SpaceVector_PWM_Inverter

PROJECT#2SPACEVECTORPWMINVERTERJIN-WOOJUNG,PH.DSTUDENTE-mail:[e-mail].:[phone]ADVISOR:PROF.ALIKEYHANIDATE:FEBRUARY20,2005MECHATRONICSYSTEMSLABORATORYDEPARTMENTOFELECTRICALANDCOMPUTERENGINEERINGTHEOHIOSTATEUNIVERSITY21.ProblemDescriptionInthissimulation,wewillstudySpaceVectorPulseWidthModulation(SVPWM)technique.WewillusetheSEMIKRON®IGBTFlexiblePowerConverterforthispurpose.Thesystemconfigurationisgivenbelow:Fig.1Circuitmodelofthree-phasePWMinverterwithacenter-tapedgroundedDCbus.Thesystemparametersforthisconverterareasfollows:ƒIGBTs:SEMIKRONSKM50GB123D,Maxratings:VCES=600V,IC=80AƒDC-linkvoltage:Vdc=400VƒFundamentalfrequency:f=60HzƒPWM(carrier)frequency:fz=3kHzƒModulationindex:a=0.6ƒOutputfilter:Lf=800µHandCf=400µFƒLoad:Lload=2mHandRload=5ΩUsingMatlab/Simulink,simulatethecircuitmodeldescribedinFig.1andplotthewaveformsofVi(=[ViABViBCViCA]),Ii(=[iiAiiBiiC]),VL(=[VLABVLBCVLCA]),andIL(=[iLAiLBiLC]).32.SpaceVectorPWM2.1PrincipleofPulseWidthModulation(PWM)Fig.2showscircuitmodelofasingle-phaseinverterwithacenter-tapedgroundedDCbus,andFig3illustratesprincipleofpulsewidthmodulation.Fig.2Circuitmodelofasingle-phaseinverter.Fig.3Pulsewidthmodulation.AsdepictedinFig.3,theinverteroutputvoltageisdeterminedinthefollowing:ƒWhenVcontrolVtri,VA0=Vdc/2ƒWhenVcontrolVtri,VA0=−Vdc/24Also,theinverteroutputvoltagehasthefollowingfeatures:ƒPWMfrequencyisthesameasthefrequencyofVtriƒAmplitudeiscontrolledbythepeakvalueofVcontrolƒFundamentalfrequencyiscontrolledbythefrequencyofVcontrolModulationindex(m)isdefinedas:A01A010Vofcomponentfrequecnylfundamenta:)(Vwhere,,2/)(dcAtricontrolVVofpeakvvm==∴2.2PrincipleofSpaceVectorPWMThecircuitmodelofatypicalthree-phasevoltagesourcePWMinverterisshowninFig.4.S1toS6arethesixpowerswitchesthatshapetheoutput,whicharecontrolledbytheswitchingvariablesa,a′,b,b′,candc′.Whenanuppertransistorisswitchedon,i.e.,whena,borcis1,thecorrespondinglowertransistorisswitchedoff,i.e.,thecorrespondinga′,b′orc′is0.Therefore,theonandoffstatesoftheuppertransistorsS1,S3andS5canbeusedtodeterminetheoutputvoltage.Fig.4Three-phasevoltagesourcePWMInverter.5Therelationshipbetweentheswitchingvariablevector[a,b,c]tandtheline-to-linevoltagevector[VabVbcVca]tisgivenby(2.1)inthefollowing:⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−−=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡cbaVVVVdccabcab101110011.(2.1)Also,therelationshipbetweentheswitchingvariablevector[a,b,c]tandthephasevoltagevector[VaVbVc]tcanbeexpressedbelow.⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−−−−−=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡cbaVVVVdccnbnan2111211123.(2.2)AsillustratedinFig.4,thereareeightpossiblecombinationsofonandoffpatternsforthethreeupperpowerswitches.Theonandoffstatesofthelowerpowerdevicesareoppositetotheupperoneandsoareeasilydeterminedoncethestatesoftheupperpowertransistorsaredetermined.Accordingtoequations(2.1)and(2.2),theeightswitchingvectors,outputlinetoneutralvoltage(phasevoltage),andoutputline-to-linevoltagesintermsofDC-linkVdc,aregiveninTable1andFig.5showstheeightinvertervoltagevectors(V0toV7).Table1.Switchingvectors,phasevoltagesandoutputlinetolinevoltages6Fig.5Theeightinvertervoltagevectors(V0toV7).SpaceVectorPWM(SVPWM)referstoaspecialswitchingsequenceoftheupperthreepowertransistorsofathree-phasepowerinverter.IthasbeenshowntogeneratelessharmonicdistortionintheoutputvoltagesandorcurrentsappliedtothephasesofanACmotorandto7providemoreefficientuseofsupplyvoltagecomparedwithsinusoidalmodulationtechniqueasshowninFig.6.Fig.6LocuscomparisonofmaximumlinearcontrolvoltageinSinePWMandSVPWM.ToimplementthespacevectorPWM,thevoltageequationsintheabcreferenceframecanbetransformedintothestationarydqreferenceframethatconsistsofthehorizontal(d)andvertical(q)axesasdepictedinFig.7.8Fig.7Therelationshipofabcreferenceframeandstationarydqreferenceframe.Fromthisfigure,therelationbetweenthesetworeferenceframesisbelowabcsdqfKf=0(2.3)where,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−−=2/12/12/1232302/12/1132sK,fdq0=[fdfqf0]T,fabc=[fafbfc]T,andfdenoteseitheravoltageoracurrentvariable.AsdescribedinFig.7,thistransformationisequivalenttoanorthogonalprojectionof[a,b,c]tontothetwo-dimensionalperpendiculartothevector[1,1,1]t(theequivalentd-qplane)inathree-dimensionalcoordinatesystem.Asaresult,sixnon-zerovectorsandtwozerovectorsarepossible.Sixnonzerovectors(V1-V6)shapetheaxesofahexagonalasdepictedinFig.8,andfeedelectricpowertotheload.Theanglebetweenanyadjacenttwonon-zerovectorsis60degrees.Meanwhile,twozerovectors(V0andV7)areattheoriginandapplyzerovoltagetotheload.TheeightvectorsarecalledthebasicspacevectorsandaredenotedbyV0,V1,V2,V3,V4,9V5,V6,andV7.ThesametransformationcanbeappliedtothedesiredoutputvoltagetogetthedesiredreferencevoltagevectorVrefinthed-qplane.TheobjectiveofspacevectorPWMtechniqueistoapproximatethereferencevoltagevectorVrefusingtheeightswitchingpatterns.Onesimplemethodofapproximationistogeneratetheaverageoutputoftheinverterinasmallperiod,TtobethesameasthatofVrefinthesameperiod.Fig.8Basicswitchingvectorsandsectors.Therefore,spacevectorPWMcanbeimplementedbythefollowingsteps:ƒStep1.DetermineVd,Vq,Vref,andangle(α)ƒStep2.DeterminetimedurationT1,T2,T0ƒStep3.Determinetheswitchingtimeofeachtrans