space _vector_modulation

42SPACEVECTORMODULATIONFORTHREE-LEGVOLTAGESOURCEINVERTERS2.1THREE-LEGVOLTAGESOURCEINVERTERThetopologyofathree-legvoltagesourceinverterisshowninFig.2.1.Becauseoftheconstraintthattheinputlinesmustneverbeshortedandtheoutputcurrentmustalwaysbecontinuousavoltagesourceinvertercanassumeonlyeightdistincttopologies.ThesetopologiesareshownonFig.2.2.Sixoutoftheseeighttopologiesproduceanon-zerooutputvoltageandareknownasnon-zeroswitchingstatesandtheremainingtwotopologiesproducezerooutputvoltageandareknownaszeroswitchingstates.Fig.2.1.Topologyofathree-legvoltagesourceinverter.LpnabcACBIaVg5pabcnV2(ppn)pabcnV3(npn)pabcnV4(npp)abcnV1(pnn)pabcnV5(nnp)pabcnV7(ppp)pabcnV6(pnp)pabcnV8(nnn)pFig.2.2.Eightswitchingstatetopologiesofavoltagesourceinverter.2.2VOLTAGESPACEVECTORSSpacevectormodulation(SVM)forthree-legVSIisbasedontherepresentationofthethreephasequantitiesasvectorsinatwo-dimensional(αβ,)plane.Thishasbeendiscussedin[1]andisillustratedhereforthesakeofcompleteness.Consideringtopology1ofFig.2.2,whichisrepeatedinFig.2.3(a)weseethatthelinevoltagesVab,Vbc,andVcaaregivenby6ancbVgpgcabcgab=-VV=V=VV0…..(2.1)Thiscanberepresentedintheαβ,planeasshowninFig.2.3(b),wherevoltagesVab,Vbc,andVcaarethreelinevoltagevectorsdisplaced120°inspace.TheeffectivevoltagevectorgeneratedbythistopologyisrepresentedasV1(pnn)inFig.2.3(b).Herethenotation‘pnn’referstothethreelegs/phasesa,b,cbeingeitherconnectedtothepositivedcrail(p)ortothenegativedcrail(n).Thus‘pnn’correspondsto‘phasea’beingconnectedtothepositivedcrailandphasesbandcbeingconnectedtothenegativedcrailFig.2.3(a).Topology1-V1(pnn)ofavoltagesourceinverter.VabVbcVca-VcaVg-VgV1(pnn)Vab=VgVbc=0Vca=-VgFig.2.3(b).Representationoftopology1intheαβ,plane.7Proceedingonsimilarlinesthesixnon-zerovoltagevectors(V1-V6)canbeshowntoassumethepositionsshowninFig.2.4.Thetipsofthesevectorsformaregularhexagon(dottedlineinFig.2.4).Wedefinetheareaenclosedbytwoadjacentvectors,withinthehexagon,asasector.Thustherearesixsectorsnumbered1-6inFig.2.4.V1V2V3V4V5V6123456Fig.2.4.Non-zerovoltagevectorsintheαβ,plane.ConsideringthelasttwotopologiesofFig.2.2whicharerepeatedinFig.2.5(a)forthesakeofconvenienceweseethattheoutputlinevoltagesgeneratedbythistopologyaregivenby000===cabcabVVV…..(2.2)Thesearerepresentedasvectorswhichhavezeromagnitudeandhencearereferredtoaszero-switchingstatevectorsorzerovoltagevectors.Theyassumethepositionatoriginintheαβ,planeasshowninFig.2.5(b).ThevectorsV1-V8arecalledtheswitchingstatevectors(SSVs).8abcnV7(ppp)pabcnV8(nnn)pFig.2.5(a).Zerooutputvoltagetopologies.VabVbcVcaV7,V8Vab=0Vbc=0Vca=0Fig.2.5(b).Representationofthezerovoltagevectorsintheαβ,plane.2.3SPACEVECTORMODULATIONThedesiredthreephasevoltagesattheoutputoftheinvertercouldberepresentedbyanequivalentvectorVrotatinginthecounterclockwisedirectionasshowninFig.2.6(a).Themagnitudeofthisvectorisrelatedtothemagnitudeoftheoutputvoltage(Fig.2.6(b))andthetimethisvectortakestocompleteonerevolutionisthesameasthefundamentaltimeperiodoftheoutputvoltage.9V1V2V3V4V5V6123456VVabVbcVcaFig.2.6(a).Outputvoltagevectorintheαβ,plane.123456VabVbcVcaV0Fig.2.6(b).Outputlinevoltagesintimedomain.Letusconsiderthesituationwhenthedesiredline-to-lineoutputvoltagevectorVisinsector1asshowninFig.2.7.Thisvectorcouldbesynthesizedbythepulse-width-modulation(PWM)ofthetwoadjacentSSV’sV1(pnn)andV2(ppn),thedutycycleofeachbeingd1andd2,respectively,andthezerovector(V7(nnn)/V8(ppp))ofdutycycled0[1]:jège=mV=+ddVVV2121…..(2.3)1021=+d+dd…..(2.4)where,86600.m≤≤,isthemodulationindex.Thiswouldcorrespondtoamaximumline-to-linevoltageof1.0Vg,whichis15%morethanconventionalsinusoidalPWMasshown[1].10d1V1(pnn)V2(ppn)1Vd2V7(ppp)V8(nnn)θFig.2.7.Synthesisoftherequiredoutputvoltagevectorinsector1.AllSVMschemesandmostoftheotherPWMalgorithms[1,4],use(2.3),(2.4)fortheoutputvoltagesynthesis.Themodulationalgorithmsthatusenon-adjacentSSV’shavebeenshowntoproducehigherTHDand/orswitchinglossesandarenotanalyzedhere,althoughsomeofthem,e.g.hysteresis,canbeverysimpletoimplementandcanprovidefastertransientresponse.Thedutycyclesd1,d2,andd0,areuniquelydeterminedfromFig.2.7,and(2.3),(2.4),theonlydifferencebetweenPWMschemesthatuseadjacentvectorsisthechoiceofthezerovector(s)andthesequenceinwhichthevectorsareappliedwithintheswitchingcycle.Thedegreesoffreedomwehaveinthechoiceofagivenmodulationalgorithmare:1)Thechoiceofthezerovector-whetherwewouldliketouseV7(ppp)orV8(nnn)orboth,2)Sequencingofthevectors3)Splittingofthedutycyclesofthevectorswithoutintroducingadditionalcommutations.FoursuchSVMalgorithmsareconsideredinthenextsection,namely:1)Therightalignedsequence(SVM1)112)Thesymmetricsequence(SVM2)3)Thealternatingzerovectorsequence(SVM3)4)Thehighestcurrentnotswitchedsequence(SVM4).Themodulationschemesaredescribedforthecasewhenthereferencevectorisinsector1:allothercasesarecircularlysymmetric.Thesemodulationschemesareanalyzedandtheirrelativeperformancewithrespecttoswitchingloss,THDandthepeak-to-peakcurrentrippleattheoutputisassessed.Theanalysisisperformedovertheentirerangeofmodulationindexandforloadpowerfactoranglevaryingfrom–90oto90o