS,,,6,R1L1,C1,ZtVFTO,66Fig.6Terminalmodelofatransformerwithleadandbushing,,,,,:1),,2)20MHz,,,(References):[1]JMeppelink,KJDiederich,KFeser,etal.VeryfasttransientsinGIS[J].IEEETrans.onPowerDelivery,1989,4(1):2232233.[2]SYanabu,HMurase,HAoyagi,etal.Estimationoffasttransientovervoltageingas2insulatedsubstation[J].IEEETrans.onPowerDelivery,1990,5(4):187521882.[3],,,(WeiYanfei,CaoHaixiang,SunXudong,etal.).PEEC(HFcircuitmodelofgeneratorstatorbarbasedonPEEC)[J].(Adv.Tech.ofElec.Eng.&Energy),2007,26(3):6210.[4](WangZanji).(Transientvoltagedistributionandits4128simulationinEHVlargetransformerwindings)[D].:(Beijing:TsinghuaUniv.),1990.[5]YShibuya,SFujita,NHosokawa.Analysisofveryfasttransientovervoltageintransformerwinding[J].IEEProc.2Gener.Transm.Distrib.,1997,144(5):4612468.[6]MPopov,LVanDerSluis,GPaap,etal.Computationofverytransientovervoltagesintransformerwindings[J].IEEETrans.onPowerDelivery,2003,18(4):126821274.[7]YPeng,JJRuan.InvestigationofveryfasttransientovervoltagedistributionintaperwindingofTeslatransformer[J].IEEETrans.onMagnetics,2006,42(3):4342441.[8]PIFergestad,THenriksen.Transientoscillationsinmultiwindingtransformers[J].IEEETrans.onPAS,1974,93(2):5002509.[9](WangZanji).(Acalculationmethodforimpulsevoltagedistributioninmultiwindingtransformers)[D].:(Beijing:TsinghuaUniv.),1985.[10]GMiano,AMaffucci.Transmissionlinesandlumpedcircuits[M].USA:AcademicPress,2001.2402263.(4):Z=R+sLY=G+sCWPUI,:U=WŽU,I=P„I,W-1ZP=P-1YW=s,,:d[ŽU]dx=-[][„I]d[„I]dx=-[][ŽU](4)ŽU„I,UI,[9],USUR,ISIR,,:IS=Pcoth(s)W-1VS-Psinh-1(s)W-1VRIR=-Psinh-1(s)W-1VS+Pcoth(s)W-1VR:IS=Y1VS+Y2(VS-VR)IR=Y1VR+Y2(VR-VS)(A1):Y2=Psinh-1(s)W-1Y1=Pcoth(s)W-1-Y2=Ptanhs2W-1(A1)1ModelingofpowertransformerinwidefrequencyrangeandanalysisoftheimpedancecharacteristicYANGYu,WANGZan2ji,SHAOChong(StateKeyLab.ofPowerSystem,Dept.ofElectricalEngineering,TsinghuaUniversity,Beijing100084,China)Abstract:InordertopreciselypredictVFTOdistributionsinthewindingsduringtransformerdesignstage,themodelingofthepowertransformerwindinginthewidefrequencyrangeisnecessary.Applyingmulti2transmissionline(MTL)theorytoestablishequivalentcircuitofthetransformerwindingandcalculatingitsdrivingpointimpedanceandvoltagetransferfunctions,thenaturalfrequenciesandtransientresponsecanbeobtained.Thevalidityoftheequivalentcircuitcanbeverifiedbycomparisonofthecalculatedandmeasuredimpedanceofamodelwinding.Inthispaper,theconsistenceoftwoMTLmodelsdevelopedonthesystemsofthecircularcylindricalcoordinatesandtherectangularcoordinatesrespectivelyforthecoretypetransformerwindingisfirstlyanalyzed.Thenthephase2modaltransformationforMTLequationsandtheparametersofthetypeequivalentcircuitforMTLaredeveloped.Finally,thedriving2pointimpedanceandthevoltagetransferfunctionsofthecircuitaresolvedusingnodeanalysis.Themeasuredimpedanceofamodelwindingverifiedthattheequivalentcircuitisvalidformodelingofthetransformerwindingsinthefrequencyrangebelow20MHz.Keywords:VFTO;powertransformer;modeling;multi2transmissionline;driving2pointimpedance511,: