SHUNTANDSERIESCONDITIONINGOFHYBRIDMATRIXCONVERTERByAmeerJanabiATHESISSubmittedtoMichiganStateUniversityinpartialentoftherequirementsforthedegreeof2016ABSTRACTSHUNTANDSERIESCONDITIONINGOFHYBRIDMATRIXCONVERTERByAmeerJanabiHybridmatrixconverterscanpotentiallyenablematrixconvertersinhighpowerappli-cationsthatconventionalmatrixconverterswillnotbeabletoattain.Itusesaconventionalnine-switchmatrixconverterinconjunctionwithanauxiliaryback-to-backac-dc-accon-verterthatconditionsthecurrentandvoltagewaveformsontheinputandoutputsideofthematrixconverter.Thematrixconverterprocessesthemainpoweratlowswitchingfrequencytoenabletreductionofswitchinglossesandtoallowforadoptionofhigh-powersemiconductordevicessuchasintegratedgatecommutatedthyristors(IGCTs).Theauxiliaryac-dc-acconverterisdedicatedtoimprovingthepowerqualityattheinputandoutputterminalsofthematrixconverterbyminimizingharmoniccurrentsdrawnfromthesourceandharmonicvoltagesappliedtotheload.Essentially,theauxiliaryback-to-backconverterfunctionsasashunt-and-seriesactive(AF).SeveralAFcontroltechniqueshavebeenpresentedintheliterature.Basedontheop-eratingprinciple,thesetechniquescanbecategorizedintotwogroups.Thegroupofmethodsarebasedoninstantaneousreactivepowertheory(IRPT)andextractthereactivecomponentofthepowerandtheoscillatorycomponentoftherealpower.TheothermethodsarebasedontechniquesandextractthefundamentalcomponentofthecurrentorvoltagesuchasnotchandfastFouriertransform(FFT)methods.ThemainlimitationforIRPTbasedmethodliesinitsenesswhentheharmonicsareconcurrentlypresentinvoltageandcurrentwhilethelimitationforFFTbasedmethodisitsinabilitytocompensatethefundamentalcomponent.Toaddresstheselimitationsoftheaforementionedmethods,anewcontrolstrategybasedonpoweraveraginghasbeenproposed.Thisproposedcontrolmethodisabletoelyobtainthecorrectactivecomponentofcurrentorvoltageincaseswhereboththecurrentandthevoltagearenon-sinusoidalandprovidefullcontroloverthepowerfactor.ACKNOWLEDGMENTSIwouldliketoexpressmyappreciationtomyadvisor,Dr.BingsenWang,forhiscontinuousguidanceandsupportduringmystudyinMichiganStateUniversity.Hisextensiveknowl-edge,meticulousandopen-mindedattitudetoresearch,andthinkingandproblemsolvingapproacheshelpmealottolearnhowtodoreachwork.WithoutDr.Wang'sguidance,Icannotthiswork.Ialsowouldliketothankmycommitteemembers,Dr.EliasStrangas,andDr.ShanelleN.FosterforservingtobemyM.S.committee.Ialsowouldliketothankmylab-matesYantaoSongandLinaHmoudfortheirsupport.Finally,butnotleast,Iwanttothankmyparents,mybrothersandmysistersfortheirconstantsupportandencouragementalongtheway.IamthankfulforallthewonderfulpeopleImethere,SymbatPayayeva,MohammedAl-Rubaiai,KhalilSinjari,MaherAl-Sahlany,AliAl-Hajjar,PetrosTaskas,MontassarSharif,HussamJabbar,SamanthaTraylor,AaronWentz,NickSetterington,MariaVeretennikova.ivTABLEOFCONTENTSLISTOFTABLES....................................viLISTOFFIGURES...................................viiChapter1Introduction...............................1Chapter2Background................................42.1TheConventioanlTopologyofMatrixConverter................42.2HighFrequencyModulationTechniquesofMatrixConverter.........52.2.1Alesina-Venturini1981..........................62.2.2Alesina-Venturini1989..........................82.2.3Space-VectorApproach..........................102.3LowFrequencyModulationTechniqueofMatrixConverter..........10Chapter3TheProposedHybridMatrixConverter..............163.1ActiveFilterModulation.............................183.1.1InputCurrentConditioning.......................183.1.2OutputVoltageConditioning......................213.2SimulationResults................................233.3conclusionandremarks..............................25Chapter4ControlSchemeofHybridMatrixConverterOperatingUnderUnbalancedConditions........................264.1UnbalancedVoltageSource............................264.2UnbalancedLoadCurrent............................304.3SimulationResults................................324.4Conclusion.....................................33Chapter5CriticalEvaluation...........................355.1AdaptiveNotchFilterMethod..........................375.2InstantaneousReactivePowerMethod.....................385.2.1ActiveCurrentontheInputSide....................395.2.2ActiveVoltageontheOutputSide...................415.3ProposedAveragePowerMethod........................435.4SimulationResultsandEvaluation.......................445.5Conclusion.....................................49BIBLIOGRAPHY....................................50vLISTOFTABLESTable5.1:Asummaryofthecomparativeevaluationofthethreemethods......46viLISTOFFIGURESFigure1.1:Conventionalninebidirectionalswitchmatrixconverter..........2Figure2.1:Illustrationofmaximumvoltagetransferratio................8Figure2.2:Illustrationofmaximumvoltagetransferratioimprovedto87%......9Figure2.3:Conventionalninebidirectionalswitchmatrixconverter..........11Figure2.4:Typicalinput/outputvoltages/currentsofamatrixconverterwithlow-frequencymodulationscheme........................13Figure2.5:Thespectraofinputcurrentsandoutputvoltages.............14Figure2.6:SwitchinglossesofIGBTsanddiodesatvariousswitchingfrequencies..15Figure3.1:HybridMatrixConverter...........................17Figure3.2:(a)Controlcircuitfortheshuntactive(b)Controlcircuitfortheseriesactive(c)Outputcurrentfundamentalcomponentextraction.22Figure3.3:(a)Inputcompensationcurrentinjectedbytheshuntactive(b)Inputcurrentafterusingtheshuntactive(c)Outputcompensationvoltageinjectedbytheseriesactive(d)Outputlinevoltageafterusingtheseriesactive.........................24Figure4.1:Controlcircuitoftheshuntactiveinthecaseofunbalancedsourcevoltage.....................................29Figure4.2:Controlcircuitoftheseriesactiveinthecaseofunbalancedload.32Figure4.3:Outputresultsunderunbalancedvoltagesourceconditions........33Figure4.4:Outputresultsunderunbalancedloadconditions.............34Figure5.1:Detailedimplementationoftheadaptivenotch...........38Figure5.2:Blockdiagramsfor(a)determiningthereferencesignalsforcompensationcurrentandvoltageusingIRPT;(b)extractingthefundamentalcompo-nentoftheoutputcurrent...........................43viiFigure5.3:Averagepowercompensationmethodcontrolfor(a)inputcurrent;(b)outputvoltage.................................45Figure5.4:Inputlinevoltagevabandcurrentia.....................47Figure5.5:InputcurrentiausingNotchFilter......................47Figure5.6:InputcurrentiausingIRPT.........................47Figure5.7:InputcurrentiausingAP...........................47Figure5.8:OutputlinevoltagevABandcurrentiA...................48Figure5.9:OutputvoltagevAusingNotchFilter....................48Figure5.10:OutputvoltagevAusingIRPT........................48Figure5.11:OutputvoltagevAusingAP.........................48viiiChapter1IntroductionMatrixconvertershaveseveraladvantagesovertraditionalfrequencyconverters.Theyareabletoprovidesinusoidalinputcurrentsandoutputvoltageswithsmallersizeandnolargeenergystoragecomponentsrequired,andtoachievefullcontrolovertheinputpowerfactorforanyload[1].Duetothequalitiesthatthematrixconverterprovides,ithasbeenaveryattractiveareaofresearchovertherecentyears.TherealdevelopmentwasstartedbyVenturiniandAlesinapublishedin1980[2][3],theyintroducedthename\MatrixConverter"andprovidedadetailedmathematicalmodeldescribingthebehaviorofthecon-verter.AnothermodulationtechniqueisbasedonaousDClinkconnectingacurrentsourcebridgeandvoltagesourcebridgepresentedbyRodriguez[4].Thisapproachisknownastheindirecttransferfunctionapproach.In1989themethodofspacevectormodulationtechniqueformatrixconvertersintroducedbyHuber[5].In1992itwaspracticallythatthenineswitchesmatrixconvertershowninFig.1.1,couldbeusedelyinvectorcontrolofinductionmotor[1].However,theusageofthematrixconverterwasstilllimitedduetotheltcurrentcommunicationofbidirectionalswitches.Recently,manysolutionshavebeenpresentedtosolvethecommuni-cationproblemsuchasthefourstepmethod[6].MatrixconvertersgeneratecurrentharmonicsthatareinjectedbackintotheACsystem.1Figure1.1:Conventionalninebidirectionalswitchmatrixconverter.Thesecurrentharmonicscanresultinvoltagedistortionsthatfurthercttheoperationoftheentiresystem.Ontheotherhandthevoltageharmonicsontheoutputsidewillcauseadisturbancetotheloadwhichinmostcasesisinductive.Inordertoreducetheseharmonicsinthesourcecurrentandtheoutputvoltage,passivearetypicallyused.toflowpasspassivehavebeenproposed[7],Thesizeanddesignofthesedependonmanyfactorssuchas:1-powerqualityrequirements;2-powersystemharmoniccontent;3-converterswitchingfrequency;4-convertermodulationtechnique[8].Passiveseemtobeanpreferredsolutioninlowpowerapplicationsofmatrixcon-verters.However,thisisnotthecasewhenamatrixconverterisintroducedforhighpower2interfaces,theoptimaldesignofthepassivewouldbeamajorchallenge.ThehighpowermatrixconverterisintroducedbyYaskawaforwindpowerappli-cations[9],inwhichthemodularconceptisusedtocopewiththevariousdemandsinthepowergrid.However,themodularconceptispresentedtobeusedinaveryhighvoltagesapplicationssuchaswindmillandlargeproblems.Inthispaperahybridmatrixconverterwillbeintroducedtooperateathighpowermediumvoltagedemands.Theproposedtopol-ogyemployaconventionalnine-switchmatrixconvertercoupledwithshuntactiveconnectedtotheinputsidetoreducethesourcecurrentharmonics,andseriesactiveconnectedtotheoutputsidetoreducetheoutputvoltageharmonics.ThetwoactiveareconnectedthroughasmallDClinkcapacitor.Themainmatrixconverterismodulatedusingthelowfrequencymodulationalgo-rithm[10]toallowmaximumvoltagetransferratio,andtheactivearecontrolledbasedontheinstantaneousreactivepowertheory[11][12].Thethesisisorganizedasfollows,Thenextchaptergiveabriefdiscussionaboutthehighfrequencymodulationtechniquesandexplainsthelowfrequencymodulationtechnique.Thethirdchapterintroducethehybridmatrixconverteranditsoperation.Thefourthchapterdiscusstheoperationofhybridmatrixconverterinabnormalconditions.Thesixthchapterdiscussotherconditioningmethodforhybridmatrixconverterandintroduceanewconditioningtechniquetoassesstheevaluationofthepreviousmethods.3Chapter2BackgroundThischapteraimtogiveageneraldescriptionofthemainfeaturesofmatrixconverter.MatrixconverterisaonestageAC-ACconverter.Ithasseveraladvantagesovertheconven-tionalAC-DC-ACconverterssuchassinusoidalinputandoutputwaveform,ithasinheredthebidirectionalwofpower,andminimalenergystoragerequirements.Matrixconverterhasalsodisadvantages.Themaximumoutputvoltageis0:866%forsinusoidalinputandoutputwaveform.ItrequiresmoresemiconductordevicesthantheconventionalAC-DC-ACconverters.2.1TheConventioanlTopologyofMatrixConverterTheninebidirectionalswitchthreephasematrixconverterisshowninFig.1.1.Theinputterminalofthematrixconverterisconnectedtoathreephasevoltagesource.whiletheoutputsideisconnectedtoathreephaseload.Theofmatrixconvertertheo-reticallyassumes(512)switchingHowever,ifwetakeintheconsiderationtheconstrainsoftheinputbeingavoltagesourceandtheoutputbeingacurrentsource,suchthattheinputsideofthematrixconvertercannotbeshortcircuitedandtheoutputsideofthematrixconvertercannotbeopencircuited.Thisyieldofonly27feasibleswitchingcombinations.42.2HighFrequencyModulationTechniquesofMatrixConverterInordertoanalysisthemodulationtechniquesofmatrixconverter,itsvalidtoconsideridealswitchingandthattheswitchingfrequencyismuchhigherthattheinputandtheoutputfrequencies[15].Theinputoutputrelationshipsofvoltagesandcurrentsareasfollows.vout=Hvin;(2.1)iin=HTiout;(2.2)wherevoutistheoutputvoltagevector[vuvvvw],vinistheinputvoltagevector[vavbvc],iinistheinputcurrentvector[iaibic],andioutistheoutputcurrentvector[iuiviw].HistheswitchingmatrixofthematrixconverterexpressedasH=2666664hauhbuhcuhavhbvhcvhawhbwhcw3777775:(2.3)Eachelementinthetransformationmatrix(2.3)correspondstooneswitchingfunctionforthedirectionmatrixconverter.Consideringthatassumptionswemadeearlierandfurthermoreneglectingallofthehighfrequencycomponentswecanreplacetheswitchingfunctionintheswitchingmatrixintothemodulationfunctionrepresentedbythedutycycle.Theconstrainsoftheinputandtheoutputsidesofthematrixconvertercanbemain-tainedviathefollowingequations5hau+hbu+hcu=1(2.4)hav+hbv+hcv=1(2.5)haw+hbw+hcw=1(2.6)Thedeterminationofanymodulationstrategyforthematrixconverterisbasicallydeter-miningtheappropriatedutycyclethattheinput-outputrelationshipsequ.(2.1)and(2.2)2.2.1Alesina-Venturini1981Themodulationofmatrixconvertercanbestatedasfollows.Givenasetofinputvoltagesandasetofoutputcurrentsvin=Vin2666664cos(!it)cos(!it2ˇ3)cos(!it+2ˇ3)3777775:(2.7)iout=Iout2666664cos(!ot+˚o)cos(!ot2ˇ3+˚o)cos(!ot+2ˇ3+˚o)3777775:(2.8)themodulationmatrixH(t)suchthat6vout=qVin2666664cos(!ot)cos(!ot2ˇ3)cos(!ot+2ˇ3)3777775:(2.9)andiin=qcos(˚o)Iout2666664cos(!it+˚o)cos(!it2ˇ3+˚o)cos(!it+2ˇ3+˚o)3777775:(2.10)whereqisthevoltagetransferratiooftheoutputandtheinputvoltages.TherearetwobasicsolutionforthisasshownbelowThemethodobtainedbyusingthedutycycleofthematrixconverter[16]representedinthefollowingequationH1=26666641+2qcos(!mt)1+2qcos(!mt2ˇ3)1+2qcos(!mt+2ˇ3)1+2qcos(!mt+2ˇ3))1+2qcos(!mt)1+2qcos(!mt2ˇ3)1+2qcos(!mt2ˇ31+2qcos(!mt+2ˇ3))1+2qcos(!mt))3777775:(2.11)andH2=26666641+2qcos(!mt)1+2qcos(!mt2ˇ3)1+2qcos(!mt+2ˇ3)1+2qcos(!mt2ˇ31+2qcos(!mt+2ˇ3))1+2qcos(!mt))1+2qcos(!mt+2ˇ3))1+2qcos(!mt)1+2qcos(!mt2ˇ3)3777775:(2.12)ForH1;!m=!o!iandforH2,!m=(!o+!i)Soforgivingthesamephasedisplacementattheinputandtheoutputports˚i=˚o7gives(2.11),where˚i=˚ogives(2.12).Combiningthetwosolutionsprovidesfullcontrolovertheinputpowerfactor.Figure2.1:Illustrationofmaximumvoltagetransferratio.Thebasicsolutionrepresentsadirecttransferfunctionapproach.duringeachswitchsequencetimetheavargeoutputvoltageequaltothetargetvoltage.Forthistobeachived,theoutputvoltagemustwithentheinvelopeoftheinputvoltageasshowninFig.2.1.Thismodulationsolutionlimittheoutputvoltageto%50oftheinputvoltage.Itispossibletoaddthecommonmodevoltagetoincreasethevoltagetransferrationto0:866asshowninFig.2.2.Itisimportanttomentionthatthecommonmodevoltagedoesnotcttheoutputline-to-linevoltage.Itonlyallowthatoutputvoltagetobewithintheinputvoltageenvelopewith0:87voltagetransferratio.2.2.2Alesina-Venturini1989CalculatingtheswitchingtimingdirectlyfromthemethodisquitedItspossibletoexpressthethemodulationfunctionas8Figure2.2:Illustrationofmaximumvoltagetransferratioimprovedto87%.hKj=tKjTseq=131+2vKvjV2in(2.13)whereK=a;b;candj=u;v;w.Equation(2.13)correspondto50%voltagetransferratio.toachievethemaximumvoltagetransferrationwemayconsiderthecommonmodevoltageasfollowshKj=tKjTseq=131+2vKvjV2in+4q3p3sin(!it+K)(2.14)whereKis0;2ˇ3;2ˇ3forK=a;b;cTheinputdisplacementfactorcanbecontrolledbyinsertingaphaseshiftbetweenthemeasuredinputvoltageandthevoltagevKin(2.14).However,controllingtheinputdis-placementangleisontheexpenseofvoltagetransferratio.92.2.3Space-VectorApproachAnotherapproachisbydetheavailablevectorsandforaspacevectorrepresentationfortheinputandoutputvoltagesandcurrent.Amongthe27availablevectorsthereareonly21voltagevectorcanbeusefullyemployedtothespacevectoralgorithm.The18vectordeterminetheoutputvoltageandtheinputcurrentandtheother3arethezerovectors.The6vectorthatcompletesthe21vectorarebasicallyconnectingeachoutputphasetoatinputphase[15].SVPWMmethodcanalsoachieve0:87voltagetransferratio.Sincewearenotinterestedinhighfrequencymodulationtechniques,weomitthedetailsofSVPWM.2.3LowFrequencyModulationTechniqueofMatrixConverterAlloftheproposedswitchingtechniquesexcepttheprogrammableoneintroducedin[17]andtheZ-sourcematrixconverterfamilypresentedin[18]werenotabletobreakp32voltagetransferratio.Thisinternsiclimitationofthematrixconverterreducestheoutputpoweroftheinductionmotorto23whenitisfedfromthematrixconverterusingaconventionalpowersource.Lowswitchingtechnique,sixstepmethodwaspresentedbyBingsenWang[10]thatisabletobreakthelimitofvoltagetransferratio.Thesix-stepmethodwillbeusedasthemodulationtechniqueforthenine-switchmatrixconverterforthewingreasons:1-Greaterthanunityvoltagetransferratio,namely1:05%2-Lowswitchingfrequencywithminimumswitchinglossescomparedtohigh-frequencysynthesismodulationtechniques103-Easytocontrolandimplement.TheconventionalmatrixconverterinFig.1.1couldberealizedtoanindirectmatrixconverterasshowninFig.2.3.Wheretheinput-outputrelationshipcanbeexpressedasvout=HVSBHCSBvin;(2.15)iin=HTCSBHVSBiout;(2.16)whereHCSBistheswitchingmatrixforthecurrentsourcebridgeconnectedtotheFigure2.3:Conventionalninebidirectionalswitchmatrixconverter.voltageandHVDBistheswitchingmatrixforthevoltagesourcebridgeconnectedtothecurrentsourceandtheyaregivenbyHCSB=264haphbphcphanhbnhcn375:(2.17)11HCSB=2666664huphunhvphvnhwphwn3777775:(2.18)whereH=HCSBHCSB(2.19)Anymodulationtechniquethatprovidessolutiontotheindirectrealizationofthematrixconvertercanbeappliedtothedirectmatrixconvertervia(2.19).InourcasetheCSBwillbetreatedasaandtheVSBwillbetreatedavoltagesourceinverter,andbothconverterareoperatinginfullsix-stepsmode.Theswitchingsignlasandtheinput-outputvoltageanscurrentareshownin2.4.Eachelementinthetransformationmatrixcorrespondstooneswitchingfunctionforthedirectionmatrixconverter.Byanappropriateselectionoftheswitchingfunctions,outputvoltagesandtheinputcurrentssimilartothoseofthevoltagesourceinverterandcurrentsourceinverter,respectively,canbeachieved.Theresultingoutputvoltagesandinputcurrentsforunitydisplacementfactoroperationattheinputandoutput,andthecorrespondingFourierspectraareshowninFig.2.4and2.5,respectively.Thespctrumoftheinputcurrentincludeslowfrequencyharmonic5thand7th.Theloadvoltageincludethe5thand7thasshowninFig.2.5.Thetotalharmonicdistortioninboththeinputcurrentandtheoutputvoltageisaround31%.Theinputcurrentandoutputvoltageswaveformcontainalowfrequencyharmonics,andforhighpowerapplicationitstodesignlowpassthatisablemitigatethese12Figure2.4:Typicalinput/outputvoltages/currentsofamatrixconverterwithlow-frequencymodulationscheme.13Figure2.5:Thespectraofinputcurrentsandoutputvoltages.14Figure2.6:SwitchinglossesofIGBTsanddiodesatvariousswitchingfrequencies.lowfrequencyharmonics.Forillustration,theswitchinglosseshavebeencalculatedanalyticallyformatrixconverterconnectedto100kWRLloadincasesoflowfrequencymodulationandhighfrequencymodulationtechniques.Fig.2.6showsthattheswitchingpowerlossesofthelowfrequencymodulationmatrixconverterareverysmallcomparedtohighfrequencysynthesismatrixconverter,Theswitchonpowerlossesforthediodeisneglectedbecausetheyareverysmall.15Chapter3TheProposedHybridMatrixConverterMatrixconverterswouldinjectasitamountofcurrentharmonicsandvoltagehar-monicsbackintothepowersourceandtheload,respectively,ifmeasuresarenotproperlyimplemented.Theseharmonicscausedistortionandadverselyimpacttheoperationofthewholesystem.Theincreasingdemandforhighpowermakestheconventionalsolutionofpassivenolongerttosolvethepowerqualityprobleminmatrixconverters,besidetheotherdrawbacksofusingbulkypassivecomponentssuchas,shortlifetime,bigsize,andhighcost.Thischapterpresentsahybridmatrixconverterformediumvoltagehighpowerapplications.Byutilizingalow-frequencymodulationtechniques,combinedwithashuntactiveimplementedtotheinputsideofthematrixconvertertoeliminatecurrentharmonicsandaseriesactiveisappliedtotheoutputsideofthematrixconvertertoeliminatethevoltageharmonics.Thisapproachismoretintermsofreducingthetotalnumberofpassivecomponentsusedinthesystem,reducingtheswitchingpowerlosses,andimprovingvoltagetransferratio.Theexplanationofpredictingthecompensa-tioncurrentandthecompensationvoltagewaveformsisbasedontheinstantaneousreactivepowertheory.Thefeasibilityandenessproposedtopologyhavebeenvbythesimulationresults.16Figure3.1:HybridMatrixConverter.Fig.3.1showstheproposedtopologyofthehybridmatrixconverter.Thetopologyconsistoftheconventionalninebidirectionalswitchesmatrixconvertercoupledwithashuntactiveimplementedontheinputsideandaseriesactiveontheoutputside.Bothactiveconsistofthree-phaseinvertersconnectedbyacommonDClink.Theshuntactivecompensatestheinputcurrentharmonicsproducedbytheswitchingoperationofmatrixconverter.Theseriesactivecompensatestheoutputvoltageharmonics.Fromasystem-modelingpointofviewthematrixconverterisconsideredasdualharmonicssources,currentharmonicsourceintheinputside,andvoltageharmonicsourceintheoutputside.ThesmallDC-linkcapacitorconnectingtheshuntandtheseriesactivelterisneededtocompensatetheoscillatorycomponentoftheinstantaneousactivepoweraswillbeexplainednext.173.1ActiveFilterModulation3.1.1InputCurrentConditioningConsideringthetwowaveformsattheinputside,thethree-phaseinputvoltageisalwayssinusoidalandthethree-phasecurrentisextremelydistortedduetotheswitchingactionofthematrixconverter.Theinstantaneousthree-phaseactivepowerattheinputsidep,canbegivenbypin=vinvin;(3.1)where""denotestheinternalproductofthetwovectors.Equation(3.1)canalsoexpressedintheconventionaldetentionofpower,pin=iiva+ibvb+icvc:(3.2)Theinstantaneousinputreactivepowervectorofthethree-phasesystemcanbeexpressedasqin=viniin;(3.3)where""denotesthecrossproductofthevoltageandcurrentvectors.qcanalsobe18expressedqin=2666664qaqbqc3777775=26666666666666666664vbvcibicvcvaiciavavbiaib37777777777777777775;(3.4)thenormofthereactivepowervectorisqin=kqink=qq2a+q2b+q2c:(3.5)Wecandecomposethesourcecurrentintoanactivecomponentiinp,andreactivecomponentIinqinwhichiinp=2666664iapibpicp3777775=pinvinvinvin;(3.6)iinq=2666664iaqibqiaq3777775=qinvinvinvin;(3.7)Itisworthnotingthattheresultantcurrentvectorfromtheadditionofthetwocur-rentsiinpandiinqisalwaysequalthesourcecurrentiin.Anotherobservationisthattheinstantaneouspowerproducedfromviniinpequaltotheinputpowerpin,andthe19instantaneouspowerproducedfromviniinqisalwaysequaltozero.Fromthisobservationwecantellthatiinqisnotcontributingtoanypowertransmissionfromthesourcetotheload.Infactiftheinstantaneousreactivecurrentiskeptiinq0,thecurrentiinwillbetransmittingthesameinstantaneousactivepowerpinwithunitypowerfactor.Consequently,theinstantaneousactivepowerpincanbeanalyzedintotwocomponents,pin=pin+~pin;(3.8)wherepinisthedirectcomponentoftheinstantaneousactivepoweranditrepresentstheenergywinthedirectionfromthesourcetothematrixconverter.And~pinrepresentstheoscillatorycomponentoftheinstantaneousactivepowerwhichistheenergyexchangedbetweenthesourceandthematrixconverter.Byeliminatingthecurrentcomponentthatproduces~pin,thesourcecurrentwillbesinusoidal.Itisimportanttonotethatwedonotneedanenergystoringcomponenttocompensatethereactivepowerqin,becauseqinrepre-sentstheenergyexchangeamongthethree-phases.Whileanweenergystoringcomponentisrequiredforcompensatingtheoscillatoryrealpower~pin,because~pinistherealpowerexchangedbetweenthesourceandthematrixconverter.Knowingthis,wecangeneratethecompensationcurrentbyselectingtheappropriatepowerportiontobeeliminated.Thethree-phasecompensationcurrentcouldbeexpressedasicomp==pcompvinvinvin+qcompvinvinvin;(3.9)wherepcompandqcompcanbedeterminedfrompinandqindependingonthecompen-sationobjectives.203.1.2OutputVoltageConditioningThecontinuouscurrentrequirementofthematrixconverterattheoutputsidemakesitaperfecttoapplytheseriesactivetocompensatetheoutputvoltageharmonics.Byusingthedualapproachoftheinstantaneousreactivepowertheorywecananinstantaneousactiveoutputpowerandinstantaneousreactiveoutputpoweraspout=voutiout;(3.10)qout=voutiout:(3.11)Inturn,weetheinstantaneousactivevoltagevectorVoutpandinstantaneousreactivevoltagevectorVoutqasvoutp=2666664vApvBpvCp3777775=pouti1outi1outi1out;(3.12)voutq=2666664vAqvBqvCq3777775=qouti1outi1outi1out;(3.13)thesuperscript"1"denotesthefundamentalcomponentoftheoutputcurrent.Inmostcases,seriesactiveltersisusedinapplicationswherethecurrentissinusoidal.However,thisisnotthecaseinthematrixconverteranditrequiresfurthercontroltoextractthefundamentalcomponentoftheoutputcurrent.21Figure3.2:(a)Controlcircuitfortheshuntactive(b)Controlcircuitfortheseriesactive(c)Outputcurrentfundamentalcomponentextraction.SimilarobservationcanbemadeintheseriesactiveTheadditionofthetwovoltagevectorsvoutpandvoutqalwaysequaltheoutputvoltagevout.Theinstantaneouspowerproducedfromvoutpioutisequaltothetotheoutputpowerpout,andtheinstantaneouspowerproducedfromvoutqioutalwaysequalszero.Theinstantaneousoutputactivepowerhasasimilarenvelopetotheinstantaneousinputactivepower.Theonlyerenceistheswitchinglosses.Wecanalsoanoscillatorycomponentoftheinstantaneousoutputactivepowerandthecorrespondingcomponentofoutputvoltagethatcausesthisoscillation.Byselectingtheappropriateportionsofpowertobecompensatedwecanwritetheequationofthecompensatingvoltageasvcomp==pcompi1outi1outi1out+qcompi1outi1outi1out;(3.14)22wherepcompandqcompcanbeassignedfrompoutandqoutaccordingtoourone'scompen-sationobjectives.ThecontrolcircuitsofthetwoactiveareshowninFig.3.2(a)includescompu-tationalcircuitsfortheinstantaneousinputreactivepowerqin,instantaneousoscillatorycomponentoftheinputactivepower~pin,andinstantaneousreactivecomponentoftheinputcurrentiinq,instantaneousoscillatorycomponentoftheinputactivecurrent~iinp.circuitFig.3.2(b)includescomputationalcircuitsfortheinstantaneousoutputreactivepowerqout,instantaneousoscillatorycomponentoftheoutputactivepower~pout,andinstantaneousre-activecomponentoftheoutputreactivevoltagevoutq,instantaneousoscillatorycomponentoftheoutputactivevoltage~voutp.Fig.3.2(c)showsthefundamentalcomponentextractionfromtheoutputcurrent.3.2SimulationResultsAsimulationmodelofthehybridmatrixconverterasshowninFig.3.1isbuildusingMATLABSimulink.Intheshuntactiveahysteresiscurrentcontrollerisusedtotracktheinstantaneouschangeoftheinvertercurrentandcompareitbackwiththereferencecurrent.ItisnecessarytocontrolthevoltageoftheDClinkcapacitorbyaddingthepowerlosscausedbytheinverterswitches.Theactivegeneratesharmonicsatitsswitchingfrequency,anditisnecessarytoouttheseharmonic,typically,smallcouplinginductorconnectedinserieswiththeinverteroutputtoeliminatethesehighfrequencyharmonics.Inourcasethecompensationpowersarethereactivepowerandtheoscillatorycomponentofthetheactivepower.Thecompensationofreactivepowerwillguaranteethatthereis23Figure3.3:(a)Inputcompensationcurrentinjectedbytheshuntactive(b)Inputcurrentafterusingtheshuntactive(c)Outputcompensationvoltageinjectedbytheseriesactive(d)Outputlinevoltageafterusingtheseriesactivenophaseshiftbetweenthecurrentandthevoltageintheinputandoutputside,andthecompensationoftheoscillatorycomponentoftheactivepowerwillguaranteethattheinputcurrentandtheoutputvoltagearesinusoidal.Fig.3.3showstheinputcurrentandtheoutputvoltageafterthecompensation.inthesamephasewiththeinputvoltagewhichmeansthatallthereactivepowerhasbeencompen-satedely.Thecompensationoftheoscillatorycomponentoftheinputactivepowerresultinthesinusoidalshapeoftheinputcurrent.Thesameexplanationcanbemadefortheoutputvoltage.243.3conclusionandremarksInthischapter,shuntandseriesactiveltershavebeenimplementedontheinputandtheoutputsidesofthelow-frequencymodulatedmatrixconverter,respectively.Theanalysisoftheinputandoutputpowershowsthattheinstantaneousreactivepowertheorycanbeappliedindeterminingthecompensationcurrentoftheinputsideandthecompensationvoltagefortheoutputsideofthematrixconverter.Theproposedtopologyisverytinmediumvoltagehighpowerapplicationsinwhichtheconventionalsolutionofpassiveisnote.Thehybridmatrixconverterreducesthesizeofenergystoragecomponents,andprovideshigherreliability.Theproposedtopologycouldbeutilizedformitigatingtheofvoltagesag,especiallywhenthematrixconverterisusedtodrivesensitiveloads.MoredetailedinvestigationswillbereportedinthefuturepublicationsTheDClinkconnectingthetwoactivecanprovidethesamevoltageintheAC-DC-ACbacktobackinverters.25Chapter4ControlSchemeofHybridMatrixConverterOperatingUnderUnbalancedConditionsHybridmatrixconverterscanpotentiallyenablematrixconverterinhigh-powerapplica-tionsthatconventionalmatrixconverterswouldnotbeabletoattain.Thehybridmatrixconverterconsistsamainmatrixconverterthatprocessesthebulkpowerconversionandanauxiliaryback-backvoltagesourceconverterthatimprovestheterminalpowerquality.Priorsimulationstudyhassuccessfullydemonstratedthatthesuperiorspectralperformancecanbeachieved.Thischapterisfocusedonthecontrolschemeofthehybridmatrixconverteroperatingunderbalancedandunbalancedconditions.4.1UnbalancedVoltageSourceInthepreviouschaptertheassumptionismadethatthesourcevoltageisbalanced,meaningtheamplitudesofthethreephasevoltagesareequaltoeachotherandthereisa120ophaseshiftamongthem.Incaseofunbalancedvoltagesource,furtheranalysisneedstobeconsideredtoobtainthecorrectcompensationcurrentfortheinputstageofthematrix26converter.Theunbalancedvoltagesourcemayincludepositive,negative,andzerosequencecompo-nentsaccordingtothesymmetricalcomponenttheory.Thesymmetricalcomponenttrans-formationisappliedonboththeinputvoltageandcurrenttodeterminethesequencecom-ponents.2666664vin0vin+vin3777775=132666664111121237777752666664vavbvc3777775;(4.1)Thesubscripts"0","+",and"-"correspondtothezero,positive,andnegativesequences,respectively.Thecomplexnumberinthetransformationmatrixcorrespondstothephaseshiftinthethreephasesystem,=1\120o=ej2ˇ3,2666664inin0inin+inin3777775=132666664111121237777752666664inainbinc3777775;(4.2)where"n"denotestheharmoniccomponentorder.Thetimedomainequivalentvoltageandcurrentcanbederivedfromthephasorsgivenby(4.1)and(4.2).Bysynthesizingthesymmetricalcomponents,theabcinputvoltagescanbewrittenas:278>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>:va=vin0z}|{p2Vin0sin(!it+˚0)+vin+z}|{p2Vin+sin(!it+˚+)+vinz}|{p2Vinsin(!it+˚)vb=p2Vin0sin(!it+˚0)+p2Vin+sin(!it+˚+2ˇ3)+p2Vinsin(!it+˚+2ˇ3)vc=p2Vin0sin(!it+˚0)+p2Vin+sin(!it+˚++2ˇ3)+p2Vinsin(!it+˚2ˇ3);(4.3)Similarly,theinstantaneousinputlinecurrentsarefoundtobe8>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>:ina=inin0z}|{p2Inin0sin(!it+˚0)+inin+z}|{p2Inin+sin(!it+˚+)+ininz}|{p2Ininsin(!it+˚)inb=p2Inin0sin(!it+˚0)+p2Inin+sin(!it+˚+2ˇ3)+p2Ininsin(!it+˚+2ˇ3)inc=p2Inin0sin(!it+˚0)+p2Inin+sin(!it+˚++2ˇ3)+p2Ininsin(!it+˚2ˇ3);(4.4)Theinputcurrentistheresultofaddingtheresultsofallthetimedomaincurrentsfromeachharmonic.ik=1Xn=1Inkk=(a;b;c):(4.5)Theabovedescriptionallowsustoanalyzethethreephaseunbalancedsystemintotwothreephasebalancedsystemspulsezerosequencecomponent.Inthematrixconvertercase28Figure4.1:Controlcircuitoftheshuntactiveinthecaseofunbalancedsourcevoltagewewillnotconsiderthezerosequencecomponenttobecompensated.Fig.4.1showsthetwobalancedsystems(positivesequencesystemvin+=[va+vb+vc+]T,iin+=[ia+ib+ic+]Tandthenegativesequencesystemvin=[vavbvc]T,iin=[iaibic]T)canbecompensatedintwoerentcontrolloops,thenthetotalcompensat-ingcurrentwillbetheadditionofthecompensatingcurrentofthepositivesequencesystemandthecompensatingcurrentofthenegativesequencesystem.icomp+=pcomp+vin+vin+vin++qcomp+vin+vin+vin+;(4.6)icomp=pcompvinvinvin+qcompvinvin+vin+;(4.7)whereIcomp=Icomp++Icomp:(4.8)294.2UnbalancedLoadCurrentIncaseofwhentloadsareconnectedtothematrixconverter,eachloadwilldrawatamountofcurrentleadingtoalinearlyindependentthreephaseoutputcurrent.Thedecompositionoftheoutputvoltageandcurrentintoit'ssymmetricalcomponentisasfollows:2666664vnout0vnout+vniout3777775=132666664111121237777752666664vnAvnBvnC3777775;(4.9)2666664i1in0i1in+i1in3777775=132666664111121237777752666664i1Ai1Bi1C3777775;(4.10)Thetimedomainequivalentvoltageandcurrentcanbederivedfromthephasorsgivenby(4.9)and(4.10).Bysynthesizingthesymmetricalcomponents,theABCvoltageandcurrentcanbewrittenas:308>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>:vnA=vnout0z}|{p2Vout0sin(!it+˚0)+vnout+z}|{p2Vout+sin(!it+˚+)+vnoutz}|{p2Voutsin(!it+˚)vnB=p2Vout0sin(!it+˚0)+p2Vout+sin(!it+˚+2ˇ3)+p2Voutsin(!it+˚+2ˇ3)vnC=p2Vout0sin(!it+˚0)+p2Vout+sin(!it+˚++2ˇ3)+p2Voutsin(!it+˚2ˇ3);(4.11)Similarly,theinstantaneouslinecurrentsarefoundtobe8>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>:i1A=i1out0z}|{p2Inout0sin(!it+˚0)+i1out+z}|{p2Inout+sin(!it+˚+)+i1outz}|{p2Inoutsin(!it+˚)i1B=p2Inout0sin(!it+˚0)+p2Inout+sin(!it+˚+2ˇ3)+p2Inoutsin(!it+˚+2ˇ3)i1C=p2Inout0sin(!it+˚0)+p2Inout+sin(!it+˚++2ˇ3)+p2Inoutsin(!it+˚2ˇ3);(4.12)thentheoutputvoltageistheresultofaddingalltheharmonicstogetherVj=1Xn=1Vnjj=(A;B;C):(4.13)Thesameconsiderationofzerosequencevoltageswillbemadehere.Thecontrolprocessissimilartotheonewehaveincaseofunbalancedsourcevoltage,utilizingtheoutput31Figure4.2:Controlcircuitoftheseriesactiveinthecaseofunbalancedloadvoltageandcurrentintoit'ssymmetricalcomponentleavinguswithtwobalancedsystems,(positivesequencesystemvout+=[vA+vB+vC+]T,i1out+=[i1A+i1B+i1C+]Tandthenegativesequencesystemvout=[vAvBvC]T,i1out=[i1Ai1Bi1C]T.ThetwobalancedsystemscanbecompensatedintotwotcontrolloopsasshowninFig.4.2.Thetotalcompensatingvoltagewillbetheadditionofthecompensatingvoltageofthepositivesequencesystemandthecompensatingvoltageofthenegativesequencesystem.vcomp+=pcomp+I1out+I1out+I1out++qcomp+I1out+I1out+I1out+;(4.14)vcomp=pcompI1outI1outI1out+qcompI1outI1outI1out;(4.15)Vcomp=Vcomp++Vcomp:(4.16)4.3SimulationResultsFig.4.3,showstheoutputresultofcompensatingthesourcecurrentwhenthesupplyvoltageisnotbalanced.Thesimulationshowsthatasinusoidalinputcurrentcanbeachieved.32Figure4.3:OutputresultsunderunbalancedvoltagesourceconditionsFig4.4,showsthesimulationinthecaseofanunbalancedloadbeingfedbythematrixconverter.4.4ConclusionInthischapter,ageneralcontrolschemeforthehybridmatrixconvertercontroloperatingundererentconditions(normalcondition,unbalancedsourcevoltage,andunbalancedload.Theanalysisoftheinputandoutputpowershowsthattheinstantaneousreactivepowertheorycanbeappliedindeterminingthecompensationcurrentoftheinputsideandthecompensationvoltagefortheoutputsideofthematrixconverter.FurtheranalysisneedstobeconsideredwhentheHybridMatrixConverteroperatesunderabnormalconditions,those33Figure4.4:Outputresultsunderunbalancedloadconditionsanalysesincludethesymmetricalcomponenttheory.Theproposedtopologycanbeutilizedformitigatingtheofvoltagesag,especiallywhenthematrixconverterisusedtodrivesensitiveloads.34Chapter5CriticalEvaluationThischapterisfocusedonconditioningthevoltageandcurrentwaveformqualityofahybridmatrixconverterthatconsistsofaconventionalnine-switchmatrixconverterandaback-to-backvoltagesourceconvertershoeninFig.3.1.Uponcriticalevaluationoftheexistingmethodsforshuntandseriescompensation,thefundamentallimitationsforachievingsu-periorresultshavebeenidenAnewstrategybasedonpoweraveragingforobtainingthereferencecompensatingcurrentandvoltagehasbeenproposed.Theenessoftheproposedmethodhasbeenevidencedbythesimulationresultsforboththeshuntandseriescompensationwithconcurrentpresenceoftheharmoniccomponentsinvoltagesandcurrents.SeveralAFcontroltechniqueshavebeenpresentedintheliterature[19][20][21].Basedontheoperatingprinciple,thesetechniquescanbecategorizedintotwogroups.Thegroupofmethodsarebasedoninstantaneousreactivepowertheory(IRPT)[22]andextractthereactivecomponentofthepowerandtheoscillatorycomponentoftherealpower.TheothermethodsarebasedontechniquesandextractthefundamentalcomponentofthecurrentorvoltagesuchasnotchandfastFouriertransform(FFT)methods[23][24][25][26].InthischaptertAFcontrolstrategiesarepresentedandcriticallyevaluated.Thelimitationsoftheexistingcontrolapproacheshavebeenclearlyidend.35Infrequency-varyingenvironment,thebestsolutionistouseadaptiveapproach.How-ever,notchisonlyableforharmonicdetectionandcannotextractthereactivecom-ponents[26].Further,suchadaptiveapproachesmighthaveconvergenceandrobustnessproblems[27].OthertechniquessuchFouriermethodsarewidelyused.FastFouriertransformrequireshighcomputationalanddiscreetFouriertransformDFTrequiressynchronizationtoolsuchphase-locked-loop(PLL).Furthermore,theysharethesamelimita-tionwithadaptivenotchofbeingunabletoextractthereactivecomponent.Therefore,onlytheanalysisofadaptivenotchispresentedinthethispaper.Instantaneousreactivepowertheoryisatimedomainmethodthatbasedonthelawofconservationofenergy.Itutilizestheconceptthatthenon-activecomponentofthevoltageandcurrentdonotcontributeinanyenergytransferfromthesourcetotheload.TheInstantaneousreactivepowertheorycouldundergocoordinatetransformationtothesynchronousreferenceframe.ThistransformationchangestheoscillatingACvariablestoaDCvariablesandtheharmonicsappearinformofrippleintheDCsignal.Althoughthisapproachprovidesextratothesystem,itsrequiredsynchronizingtoolsuchasPLL.Theinstantaneousreactivepowertheoryseemstobeagoodsolutioninobtainingthereactivecomponents,itfailswhenboththecurrentandthevoltagecontainharmonics.Thisbecauseoftheoverlapinthefrequenciesofthecurrentandthevoltageharmonics.Therefore,itisincapabletoobtainthecorrectcompensatingcurrentorvoltagewhenharmonicsarepresentinboththecurrentandthevoltage.Toaddresstheselimitationsoftheaforementionedmethods,anewcontrolstrategyisproposed.Thisproposedcontrolmethodisabletoelyobtainthecorrectactivecomponentofcurrentorvoltageincaseswhereboththecurrentandthevoltagearenon-36sinusoidalandprovidefullcontroloverthepowerfactor.5.1AdaptiveNotchFilterMethodAdaptivenotchisthetechniquethatselectivelyextractsofaharmoniccomponentofcertainfrequency.Itfeaturesverypowerfulqualitieswhereeliminationofcertainhar-monicsisrequired.Notchtercanestimateinformationembeddedinthesignalsuchastheamplitude,frequencyandphaseangle,thesignalfrequency.Thedynamicbehavioroftheadaptivenotch(ANF)canbecharacterizedbythefollowingdeferentialequations.x00+i2!2x=2!(u(t)x0)(5.1)!0=x!(u(t)x0)(5.2)wherexistheintegralofthefundamentalcomponentoftheinputsignalu(t),!istheestimatedfrequencyofthefundamentalcomponent;andareadjustablerealpositiveparametersthatdeterminetheaccuracyandconvergencespeedoftheANF;u(t)isthesignalfromwhichthefundamentalcomponentistobeextracted.Forasinusoidalinputsignal,thesystemdescribedby(1)and(2)hasauniqueperiodicalorbitlocatedat0BBBBB@xx0!1CCCCCA=0BBBBB@A!1cos(!1t+˚1)Asin(!1t+˚1)!11CCCCCA;(5.3)wheretheestimatedcomponentofthefrequency!isidenticaltoitsactualvalue!1,whichismathematicallyexplainedin[26].AdetailedimplementationoftheANFisshowninFig.5.1.37Figure5.1:DetailedimplementationoftheadaptivenotchThesamecontrolcircuitisusedtoobtainthefundamentalcomponentoftheoutputvoltage.5.2InstantaneousReactivePowerMethodTheinstantaneousreactivepowertheoryprovidestinsightforunderstandingthepowertransferredfromthesourcetotheloadandamongthethreephases.Byeliminationofthepowercomponentthatdoesnotcontributetotheenergytransmissionfromthesourcetotheload,sinusoidalinputcurrentandsinusoidaloutputvoltagecanbeachieved.Thecompensationsystemininstantaneousreactivepowertheoryconsistofonlypassivecompo-nentsandswitches.Therefore,thenetenergyaddedordrownbythecompensatingsystemiszero.PC=0;PS=PL=P(5.4)wherePCistherealpowerfromthecompensator,PSandPLarethesourceaveragepower,loadaveragepower,respectively.Theaveragepowerisgivenby38P=PX=1TXZttTXp(˝)d˝:(5.5)whereTXdenotetheaveragingintervalthatcanbezero,onefundamentalcycle,one-halfcycle,ormultiplecycles,dependingoncompensationobjectivesandthepassivecomponentsenergystoragecapacity;p(˝)istheinstantaneousrealpower.Theinstantaneousreactivepowertheoryworkcanbeexplainedfromearlyonofnon-activecurrentbyFryze[28].ip(t)=(v;i)(v;v)v(t);iq(t)=i(t)ip(t);(5.6)whereipistheactivecurrentcomponent,v(t)andi(t)isthereferencevoltageandcurrent,respectively,andiqisthenon-activecurrentcomponent;(v;i)istheinnerproductofthevoltageandthecurrentovertheintervalftTX;tgwithrespecttoweightingfactorequalone,(v;v)istheinnerproductofthevoltageanditselfovertheintervalftTX;tgwithrespecttoweightingfactorequalone.Theycanbeexpressedasfollows(v;i)=kv(t)i(t)k=1TXZttTXv(˝)i(˝)d˝=P(5.7)(v;v)=kv(t)k2=1TXZttTXv2(˝)d˝=v2rms(5.8)5.2.1ActiveCurrentontheInputSideOntheinputsideofthematrixconverterthesourcevoltageissinusoidalandthesourcecurrentisnotsinusoidalasitshowninFig.5.2(a).Therefore,theycanbeexpressedbythe39followingequationsva(t)=VSfsin(!it)(5.9)ia(t)=ISfsin(!it)+IShsin(!int+h)(5.10)whereVSfistheamplitudeofthevoltagefundamentalcomponent;ISfistheamplitudeofthecurrentfundamentalcomponent;IShistheamplitudeoftheh-thorderharmonic,thecorrespondingaveragepowerisP=VSfISf2cos(5.11)Itcanbevthatthesetofallharmonicsinthecurrentwaveformia(t)areorthogonalwithrespecttothevoltageva(t)overtheintervaloftheintegral.Thereforethecorrespondingaveragepowerisonlyaresultofthefundamentalcomponentsofthecurrentiaandthevoltageva(t).Likewise,substituting(5.9)and(5.10)in(5.8)yieldsvarms=VSfp2(5.12)Bysubstituting(5.7),(5.9),and(5.12)in(5.6),wecanobtaintheactivecurrentcomponentip(t)=ISfcos()sin(!t)(5.13)Thisprovesthattheinstantaneousreactivepowertheoryisabletoobtaintheactivecom-ponentofthecurrentwhenthesourcevoltageissinusoidalandthesourcecurrentcontainsharmonics.405.2.2ActiveVoltageontheOutputSideOntheoutputsideofthematrixconverter,bothloadvoltageandcurrentincludeharmonicsasshowninFig.5.2(a).Usingadualanalogytotheactivecurrentin(6),wecantheactivecomponentvpandthenon-activecomponentvqofthevoltageasvp(t)=(v;i)(i;i)i(t);vq(t)=v(t)vp(t);(5.14)where(i;i)istheinnerproductofthecurrentanditselfovertheintervalftTX;tgwithrespecttoweightingfactorequalone.Itisexpressedasfollows(i;i)=ki(t)k2=1TXZttTXi2(˝)d˝=i2rms(5.15)TheloadvoltagevA(t)andtheloadcurrentiA(t)canbeexpressedbythefollowingequationsvA(t)=VLfsin(!ot)+VLhsin(!oht+h)(5.16)iA(t)=ILfsin(!ot)+ILhsin(!ont+h)(5.17)whereVLfistheamplitudeofthevoltagefundamentalcomponent;VLhistheamplitudeoftheh-thorderharmonic;ILfistheamplitudeofthecurrentfundamentalcomponent;ILhistheamplitudeoftheh-thorderharmonic,thecorrespondingaveragepowerisP=VLfILf2cos+VLhILh2cosh(5.18)andthecorrespondingrmscurrentis41iArms=si2Lf+i2Lh2(5.19)Bysubstituting(5.15),(5.17),and(5.18)in(5.14)wecanobtaintheactivecomponentofthevoltagevp(t)=VLfILfcos+VLhILhcoshI2Lf+I2Lh(ILfsin(!ot)+ILhsin(!ont+h))(5.20)Itisobservedfrom(5.20)thattheactivecomponentofthecurrentisnotsinusoidal.Therefore,theinstantaneousreactivepowertheoryisnotabletoachieveasinusoidalloadvoltage.AnFFTisusedtoobtainthefundamentalcomponentoftheloadcurrentbeforeitisusedinthecontrolloop[29].Thislimitationoftheinstantaneousreactivepowertheorywillberesolvedbytheproposedmethodinthenextsection.Byexpandingthesameapproachforathreephasesystemwecanthecompensationcurrentandthecompensationvoltageasfollowsicomp=~pvinvinvin+qvinvinvin(5.21)vcomp=~pi1outi1outi1out+qi1outi1outi1out(5.22)wherevin=[vavbvc]Tistheinputvoltagevector;i1out=[iAiBiC]Tisthefundamentaloutputcurrentvector;~pistheoscillatorycomponentoftherealpower;qisthereactivepower.ThecontrolblockdiagramsfortheinputcurrentcompensationandtheoutputvoltagecompensationareshowninFig.3(a).Bothoutputcurrentandvoltageofthe42Figure5.2:Blockdiagramsfor(a)determiningthereferencesignalsforcompensationcurrentandvoltageusingIRPT;(b)extractingthefundamentalcomponentoftheoutputcurrent.matrixconvertercontainatamountofharmonics,insuchcasesthetypicalcontrolapproachofinstantaneousreactivepowertheorywillnotbeabletoobtainthecorrectactivevoltagecomponent.ForsuchreasonthefundamentalcomponentoftheoutputcurrenthastobeextractedbeforeitisemployedinthecontrolcircuitasshowninFig.5.2(b).5.3ProposedAveragePowerMethodAveragepowercompensation(APC)isbasedontheassumptionthatthetotalaveragedpowerdrawnfromthesourceisequaltothepowerobtainedbythesinusoidalactivecompo-nentsofthecurrentorthevoltage.Thisassumptionismathematicallyrepresentedin(5.23)forsingle-phasesystem,ZttTXv(t)i(t)dt=ZttTXvp(t)i(t)dt(5.23)43wherevpistheactivecomponentofthevoltage.Assumingthetheactivecomponentofthevoltageissinusoidal,therefore,vp(t)=Asin(!ot)(5.24)Wecanestimatetheamplitudeoftheactivevoltagecomponentbysubstituting(5.16)and(5.17)in(5.23),theamplitudeAisdeterminedbyA=vafcos()+vahiahcos(h)iaf(5.25)Fromtheactivevoltageamplitudein(5.25),itcanbeobservedthattheactivecomponentofthecurrentvpisnotequaltothefundamentalcomponent,whichisthefundamentalreasonthattheANFmethodswillnotachievemaximumpowertransfer.Adualapproachcanbeeasilyimplementedtoobtaintheactivecomponentoftheinputcurrent.TheblockdiagramofaveragedpowermethodfortheinputcurrentandtheoutputvoltagecompensationareshowninFig.5.3(a)and(b),respectively.5.4SimulationResultsandEvaluationToevaluatetheperformanceofthepresentedmethodsdetailedsimulationmodelshavebeenconstructedbasedonthethreephasehybridmatrixconvertershowninFig.??.Ineachsimulationmodelthecontrolmethodisappliedtocompensateboththeinputcurrentandtheoutputvoltageharmonics.ThetypicalinputandoutputcurrentandvoltagewaveformsofthemainmatrixconverterareshowninFig.5(a)and(b).Fig.8(c)showstheinputsourcecurrentaftercompensationusingadaptivenotchmethod,bywhichthefunda-mentalcomponentoftheinputcurrentiscalculated.Theharmoniccontentisobtainedby44Figure5.3:Averagepowercompensationmethodcontrolfor(a)inputcurrent;(b)outputvoltage.subtractingthefundamentalcomponentfromtheoriginalcurrentwaveform.Althoughthenotchiseasytoimplement,itisunabletocorrectthephaseshiftbetweentheinputvoltageandtheinputcurrent,Therefore,theANFmethodisewhenpowerfactorcorrectionisrequired.AnotherdisadvantageforANFisitsenesswhenboththevoltageandthecurrentcontainharmonicssuchastheoutputvoltageandcurrentofthematrixconverter.Inthiscasesomeofthepowertransferredtotheloadtakesplaceatharmonicfrequencies.Compensationtoachieveoutputvoltageequaltoitsfunda-mentalcomponentsimplywillnotachievemaximumpowertransfer.TheoutputvoltageusingANFisshowninFig.5(d).Theinstantaneousreactivepowertheoryallowforfullcontrolofthephaseshiftoftheinputcurrentandsubsequentlyaunitypowerfactorcouldbeachieved.However,IRPmethodisstillunabletocompensatetheoutputvoltagebecausebothoutputcurrentand45Table5.1:AsummaryofthecomparativeevaluationofthethreemethodsMethodsANFIRPAPCPowerfactorcontrolUnabletocontrolthePF,Becauseitisonlyobtainsthefundamen-talcomponentwithitsphaseshift.CanachieveunityPFbycompensatingallthereactivecompo-nentq.FullycontrolthePFbyselectingtherequiredphaseshiftintheref-erencesignal.Obtainingtheactivecom-ponentofcurrentandvoltageOnlyabletoobtainthefundamentalcom-ponentofthecurrentorthevoltage,there-foreitfailstoachievemaximumpowertrans-ferwhenboththecur-rentandvoltagecon-tainharmonics.Failtoobtaintheac-tivecomponentofloadvoltage,because,bothloadvoltageandcur-rentcontainharmon-ics.Therefore,itisre-quiredtotheloadcurrentbeforeitisemployedinthecon-trolcircuit.,Abletosuccessfullyobtaintheactivecom-ponentoftheoutputvoltagewithoutanyneedofteringtheoutputcurrent.TransientResponse(duetoinputvoltageincreasebyby0:3pu).Requiresatleastonecycletoreachthesteadystate.currentdropsduringthetransientperiod.Requiresonecycletoreachthesteadystatewithoutanyovershootinthecurrent.ComplexlyofImplemen-tation.Manydesignpa-rametersneedtobeoptimizedtoachievelowTHD.HigherorderthanIRPandAPC.Obtainingtheloadcurrentfundamentalcomponentincreasesthecomputationaltly.Requireslesscomputa-tionalThesamecontrolcircuitcanbeusedforallcases.TotalharmonicdistortionTHD7:8%2:5%2%voltagepresentharmonic.TheonlywaytoachievesinusoidaloutputloadvoltageistoobtainthefundamentalcomponentofthecurrentbeforeitisemployedinthecontrolcircuitasshowninFig.3(b).ThecompensatedinputsourcecurrentandtheoutputloadvoltageusingIRPareshowninFig.5(e)and(f).Theaveragepowermethodincontrastcanprovideunitypowerfactorwhencompensatingtheinputcurrent.Itisalsoabletoobtaintheactivecomponentoftheoutputvoltagewithoutanyneedoftheoutputcurrent.TheinputsourcecurrentandtheoutputloadvoltageusingAPCareshowninFig.5(g)and(h).AsummaryofthecomparativeevaluationofthemethodsislistedinTable1.46Figure5.4:Inputlinevoltagevabandcurrentia.Figure5.5:InputcurrentiausingNotchFilter.Figure5.6:InputcurrentiausingIRPT.Figure5.7:InputcurrentiausingAP.47Figure5.8:OutputlinevoltagevABandcurrentiA.Figure5.9:OutputvoltagevAusingNotchFilter.Figure5.10:OutputvoltagevAusingIRPT.Figure5.11:OutputvoltagevAusingAP.485.5ConclusionThispaperhaspresentedthepreliminaryresultsfortheevaluationofexistingapproachestoshuntandseriesconditioningofthecurrentsandvoltages.ThecriticallyevaluatedmethodsarebasedoneitherinstantaneousreactivepowertheoryorfastFouriertransform.ThemainlimitationforIRPTbasedmethodliesinitsenesswhentheharmonicsareconcurrentlypresentinvoltageandcurrentwhilethelimitationforFFTbasedmethodisitsinabilitytocompensatethefundamentalcomponent.Toaddressthelimitationsassociatedwiththeexistingmethods,anewmethodbasedonpoweraveraginghasbeenproposed.TheenessoftheproposedmethodhasbeenvdbythesimulationresultsobtainedfromadetailedMathCAD/Simulinkmodel.Furthermore,experimentalworkhasbeenplannedandtheexperimentalresultswillbeincludedinthemanuscript.49BIBLIOGRAPHY50BIBLIOGRAPHY[1]Wheeler,P.W.;Rodriguez,J.;Clare,J.C.;Empringham,L.;Weinstein,A.,\Matrixconverters:atechnologyreview,"IEEETransactionsonIndustrialElectronics,vol.49,no.2,pp.276,288,Apr2002[2]M.Venturini,\Anewsinewaveinsinewaveout,conversiontechniquewhicheliminatesreactiveelements",Proc.POWERCON7,pp.E31-E3151980[3]M.VenturiniandA.Alesina,\Thegeneralizedtransformer:Anewbidirectionalsinu-soidalwaveformfrequencyconverterwithcontinuouslyadjustableinputpowerfactor",Proc.IEEEPESC',80,pp.242-2521980[4]J.Rodriguez,\AnewcontroltechniqueforAC-ACconverters",Proc.IFACControlinPowerElectronicsandElectricalDrivesConf.,pp.203-2081983[5]L.HuberandD.Borojevic,\Spacevectormodulatedthree-phasetothree-phasematrixconverterwithinputpowerfactorcorrection",IEEETrans.Ind.Applicat.,vol.31,pp.1234-12461995[6]Burany,N.,\Safecontroloffour-quadrantswitches,"IndustryApplicationsSocietyAnnualMeeting,1989.,ConferenceRecordofthe1989IEEE,vol.,no.,pp.1190,1194vol.1,1-5Oct.1989[7]A.Popovici,V.Popescu,M.Babaita,D.Lascu,D.Negoitescu,\Modeling,SimulationandDesignofInputFilterforMatrixConverters",2005WSEASInt.Conf.onDYNAM-ICALSYSTEMSandCONTROL,Venice,Italy,November2-4,2005(pp439-444)[8]Empringham,L.;Kolar,J.W.;Rodriguez,J.;Wheeler,P.W.;Clare,J.C.,\Technolog-icalIssuesandIndustrialApplicationofMatrixConverters:AReview,"IEEETrans-actionsonIndustrialElectronics,vol.60,no.10,pp.4260,4271,Oct.2013[9]JunKang;Takada,Noriyuki;Yamamoto,E.;Watanabe,E.,\Highpowermatrixcon-verterforwindpowergenerationapplications,"PowerElectronicsandECCEAsia(ICPE-ECCE),2011IEEE8thInternationalConferenceon,vol.,no.,pp.1331,1336,May302011-June3201151[10]BingsenWang;Venkataramanan,G.,\SixStepModulationofMatrixConverterwithIncreasedVoltageTransferRatio,"PowerElectronicsSpecialistsConference,2006.PESC'06.37thIEEE,vol.,no.,pp.1,7,18-22June2006[11]H.Akagi,Y.Kanazawa,andA.Nabae,\Instantaneousreactivepowercompensatorscomprisingswitchingdeviceswithoutenergystoragecomponents",IEEETrans.Ind.Appl.,vol.20,pp.625-6301984[12]FangZhengPeng;Jih-ShengLai,\Generalizedinstantaneousreactivepowertheoryforthree-phasepowersystems,"IEEETransactionsonInstrumentationandMeasure-ment,,vol.45,no.1,pp.293,297,Feb1996[13]P.D.Ziogas,S.I.Khan,andM.H.Rashid,\Analysisanddesignofforcedcommutatedcycloconverterstructureswithimprovedtransfercharacteristics,"IEEETransactionsonIndustrialElectronics,vol.IE-33,no.3,pp.271,1986.[14]BaomingGe;QinLei;WeiQian;FangZhengPeng,\AFamilyofZ-SourceMatrixConverters,"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