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AHighPerformancePWMCurrentSourceInverterFedInductionMotorDrivewithaNovelMotorCurrentControlMethodMikaSal0andHeikkiTuusaDepartmentofElectricalEngineering,PowerElectronicsTampereUniversityofTechnologyP.O.Box692,FIN-33101Tampere,FinlandAbstract-Thispaperpresentsahighperformancevectorcontrol-ledPWMcurrentsourceinverter(PWM-CSI)fedinductionmo-tordrivewhereonlythemeasuredrotorangularspeedandthede-linkcurrentareneededformotorcontrol.Novelmethodsforcompensatingthecapacitivecurrentsofthemotorfilteranddampingthemotorcurrentoscillationsinthetransientconditionsarepresented.Thevalidityoftheproposedmethodsareverifiedbysimulation.I.INTRODUCTIONTherapiddevelopmentofpowerandmicroelectronicsinre-centyearsallowtheuseofinductionmachinealsoinhighper-formancemotordrives.Atlow-andmediumpowerlevelthevariablespeedinductionmotordrivesareusuallyrealizedus-ingaPWMvoltagesourceinverters(PWM-VSI).However,theswitchedvoltagesyieldhighdddt-voltageslopesoverthestatorwindings,whichstressestheinsulationsandcausesbear-ingcurrentploblems.ApossiblesolutionforthisploblemistheuseofPWMcurrentsourceinverter(PWM-CSI)(Fig.1).Boththevoltagesandthecurrentsofthemachinearenearlysinusoi-dalandthereforethevoltagestressesinthemachinewindingsarelow.InthePWMcurrentsourceinvertersaCfilterhastobein-sertedontheloadsidetoreducethecurrentharmonics.Duetothecapacitivecurrentsofthefilterthemotorcurrentreferencesarenotrealizedaccurately,whichcanbethecauseforunsatis-factoryperformanceandinstabilityproblems.Afewmeth-odsl,2,whicharebasedonthemeasurementoftheloadcapacitorvoltages,havebeenreportedtosolvetheproblem.However,withthecompinedsteadystateequationsoftheloadfilterandmotorthecapacitivecurrentscanbecompensatedwithoutanymeasurements.LinebridgeOntheotherhand,theCfilterandthemachineinductancesformaresonancecircuitwhichisstimulatedespeciallywhenthemotorcurrentreferencesarechanged.Somemethods3,4,basedonthemeasurementofthemotorvoltagesand/orcur-rentshavebeenproposedtodampthemotorcurrentoscilla-tionsinthetransientconditions.However,inPWM-CSIdrivesmotorcurrentmeasurementsarenotneededforprotectionsincetheovercurrentcanbedetectedwiththedc-linkcurrentsensor.So,itispreferredtousecontrolmethodswheremotorcurrentmeasurementsarenotneededbecauseinthatcasethemotorcurrentsensorscanbetotallyeliminated.InthepresentworkthecontrolsystemofthePWM-CSIfeddriveisunderinvestigation.Thelinesideconverterhasbeenstudiedearlier5,6whenalsotheprototypesof5kWand100kWhavebeenbuilt.Thefinalgoalistodevelopahighper-formancemotordrivewithminimumhardwarerequirements.Theproposedvectorcontrolsystemisrealizedintherotorfluxorientedreferenceframe.Thecapacitivecurrentsoftheloadfilterarecompensatedwithoutanymeasurementsusingthecombinedsteadystateequationsoftheloadfilterandthemo-tor.Also,anewmethodfordampingthemotorcurrentoscilla-tionsinthetransientconditionsispresented.Themethodisbasedonthecombineddynamicequationsoftheloadfilterandthemotoranddoesnotneedanymeasurements.However,thespeedsensorisincludedtogetthedrivealsotoworkwellnearzerospeed.11.VECTORCONTROLOFTHEPWMCURRENTSOURCEINVERTERFEDINDUCTIONMOTORDRIVEFig.1showsthemaincircuitofthePWMcurrentsourcein-verterfedinductionmotordrive.LlifandClifaretheinduct-anceandcapacitanceofthelinefilterandusupthesupplyLrlrLoadbrideeFig.1.ThemaincircuitofthePWMcurrentsourceinverterfedinductionmotordrive0-7803-5421-4/99/$10.0001999IEEE506voltage.Clofistheloadfiltercapacitance.Thelineandloadbridgesareidentical.BothbridgesconsistofsixcontrollableswitchessuchasIGBtransistors(IGBTs).AntiparalleldiodesoftheIGBTsinthecommercialpowermodulesarealsoshowninthefigure.BecauseofthesediodesandverylowreversevoltageblockingcapabilityoftheIGBTs,additionaldiodeshavetobeconnectedinserieswiththetransistors.Asmoothinginductor(Ldc)isconnectedbetweenthebridges.InthePWM-CSIdrivesthelineconverterisusedtocontrolthedc-linkcurrent.Thefunctionofthelineconverterissyn-chronizedwiththesupplyvoltages.Bychangingthemodula-tionindexinthelinebridgethedc-linkvoltage,i.e.thedc-linkcurrent,canbecontrolled.Intheline-voltage-orientedrefer-enceframetheactiveandreactivepowerofthelineconvertercanbesimplycontrolledwiththerealandandimaginaryaxiscomponentsofthesupplycurrentvector5,6.Thelinefiltertakesreactivepowerwhichcanbecompensatedbythecontrolsystem5,6.Thestatorcurrentsaregeneratedbytheloadconverter.Theloadfiltertakescapacitivecurrentswhichareproportionaltothesquareofstatorfrequencyintheconstanttorqueregionandlinearlyproportionaltothestatorfrequencyinthefieldweak-eningregion.A.RotorfluxbasedvectorcontrolsystemInthevectorcontrolstrategiestheACmotorsarecontrolledlikedcmotorswhichhaveindependentchannelsforfluxandtorquecontrol.Fig.2(a)showsthevectorcontrolsystemwhichisrealizedintherotor-flux-orientedreferenceframeandisbasedonindirectvectorcontrolscheme7.Itshouldbenotedthatthecontrolsystemofthelineconverterisnotshowninthefigure.Detaileddescriptionofthelineconvertercontrolcanbefoundin5,6.Theelectromagnetictorqueoftheinductionmotorinthero-tor-fluxorientedreferenceframecanbewrittenas3Lm-te=2-p+$LrSYwherepisthenumberofpolepairs,L,magnetizinginduct-ance,Lrrotorselfinductance,limdrotormagnetizingcurrentanditheimaginaryaxiscomponentofthestatorcurrentvectorintherotorfluxbasedcoordinatesystem.Belownomi-nalrotorspeediskeptconstantandtheelectromagnetictorqueiscontrolledwithis,ofwhichreferencevalueistheoutputofthespeedcontroller.Abovenominalrotorspeedthereferencevalueofthemagnetizingcurrentisinverselypropor-tionaltothestatorfrequency.lirnr1canbecontrolledwiththerealaxiscomponentofthestatorcurrentvectoris,expressedintherotor-flux-orientedreferenceframe,asfollows:sYd-T-limd+=is,dtrefdcIMachineLoadConverterSoeedController+.I+Trita).ref+invyrefSYcampyPhase-errorcompensationeompx.ref+.refLgXinvxb)+invyReferencfilterOscillationsdampingReferenfilter+.refref8x1inv.xe)Fi2a)VectorcontrolofthePWM-CSIfeddriveintherotor-flux-orientedreferenceframe.b)Compensationofthemotorcurrentphase-error.c)Damp-ingofthemotorcurrentoscillations.Intheindirectvectorcontrolsystemtherotorfluxangleiscalculatedasasumofthemeasuredrotorangleandtherefer-encevalueoftheslipangleinthefollowingway:refe,=er+-sydtT:I(3)Iftheangularrotorvelocityw,insteadof8,ismeasured,asisthecaseinFig.2(a),(3)canbewrittenas(4)Rotorfluxangleisneededtotransformtheinvertercurrentref-erencevector;:$tothestationarycoordinates&$.Su-perscriptmrreferstotherotorfluxbasedreferenceframe.Intheproposedvectorcontrolsystemonlytherotorangularspeedandthedc-linkcurrentmeasurementsareneededformo-torcontrol.Themeasureddc-linkcurrentisneededforthemodulatorrealization8,9inbothconvertersandfordc-linkcurrentcontrolinthelineconverter.Thedc-linkcurrentrefer-encevalueisgeneratedintheloadconverterasfollows:507wheretheconstantc21i.e.themagnitudeofthedc-linkcur-rentshouldbeequalorgreaterthanthelengthoftheinvertercurrentreferencevectorinordertokeepthemodulationinthelinearregion.B.Compensatingthemotorcurrentphase-errorTheprobleminFig.2(a)controlsystemisthatthestatorcur-rentreferencevectorisnotrealizedaccuratelybecauseofthecapacitivecurrentsoftheloadfilter.Withthecombinedsteadystateequationsoftheloadfilterandmotorthecapacitivecur-rentscanbecompensatedwithoutanymeasurements.Next,theequationsneededforcompensationcontrolarederived.Thestatorvoltageequationoftheinductionmotorinthesta-tionaryreferenceframecanbeexpressedaswhereoistheresultantleakageconstant.Theloadfilterca-pacitorvoltagecanbewrittenas(7)andtheloadcapacitorcurrentasilofc=iinv-is.(8)Bysubstituting(8)into(7)andtheresultingequationinto(6)(Es=Elofc)followingexpressionisobtained:didimr(inV-,)dt=RSis+oL-+(I-o)L-(9)SdtSdtWhen(9)isexpressedusingthequantitiesoftherotorflux-ori-entedreferenceframewehave-mrBysolving(10)foriinvthefollowingequationisobtained:-mrdi,-mrmrzamriswherewmr=&,/dt.Accordingto(11)theeffectofloadfil-terinsteadystatecanbecompensatedasfollows:When(12)isexpressedintermsofdirectandquadratureaxiscomponentswehaveand2.ref=Rc0jref.refcompyslofmrsx-(3Lsclofwmrsy(14)Lwherethereferencevaluesofthestatorcurrentcomponentsandtherotormagnetizingcurrentareused.IntheconstantfluxregionIimrl=is,and(13)canbewrittenas.refref2.refcompx=-RsClofWmrisy-Lsclofwmrsx(15)TheproposedcompensationmethodisshownintheblockdiagramforminFig.2(b)whichreplacestheareasurroundedbythebrokenlineinFig.2(a).C.DampingthemotorcurrentoscillationsTheloadfiltercapacitanceandthemachineinductancesformaresonancecircuitwhichisstimulatedespeciallywhenthemotorcurrentreferencesarechanged.Onesolutiontoover-comethisproblemistousecombineddynamicequationsoftheloadfilterandthemotor.Bytakingintoconsiderationthedynamictermsofthestatorcurrentvectorin(11)wehave-mr7-mrThedynamictermsofrotormagnetizingcurrentarenotin-cludedin(16)becauselimrlchangesmuchmoreslowlythan.mrLandalsobecausetherotormagnetizingcurrentisnormallykeptconstant.When(16)isexpressedintermsofdirectandquadratureaxiscomponentswehaveand508However,becauseinpracticerealstatorcurrentscannotfollowstepresponsesofthesupplycurrentreferences,modified(fil-tered)currentreferences(z;lfandisryef)areusedin(17)and(18).TheproposeddampingmethodisshowninblockdiagramforminFig.2(c),whichreplacestheareasurroundedbythebrokenlineinFig.2(a).Anexampleoffilteringthestatorcur-rentreferencesindiscretecaseisshowninFig.3whereachangeinstatorcurrentreferencevalueisobtainedattimetk.Therealizationofthereferencevalueisbegunattimetk+lbe-causeoftheonetimeintervalcalculationdelay.Afterthattheorginalreferencevalueisrealizedduringfourtimeintervals.Formicroconpollerimplementation(17)and(18)havetobediscretizedwhenwehaveAt-.k+1ldampx=RsClof-refAtAis,k+1+oLsCl0fLAtk+l(19)andk+l-refk+1-refk=(A*-%)/At(22)IndiscreterealizationtheaveragevaluesofmodifiedstatorcurrentreferencesduringatimeintervalshouldbeusedinthesummingpointshowninFig.2(c).Thesecanbeexpressedas:ref,k+1:ref,k+l-ref,k+2lsxy,av=(zsxy+isxy)/2(23)Finally,themodifiedcurrentreference,whichisfilteredac-cordingtoFig.3,canbewrittenasSXYref,k+l-i-ref,k+2-:ref,k+lisxy-zsxy+0.25(isxyref,k.ref,k-1ref,k-1-irefk-2)(24)+0.3(isxySXY+0.45(isxy-zsxyandrik+1111.SIMULATIONRESULTSLJwhere(bothcomponentscombinedinoneexpression)-ref,k+2:ref,k+l=(isxy-xy/At%.reftktk+ltk+2tk+3tk+4tk+5Fig.3.Exampleoffilteringthestatorcurrentreferences.ThesimulationisbasedontheparametersshowninTableI.However,duetotheskineffectthestatorresistanceintheres-onancefrequencyoftheloadfilter(360Hz)isconsiderablylargerthanthatshowninthetable.Therefore,threetimesthevaluegiveninthetablehasbeenusedinthesimulationmodel.Themodelhasbeenbuiltindiscreteformtohavecloseanalogywiththefuturemicrocontrollerimplementation.Themodelhasbeenbuiltusingperunitvalues.Thebasevaluesare:currentio=A,voltageuo=./zUs,angularspeedwo=21150/p,fluxwo=U,/(21150)andtorqueto=(3/2)uoio/wo.Fig.4showssimulationresultsoftheproposeddampingmethodwherethey-axiscomponentofthestatorcurrentrefer-encevectorissuddenlychanged.ThestatorcurrentreferencesarefilteredasshowninFig.3.ThediscretetimeintervalAtin(19)-(24)is200ps.Fig.4(a)showsthephase-Astatorcurrentwhenthedampingmethodisnotused.Fig4(b)showsthesim-ulationresultwhenthedampingmethodisused.Itcanbeseenthatwiththeproposeddampingmethodthecurrentoscillationscanbeconsiderablyreduced.Fig.5showsthesimulationresultsoftheentirevectorcon-trolsystem.Thereferencevaluesareshownwiththebrokenlineandrealizedvalueswiththesolidline.Theproposedcon-trolmethodsofcompensatingthereactivepowerdrawnbytheloadfilteranddampingthestatorcurrentoscillationsareused.Themagnetizationofthemotorisbeginnedat10ms.Theref-erencevalueoftherotorfluxisratelimitedinordertokeepiLE*atanacceptablelevel.Thefinalvalueoftherotorfluxintheconstantfluxregionissetto0.9p.u.Then,at100msthe509TABLEISIMULATIONPARAMETERSNominalStatorphaseVoltageus230vNominalstatorcurrent1,16ANOmindlShaftpowerPN1.5kWMagnetizinginductanceL,80mHStatorleakageinductanceL,I4.5mHRotorleakageinductanceL,I4.5mHStatorresistance50HzRs0.6QRotorresistance50HzR,0.7QInertiamomentJ0.1kgm2FrictionconstantB0.01NmsNominalspeednN1440r/minLoadfiltercapacitanceCI,LinefiltercapacitanceClifLinefilterresistance50HzRlifNumberofpo:epairsp222.5pF22.5pF1.2mH0.1QDc-linkinductanceLdc20mHLinefilterinductanceLlifI00.050.0750025f,rne(s)II00.05007507,me(=)0025Fig,4.Simulatedwaveformsofphase-Astatorcurrentatsuddenchangeinig&.a)Withoutoscillationdampingcontrol.b)Withoscillationdampingcontrol.-I/I020304I020.30.4tirne(s)0.1Fig.5.SimulatedwaveformsofPWMcurrentsourceinverterfedinductionmotordrive.a)Rotorflux.b)x-axiscomponentofthestatorcurrent.c)Angularrotorspeed.d)y-axiscomponentofthestatorcurrent.e)Electromagnetictorque.f)dc-linkcurrent.g)Phase-Astatorcurrent.h)Phase-Astatorvoltage.510referencevalueoftheangularrotorspeedischangedfrom0tonominalvalue(0.96P.u.)andat250msto0.7p.u.Finally,at350mstheloadtorqueischangedfrom0tonominalvalue(0.71P.u.).Thereferencevalueofthedc-linkcurrentiscaluc-ulatedusingc=1.2in(5).Negativeslopesofthedc-linkcurrentreferencevaluearefilteredusingtimeconstantof100ms.Theoutputofthespeedcontrollerislimitedto1.5p.u.AccordingtoFigS(b)and5(d)itcanbeseenthatthestatorcurrentsfollowthestatorcurrentreferenceswellandthattheoscillationsinthestatorcurrentarelow.I213141IV.CONCLUSIONSInthispaper,thecontrolofthePWMcurrentsourceinverterfedinductionmotordrivehasbeendiscussed.Thecontrolsys-temhasbeenrealizedintherotor-flux-orientedreferenceframe.Newmethodsforcompensatingthereactivepowerdrawnbytheloadfilteranddampingthestatorcurrentoscilla-tionswithoutanymeasurementshavebeenpresented.Thetestswithsimulationmodelshowexcellentperformanceinbothsteadyandtransientstateconditions.REF
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