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IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.54,NO.1,FEBRUARY2007495PredictiveCurrentControlofaVoltageSourceInverterJoséRodríguez,SeniorMember,IEEE,JorgePontt,SeniorMember,IEEE,Cé,Member,IEEE,PabloCorrea,PabloLezana,Member,IEEE,PatricioCortés,StudentMember,IEEE,andUlrichAmmannusedincurrentcontrolforinverters[6],[7],aswellasforrecti-fiersandactivefilters[8].AvariationtothismethodcalculatesthedutycycleofthePWMpulsesnecessaryforthecurrentcon-trol[9],[10].Oneadvantageofpredictivecontrolisthepossibilitytoin-cludenonlinearitiesofthesysteminthepredictivemodel,andhenceopertywasexploitedinanearlierstudy[12],wherepredictivec[11],thispropertyofpredictivecontrolisusedtoevaluatethebehaviorofthecur-renterrorforeachswitchingstateinasingle-phaseactivefiptuallydifferentapproachispresentedin[13],elofthesystemisusedtopre-dictthebehavioroftheloadanthoddemon-stratesthattheusperpresentsthemethodintroducedin[13]ledexplanationofthemethodispresented,includingthemodelsusedforcurre-tionresultscomparingtheperformanceoftheproposedstrategywithwell-knownhysteresisandPWMcontrol,-nally,esisCurrentControlInthiscontrolstrategy,showninFig.1,measuredloadcmparatordeterminestheswitchingstateofthecorrespondinginverterleg(,,and)thodisconceptuallysimpfor-manceofthehysteresiscontrollerisgood,heinteractionbetweenthephases,ttchingfrequencychangeoneofthemajordrawbacksofhysteresiscontrol,tion,theswitchingloct—Thispaperpresentsapredictihodusesadiscrete-timemodelofthesystemtopredictthefuturevalueoftlityfunc-formanceoftheproposedpredictivecontultsshowthatthepredictivemethodcontrolsveryeffectivelytheerms—Currentcontrol,digitalcontrol,inverters,UCTIONCURRENTcontrolofathree-phaseinverterisoneofthemostimportantandclassicalsubjectearmethods,likehysteresiscontrolandlinearmethods,likepropor-tional-integralcontrollersusingpulsewidthmodulation(PWM)arewelldocumentedinliterature[1]–[3].Withthedevelopmentofpowerfulandfastmicroprocessors,method,loadandconvertermodelsareusedtopredictcurrentbehavior,andtherebyselectthemostappro-priateactuationfollowinganarbitrarycontrolcriteria[4]–[11].Predictivecontrolisaverywideificationofthemispresentedin[4].Oneapproachusespredictivecontrol,approach,rategyhasbeenManuscriptreceivedJune10,2005;revisedNovember2,ctpub-lishedontheInternetNovember30,rkwassupportinpartbytheChileanResearchFundCONICYTunderGrant1050549andGrant1030368,inpartbytheIndustrialElectronicsandMechatronicsMillenniumScienceNu-cleus,andinpartbytheUniversidadTécnicaFedericoSantaMarííguez,,,,ésarewiththeDe-partamentodeElectrónica,UniversidadTécnicaFedericoSantaMaría,Casilla110-V,Valparaíso,Chile(e-mail:jrp@;@;@).waswiththeInstitutfürLeistungselektronikundElektrischeAntriebeUniversitätSiegen,D-57068Siegen,wwiththeDepartamentodeElectrónica,UniversidadTécnicaFedericoSantaMaría,Casilla110-V,Valparaíso,iswiththeInstituteforPowerElectronicsandElectricalDrives,UniversitätStuttgart,70569Stuttgart,lObjectIdentifier10.1109/TIE.2006.8888020278-0046/$25.00©2007IEEE

496IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.54,NO.1,,theerrorbetweenthereferenceandthemeasuredloadcurrentisprocessedbyaproportional-integral(PI)erenceloadvoltagesarecomparedwithatriangularcarriersignal,ismethod,constantswitchingfrequency,fiformanceofthiscontrolschemede-pendsonthedesignofthecontrollerparameters,ghthePIcontrollerassureszerosteady-stateerrorforcontinuousreference,rorin-creaseswiththefrequencyofthetrolStrategyTheproposedpredictivecontrolstrategyisbasedonthefactthatonlyafinitenumberofpossibleswitchingstatescanbegen-eratedbyastaticpowerconverterandthatmodelsofthesystemcselectionoftheappropriateswitchingstatetobeapplied,aselectioncriteriamustbedefi-lectioncriteriaisexpressedasaqualityfunctionthatwitionofthefuturentrolstrategycanbesummarizedinthefollowingsteps.•Defitivecurrentcontrolblockdiagram.•Buildamodeloftheconverteranditspossibleswitchingstates.•ete-timemodeloftheloadisneededt,diagramofthepredictivecontrolstraterentcontrolisperformedinthefollowingsteps.1)Thevalueofthereferencecurrentisobtained(fromanoutercontrolloop),andtheloadcurrentismeasured.2)Themodelofthesystem(block1)isusedtopredictthevalueoftheloadcurrentinthenextsamplingintervalforeachofthedifferentvoltagevectors.3)Inthiscase,thequalityfunctionevaluatestheerrortagethatminimizesthecurrenterrorisselectedandappliedtotheload(block2).yFunctionThecurrenterrorforthenextsamplinginstantcanbeex-pressedinorthogonalcoordinatesasfollows:(1)whereandaretherealandimaginarypartofthepredictedloadcurrentvector,work,ualityfunctionscouldevaluatetheerrorintegraloverasamplingperiod,orthesquareerror,[14],thetorqueandfluxaredirectlycontrolledbyevaluatingthetorqueandflameway,activeandreactivepoweraredirectlycontrolledin[15]foranAC/DC/,additionaltermscanbeaddedtothequalityfunctiontoimproveotheraspectsofthecontrollikeminimizingtheswitchingfrequencyandDClinkvoltagebalancing,aspresentedin[16],erModelThepowercircuitoftheconverterconsideredinthisworkisshowninFig.4.

RODRÍGUEZetal.:tchingstatesoftheconverteraredeterminedbythegatingsignals,,andasfollows:ifonandoffifoffandon(2)ifonandoffifoffandon(3)ifonandoffifoffandon(4)andcanbeexpressedinvectorialformby(5)putvoltagespacevectorsgeneratedbytheinverteraredefinedby(6)where,,andarethephasetoneutralvoltagesoftheinverter(Fig.4).Then,theloadvoltagevectorcanberelatedtotheswitchingstatevectorby(7)eringallthepossiblecombinationsofthegatingsig-nals,,and,eightswitchingstates,andconsequently,at,resultinginonlysevendifferentvoltagevectors,odulationtechniqueslikePWM,heless,inthispaper,thein-verterisconsideredasanonliccuratemncludedeadtime,in-sulatedgatebipolartransistor(IGBT)saturationvoltage,anddiodeforwardvoltagedrop,work,emphasishasbeenputinsimplicity,delInabalancedthree-phaseload,thecurrentcanbedefinedasaspacevectorby(8)andtheloadEMFas(9)Inthisway,theloadcurrentdynamicscanbedescribedbythevectorequation(10)whereistheloadresistance,theloadinductance,thevoltagegeneratedbytheinverter,ulationandexperimentalresults,theloadback-EMFisate-TimeModelAdiscrete-timeformoftheloadcurrent(10)forasamplingtimecanbeusedtopredictthefuturevalueofloaimatingthederivativeby(11)andreplacingitin(10),thefollowingexpressionisobtainedforthefutureloadcurrent:(12)wherethetermcouldbeneglengthediscrete-timeonestepforwardin(12),thefutureloadcurrentcanbedeterminedby(13)

498IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.54,NO.1,FEBRUARY2007Theloadback-EMFcanbeestimatedusing(12)andmeasure-mentsoftheloadvoltageandcurrent,resultinginthefollowingexpression:(14)ureback-EMFcanbecalculatedusinganextrapolationofthepresentandpastvaluesoftheestimatedback-EMF,oritcanbesupposedthattheback-EMFdoesnotchangeconsiderablyinonesamplingintervaland,inthatcase,eVectorSelectionIntheproposedpredictivealgorithm,(13)isevaluatedforeachofthepossiblesevenvoltagevectors,tagevectorwhosecurrentpredictionisclosesttotheexprwords,theselectedvectorwillbetheonethatminimizesthequalityfunction(15)However,thefuturereferencecurrentvaluere-quiredby(1)ore,ithastobepredictedfromthepresentandpreviousvaluesofthecurrentreferenceusingasecond-orderextrapolationgivenby(16)obtainedfromtheLagrangeextrapolationformulafor(quadratic)andisappropriateforawidefrequencyrangeof[7].ficientlysmallsamplingtimes,calConsiderationsThecontrolstrategyhasbeenimplementedonadigitalsignalprocessor(DSP).eelapsedbeobservedinFig.7thatthevaluesforswitcdoneinordertodealwiththeprocessingtimedelay,whichisthemostimportantdelayonthesystem,filayhasbeenincludedinthedesignofthecontrollawfortheexperimentalresults,associatedwiththeresponseofthegatedrivecircuitryandswitchingofthedevicescanbeneglected,duetotheirsmallmagnitude,itsesofthelo,speedcontrolloop).Atablewithallthepossibleswitchingstatspondingtablewiththepossiblevolteginningofthenextsamplingperiod,theindexvalueisusedtoreadthetableofslAlgorithmThecontrolalgorithmisdetailedinFig.6asaflninthediagram,theminimizationofthequalityfunctioncanbeimplementedasacyclepredictingfor

RODRÍGUEZetal.:ltagevector,evaluatingthequalityfunction,andstoringtrolalgorithmisimplementedinaverysimplewaywiththefollowingprogramlines:TIONRESULTSSimulationsofaninvertercontrolledbythethreedif-ferentcurrentcontrolmethodshavebeencarriedoutwithMatlab/Simulink,inordertoassesstheperformanceofthepro-posedpredictivemethod,ametersofthesimulatedsystemare:,,,andtheback-EMFissinusoidalwithfitionr.8showeobservedthatthewaveformofloadvoltageisvfirstpart,thisresultpresentsthetransientbehaviorofthecontrolsystem,parisonpurposes,controllerparametersoftheclassicalmethodsconsideredint,risonoftheproposedpredictivecurrentcontrolwiththeconventionalhysteresisandPWMcontrolispresentedinFigs.9–,theamplitudeofreferencecurrentisre-ducedfrom13Ato5.2Aatinstant,whilekeeping

500IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.54,NO.1,tionrum,quencyspectrumofFig.12(b)showsthattheharmoniccontentgeneratedwhenusingPWMcurrentcontrol,y,Fig.12(c)ptagespectrumoftheproposedmethodischaracterizedbydiscretespectrallinessimilartothoseofPWMcurrentcon-trol,bleexplanationforthis,isthefactthattheswitchingstateoftheinvertercanbechangedonlyonceduringeachsamplinginstant,r,switchingstates1/2ofthesamplingfrequencydonotchangeineverysamplinginstant,sshowthatswitchingfrequencyisaofLoadModelErrorsConsideringthatthequalityofthecontrolstrategydependsonthemodelusedtopredictthebehavioroftheloadcurrents,ectoferrorsinthevalueoftheloadinductanceandresistancehasaverysmalleffectoverthepredictionand,infact,r,errorsintheloadinductancehaveamajorimportancefortheloadcur-rentprediction,andhence,ninFig.13,estimatingalowervalueoftheinductasmallervalueofcanincreasethedelayinthereferencetracking,asshowninFig.14(a).Forahighervalueof,thebehavioroftheloadcurrentsisshowninFig.14(b).MENTALRESULTSAnexperimentalsetupwasdevelopedusingaDSPmodelandTMS320F2812forasamplingtime,andtestedwithanactiveloadwithvaluestheamplitudeofcurrentfiesiscon-trol,showninFig.9,presentsgou-latedcurrentsusingPWMmodulation,showninFig.10,presentand,andaslowerre-similarcoupl-sponseoftheproposedpredictivecurrentcontrol,forthesametest,amicresponseisasfastastheoneobtainedbyhysteresissthereferencetrackingcapabilitiesofanycurrentcontrolmethod,anotherimportantper.12(a),itcanbeobservedthathysteresiscontrolpro-ducesacontinuousandwidefrequencyrangeoutputvoltage

RODRÍGUEZetal.:ofmodelerrorsintheloadcurrent.a)Witha050%errorintheloadinductanceL.b)Witha+50%,inkcapacitorisfedbyasingle-phaserectifier,rentsaremeasuredtoclosethecurrentcontrolloopandtheDSPisprograimplementation,asimplifiedversionof(13)wasused,ationisreducedto(17)ThedynamicresponseofthesystemwithasamplingtimeisshowninFig.16forastepchangeintheampli-tudeof(from4Ato2Aattime),sultisverysimilartotheonepresentedinFig.11,mentalresultswithT=100