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2019年中国电机工程学会年会论文集特高压变压器直流偏磁快速计算王欢国网上海青浦供电公司，上海201799FASTCALCULATIONOFDC-BIASEDUHVTRANSFORMERHuanWANGStateGridShanghaiQingpuelectricpowersupplycompany/Shanghai,China.摘要：随着我国特高压直流电网的大规模建设，特高压变压器在电力系统中的重要性日益攀升。高压直流输电和地磁暴引起变压器直流偏磁，进而影响供电可靠性。本文针对特高压变压器三维模型直流偏磁计算复杂的问题，从场路耦合方法的特点出发，通过建立特高压变压器的二维仿真模型提升磁场求解速度，并验证了该模型的正确性。在二维仿真模型的基础上，分析了不同网格划分程度对直流偏磁计算的影响。相较于三维模型，特高压变压器轴对称二维有限元模型规模小，受网格划分程度的影响较小，可在比较短的时间内进行多个周期计算，大幅度减少了直流偏磁的计算工作量。关键词：特高压变压器；二维仿真模型；直流偏磁效率；快速计算ABSTRACT:Withthelarge-scaleconstructionofUHVDCpowergridinChina,theimportanceofUHVtransformerinpowersystemisincreasing.Highvoltagedirectcurrent(HVDC)andgeomagneticstormscauseDC-biasedtransformer,thusaffectingthereliabilityofpowersupply.Aimingatthecomputationalcomplexityinthethree-dimensionalmodelofDC-biasedUHVtransformer,startingfromthecharacteristicsofthefield-circuitcoupledprinciple,thetwo-dimensionalsimulationmodelofUHVtransformerisestablishedtoimprovethesolvingspeedofmagneticfield,andthecorrectnessofthemodelisverified.Basedonthetwo-dimensionalsimulationmodelofUHVtransformer,theinfluenceofmeshingontheDC-biasedcalculationisanalyzed.Comparedwiththethree-dimensionalmodel,thetwo-dimensionalfiniteelementmodelofUHVTransformerissmallinscale,lessaffectedbymeshsize.Itcancarryoutmanycyclescalculationinarelativelyshorttime,whichgreatlyreducestheDC-biasedcomputationworkload.KEYWORD:UHVtransformer;two-dimensionalsimulationmodel;DC-biasedefficiency;fastcalculation1Introductioncurrentseriousdistortion,increasesreactivepowerconsumption,vibrationenhancement,andreducesInrecentyears,thedemandforelectricpowertheperformanceofinsulatingmaterials,therebyinourcountryhasbeenincreasingrapidly,andreducingtransformerlife[6].UHVDCeffectivelysolvestheproblemofpowergridandenergydevelopmentinChina[1].AsoneofAtpresent,someresearcheshavebeencarriedoutontheDCbiasoftransformers.TheharmonicthekeyequipmentofUHVpowergrid,thesafebalancefiniteelementmethodobtainstheharmonicandstableoperationofUHVtransformerisveryimportant[2-3].componentofunknownquantitybysolvingthemagneticfieldequationandthecircuitequation,butTheDC-biasphenomenonoccurswhentheitconsumesmoreresourcesandthecalculationDCcur-rentismixedfromtheneutralpointofthetransformer[4],themonopole-groundoperationefficiencyisnothigh[7].Jiles-AthertonferromagnetichysteresisprincipleanalysismodeofHVDCtransmissionandgeomagnetictransformercoreDCbiasconditionsunderthestormarethemaincausesofDCbiasontransformers[5].TheDCbiascausesthecoreoftheexcitationcharacteristicsoftheparametersinvolvedinalargenumberofcalculations[8].Inthetransformerthehalfwavesaturation,theexcitationliterature[9],thefield-circuitcouplingmodelofthe
12019年中国电机工程学会年会论文集transformerisestablished,andthemagneticfieldmodelofthethree-dimensionaltransformerisestablishedbyusingthefiniteelementmethod.Themethodcancarryoutde-tailedelectromagneticcharacteristicanalysisunderDCbias,butitscomputationalefficiencyisverylow.BecauseofthecomplexityofUHVTransformermagneticcircuitstructureandelectricalconnections,aswellasthestrongFig.1TheDCmagnetizationcurvenonlinearityofthetransformerpermeability.ItisAccordingtothesizeofeachcomponentofparticularlydifficulttoperformDC-biasedUHVtransformerandtherelatedcalculationanalysisefficiently.parameters,the1/8three-dimensionalmodeloftheInthispaper,wefocusontheefficiencyofUHVTransformerisconstructed,asshowninDC-biasedcalculationforUHVtransformeronFigure2.loadthroughtheestablishmentoftwo-dimensionalsimulationmodeltoimprovethesolvingspeedofmagneticfield,onthisbasis,throughthestep-sizestrategytofurtherreducethecalculationworkofcircuitmodel.ThefastcalculationmethodguaranteestheaccuracyandefficiencyofDC-biasedcalculationforUHVTransformer,whichcanbeusedasreferenceforthedesignandoperationofUHVtransformers.2ProblemofDC-biasedcalculationefficiencyforUHVtransformer2.1ThestructurefeaturesofUHVFig.2Thethree-dimensionalmodeloftransformertransformer2.2TheproblemofDC-biasedcalculationInthispaper,the1000kVsingle-phaseefficiencyfour-columnUHVautotransformerisstudied.TheThetime-domainmagneticfield-electricalcoreismadeofhigh-magneticallyorientedcircuitcoupledmethodissimple,accurateandgrain-orientedcold-rolledsiliconsteelsheet,stable.Itisrelativelymaturetosolvetheincludingtwomaincolumntwosidecolumnandelectromagnetictransientanalysisoftransformer.theupperandlowerironyoke.TheDCThemethodisanindirectcouplingalgorithminmagnetizationcurveisshowninFigure1,Wherewhichthetime-domaincurrentandthedynamicBdenotesthemagneticinductionintensityandHinductanceareusedasthecouplingparameters.Thedenotesthemagneticfieldstrength.Thedynamicinductorisobtainedbythemagneticfieldtransformerismadeofcopperwire,andthelow,model,thetransientcurrentissolvedbythecircuitmiddleandhighwindingsarearrangedfrominsidemodelthroughthefourth-orderRunge-Kuttatooutside,andaresheathedonthetwomainmethod,andthecouplingofnonlinearmagneticcolumninturn.fieldandcircuitcalculationisrealized.Itisan
22019年中国电机工程学会年会论文集importantguidingsignificancefortheanalysisofDC-biasedtransformer.DC-biasedcalculationefficiencyproblemsforUHVtransformer:Ontheonehand,duetothecomplexstructureofUHVtransformer,thesizeofeachcomponentisverydifferent.Whenthemagneticfieldmodelisestablished,thenumberofnodesandelementsarelarge,soitisdifficulttoFig.3ThemagneticcircuitmodelofUHVquicklycalculatethebias;Ontheotherhand,transformerbecauseofthelargeinductanceseriesofsmallTheequivalenttwoaxialsymmetrymodelsresistanceoftheUHVtransformercircuitmodel,haveexactlythesamestructure,inwhichthe1/8thetimeconstantisgreat,makingthecalculationaxissymmetrymodelofasingle-phasethreeoftransientprocessisverylong,sothesolutioncolumntransformerwithisshowninFigure4.efficiencyisverylow.Tosolvetheaboveproblems,thefastcalculationofDCbiasedUHVtransformerisrealizedbysimplifyingthemagneticfieldmodel.3SimulationmodelofDC-biasedUHVtransformer3.1Thetwo-dimensionalmodelofUHVtransformerAccordingtothebasiclawofmagneticcircuitandtheelectromagneticrelationship,twoidenticalaxialsymmetrymodelsareusedtobeequivalenttoFig.4TheaxisymmetricmodelofUHVtransformertheactualmodelofUHVtransformer,whichWhenusingANSYStosolvethetransformerensuresthatthemaincolumnmagneticdensityofmagneticfield,itcanbefurthersimplifiedtothetwomodelsisconsistentinthelinearcase.Thetwo-dimensionalmodel.Accordingtotheupperandactualthree-dimensionalmagneticcircuitmodeloflowersymmetryofthemodel,the1/2thetransformerandtheequivalentaxialsymmetrytwo-dimensionaltransformergeometrymodelismagneticcircuitmodelareshowninFigure3.showninFigure5.Fig.5Thetwo-dimensionalmodelofUHVtransformer
32019年中国电机工程学会年会论文集3.2SimulationandcomparisonAfterformingthetwo-dimensionalDC-biasedcalculationmodelofUHVtransformer,themodeliscomparedwiththethree-dimensionalmodeltoverifythecorrectnessofthemodel.3.2.1Thecomputationalcorrectnessunderno-loadconditionTheelectricalwiringofUHVautotransformerismorecomplicatedthanthatofconventionalFig.7Theno-loadcurrentcurvewithtimetransformer.ThereareelectricalandmagneticThecomparisonresultsshowthatthevariationconnectionsbetweenwindings.Fourwindingsofofno-loadcurrentcalculatedinthetransformerhighvoltagewindingareconnectedintwo-dimensionalmodeloftransformerisbasicallyparallel,thecommondoublewindingsofhighthesameasthatcalculatedinthethree-dimensionalvoltagewindingandmediumvoltagewindingaremodeloftransformer.connectedinparallel,andthedoublewindingsof3.2.2Thecomputationalcorrectnessunderlowvoltagewindingarealsoconnectedinparallel.loadconditionTheequivalentcircuitdiagramunderno-loadconditionisshowninFig.6.Inviewofthehigh-mediumvoltagerunningGiventhattheDC-biasedcurrentis10A,thestateofUHVtransformer,theequivalentcircuitno-loadDCbiasedcurrentiscalculatedbymodelunderDCbiasisshowninFigure8.time-domainfield-circuitcoupledprinciple,andthecalculationresultsoftwo-dimensionalmodelandthree-dimensionalmodelareobtained.Theno-loadcurrentafterstabilizationisshowninFig.7.Fig.8TheequivalentcircuitmodelUndertheconditionofratedload,theFig.6Theequivalentcircuitdiagramunderno-loadconditionDC-biasedcurrentof100Aisapplied,andthefield-currentcoupledmethodisusedtosimulatetheDCbias.Theexcitationcurrentisobtainedunderthetwo-dimensionalmodelandtheactualmodel.SeveralperiodicwaveformsafterexcitationstabilizationareshowninFigure9.
42019年中国电机工程学会年会论文集Fig.9TheexcitationcurrentversustimecurveTheresultsshowthatthecurrentcalculated(a)Thesparsemeshingunderthetwo-dimensionalmodelofthetransformerisbasicallythesameastheactualmodel.Soitisandcorrecttousethetwo-dimensionalmagneticfieldmodelforDC-biasedcalculation.4Computationalefficiencyoftwo-dimensionaldc-biasedmodel4.1TheinfluenceofmeshingInthispaper,AnsysisusedtosolvethemagneticfieldofUHVtransformer.Therefore,the(b)ThedensemeshingmeshingdegreeofmagneticfieldmodelisveryFig.10Thetwo-dimensionalfiniteelementmodelofimportantfortheaccurateandfastsolutionofUHVtransformerdynamicinductanceparameters,whichaffectstheUnderthesamecalculationparameters,thecorrectnessandefficiencyofDCbias.excitationcurrentofthetransformerisobtained,WhencalculatingtheDC-biasedUHVandthewholeperiodaftercurrentstabilizationistransformer,thethree-dimensionalmodelisgreatlytaken.Thetime-varyingcurvesoftheexcitationaffectedbythegrid.Whenthegridistoosparse,currentcalculatedunderthetwofiniteelementthecalculationresultsareincorrect[8],andtheDCmodelsareobtained,asshowninFig.11.componentobtainedisquitedifferentfromtherealvalue.Inaddition,becauseofthecomplexityofthethree-dimensionalmodel,tosomeextent,itaffectsthesolvingspeed.Forthetwo-dimensionalmodel,two-dimensionalfiniteelementmodelswithregularmeshesareestablishedasshowninFig.10.InthecaseofUHVautotransformeroperatingundermediumandhighvoltageload,theinfluenceofmeshingonDC-biasedcalculationundertwo-dimensionalmodelsisanalyzed.Fig.11TheexcitationcurrentversustimecurveThesimulationresultsshowthatthenumberof
52019年中国电机工程学会年会论文集nodesinthefiniteelementroughmodelis181,thenumberofelementsis50,thenumberofnodesinthefiniteelementdensemodelis647,andthenumberofelementsis196,whichismuchsmallerthanthescaleofthree-dimensionalfiniteelementmodel.Thesimulationsolutionspeedisfast,andthefewerthefiniteelementmeshes,thefasterthesolutionspeedis.Inaddition,thetwo-dimensionalmodelofUHVtransformerDCbiasanalysisislessFig.12Thecurrentchangeprocessaffectedbymeshing,andtheresultsofcalculationWhenusingthetwo-dimensionalmodeltoarenotverydifferent.Thereasonisthatbecauseofsolvethebiasedcurrent,theCPUconsumptionintheaxisymmetriccharacteristicsofthemodel,itseachcycleeachismuchlowerthanthatofthecircumferentialmeshingisequivalenttoinfinitethree-dimensionalmodel,andthespeedofsolutiondensity,sothereisnocircumferentialerrorintheisfasterwhenthegridismoresparse,whichcalculationofmagneticbias,andtherequirementeffectivelyimprovestheefficiencyofDC-biasedfortangentialmeshingislow.currentsolution.Duetothecorrectnessandhighefficiencyof4.2Thehighefficiencythetwo-dimensionalDC-biasedsimulationmodelInordertoverifythehighcomputationalofUHVtransformer,aseriesofdiscussionscanbeefficiencyunderthetwo-dimensionalmodel,thecarriedoutonthebasisofthismodel.actualmodelandthetwo-dimensionalmodelare5ConclusionsusedtocalculatetheDCbiasinthesamecalculationconditions,andtheCPUconsumptionAimingattheinefficiencyproblemofoftheDC-biasedcalculationunderdifferentDC-biasedUHVtransformer,anequivalentmodelsiscompared,asshowninTable1.Theaxisymmetrictwo-dimensionalmodelofUHVtransitionfromtheinitialstatetothestablestateoftransformerisestablished.Andtheresultsarethecircuitdependsonthetimeconstantofthecomparedwiththoseofthree-dimensionalmodel,circuitdifferentialequation.ThecurrentvariationwhichverifiesthecorrectnessoftheaxisymmetricprocessisshowninFig.12.two-dimensionalmodel.Tab.1TheCPUtimeofDCbiasedcalculationBasedonthetwo-dimensionalsimulationmodelofUHVtransformer,theinfluenceoftheFiniteelementTotalmodelCPUtime(min/T)time(min)meshingontheDC-biasedcalculationisanalyzed.3Dmodel313.2627253Thesimulationresultsshowthattheaxisymmetric2Dmodelundertwo-dimensionalmodelofUHVtransformerissparsemeshing60.585444smallinscale,lessaffectedbymeshing,and2DmodelundereffectivelyreducethecalculationworkloadofDCdensemeshing70.246110bias.Comparedwiththethree-dimensionalmodel,theaxisymmetricmodelhasobviousadvantages.References[1]ZHANGWenliang,WUWeining,HUYi.ResearchonUHVTransmissionTechnologyandDevelopmentofChina'sPower
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