CircuitTheoreticClassificationofParallelConnected
DC–DCConverters
YuehuiHuang,StudentMember,IEEE,andChiK.Tse,Fellow,IEEE
Abstract—Thispaperdescribesaclassificationofparallelingschemesfordc–dcconvertersfromacircuittheoreticviewpoint.Thepurposeistoprovideasystematicclassificationofthetypesofparallelconvertersthatcanclearlyidentifyallpossiblestructuresandcontrolconfigurations,allowingsimpleanddirectcompar-isonofthecharacteristicsandlimitationsofdifferentparallelingschemes.Intheproposedclassification,convertersaremodeledascurrentsourcesorvoltagesources,andtheirconnectionpos-sibilities,asconstrainedbyKirchhoff’slaws,arecategorizedsystematicallyintothreebasictypes.Moreover,controlarrange-mentsareclassifiedaccordingtothepresenceofcurrentsharingandvoltage-regulationloops.Computersimulationsarepresentedtoillustratethecharacteristicsofthevariousparallelingschemes.IndexTerms—Controlmethods,current-sharingschemes,dc–dcconverters,parallelconnectedconverters,topology.
I.INTRODUCTION
OWERsuppliesbasedonparallelinganumberofswitchingconvertersofferseveraladvantagesoverasinglehigh-powercentralizedpowersupply,suchaslowcomponentstresses,increasedreliability,easeofmaintenanceandrepair,improvedthermalmanagement,etc.[1]–[4].Parallelingofstandardizedconverterswillcontinuetobeapopularapproachadoptedindistributedpowersystemsforbothfront-endandloadconverters.
Onebasicobjectiveofparallelconnectedconvertersistosharetheloadcurrentamongtheconstituentconverters.Todothis,someformofcontrolhastobeusedtoequalizethecur-rentsintheindividualconverters.Avarietyofapproaches,withvaryingcomplexityandcurrent-sharingperformance,havebeenproposedinthepasttwodecades[5]–[9].Ingeneral,methodsforparallelingdc–dcconvertersaredescribedintermsofcon-nectionstyles,controlconfigurationsandfeedbackfunctions.Althoughsomeformsofclassificationsandcomparisonshavebeengivenforparallelingschemes[10]–[12],mostfallshortofasystematicidentificationofallpossiblestructuresandcontrolconfigurations.Forinstance,inLuoetal.[10],aclassificationhasbeengivenbasedontheexistingparallelingmethods.Ba-sically,Luoetal.categorizedthemethodsintotwocategoriesaccordingtothetypeofcurrent-sharingmethod,namely,pas-sivedroopmethodsandactivecurrent-sharingmethods.Theyreportedfivespecificschemesthatexploitthedroopcharac-teristicsoftheconverters,andtwospecificschemesthatuse
ManuscriptreceivedJuly10,2006.ThisworkwassupportedbytheHongKongResearchGrantsCouncilunderCERGProjectPolyU5237/04E.ThispaperwasrecommendedbyAssociateEditorS.Banerjee.
TheauthorsarewiththeDepartmentofElectronicandInformationEngi-neering,HongKongPolytechnicUniversity,Hunghom,HongKong(e-mail:encktse@polyu.edu.hk).
DigitalObjectIdentifier10.1109/TCSI.2007.890631
P
active-currentsharingmethods,i.e.,themaster–slaveschemeandtheaveragescheme.Inaddition,threecontrolstructures,namely,innerloopregulation,outerloopregulationandexternalcontrol,wereidentified.Theirclassificationisthusbasicallyasystematiccollectionofexistingschemes.Otherclassificationworks,suchasLiuetal.[11]andChoi[12],focusonthecon-trolloopconfigurationsofselectedactivecurrent-sharingparal-lelingschemes.
Inordertofacilitatedesignandchoiceofappropriatepar-allelingconfigurations,asystematicclassificationoftheparal-lelingschemesthatpermitsaclearexposureofthestructures,behaviorsandlimitationsofallpossibleschemes,isneeded.Inthispaper,weinvestigatetheclassificationproblemandutilizebasiccircuittheorytoidentifythebasicstructuresandcontrolmethodsofparalleleddc–dcconverters.Ourobjectiveistopro-videasimpleclassificationthateliminatesredundancy,includesallpossiblebasicstructures,permitscomparativeanalysisofdifferentstructures,andhenceallowssystematicderivationofparallelingschemes.
OurstartingpointwillbethetwoKirchhoff’slawsthatdictatethepossibleconnectionstyles.Consideringconvertersaseithervoltagesourcesorcurrentsources,wedefinethreebasicstruc-turesforparallelingconverters.Aswewillsee,thesestructuresactuallyformthebasisofallpracticalparallelingschemes.Wewilldevelopequivalentmodelswhichcanbeusedinanalysis.Furthermore,controlmethodswillbesystematicallyintroducedtocompletetheoutputregulationandcurrent-sharingfunctions.Finally,computersimulationswillbepresentedtoprovideafullcomparisonofthevariousconfigurations.
II.BASICCIRCUITTHEORYOFPARALLELCONNECTIONSA.BasicConstraintsinParallelingIndependentSources
Theoutputofanyconverterisnormallyexpectedtoprovideregulatedvoltageorcurrent.Thus,anappropriatemodelforaconverter(seenatoutputterminals)iseitheravoltagesourceoracurrentsource.Twobasiclawsmustbeobeyedwhenconnectingsourcestogether.First,Kirchhoff’svoltagelaw(KVL)dictatesthatthesumofvoltagesofallbranches(inthesamesense)formingaloopmustequalzero.Thismeansthatnotwoinde-pendentvoltagesourcesarepermittedtobeconnectedinpar-allel.Theoretically,evenifthevoltagesourcesareofthesamemagnitude,parallelingthemisstillnotpermittedasitmakesthecurrentvaluesundefined[13].Likewise,Kirchhoff’scur-rentlaw(KCL)dictatesthatthesumofcurrentsofallbranchesinacutset(emergingfromthesamesub-graph)mustequalzero.Thisclearlyeliminatesthepossibilityofconnectingtwoinde-pendentcurrentsourcesinseries.Inthispaper,asourfocusisparallelingsources,wedonotconsiderthecaseofconnectingsourcesinseries.
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Fig.1.Structuresforparallelingidealindependentsources.
Fig.2.Equivalentcircuitsforpowerconverters.(a)Théveninform.(b)Nortonform.
Fromtheabovediscussion,itisclearthatindependentsourcescanbeconnectedinparallelunderonlytwopossiblecircumstances,asshowninFig.1.First,onlyoneofthemcanbeanindependentvoltagesource,andtherestmustbecurrentsources,asshowninFig.1(a).Theoutputvoltageisdecidedbythevoltagesourcebranch,andthecurrentinthevoltagesourceisdeterminedbytheload.Second,allparallelbranchesarecurrentsources,asshowninFig.1(b).Theoutputvoltageisdecidedbytheload.
Itshouldbeclearthatinpractice,thevoltageandcurrentsourcesarenotindependentbutarecontrolledsourcesinordertoallowregulatedoutputvoltageandspecificsharingofcurrenttobemaintained.Nonetheless,theaforementionedtwobasicconfigurationswillformthebasisofparallelconnectionstyles.Theapplicationsoftheseconnectionstylesandtheassociatedcontrolproblemwillbethemainsubjectsofdiscussionofthispaper.
B.EquivalentCircuitsforDC–DCPowerConvertersDC–DCconvertersaredevicesforprocessingpower.Formostpracticalpurposes,aregulatedoutputvoltageorcurrentisrequiredofaconverter,mandatingtheuseofsomefeedbackcontroltokeeptheconverterunaffectedbyloadandinputdisturbances.Asaresult,adc–dcconvertercanbeviewedasanimperfectvoltageorcurrentsourcewithappropriatecontrolofitsmagnitudeinresponsetooutputand/orinputvariations[14].Ingeneral,wemaysimplyandgenericallyrepresentadc–dcconverterinThéveninformorNortonform,i.e.,adependentvoltagebehindasmallimpedance(atlowfrequency)oradependentcurrentsourceinparallelwithalargeimpedance(atlowfrequency),asshowninFig.2.1Theoretically,thetworepresentationsarearbitrary.However,itshouldbeclearthattheThéveninformismoresuitedforconverterswhosepurposeistoachievearegulatedoutputvoltage,whereastheNortonformissuitedforconverterswhosepurposeistoachievea
1By“small”impedanceand“large”impedance,weactuallyrefertothemod-
ulusoftheimpedance.regulatedoutputcurrent.Obviously,voltagefeedbackisneededfortheformercase,andcurrentfeedbackforthelatter.
Weshouldreiteratethatthetwoequivalentrepresentationsareinterchangeableexceptforthecasewheretheequivalentoutputimpedanceiszero.Denotingtheoutputimpedancebyandtheloopgainby,wemaywrite
forThéveninformforNortonform
(1)
whereistheopen-loopoutputimpedance.Iftheloopgainishighenough,becomesnegligiblysmallforthevoltagesourcerepresentationorverylargeforcurrentsourcerepresen-tation.Theoutputcharacteristicoftheconverterresemblesthatofanearlyindependentsource.
III.GENERALCLASSIFICATIONOFPARALLELCONNECTED
DC–DCCONVERTERS
Fromtheforegoingdiscussion,itisclearthatanyparallelingschemeinvolvingvoltageandcurrentsourcesmustcomplywiththetwobasicstructuresdescribedearlier.Moreover,ifthevoltagesourcesareimperfect(i.e.,withanonzerooutputimpedance),theycanstillbeconnectedinparallel.Thus,wehavethreebasicconfigurationsforparallelingimperfectsources.2
Whendc–dcconvertersaretreatedasimperfectvoltageorcurrentsources,threebasicconfigurationsforparallelingpracticaldc–dcconverterscanbedeveloped,assummarizedinFig.3.Forbrevity,werefertotheseconfigurationsasTypesI,II,andIIIconnections.Foravoltagesourcebranch,wehave
(2)
wheresubscript(1to)indicatesthebranchnumber,andistheoutputcurrentofthethbranch,i.e.,thepartofloadcur-rentsharedbythethbranch.Foracurrentsourcebranch,wehave
(3)
whereistheequivalentcurrentsourceofthethbranch.Inpractice,weneedtoapplyappropriatecontroltodc–dcconvertersinorderto“cast”themasvoltageorcurrentsources.Forinstance,avoltagefeedbackloopisobviouslyneededforcontrollingadc–dcconvertersothatitbehavesasavoltagesource.Thus,theparallelingconfigurationsarecloselyrelatedtothecontrolmethodwhicheffectivelydetermineswhetheradc–dcconverterwouldbehaveasavoltageorcurrentsource.Inadditiontothedefiningcontrolofcurrentandvoltagesources,acurrentsharingcontrolcanbeusedtoensureevensharingoftheloadcurrentamongtheconverters.Inaparallelconvertersystem,eachconstituentconverterisapowersupply.Toavoidconfusion,wewillusethetermcurrent-sharingloopinaspecificcontext.Ifacurrent-sharingreferenceisderivedfromtheoutputcurrentsofone/allconstituentconverters,thecontrolschemeissaidtocontainacurrent-sharingloop.
2Byimperfectsources,wemeanthosevoltagesourceshavingnonzerooutput
impedanceandthosecurrentsourceshavingfiniteoutputimpedance.
HUANGANDTSE:CIRCUITTHEORETICCLASSIFICATIONOFPARALLELCONNECTEDDC–DCCONVERTERS1101
Fig.3.Threeconfigurationsforparallelingconverters.(a)TypeI.(b)TypeII,withpracticalformontheright.(c)TypeIII,withpracticalformontheright.
Fig.4.Systematicclassificationofparallelconnectedconverters.
Otherwise,thecontrolschemedoesnothaveacurrent-sharingloop.
Wemaythereforefurtherclassifyparallelconvertersystemsaccordingtothepresenceofacurrent-sharingloop,resultinginasimple,systematicclassification,asshowninFig.4.Twolayersareincludedintheclassification.Inthefirstlayer,wegetthreeconfigurations,TypesI,II,andIII,basedonthecircuittheoreticconnectionstyles.Inthesecondlayer,thepresenceofacurrent-sharingloopistheclassifyingcriterion.
IV.THREETYPESOFCONNECTIONSTYLESAND
ASSOCIATEDCONTROLMETHODS
Inthissection,inlightoftheclassificationframeworkmen-tionedintheforegoing,thevarioustypesofparallelconnecteddc–dcconvertersaredescribedindetail.Ouremphasesherearethegenericcircuittheoreticstructuresandthenecessarycontrolmethods.Asaprerequisite,wenotethatconvertersaimingtoimitatevoltagesourcesshouldhavetightvoltagefeedbackloopsforvoltageregulationpurposes,whereasconvertersimitatingcurrentsourceswouldnecessitatesomeformofcurrent-modecontrolinordertosetthecurrentmagnitudes.Thepresenceof
Fig.5.Outputcharacteristicsoftwoparallelconnectedconverters.
current-sharingloopisanadditionalfeature,contributingtothecurrentsharingoftheconstituentconverters.A.TypeI
TheType-IconnectionisshowninFig.3(a).Eachbranchrepresentsaconverter,whichisbasicallyaThévevinsource,i.e.,adependentvoltagesourcebehindanoutputimpedance.Forthecontrolwithoutcurrent-sharingloop,thebranchesaresimplyconnectedinparallel.However,theabsenceofacur-rent-sharingloopimposessomespecificrequirementsontheindividualbranchesinordertoprovidenaturalcurrentsharing[15],[16].Thishasbeencommonlyknownasthedroopmethod[7],[17].Specifically,eachconverter(branch),intheabsenceofacurrent-sharingloop,shouldhaveafiniteoutputresistanceatsteadystate.
Asanexample,Fig.5showstheoutputcharacteristicsoftwoconvertersconnectedinparallel,withoutemployingacurrent-sharingloop.Supposetheoutputcurrent,equivalentThéveninvoltageandoutputresistanceofconverter(branch)is
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Fig.6.ControlstructureforType-Iconfigurationwithcurrent-sharingloop.
and,respectively,andthecommonoutputvoltageis.The
currentsharingerrorisexpressedas
(4)
where
istheloadresistanceand.Thecurrenterrorwillbezeroonlyifand.Thus,inpractice,currentsharingcanbeachievedby
adjusting
and.ForType-Iconnectionwithcurrent-sharingloop,sinceallconvertersareThéveninsources,outputregulationandcurrent
sharingareachievedbycontrolling
and/ortheoutputimpedance
.ThecontrolstructureisshowninFig.6,wheretheequivalentvoltagesourcesarecontrolledtoobtaincurrentsharing.Inthisconfiguration,eachconverterisandependantvoltagesourceundervoltagefeed-backcontrol.InFig.6,
representsthecontrolinformationprovidedbycurrentsharing,
andarethefeedbackvoltageandswitchcontrolsignalofconverter,respectively.Inthecurrent-sharingnetwork,thecurrentssensedfromdifferentconvertersarefirstprogrammedtoobtainacommoncurrentcontrolsignal,whichwillbecomparedwiththeindividualcur-rentstogenerate
.Then,isusedtoregulateindividualequivalentvoltages.Thecontrolobjectiveistoensurethatallconverterssharetheloadequally.B.TypeII
FortheType-IIconnectionshowninFig.3(b),oneconverterservesasthevoltage(Thévenin)sourceandothersarecurrent(Norton)sources.Thecontrolstructurewithoutcurrent-sharingloopisshowninFig.7(a).Thereisamainvoltagefeedbackloop,whichactsonthevoltage(Thévenin)sourcetoregulatetheoutputvoltage.Otherbranchesareundercurrent-modecon-trol,whoseobjectiveistomakeallindividualoutputcurrentssharethesameportionoftheloadcurrent[18].Thecurrentinthevoltagesourcebranchisthuscontrolledindirectly(automat-ically)intheequilibriumstate,i.e.,
.Thus,thecurrentforeachconverterisequalto
,where.
FortheType-IIconfigurationwithcurrent-sharingloop,avarietyofcontrolmethodscanbeusedtofabricatethevoltageFig.7.ControlstructuresforType-IIconfiguration(a)withoutcurrent-sharingloop,and(b)withcurrent-sharingloop(alsoknownasmaster–slavecurrentsharing).
sourceandcurrentsources.ThecontrolstructureisshowninFig.7(b).Again,thereisamainvoltagefeedbacklooptocontrolthevoltagesourcebranch.Thecurrentcontrolsignal
forthecurrentsourcebrancheswillbederivedfromthevoltagesourcebranch.Thiscontrolsignalisthencompared
withtheindividualcurrentofthe
converterstoachievecurrentsharing.Thiscontrolmethodiscommonlyknownasmaster–slavecurrent-sharingmethod[19]–[21],wherethevoltagesourceisthemasterandthecurrentsourcesaretheslaveswhosecurrentsareprogrammedtofollowthemaster’s.C.TypeIII
IntheType-IIIconfigurationshowninFig.3(c),allconvertersarecurrent(Norton)sources.Intheabsenceofacurrent-sharingloop,allconvertershavetofollowacurrentcontrolsignalwhichisderivedfromtheoutputvoltagefeedbackloop,asshowninFig.8(a).Thevoltagefeedbackloopaimstoachievevoltageregulationaswellascurrentsharing.Intheidealcase,
theloadcurrentisdistributedequally,i.e.,
.AsimpleimplementationcanbefoundinIuetal.[22].
Finally,fortheType-IIIconfigurationwithcurrent-sharingloop,allconvertersareundercurrent-modecontrolsothattheybehaveasgoodcurrentsources.Current-programmingmethods,suchasmaster–slavemethodoraveragemethod,canbeusedtogeneratethecommoncurrent-sharingcontrolsignal[23],[24].Theamplifiederrorsbetweenthecurrent-sharingcontrolsignal
andthefeedbackcurrents
,areinjectedtothefeedbackloop,adjustingthecurrentcontrolsignals
.ThebasicstructureisshowninFig.8(b).
HUANGANDTSE:CIRCUITTHEORETICCLASSIFICATIONOFPARALLELCONNECTEDDC–DCCONVERTERS1103
Fig.8.ControlstructuresforType-IIIconfiguration(a)withoutcurrent-sharingloopand(b)withcurrent-sharingloop(alsoknownasdemocraticcurrentsharing).
V.COMPARISONOFPARALLELINGSCHEMES
Intheforegoingsection,wehavediscussedthestructuresandtheassociatedcontrolmethodsforparallelingdc–dcconverters.Inthissection,wecomparethedifferentstructuresandcontrolmethodsintermsofcurrent-sharingaccuracy,voltageregula-tion,dynamicalperformance,etc.Intuitively,wecanmakethefollowinggeneralobservations:
1)Type-Ischemesaresimplebutsufferfundamentallyfromparallelingvoltagesources.Theadjustmentrangeforcur-rentsharingissmallsinceeachconstituentconverterisde-signedprimarilytoregulateitslocaloutputvoltage,andthecurrentsintheconverterscanonlybeadjustedbycontrol-lingthevoltageswhicharenotallowedtovarytoomuch.2)Type-IIschemesaretheoreticallymoreviableasthereisonlyonevoltagesource,parallelingwithcurrentsources.Thedynamicsofthevoltageregulationthusdependsonthecontrolmethodbeingemployedbythevoltageregulatingloop.Theothercurrentsourceconverterscontroltheircur-rentsdirectlytoachievethedesiredcurrentsharing.Thus,thecurrent-sharingperformanceisgenerallymuchbettercomparedtoType-Ischemes.
3)Type-IIIschemesaremorecomplicatedintermsofimple-mentationduetosubstantialcurrentprogrammingrequire-ments.However,Type-IIIschemesaregenerallybestintermsofcurrentsharingasallconvertersarefundamentallycurrentcontrolled.Thevoltageregulationcanalsoenjoyfastresponseduetothedirectloadvoltagecontrol.
Foradetailedcomparison,weconsiderasystemofthreebuckconvertersconnectedinparallel,asshowninFig.9(a).
Fig.9.Paralleledconvertersandthecompensatornetworks.(a)Threeparallel-connectedbuckconverters.(b)Two-zerotwo-polecompensator.(c)Propor-tional-integralcompensator.(d)Single-polecompensator.
Fig.9(b)–(d)showsthecontrollersusedinthesimulationsforvoltageregulationandcurrentsharing.Inoursimulations,modelsareconstructedusingMATLAB/SIMULINK.
Asitisimportanttoensuregeneralityofanyconclusionmadeinourstudy,wehaveconsistentlyusedthesametypeofcom-pensationnetworksandequivalentvaluesofcontrolparametersinordertoensurethatfaircomparisoncanbemadeandgen-erallyvalidconclusionsaredrawn.Here,wehavechosenthemosttypicalcompensationnetworksforthedifferentcontrolsituations.Specifically,forvoltage-modebuckconverters,weemployatypicaltwo-zerotwo-polecompensator,asshowninFig.9(b).DenotingtheLaplacetransformsofthecontrolsignal
andconverteroutputsignalas
and,respectively,thetransferfunctionis
(5)
where
.Forthecurrent-modecontrol,more-over,theoutervoltagefeedbackloopemploysaPIcontroller,asshowninFig.9(c).Thetransferfunctionis
(6)
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TABLEI
POWERSTAGECOMPONENTVALUESUSEDINSIMULATIONS
TABLEII
CONTROLLERPARAMETERSUSEDINSIMULATIONS(UNITFORALL!’S:RAD/S,
UNITFORK:RAD/S,UNITFORK:)
where.Finally,forcur-rent-sharingloops,weemployasimplesingle-polecompen-sator,asshowninFig.9(d).DenotingtheLaplacetransformsof
thecontrolvoltageandtheinductorcurrentas
and,thetransferfunctionisgivenby
(7)
where.Thecurrent
sharingcontrolsignal,,istheaveragevalueofallinduc-tancecurrents,i.e.,.
ThecomponentvaluesusedinthesimulationsarelistedinTableI.Fordifferenttypesofparallelingschemes,appropriatecontrollers,asshowninFig.9(b)–(d),areselectedanddesignedtoensurethatthesamevoltageloopbandwidthisachieved,i.e.,about10kHz.TheparametersusedinthecontrollersareshowninTableII.
FortheType-Iconfiguration,eachconverterisundervoltage-modecontrol.Fortheparallelingschemewithoutcurrent-sharingloop(droopscheme),extracurrentfeedbackisusedtoproduceadroopintheoutputvoltage,wheretheequiv-alentdroopresistanceisproportionaltothecurrentfeedbackgain[10].Figs.10and11showtheoutputvoltageandcurrentwaveformsunderasteppedloadcondition.InFig.10,wealsoillustratetheeffectoftheoutputresistance,whichiscrucialtothiskindofdroopscheme.TheoutputresistanceusedforsimulationsofFig.10(a)and(b)istentimeslargerthanthat
Fig.10.SimulationresultsforsteppedloadforType-Ischemewithoutcur-rent-sharingloop.(a)Outputvoltagewithlargeoutputresistance.(b)Converteroutputcurrentswithlargeoutputresistance.(c)Outputvoltagewithsmalloutputresistance.(d)Converteroutputcurrentswithsmalloutputresistance.
Fig.11.Simulationresultsforplug-intransientforType-Ischemewithoutcur-rent-sharingloop.(a)Outputvoltage.(b)Converteroutputcurrents.
usedforthesimulationsofFig.10(c)and(d).Fromthesim-ulationresults,weclearlyseethattheType-Ischemewithoutcurrent-sharingloopdoesnotperformverysatisfactorily.Normally,withlargeoutputresistance,wemayachievegoodcurrentsharingbutpooroutputregulation.However,thecurrentsharingbecomesworseandoutputregulationbecomesbetterwithsmalleroutputresistance.Thisremainsthefundamentallimitationofsuchdroopschemes,asmultiplenonidenticalvoltagesourcesareparalleledandthereisonlyaverynarrowadjustmentrangeforcontrollingthecurrentsviathevoltagedropsintheoutputresistances.
Anotherdynamicaltestistheplug-intransient.Initially,twoconverterssharetheload.Then,athirdconverterplugsinandsharestheloadwiththeothertwooperatingconverters.TheresultsareshowninFig.11fortheType-Iparallelingschemewithoutcurrent-sharingloop.Thecurrentsinthetwooperatingconvertersdroptozeroduringtheplug-intransient.Suchblackoutisundesirableasitimposeshighcurrentstressonthethirdconverterduringthetransient.
HUANGANDTSE:CIRCUITTHEORETICCLASSIFICATIONOFPARALLELCONNECTEDDC–DCCONVERTERS1105
Fig.12.SimulationresultsforsteppedloadforType-Ischemewithcurrent-sharingloop.(a)–(b)StableoperationwithparametervaluesshowninTableII.(c)–(d)Unstableoperationforlargecurrent-sharinggain(K=5).(e)–(f)Unstableoperationforlargevoltagefeedbackgain(!=3:1210rad/s).
Withcurrent-sharingloop,theType-Ischemeperformsbetter,asdemonstratedinFig.12(a)and(b)andFig.13.More-over,aswouldbeexpected,increasingthecurrent-sharinggainand/orthevoltagefeedbackgainwouldaffectthestabilityofthesystem.AsshowninFig.12(c)and(d),thesystembecomesunstablewhenthecurrent-sharinggainincreases.Likewise,thesystembecomesunstablewhenthevoltagefeedbackgainislarge,asshowninFig.12(e)and(f).Thisisbecausethecurrent-sharingerrorsignaloutsideofthevoltageloopisamplifiedandfedbacktothevoltageloopcausingpossibleunstablebehaviorifthecurrent-sharinggainorthevoltagefeedbackgainistoolarge.Togetstableoperation,wehavetolimitthesegains,whichalsolimitthedynamicresponse.Theplug-intransientisshowninFig.13.Thesystemrebalancesitselfwithoutdrasticblackoutofindividualconvertercurrents.ThisisanimprovementovertheType-Ischemewithoutcur-rent-sharingloop.
ShowninFigs.14and15aresimulationresultsfortheType-IIschemewithoutcurrent-sharingloop.AsshowninFig.14,satisfactorydynamicresponseundersteppedloadchangeisdemonstrated.However,thecurrent-sharingaccuracyreliesontheprecisionofthecurrentdivider.Smallvariation
Fig.13.Simulationresultsforplug-intransientforType-Ischemewithcurrent-sharingloop.(a)Outputvoltage.(b)Converteroutputcurrents.
Fig.14.SimulationresultsforsteppedloadforType-IIschemewithoutcur-rent-sharingloop.(a)Outputvoltage.(b)Converteroutputcurrents.
Fig.15.Simulationresultsforplug-intransientforType-IIschemewithoutcurrent-sharingloop.(a)Outputvoltage.(b)Converteroutputcurrents.
ofthecurrentdividercangivelargecurrent-sharingerrorsbetweenthevoltageconverterandcurrentconverters.Inthiscase,weobservecurrent-sharingerrorsfrom6.25%to13.25%
(
A,A,A).Also,theplug-intransientisshowninFig.15.Thesystemisabletorebalanceitselfwithoutcausingcurrentblackout,thoughfairlyslowlywithsettlingtimeofaround2msinthiscase.
InFigs.16and17,weshowthesimulationresultsfortheType-IIschemewithcurrent-sharingloop.AsseenfromFig.16,satisfactorydynamicresponseundersteppedloadchangeisdemonstrated.Also,thecurrent-sharingaccuracyisimprovedcomparedtotheType-IIschemewithoutcurrent-sharingloop,withcurrent-sharingerrorsfrom1.25%to5%(A,A,A)inthiscase.Thisisbecausetheslavessettheircurrentstoequalthatofthemastervia
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Fig.16.SimulationresultsforsteppedloadforType-IIschemewithcurrent-sharingloop.(a)Outputvoltage.(b)Converteroutputcurrents.
Fig.17.Simulationresultsforplug-intransientforType-IIschemewithcur-rent-sharingloop.(a)Outputvoltage.(b)Converteroutputcurrents.Fig.18.SimulationresultsforsteppedloadforType-IIIschemewithoutcur-rent-sharingloop.(a)Outputvoltage.(b)Converteroutputcurrents.comparisontheircurrentswiththemaster’s.Here,weclearlyconfirmourearliertheoreticalanalysisthatonlyonevoltageloopisenoughtoregulatetheoutputvoltage.However,themastershouldbeasfastaspossibletoprovidestablereferencefortheslaves.Moreover,Fig.17showssatisfactoryrebalancingafteraplug-intransient,withasettlingtimeofaround1.2ms.ResultsfortheType-IIIschemewithoutcurrent-sharingloopareshowninFigs.18and19.Here,weobservesatisfactorydy-namicresponseforlargeloadchange.However,thecurrent-sharingerrorsarequitelarge(1.25%to8.75%inthiscase,
A,A,A)becauseitissen-sitivetothecurrentcomparatorduetotheabsenceofcurrent
sharingcomparison.Moreover,asshownintheplug-intransientofFig.19,there-balancingcanbeachievedveryquicklywithasettlingtimeoflessthan1ms.
Finally,fortheType-IIIschemewithcurrent-sharingloop,thesimulationresultsareshowninFigs.20and21.InthiscaseFig.19.Simulationresultsforplug-intransientforType-IIIwithoutcurrent-sharingloop.(a)Outputvoltage.(b)Converteroutputcurrents.
Fig.20.SimulationresultsforsteppedloadforType-IIIschemewithcurrent-sharingloop.(a)Outputvoltage.(b)Converteroutputcurrents.
Fig.21.Simulationresultsforplug-intransientforType-IIIschemewithcur-rent-sharingloop.(a)Outputvoltage.(b)Converteroutputcurrents.
weobserveveryfastdynamicresponse,andveryprecisecur-rentsharing,withcurrent-sharingerrorsfrom0%to3.75%in
thiscase(
A,A,A).Furtherim-provementofcurrentsharingcanbeobtainedbyadjustingthecurrent-sharingcompensator.Also,veryfastre-balancingafteraplug-intransientcanbeobserved,asshowninFig.21.
Fromtheforegoingsimulationresults,wemaysummarizethegeneralfeaturesofthethreeconfigurationsandtheircontrolmethods.Inshort,Type-Ischemes,thoughsimple,sufferfromsomefundamentallimitationsasvoltagesourcesarebeingparalleled.Type-IIschemeshaveonevoltagesourceparallelinganumberofcurrentsources.Thevoltageregulationperfor-mancethusdependsofthefeedbackarrangementofthevoltagesource.CurrentsharingismucheasytobeobtainedthanthatofType-Ischemes.Type-IIIschemesarebasicallyparallelcurrentsources.Theyachieveveryfastresponseandgenerallygoodcurrentsharingasvoltageregulationisbasedontheload
HUANGANDTSE:CIRCUITTHEORETICCLASSIFICATIONOFPARALLELCONNECTEDDC–DCCONVERTERS1107
TABLEIII
COMPARISONOFPARALLELINGSCHEMES
voltagefeedbackandcurrentsharingisdoneviadirectcurrentcontrol.TableIIIcomparestheirrelativeprosandconsintermsofeaseofexpansion,dynamicperformance,current-sharingaccuracyandregulationcapability.
VI.CONCLUSION
Inthispaper,asystematicclassificationofparallelconnectedswitchingpowerconvertersisgiven.Ourstartingpointiscircuittheoryofconnectingvoltageandcurrentsourcesasconverterscanberegardedasvoltageorcurrentsources.Threebasictypesofparallelingschemescanbeidentified,correspondingto:i)connectingThéveninsourcesinparallel;ii)connectingoneThéveninsourcewithmanyNortonsourcesinparallelandiii)connectingNortonsourcesinparallel.Thepresenceofcurrent-sharingloophasbeenconsideredasanoptionalfeature,thoughitsusehasbeenclearlyproventobeimportantforachievinggoodperformanceincurrentbalancing.Theclassificationpresentedinthispaperallowsthestructuresandcontrolrequirementsofparallelingschemestobesystemati-callyanalyzed.
ACKNOWLEDGMENT
Theauthorswishtothankthereviewersfortheircommentsandsuggestionsthathaveledtovariousimprovementsinthepresentationofthepaper.
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YuehuiHuang(S’07)receivedtheB.Eng.andM.Eng.degreesfromXi’anJiaotongUniversity,Xi’an,China,in2002and2005,respectively.SheiscurrentlyworkingtowardthePh.D.degreeintheDepartmentofElectronicandInformationEngi-neeringattheHongKongPolytechnicUniversity,HongKong.
Herresearchinterestsincludemodelingandanal-ysisofpowerelectronicscircuitsandthecircuitthe-oreticaspectsofpowerelectronics.
ChiK.Tse(M’90–SM’97–F’06)receivedtheB.Eng.degreewithfirstclasshonorsinelectricalengineeringandthePh.D.degreefromtheUni-versityofMelbourne,Australia,in1987and1991,respectively.
HeispresentlyChairProfessorandHeadofDe-partmentofElectronicandInformationEngineeringattheHongKongPolytechnicUniversity,HongKong,andhisresearchinterestsincludenonlinearsystems,complexnetworksandpowerelectronics.HeistheauthorofLinearCircuitAnalysis(London,
U.K.:Addison-Wesley,1998)andComplexBehaviorofSwitchingPowerCon-verters(CRCPress,2003),coauthorofChaos-BasedDigitalCommunicationSystems(Heidelberg,Germany:Springer-Verlag,2003),CommunicationswithChaos(London:Elsevier,2006)andSignalReconstructionWithApplicationstoChaos-BasedCommunications(TsinghuaUniversityPress,2007),andco-holderofaU.S.patent.
Dr.TsewasawardedtheL.R.EastPrizebytheInstitutionofEngineers,Aus-tralia,in1987.HewontheIEEETRANSACTIONSONPOWERELECTRONICSPrizePaperAwardfor2001andtheInternationalJournalofCircuitTheoryandAp-plicationsBestPaperAwardfor2003.In2005,hewasnamedanIEEEDistin-guishedLecturer.WhilewithHongKongPolytechnicUniversity,hereceivedtwicethePresident’sAwardforAchievementinResearch,theFaculty’sBestResearcherAward,theResearchGrantAchievementAwardandafewotherteachingawards.From1999to2001,heservedasanAssociateEditoroftheIEEETRANSACTIONSONCIRCUITSANDSYSTEMS—I:FUNDAMENTALTHEORYANDAPPLICATIONS,andsince1999hehasbeenanAssociateEditorfortheIEEETRANSACTIONSONPOWERELECTRONICS.HecurrentlyalsoservesasanAssociateEditoroftheInternationalJournalofSystemsScience,aGuestAsso-ciateEditoroftheIEICETransactionsonFundamentalsofElectronics,Com-municationsandComputers,andaGuestEditorofCircuits,SystemsandSignalProcessing.
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