Small-Signal Methods for AC Distributed Power

Small-Signal Methods for AC Distributed Power

IEEETRANSACTIONSONPOWERELECTRONICS,VOL.24,NO.11,NOVEMBER20092545

Small-SignalMethodsforACDistributedPower

Systems–AReview

JianSun,SeniorMember,IEEE

Abstract—ACdistributedpowersystems(DPS)canbefoundinseveralnewandemergingapplications.Similartodcdistributedpowersystems,anacDPSreliesonpowerelectronicsandcontroltorealizeitsfunctionsandachievetherequiredperformance.Systemstabilityandpowerqualityareimportantissuesinbothtypesofsystemsduetothecomplexsystembehaviorresultedfromactivecontrolatboththesourceandtheloadside.Traditionalsmall-signalanalysismethodscannotbedirectlyappliedtoanacDPSbecauseoftheperiodicallytime-varyingsystemoperationtrajec-tory.Possiblesolutionstothisproblemincludetransformationintoarotating(dq)referenceframe,modelingusingdynamicphasors,reduced-ordermodeling,andharmoniclinearization.Thispaperreviewsthesesmall-signalmethodsanddiscussestheirutilitiesaswellaslimitations.Compatibilityofeachtypeofmodelswithstate-spaceandimpedance-basedsystemanalysisapproacheswillalsobediscussed.Problemsrelatedtothelinearizationofphasor-basedmodelsandtheiruseinimpedance-basedsystemanalysisarehigh-lightedinparticular.

IndexTerms—AC–DCpowerconversion,aircraftpowersys-tems,impedance,modeling,powersystemstability.

I.INTRODUCTION

D

ISTRIBUTEDpowersystem(DPS)technologywas?rstdevelopedforcomputerandcommunicationapplicationstoreplacethetraditionalcentralizedpowersystemarchitec-ture[1].Despitetheon-and-offdiscussionofhigh-frequencyacdistribution[2],practicalapplicationsincomputers,commu-nication,andotherelectronicsystemshaveallbeenbasedondcDPS(withdifferentinternaldcbusvoltages).AnimportantfeatureofDPSistheconditioningofpowerbyswitchingcon-vertersforindividualloads(aswellassourcesinmanycases.)Activecontroloftheseconvertersandtheresultingnonlineardynamicscreatecomplexsysteminteractionsthatcanleadtovariousstabilityandpowerqualityproblems,necessitatingsys-temmodelingandanalysis[3],[4].

ACDPSisarelativelynewdevelopment,butisbeingusedinseveralnewandemergingapplicationssuchasmore-electricandall-electricaircraft[5],[6],electricships[7],[8],renew-ableenergyanddistributedgeneration[9],microgrid[10],andsmartgrid[11].SimilartodcDPS,anacDPSreliesonpowerelectronicsandcontroltorealizeitsfunctionsandachievethere-quiredperformance.Examplesofsuchpowerelectroniccircuits

ManuscriptreceivedMarch11,2009;revisedJune28,2009.CurrentversionpublishedDecember18,2009.RecommendedforpublicationbyAssociateEditorJ.M.Guerrero.

TheauthoriswiththeDepartmentofElectrical,ComputerandSystemsEngineering,RensselaerPolytechnicInstitute,Troy,NY12180-3590USA(e-mail:jsun@rpi.edu).

Colorversionsofoneormoreofthe?guresinthispaperareavailableonlineathttp://ieeexplore.ieee.org.

DigitalObjectIdenti?er10.1109/TPEL.2009.2029859

includepulsewidthmodulation(PWM)invertersforgridinte-grationofrenewableenergyresources;powerconditioningforvariable-speeddrives,solid-statelighting,andenergy-ef?cientappliances;interfaceforenergystoragedevicesandelectric–hybridelectricvehicles;recti?er–inverterunitsforpropulsionmotorsonelectricships,aswellasenginestarter,fuelpumps,andothermotorapplicationsonmore-electricaircraft.Thewide-spreaduseofpowerelectronicsinanacDPSdistin-guishesitfromconventionalacpowersystems,wherepowerisalmostexclusivelygeneratedbylargesynchronousgeneratorsandmostlyconsumedbylinearandpassiveloads.TheresultingcomplexnonlinearsystemdynamicsnecessitatesimilarsystemmodelingandanalysisasrequiredfordcDPS.

Analysisanddesignofdcdistributedpowersystemsareusu-allybasedonimpedancemodelsdevelopedusingaveraging–linearizationtechniques.Inthisapproach,averagingmethods[12]and[13]areapplied?rsttoindividualconvertermodelstoeliminatetheirdiscontinuity.Theresultingaveragedmodelsaretypicallynonlinearandcanbelinearizedaboutagivensystemoperationpointtodevelopsmall-signallinearmodels,usuallyexpressedintheformofinputandoutputimpedance.Stabilityofthesystemcanthenbedeterminedbydividingitintoasourceandaloadsubsystem,andapplyingtheNyquistcriteriontotheratiobetweenthesourceoutputimpedanceandtheloadinputimpedance[14].Thisimpedance-basedsystemanalysismethodwas?rstdevelopedforstudyingdynamicinteractionsbetweendc–dcconvertersandtheirinput?lters[14],andlaterbecamethebasisforstabilityanalysisofcomplexdistributedpowersys-tems[3].Theimpedance-basedsystemstabilityrequirementscanalsobeusedtode?neimpedancespeci?cationsforindivid-ualloadssuchthatsystemstabilitycanbeguaranteedbydesign[4].However,suchspeci?cationsarealmostalwaystooconser-vative,resultinginincreasedsizeandcostofsystemdesign.Mostaveragingmethodscanalsobeappliedtoconverterswithacinputand/oroutput,whicharecommonlyfoundinacdistributedpowersystems.Theresultingaveragedmodels,however,arenonlinearingeneralandcannotbelinearizedbyconventionalsmall-signallinearizationmethodsbecauseoftheperiodicallytime-varyingoperationtrajectories.Sinceapply-ingnonlinearcontroltheoriestosuchcomplexsystemsisnotpractical,oneoftenhastoresorttonumericalsimulationinordertounderstandsystembehaviorandinteractions.How-ever,simulationalonedoesnotproducethequalitativeinforma-tionandinsightthatanalyticalmodelscanprovide.Evenwiththeabundantcomputingpoweravailabletoday,thesimulationtimecanbeprohibitivelylongforacomplexpowersystem,particularlywhensimulationhastoberepeatedoveralarge,multi-dimensionalparameterspaceinordertocovervariousde-signscenariosandtodevelopgeneralconclusions.Numerical

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