变压器comsol

SolvedwithCOMSOLMultiphysics5.01|E-CORETRANSFORMERE-CoreTransformerIntroductionTransformersareelectricalcomponentsthatareusedforpowertransmission.Mosttransformersworkontheprincipleofelectromagneticinduction.Atypicaltransformerconsistsofaprimarycoil,asecondarycoilandaferromagneticcore.TheprimarycoilreceivestheACelectricalinputsignal.Asaresultofmutualinduction,aninducedvoltageisobtainedacrossthesecondarycoil.Theferromagneticcoreservesthepurposeofamagneticfluxconcentratortherebyminimizinglossesduetofluxleakage.Commercialtransformersuseseveraltypesofcores,whicharenamedbasedontheirgeometricshapes,forexampleI-core,U-core,E-core,potcore,toroidal,andplanar.ThismodelusesapairofE-coresformagneticfluxconcentration.Thismodeldemonstrateshowtoperformtransientsimulationsofasingle-phaseE-coretransformer.IncludingtheeffectofanonlinearB-Hcurveinthesoft-ironcore,themodelcomputesthespatialdistributionofthemagneticandelectricfields,themagneticsaturationeffect,thetransientresponse,andthefluxleakagetothesurroundings.Twodifferentversionsofthetransformeraresimulated:thefirstonewithaturnratioofunityandthesecondonewithaturnratioof1000.ModelDefinitionThecoreofthesingle-phaseE-coretransformerconsideredhereconsistsofapairofE-cores,whichformaclosedmagneticfluxpath.TheprimaryandsecondarycoilsinthetransformerareplacedaroundthecentrallegofthecoreasshowninFigure1.AnonlinearB-Hcurvethatincludessaturationeffectsisusedtosimulatethemagneticbehaviorofthesoft-ironcore.Hysteresiseffectsinthecoreareneglected.Themodelassumesthattheprimaryandsecondarywindingsaremadeofthinwireandhavemultipleturns.Usingtheassumptionsthatthewirediameterislessthantheskindepthandthattherearemanyturns,thesewindingsaremodeledwithMulti-TurnCoilfeatures.Furthermore,themodeldoesnotaccountforeddycurrentsintheindividualturnsofthecoil.Theprimarywindingisconnectedtoaprimaryresistor,RpandtheACvoltagesource,VacwhilethesecondarywindingisconnectedtothesecondarySolvedwithCOMSOLMultiphysics5.02|E-CORETRANSFORMERloadresistor,RsasshowninFigure2.PrimarywindingsSecondarywindingsIroncoreFigure1:ModelillustrationofanE-coretransformer.Figure2:Atransformerconnectedtoanexternalcircuitwithvoltagesourceandresistors.Themodelissolvedintimedomainforalinefrequencyof50Hz.Severalimportantdesignparameterssuchasthemagnitudeoftheinputvoltage,thelinefrequency,thenumberofturnsinthecoils,andthecoilresistanceareparameterizedandcanthereforeeasilybechanged.AtransformerworksbytheprincipleofFaraday’slawofinductionwhichstatesthattheinducedvoltage(Vin)inacoilisproportionaltotherateofchangeofmagneticflux(φ)andthenumberofturns(N)inacoilasshowninEquation1.SolvedwithCOMSOLMultiphysics5.03|E-CORETRANSFORMER(1)Iftwocoilsarecoupled,Equation1canbeusedtodeducethattheinducedvoltageinthesecondarycoil(Vs)isproportionaltotheinducedvoltageintheprimarycoil(Vp):(2)HereNsandNparethenumberofturnsinthesecondaryandprimarycoils,respectively.Np/Nsisknownastheturnratio.ResultsandDiscussionFigure3showsthesurfaceplotofthemagneticfluxdensitynormdistributionandthearrowplotsofthecurrentsinthewindingsatt=50ms.Figure4showsthesliceandthearrowplotofthemagneticfluxdensitynorminthecoreatt=50ms.Figure5andFigure6displaytheinducedvoltageintheprimaryandsecondarywindingsrespectively.Sincethenumberofturnsoneachwindingisequal,theinducedvoltageinbothwindingsissameasgivenbyEquation2.ThecurrentsflowingthroughtheprimaryandsecondarywindingsareshowninFigure7andFigure8,respectively.Figure9displaysthevoltageinducedintheprimarywindingforastep-downtransformerwithaturnratioofNp/Ns=1000andsupplyvoltageof25kV.Finally,theinducedvoltageinthesecondarywindingforastep-downtransformerisdisplayedinFigure10.Thisinducedvoltageis1000timessmallercomparedtothevoltageintheprimarywindingofFigure9.VinNdφdt-------–=VsVp-------NsNp-------=SolvedwithCOMSOLMultiphysics5.04|E-CORETRANSFORMERFigure3:Magneticfluxdensitynormandthecurrentsinthewindingsatt=50ms.Figure4:Magneticfluxdensityinsidethetransformercoreatt=50ms.SolvedwithCOMSOLMultiphysics5.05|E-CORETRANSFORMERFigure5:Theinducedvoltageintheprimarywindingversustime.Figure6:Inducedvoltageinthesecondarywindingsversustime.SolvedwithCOMSOLMultiphysics5.06|E-CORETRANSFORMERFigure7:Currentintheprimarywindingversustime.Figure8:Currentinthesecondarywindingversustime.SolvedwithCOMSOLMultiphysics5.07|E-CORETRANSFORMERFigure9:Inducedvoltageintheprimarywindingversustimeforastep-downtransformer.Figure10:Inducedvoltageinthesecondarywindingversustimeforastep-downtransformer.SolvedwithCOMSOLMultiphysics5.08|E-CORETRANSFORMERNotesAbouttheCOMSOLImplementationUsetheMagneticFieldsphysicsinterfacetomodelthemagneticfieldsofthetransformer.ModeltheprimaryandsecondarywindingswithMulti-TurnCoilfeatures.ConnecttheprimaryandsecondarywindingstoanexternalcircuitwiththeACvoltagesourceandresistorsusinganElectricalCircuitphysicsinterface.AddCoilCurrentCalculationstudystepstocalculatethecurrentinthecoils.PerformaTimeDependentstudytodeterminethevoltageandcurrentsinboththeprimaryandsecondarywindings.ModelLibrarypath:ACDC_Module/Other_Industrial_Applications/ecore_transfor