Losses-in-PWM-inverters-using-IGBTs

LossesinPWMinvertersusingIGBTsF.Casanellas,CEng,MlEEIndexingterms'IGBTY,PWMrnt,errer,Powerlosse5Abstract:TheaimofthispaperistocalculatetheforwardandswitchinglossesofaPWMinverteremployingIGBTsusingarelativelysimplemethodfrommanufacturers'catalogueparam-eters,thatis,findingareasonablecompromisebetweenaccuracyandcomplexity.Thesystemwillbeabletocalculatelossesfordifferentmodulationmethods,providedthecurrentoutputissinus-oidal.Partoftheresultscanbeusedforotherdevices,suchasbipolartransistorsorMOSFETs.ListofsymbolsE,,=turnonenergylossE,,,=turnoffenergylossE,=energylossindiodeEi=energylossinIGBTF,=switchingfrequencyI,=collectorcurrentI,,=ratedI,I,,=maximumcollectorcurrenti,=instantaneouscollectorcurrentI,,=recoverycurrentI,,,=ratedrecoverycurrentM=modulationdepthPi=powerlossinIGBTP,=powerlossindiodePo,=turnonpowerlossPo,,=turnoffpowerlossP,,=recoverypowerlossQ,,=recoverychargeQlrN=ratedrecoverycharget=periodt,=falltimet,..=ratedfalltimet,=risetimet,,=ratedrisetimet,,=recoverytimef,,N=ratedrecoverytimeV,,=DCbusvoltageV,,=collector-to-emittervoltageV,,,=ratedV,,V,,,=thresholdV,,V,=diodeforwardvoltageV,,=ratedV,VFo=diodethresholdvoltageI6=dutycycle=angleofcurrentfunctionCIEE,1994Paper13498(P6).firstreceived11thNovember1993andinrevisedform13thApril1994TheauthorISConsultantEngineeratC.Notariat3,08001Barcelona,SpainIEEProc.-Electr.PowerAppl..Vol.141,No.5,September19940T=carrierperiod1IntroductionTocalculatesemiconductorlossesinaninvertertheenergylossineverypulseduringacycleneedstobecal-culatedandthenadded.Inathree-phaseinverterthecurrentinonephasedependsonthestateoftheswitchesoftheotherphasesandonthemotorcharacteristicssothewaveformisverycomplex.Thecalculationofsemi-conductorlossesisfeasibleusingacomputerprogramwhichproducesthepulsepatternandhasamotormodel.Todothisbyusingequationsderivedfromanalyticalmethods,wouldbeaquiteimpossibletask,mainlybecauseofthecomplexmodulationstrategiesdesignofthethirdharmonicinjection.ThisapproachhasbeentriedusingthemethodgiveninReference1,whichstartswithapulsebypulsecalcu-lation(foronlyonekindofmodulationstrategy),butwiththecontradictorystatementthatthecurrentissinusoidal(noripple),whichonlymakessenseifthenumberofpulsestendstoinfinity.(Infinityheremeans'aslargeanumberasnecessarytoobtainaresultthatisbelowtheallowederror'.)Tosimplifytheequations,attheendofthecalculationsitisassumedthatthenumberofpulsesishigh.Aswillbeseen,ifthisisassumedfromthestart,calculationismucheasieranditisfeasibletoobtainequationsforothermodulationstrategies.Reference2,onbipolartransistors,assumesthatthecollector-to-emittervoltageisconstant,whichcannotbeassumedwithIGBTs.Itseemstouseawrongswitchingpattern(assumingthatcurrentdoesnottransferfromtheflywheelingdiodetothetransistor).Highswitchingfrequenciesusedtoday(3kHzminimum),giveharmoniccontentoflessthan5%.Asforwardlossesdependoncurrent,evenifthedeviceisonlyresistive(MOSFET),thiscannotintroduceanerrorgreaterthanabout10%.BecauseanIGBTisnotpurelyresistive,theerrorwillbelower.InausualIGBTinverter,switchingataround6kHz,switchinglossesaccountforabout50%oftheoveralllosses,sothetotalerrorinforwardlosseswillbehalved.Anerrorof5%foratemperaturedropof40°Cwouldgiveanerrorofonly2°Cinheatsinktemperatureinthejunction.Theerrorintroduced,assumingasinusoidalcurrent,willbelowforpracticalapplications.Itwillalwaysbemuchlowerthanthedeviceparametervariation.2ForwardlossesThetypicalvoltage/currentgraphVcE/I,,(Fig.1)isapproximatedbythefollowinglinearequation(thisimpliesathresholdvoltageplusaresistivevoltagedrop,thesameassumptionismadeinReference1):=currentlaggingangletovoltage235whereIC,vandVCENaretherated(manufacturerscatalogue)currentandthecollector-to-emittervoltageattheratedcurrent.130-.-c-a.Notethatalldatashouldbetakenat=125C,theerrorsindatawiththeusualT,100-willbemuchlowerthanthoseobtainedat25°C.)ThevalueofthethresholdvoltageVcodependsonthetypeofIGBTusedandtheratedvoltage.Forsecondgeneration1200Vtypes,aconvenientvalueforVcoisabout1V(at125°C).Thediodeforwardvoltagefollowsanexponentiallaw.Intheworkingrange,wemaysimplifytheequation,approximatingittoalinearlawwiththeoriginatVFo(seeFig.1).Thisthresholdvoltagemaybetakenas0.7VwhereVFNisthediodevoltagedropatratedcurrent.IfF(z)isthemodulatingfunction(-1F(a)l),HtheanglebetweencurrentandvoltageandMthemodu-lationindex(0Ml),thenthedutycycle6ofthevoltagepulses,referredtothecurrentanglea(Fig.2)is(3)6=t[l+MF(a+O)]1GBTUdmdeFig.2IGBTnnddiodecurrentsAsshowninFig.2,fromz=0toz=n,thecurrentcir-culatesthroughthemainswitchduringatime67ofthecarrierperiodT,andthroughtheoppositediodeduring236thetime(1-6)~.Duringtheotherhalfcycle(a=rr-2n),theIGBTisoff,andonlyitsparalleldiodeworks.Consequently,weneedtocalculateonlytheoveralllossesduringhalfaperiod.inordertoobtainthetotallossesofaswitch(IGBT+diode).TheenergylossofanIGBTduringacarrierperiodisE,=vCEi,ii~Asweassumethecurrenttobesinusoidal,i,=I,,sinaand01(6)Steadystatepowerlosseswillnotchangeifthenumberofpulsesincreases,becauseenergyperpulsedecreases(because7decreases)inthesameproportionasthenumberofpulsesincreases,sot