外文翻译原文-负载电流共享输出并联DC-DC转换器的改进下垂控制策略

AnImprovedDroopControlStrategyforLoadCurrentSharinginOutputParallel-ConnectedDc-dcConvertersV.P.Oberto,M.D.Depexe,T.C.NaidonandA.CamposGroupofIntelligenceinLighting(GEDRE)FederalUniversityofSantaMaria(UFSM)SantaMaria,97105-900,Brazilvictor.obertogedre.ufsm.br,camposct.ufsm.brAbstractThisworkpresentsanovelcurrentsharingcontroltechniquebasedonanimproveddroopcontrolschemeforamodularpowersupplycomposedofnoutputparallel-connectedDC-DCconverters.Eachconverterisconnectedtotheloadthroughindividuallineresistanceandmodeledasadependentvoltagesource.Inordertoprovideproperloadsharing,avoltagereferenceadjustmentforthemaincontrolloopisdonethroughtheloadcurrentcontrolleroutput.Adistributedpowersupplycomposedbythreebuckconverterswiththeiroutputsconnectedinparalleldesignedfora75WLightEmittingDiode(LED)streetlightingfixtureistestedthroughsimulationstoprovethefeasibilityoftheidea.KeywordsDistributedcontrol,DC-DCconverters,Parallelism,Currentsharing.I.INTRODUCTIONFromthepastdecades,theuseofmultipleconvertershavebeenmarkedasanvaluablealternativetoachieveseveralperformancemetricsinpowerelectronicsupplies,suchasredundancy,improvedthermalmanagement,modularityandgreaterreliability1.Onthepresentdays,therapidgrowthofmoredemandingloadssuchastelecommunicationsystems,distributedcomputerserversanduninterruptiblepowersup-pliesstrengthenedsuchtopicofresearch25.Adistributedpowersupply(DPS)iscomposedofmultipleDC-DCconverterswithinputsandoutputsconnectedinseriesorinparallelwitheachother.Itsmainobjectiveistoshareequally(orproportionallytoitspower)theoutputcurrent(unitswithoutputsconnectedinparallel)oroutputvoltage(unitswithoutputsconnectedinseries)betweenconverters.Inpractice,theachievementofoptimaloutputsharingbe-tweenconnectedconvertersneedstheaidofadditionalcontrolstructuresinthedistributedpowersupply.Fortheparticularcaseofoutputparalleledconvertersdesignedtoshareoutputcurrent,individualcomponenttolerancesandimbalanceinlineimpedancescangenerateseverecurrentsharingdeviation,consequentlyexposingoneormoreconverterstoexcessivethermalstress,increasingtheirrateoffailure6.Inthiscontext,severalcurrentsharingstrategiesdevelopedforparalleledconvertersshowninliteraturecanbeappliedtoreducecurrentimbalancebetweenunits.Theonescalledpassivecurrentsharingarebuiltusingonlylocalvariablesforoutputcurrentadjustment,whileactivecurrentsharingtechniquesusuallymakeuseofaglobalcurrentsharingcontrolstrategy7,8.Amongthepassivetechniques,thedroopcon-trolstrategy9doesnotrequirecontrolinterconnectionsbe-tweencontrollers,buthassomedisadvantages,likedecreasedoutputvoltageregulationfordesireddroopcharacteristicandpoorcurrentsharingduetoopenloopconfigurationforparallelconnection10.Theactivecurrentsharingtechniques8canbecomposedbyspecificcontrollersforeachconverteroracentralizedcontrolloopinchargeofallcontroltasksforallpowerunits.Activetechniqueshavebetterperformancebothfortransientandsteadystates,buttheyhavereducedmodu-larityandincreasedcomplexityofimplementationcomparedtopassivecurrentsharingstrategies.Inthiswork,theauthorsproposeanimproveddroopcon-trolstrategyforloadcurrentsharingappliedforoutputparallel-connectedDC-DCconverters.Eachconverterismodeledasadependentvoltagesourceandconnectedtoacommonoutputvoltagebusthroughindividuallineresistance.Localoutputvoltageisregulatedthroughfeedbackcontrollooptogetherwithindividualvoltagesensor.Forthecurrentsharingregula-tion,astandarddroopcontrolstrategyisusedandimprovedbyusingaloadcurrentsensorandacurrentfeedbackcontrollooptoadjustoutputvoltagereferenceinthemaincontrolloop.InSectionII,abriefreviewofexistingcontrolstrategiesdesignedforcurrentsharingbetweenconvertersisdone.TheproposedcontrolstrategyisintroducedinSectionIII.SimulationresultsforaDPScomposedbythreeparalleledconvertersfeedinga75WLEDstreetlightingfixturewiththreecontrolstructuresareshownandcomparedinSectionIV.SectionVpresentstheconclusionsofthispaper.II.REVIEWOFCONTROLSTRATEGIESFORCURRENTSHARINGForbetterunderstandingofthethemeandtheproposedtechniqueinthiswork,passiveandactivecurrentsharingcon-trolstrategieswillbebrieflyreviewedinthenextparagraphs.A.PassivecurrentsharingcontrolInapowersupplycomposedbytwoormorepowercon-verterswiththeiroutputsconnectedinparallel,eachconverterisconnectedtothemainloadbusthroughadistinctlineimpedance.Tosimplifythestudy,theselineimpedancesareconsideredhereaslineresistances.Consideringthesetupdescribed,theoutputcurrentofeachconverterdependson978-1-4799-5551-0/14/$31.002014IEEEtherespectivelineresistanceinrelationtothesumofalllineresistances.Aspreviouslycited,individualcomponenttolerancescanplayasignificantroleincurrentdeviation,speciallytheimbalancebetweenlineresistances.Originallydesignedforconvertersconnectedinparallel,thedroopcontrolstrategy8-10isapassivecurrentsharingstrategybasedonaoutputvoltagefeedbackloopwithrespectivereferenceadjustedbytheconvertersmeasuredoutputcurrent.Oneimportantadvantageofapowersupplywithdroopcontrolistheabsenceofcontrolinterconnectionsbetweenconverters,makingthepowersupplydesignmoremodularandimprovingreliabilityandredundancyofthesystem.Sincetheobjectiveofthedroopstrategyistoregulatelocaloutputvoltageusingthemeasuredoutputcurrent,thebetterthecurrentsharingachieved,theworseistheoutputvoltageregulationineachconverter9.B.ActivecurrentsharingcontrolForthiskindofcontrolimplementation,acentralcurrentcontrollooporcontrollercanbeusedtoprogrameachcon-verterscurrentreferenceinaparalleledpowersupply.Also,oneunitcanactasthemasterunitforcurrentprogrammingofitsownandslaveconverters.Themainadvantageisprecisecurrentsharingratioachieved,whilefundamentaldisadvan-tagesareincreasedcomplexityofthecontrolsystemandthepresenceofoneormorepossiblespointsoffailure(centralcurrentlooporcentralcontroller),whichreducesthereliabilityofthepowersupply.Moreactivecurrentsharingtechniquescanbefoundin8,1113.III.PROPOSEDCONTROLSTRATEGYA.Modelofanoutputparallel-connectedDPSADC-DCconverterisdesignedtoprovideregulatedvolt-ageorcurrentaccordingtotheloadrequirements.InaDPS,eachconvertersoutputcanberepresentedasavoltageoracurrentsource.Also,thepossibilitiesofconnectionandconstraintsofoperationfortheparalleledunitsaredepictedin15.Inthesamepaper,itisshownthattheonlytypeofconnectionthatdoesnotrequireacentralcontrollerormasterunitisTypeIconfiguration.Therefore,inordertoachieveallthedesiredrequirementsdescribedintheprevioussection,apropersteadystateoutputmodelforeachconvertermustbeadoptedandanalyzed.Inthiswork,eachparalleledconverterismodeledasadependentvoltagesource,togetherwithindividuallineimpedance(simplifiedasalinearresistance)connectingre-spectiveunittotheload.Fig.1showsageneralDPSrep-resentedbythecitedmodel,withtheoutputcurrent,outputvoltage,outputresistanceforthei-thconverterbeingIi,ViandRiandtheloadvoltageandcurrentasVoandIo,respectively.ThroughKirchhoffsvoltagelaw,thevoltagesandcurrentsineachbrancharerelatedtoeachotherinthefollowingmanner:V1I1:R1=V2I2:R2=:=ViIi:Ri=Vo(1)Withtwoconvertersconnectedinparallel,theoutputcurrentsI1andI2aredefinedas:I1=(V1V2):Ro+V1:R2R1:R2+Ro:(R1+R2)(2)Fig.1.Generalmodelofanoutputparallel-connectedDPS.I2=(V2V1):Ro+V2:R1R1:R2+Ro:(R1+R2)(3)Forthreeconvertersconnectedinparallel,theoutputcur-rentforeachconverterisfoundaftersomealgebraicmanipu-lationof(1).Thus,I1=Ro:V1:(R2+R3)V2:R3V3:R2+V1:R2:R3R1:R2:R3+Ro:(R1:R2+R1:R2:R3)(4)I2=Ro:V2:(R1+R3)V1:R3V3:R1+V2:R1:R3R1:R2:R3+Ro:(R1:R2+R1:R2:R3)(5)I3=Ro:V3:(R1+R2)V1:R2V2:R1+V3:R1:R2R1:R2:R3+Ro:(R1:R2+R1:R2:R3)(6)From(2)to(6),itfollowsthatanyoutputcurrentisalsodependentofoutputvoltagesandlineimpedancesfromotherconvertersandeachlineresistancecausesavoltagedropintherespectiveconverter.Knowingtheserestrictionsandthechosenconvertersoutputmodel,apropercontrolstrategymustbedevelopedtovalidatethepowersupplyrequirements.B.LoadanddesignrequirementsTounderstandtheproposedcontroltechnique,theparticu-larrequirementsoftheloadmustbeanalyzed.ForaloadwithvoltagesourcebehaviorsuchasaLightEmittingDiode(LED),astablecurrentisneededtoprovidethedesiredluminousflux14.Thus,thepowersupplymustprovideregulatedcurrentundersteadystateoperationandrejectanycurrentdisturbanceintheoutput.AnLEDdriverisapowersourcedesignedspecificallytointerfacebetweenavoltagesource(eg.mainsvoltage)andaLEDlamp.InsteadofusingasingleconverterasthedriverfortheLEDlamp,agroupofidenticalconvertersweredesignedandtestedinthiswork.Thisworkfocusmainlyonpresentingtheproposedcontrolstrategyforadistributedpowersupplyappliedtoaloadwithvoltagesourcebehaviorandnotontheparticularbenefitsordisadvantagesforthespecificapplication.Giventhoserequirements,themainobjectiveofthedis-tributedpowersupplywiththeproposedcontrolstrategyistosupplyregulatedcurrenttoastreetLEDlightingfixturecomposedby40LuxeonRebelLXML-PWN1-0100LEDsconnectedinseries.AbasiccircuitmodelfortheLED14isusedtodeterminetheoperatingpointofthefixture.Thus,inordertoprovidethedesiredcurrentof0:6Atothelamp,avoltageof126:4Vmustbeappliedtoitsterminals.C.PowerstagedesignGivendesiredrequirementsfortheload,thenextstepintheDPSdevelopmentisthepowerstagedesign.Thewell-knownbuckconvertertopologyoperatingincontinuousconductionmode(CCM)waschosenasthepowerstagestructureforthepowerconverters.Consideringa220Vinputmainvoltageat60HzfrequencyfortheDPS,acontinuouspeakvoltageVinof311Vwasusedastheinputvoltagefortheconverters.ThenominaldutycycleDnomisdeterminedastheratiobetweentheoutputvoltageandtheinputvoltage,whilechosenswitchingfrequencyfsivalueforthepulsewidthmodulation(PWM)unitoftheconvertersis40kHz.TheluminousefficacyofaLEDisdirectlydependentoftheforwardcurrentrippleinthedevice17.Asstatedinthesamestudy,aloadcurrentrippleof50%isusedhereasaparameterforthepowersupplydesign.Therefore,along-lastingLEDdriverwithhighluminousefficacycanbedeveloped,avoidingtheuseofelectrolyticcapacitors.Toimprovereliabilityandmodularity,theDPSmusthaveaminimalnumberofcentralizedcomponents,suchasextracontrollersorsensors.Also,itmustpresentredundancyinthecaseofoneormoreconvertersfail,bymakingtheremainingunitsassumethepowershareproducedbythedefectiveunits.Therefore,theDPSwillbecomposedbythreeidenticalandindependentoutputparallel-connectedbuckconverters.ForthisDPStopology,theloadcurrentisthesumofthecurrentsofeachconverter.Assumingtheworstcasescenariowherealloutputcurrentsareinphasewitheachother,themaximumcurrentrippleallowedforeachconverter,Ioutmaxiwaschosentobeunder16:67%,resultinginamaximum50%loadcurrentripple.Accordingto14,a9:81%variationoftheoutputvoltagedepicts100%variationinthelampforwardcurrent.Thus,withdesiredIoutmaxiunder16:67%,Voutmaximustbekeptunder1:6353%.Asfollows,thedesignofthebuckconverterswasdoneaccordingto16.ThebuckinductanceLbiandtheoutputcapacitanceCbiwerecalculatedbelow,respectively:Lbi=Vin:Dnom:(1Dnom)fsi:Ioutmaxi(7)Cbi=Vin:Dnom:(1Dnom)8:Lbi:Voutmaxi:(fsi)2(8)D.LocalfeedbackcontrolloopAfterthepowerstagedesign,themaincontrolloopofeachconverterisdeveloped.Inthisloop,atypicalfeedbacktopologyisusedwithoutputvoltagereferencev00refi(s)andmeasuredoutputvoltagevmedi(s).ThecontrollerCvdi(s)providesacontrolsignaluvi(s)aimingtominimizetheerrorverri(s).Also,ineachconvertersoutputacurrentfilterHii(s)isemployed.Thetransferfunctionofthedesignedbuckconverter,Gvi(s),isshownbelowin(9):Gvi(s)=Vouti(s)Di(s)=VinLbi:Cbis2+1Rlamp:Cbi:s+1Lbi:Cbi(9)whereRlampisthedynamicresistanceofthelampforchosenconfigurationandoperatingpoint.ThefrequencyresponseofGvi(s)isshowninFig.2below.Theplantexhibitsanstableopenloopresponsewith80:2degreesofphasemarginat55:1kHzandinfinitedBsofgainmargin.Fig.2.Bodediagramfortheoutputvoltageplantofthebuckconverter.Aproportional-integral-derivative(PID)compensatorwasdesignedinMATLABSISOToolRsoftwareandemployedforeachconverter,withtransferfunctionCvi(s)statedin(10).Aphasemarginandgainmarginhigherthan60degreesand40dB,repectively,wereconsideredasrequirementsforthecontrollerproject.Cvi(s)=0:0041772:(s+52:84):(s+1097)s:(s+265:9)(10)FrequencyresponseoftheclosedloopbuckconverterwithdesignedcontrollerisdepictedinFig.3below.Againmarginof62:9dBat18kHzandaphasemarginequivalentto86:9degreesat222Hzwereobtained.Fig.3.Frequencyresponseoftheclosedloopconverter.Fig.4.Improveddroopcontrolstrategyschematic(i-thconverterwithplantmodelGvi(s).E.ConventionaldroopcontroldesignTominimizethecurrentsharingerrorbetweenconvertersconnectedwiththeiroutputsinparallel,theconventionaldroopcontroldesignisfirstapplied.TheoutputfromHii(s),togetherwithdroopgainkdri,providesasignalvdri(s)usedtoadjustthevoltagereferencev0refi(s)inthemainloopfortherespectiveconverter.Thedroopgainvalues(kdri=1)werechosentodisplaythedroopcontrolfunctionality.Forthebestcurrentsharingaccuracyandoverallsystemsstability,thosegainscanbesettodistinctvalues.F.ImproveddroopcontroldesignFortheproposedcontrolstrategy,anextrafeedbackloopisaddedtotheconventionaldroopcontrolstrategyformerlydesigned.AcurrentsensorHiload(s)isusedthemeasureandfiltertheloadcurrentiload(s),thusprovidinganerrorierri(s)betweenfilteredloadcurrentifiltload(s)andloadcurrentreferenceirefload(s).ThiserrorisfedtoacurrentcontrollerCii(s),whichprovidesanoutputuii(s)designedtoadjustthevoltagereferencevrefi(s)inthemaincontrolloop.Inthisway,whenthelampcurrentisnotequaltothedesiredreference,eachconvertersvoltagereferenceisindi-viduallyadjustedbytherespectivesignaluii(s).Therefore,anyvoltagedropthatmayoccurbetweenthemainvoltagebusandtheoperatingconvertersiscompensatedwithoutharmingthedecentralizedcurrentsharingmodeprovidedbytheconventionaldroopcontrolstrategy.Thecompletediagramblockoftheimproveddroopcon-trolloopforoneconverterisshowninFig.4.ThecurrentcontrollerCii(s)mustminimizetheerrorierri(s),thusaintegralcompensationwasdesignedtoachievethisgoal.Thetransferfunctionofthiscontrollerisdepictedin(11).TableIpresentsdesignedcontrolandcircuitparameters.Low-passfiltersHii(s),Hvi(s)andHilamp(s)wereusedtominimizethehighfrequencycontentofthemeasuredvariables.Cii(s)=200s(11)TABLEI.DPSPARAMETERS.ComponentSpecificationValue1.DC-DCConverter.LbiBuckinductor11.3mHCbiBuckcapacitor31.856FRiLineresistances0.5,1.0,1.5LbiBuckinductor18.3mHCbiBuckcapacitor4.7pFRiLineresistances0.5,1.0,1.5fsiSwitchingfrequency40kHzVinInputpeakvoltage311V2.Load.nLEDNumberofLEDsinthelamp40VfLEDForwardvoltageofLED2.85VRLEDDynamicresistanceofLED0.5166RlampDynamicresistanceoflamp20.6643.Mainloopcontroller.vrefiOutputvoltagereference126.4VCvi(s)VoltagecontrollerEq.(10)4.Referenceadjustmentblock.irefloadOutputcurrentreference0.6ACii(s)CurrentcontrollerEq.(11)kdriDroopgains14.1.Low-passfilters(Hii(s),Hvi(s)andHilamp(s).fclpfiCutofffrequency4kHzklpfiFiltergain1Comparedtotheconventionaldroopcontrolstrategy,theimprovedcontrolloopproposedinthisworkrequiresonlyanextrafeedbackloopineachconverterandasinglecurrentsensorlocatedintheload.Thecurrentsensormustbroadcastthemeasuredloadcurrentforallconverterspresentinthepowersupplyforpropercurrentregulation.IV.SIMULATIONRESULTSToprovethefeasibilityoftheproposedcontrolstrategy,simulationsresultswereobtainedinsoftwarePSIMRforthedesignedDPSfeedingtheLEDlamp.OnebuckconverterwithitsimproveddroopcontrolloopandthefulldistributedpowersupplyfeedingthelampareshowninFigs.5and6,respectively.Fig.5.OnebuckconverterandproposedcontrolschematicinPSIMR.Fig.6.DistributedpowersupplyfeedingandtheLEDlampfixtureinPSIMR.StartupbehavioroftheconvertersandloadcurrentforthedistributedpowersupplyemployingonlylocalvoltagecompensationareshowninFig.7.Consideringtheimbalanceamonglineresistances,thecurrentsharingbetweenconvertersispenalizedbythelackofdedicatedcurrentcontrolineachunit.Fig.7.Outputcurrents(startup)fortheDPSwithoutcurrentsharingcontrolinPSIMR.Now,steadystatecurrentbehavioroftheDPSwithoutcurrentsharingcontrolareshowninFig.8.Sinceonlyavoltageloopcontrolisusedperconverter,eachunitcannotcompensateforthevoltagedropcausedbyindividuallineresistances,therebycompromisingindividualandloadcurrentregulation.Fig.8.DPSoutputcurrents(steadystate)fortheDPSwithoutcurrentsharingcontrolinPSIMR.ShowninFig.9,enablingtheconventionaldroopcontrolbranch(localoutputcurrentmeasurement)int=0.4sdepictsthechangesincurrentsbehaviorfortheDPS.Thecurrentdeviationbetweenconvertersisminimizedatthecostofpoorerloadcurrentregulation.Fig.9.Enablingconventionaldroopcontrolloop(t=0.4s)andoutputcurrentbehaviorforthesupply.Providedaloaddisturbance(oneLEDshort-circuitedatt=0.4s)intheDPSwithconventionaldroopcontrol,transientbehaviorofoutputcurrentsaredepictedinFig.10.Aspredicted,thepowerconverterscannotregulatetheiroutputcurrents,causingasevereincreaseinthelampcurrent.Fig.10.ShortcircuitofoneLEDatt=0.4sasloaddisturbanceforoutputbehavioranalysisoftheDPS(withconventionaldroopcontrol).InFig.11,outputstartupbehavioroftheconvertersandloadcurrentforthedistributedpowersupplyemployingtheim-proveddroopcontrolstrategyareshown.Thecontrolstrategyprovidesdesiredstartupforthedistributedpowersupplyandsimultaneouslyminimizescurrentsharingdeviationbetweenconverters.Fig.11.DPSoutputcurrents(startup)forimproveddroopcontrolimple-mentationinPSIMR.Next,steadystateofpowersupplycurrentsaredetailedinFig.12.Itcanbeobservedthattheextracurrentloopineachconvertercompensatesforthevoltagedropacrossrespectivelineresistance,providingcurrentregulationwhilestillmaintainingdesiredmodularityforthesystem.Fig.12.DPSoutputcurrents(steadystate)forimproveddroopcontrolimplementationinPSIMR.Here,oneLEDisshort-circuitedatt=0.8storepresentaloaddisturbanceinthesystem.ThecurrentwaveformsareshowninFig.13.Theimprovedcontrolloopisabletorejectthedisturbance,thusmakingthecurrentstrackpropervaluessothattheloadcurrentremainsatthedesiredmagnitude.Fig.13.ShortcircuitofoneLEDasloaddisturbanceforoutputbehavioranalysisoftheDPS(withimproveddroopcontrol).InFig.14,outputcurrentsbehaviorisshownwhencon-verter3isturnedoffatt=0.8s.Theremainingconvertersinoperationprovidecurrents(withmagnitudesclosetoeachother)fortheloadwhileassumingtheoutputcurrentcapabilityofthedisconnectedconverter.Fig.14.ThirdconvertershutdownforredundancyanalysisoftheDPS(withimproveddroopcontrol).V.CONCLUSIONSInthiswork,acontrolstrategyaimingloadcurrentsharingfordistributedpowersupplieswaspresented.Fortheproposedstrategy,anextracurrentfeedbackloopwasemployedineachconvertertoa