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1、182IEEETRANSACTIONSONPOWERELECTRONICS.VOL.5.NO.2.APRIL1990OntheUseofAveragingfortheAnalysisofPowerElectronicSystemsAbstract-Averagingtheoryasarigorousframeworkforevaluating,2)Dothetrajectoriesoftheaveragedmodelrepresentrefining,andextendinghehsticaveragedmodelsnowusedinpow
2、erthemovingaveragesalongthetrajectoriesoftheelectronics,isintroduced.Itisalsoshownthataveragingtheorypro-originalsystem?videsdirecttechniquesforrecoveringoscillatoryeffectssuchasripplefromtheaveragedmodel.Asanapplicationofthetheory,examplesof3)Arethestabilitypropertiesofth
3、eoriginalandap-theanalysisofsimpledc-dcconvertersarepresented.proximatesystemsidentical?4)Hobcanonequantifytheerrorsincurredintheap-proximation?I.INTRODUCTION5)IsitpossibletorecovertheexactsolutiondirectlyANALYSISofpowerelectronicsystemsiscompli-fromtheaveragedequation?cat
4、edbytheirswitchingbehavior.Onewell-known6)Istheapproximationvalidforlargesignals?approachtothemodelingofsukhsystemsistoapproxi-7)Whatisthelowerlimitontheswitchingspeedformatetheiroperationbyaveragingtechniques.Forexam-averagingtobevalid?ple,thepopularstate-sqaceaveragingme
5、thod[I],which8)Cantheopen-loopapproximatemodelbeusedforaveragestheseveralpossiblecircuitconfigurations,hasclosed-loopdesign?becomeausefultoolforsmall-signalmodelingofswitch-ingconverters.Thesemethods,however,areheuristicinAnalternativeformofaveraginghaslongbeenusedfornatur
6、e,andtherelationshipsbetweentheaveragedmodelsanalyzingdifferentialequationswithoscillatoryright-handandtheoriginalsystemareunclear[2],[3].sides(RHS)[12].Thistechniquehasbeenexaminedex-Theresultsofanyapproximationprocess,includingav-tensivelyinthemathematicalliterature,anda
7、substantialeraging,mightdifferdependingontheassumptionsin-bodyoftheoryhasbeendevelopedconcerningtherela-volved.Thisisparticularlyevidentinpowerelectronics,tionshipsbetweentheoriginalandtheaveragedequa-wherenumeroussmall-signalmodelshavebeenproposedtions.Thisapproachhasalso
8、beenextendedtoequations[4]-[9].Inthisliterature,bothaveragingandlinearizationwithtimedisc
