Three phase PWM boost-buck recti

滑膜控制

ThreePhasePWMBoost-BuckRecti erswithPowerRegeneratingCapability

DepartmentofElectricalandComputerEngineering

UniversityofWisconsin–Madison

1415EngineeringDriveMadison,WI53706-1691USA

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JunKikuchiThomasA.Lipo

-+

-+

Abstract—ThreephasePWMboost-buckrecti erswithpowerregeneratingcapabilityareinvestigated.TheconvertersunderconsiderationarecapableofI)bothvoltagestep-upandstep-down,II)bidirectionalpowerprocessing,andIII)almostunitypowerfactoroperationwithnearlysinusoidalaccurrent.Expectedadvantagesare1)applicabilitytolowervoltageappli-cationse.g.directretro ttoreplacediodeorthyristorrecti ers,2)switchinglossreductionintheinverterload,3)loworderharmoniccontrolintheinverterloadoutputvoltage,4)blankingtimee ectmitigationintheinverterload,and5)amodestlevelofvoltagesag/swellcompensation.

Inthispaper, rstly,astep-by-steppowerstage

´derivationprocessisdescribed.Then,takingtheCuk-´Cukrealizationasanexample,itsoperatingprinci-pleandmodulationschemearedescribed.Steady-satemodelanddynamicmodelforcontrollerdesign

arealsodescribed.Representativeresultsofcircuitsimulationsandhardwareexperimentsarepresented.Throughtheseprocedures,thefeasibilityofthepre-sentedthreephasePWMboost-buckrecti erwithpowerregeneratingcapabilityisdemonstrated.

ofvoltagesag/swellcompensationispossible.

Inthefollowingsections,apowerstagetopologyderiva--tion,operatingprincipleandmodulationscheme,steady--++

stateanddynamicmodelingforcontrollerdesign,andrepresentativeresultsofcircuitsimulationsandhardwareexperimentsarepresented.

+

II.PowerStageTopologies

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+

I.Introduction

Theactiverecti erfront-endofaPulseWidthMod-ulated(PWM)inverterdrivehasbeenattractingin-creasedattentionduetoincessantlygrowingpowerqual-ityconcerns[1],[2].AgreatamountofworkhasalreadybeendoneconcerningthethreephasePWMboostrecti er[3],[4],[5],[6],[7],andthebuckrecti- er[8],[9],[10],[11],[12].Theboost-buckbasedac-tiverecti erhas,however,notyetbeenfullyinvestigated.Althoughseveralthreephaseboost-buckrecti ershavebeenreportedthusfar[13],[14],[15],noneoftheseo erspowerregeneratingcapability.Althoughreference[16]hasshownapossibletopology,nospeci cdescriptionofitsoperationhasbeenpresented.

Inthispaper,threephasePWMboost-buckrecti erswithpowerregeneratingcapabilityarediscussed.TheconvertersunderfocusarecapableofI)bothvoltagestep-upandstep-down,II)bidirectionalpowerprocessing,andIII)almostunitypowerfactoroperationwithnearlysi-nusoidalaccurrent.Expectedadvantagescomingfromthesecapabilitiesare1)applicabilitytolowervoltageap-plications,e.g.directretro ttoreplacediodeorthyristorrecti ers,2)switchinglossreductionintheinverterload,3)loworderharmoniccontrolintheinverterloadoutputvoltage,and4)blankingtimee ectmitigationinthein-verterload,bydecreasingthedclinkvoltagedependingontheoperatingcondition.Inaddition,5)amodestlevel

´´Fig.1.DerivationofCuk-Cukbidirectionalac-dc

converter

Fig.2.DerivationofSEPIC-Zetabidirectionalac-dcconverter

Fig.1andFig.2illustratepowerstagederivationoftwothreephaseac-dcboost-buckbidirectionalpowerconvert-ers.TheirbuildingblocksarethreephaseVoltageSti Converter(VSC)andboost-buckbasedbidirectionaldc-dcconverters.

0-7803-7116-X/01/$10.00 (C) 2001 IEEE

滑膜控制

diLaca

rectification

~~

jωeLacIa

inversion

(a)Per phase fundamentalcomponent equivalentcircuit for steady-state

(b) Per phase phasor diagrams for unity power factor operation (δ is power angle and ω is ac souce angular frequency)e

Fig.3.Simpli edperphaseequivalentcircuitandphasordiagramsforunitypowerfactoroperation

Thereexisttwoboost-buckbaseddc-dcconverters,

´namelytheso-calledCuk[17]andtheSingleEndedPri-maryInductorConverter(SEPIC)[18].Atthetopof

Fig.1andFig.2areshownthesetwodc-dcconvert-ers.Theycanbemadebidirectionaldc-dcconvertersbyaddingananti-paralleldiodetotheactiveswitchandananti-parallelactiveswitchtothefreewheelingdiode.Thismodi cationisshowninthemiddleofthese gures,wherethereactivecomponentsoriginallyonlyontheupperrailaresplitintotheupperandlowerrails.Althoughthesplittingofthereactivecomponentsdoesnotmakeanychangefromdi erentialmodebehaviorviewpoint,itisexpectedtohaveacommonmodeElectro-MagneticIn-terference(EMI)suppressione ectbecauseoftheirsym-´metricalstructure.ItmaybenotedthattheCukbased´bidirectionaldc-dcconverterappearstobeaCukcon-verterfrombothsidesbuttheSEPICbasedbidirectional

dc-dcconverterisseentobeaSEPIConlyfromtheleftsideandappearsasaZeta[19]fromtherightside.Thesebidirectionaldc-dcconverterscanbemadeac-dcconvert-ersbyreplacingtheiractiveswitch/diodepairontheleftsidewithathreephaseVSCbridgeasshownatthebot-´´tomofthe gures.Inthefollowing,theCuk-Cukreal-izationwillexclusivelybediscussedduetothelimitof

space.

-Similarpowerstagederivationispossiblefromthree+

phasecurrentsti converterandbuck-boostbasedbidi-rectionaldc-dcconverters.Thisalternativeiscurrentlyunderinvestigationbytheauthors.

III.OperatingPrincipleandModulationSchemeWhetherduringrecti cationorinversion,sinusoidalcurrentshapingcanbereducedtoavoltagecontrolinwhichthecontrolledvoltagesource(recti er/inverter)isconnectedtoanacsourcethroughaninductanceasshowninFig.3(a).Thefundamentalcomponentphasordia-gramsforunitypowerfactorrecti cationandinversionareshowninFig.3(b).Thedesiredconverteractermi-nalvoltagecanbede nedasthehypotenuseoftherighttrianglecomposedofthreevoltagephasors.Themodula-tionschemeisthendiscussedfromtheacterminalvoltagesynthesisandpowertransferviewpoint.A.Recti erOperation

Fig.4showsthepowerstageschematicforthepurposeofrecti eroperationanalysis.ThefollowingdiscussionsarebasedonthenotationinFig.4.Theoperatingprin-cipleoftheboost-buckbasedrecti cationhasbeenpre-

vccLoadLoad

ccdc´´Fig.4.Cuk-Cukbidirectionalac-dcconverterforanalysisof-+recti eroperation

sentedin[14]and[15].Ithasbeenmadeclearinthese

referencesthenecessityofbridge-leg-shortrealizedasun-conventionalzerovoltagespacevectorstomakepowertransferhappen.Avarietyofzerovoltagespace-+such

vectorscanbeclassi edintothreegroups,viz.theone-leg-short,two-leg-shortandthree-leg-shortzerovoltagespacevectors[14].Inthispaper,takingintoaccountatrade-o betweenaverageswitchingfrequencyandcur-rentcarryingcapabilityrequiredintheswitchingdevices,thetwo-leg-shortzerovoltagespacevectorsareselectedasareasonablecompromise[20].

Fig.5illustratesthemodulationschemeandthepowertransferfromtheacsourcetodcloadduringonetri-

>vacb>vaccisas-anglecarrierperiod,wherevaca

sumedintherecti eracterminalvoltagecommandandia>0>ib>icisassumedinthethreephaseaccurrent.Oncetheoperatingprincipleinthisparticularconditionisunderstood,alltheotherpossibleoperatingconditionscanreadilybederivedwiththesamemanner.Immedi-atelybelowthetrianglecarrierwaveform,vcarrier,areshownthewell-knownboostrecti erswitchingfunctionsforreferencepurposes.

InFig.5(a),switchingfunctionsHa～Hcandgatepulsesg1～g6arethesamebetweentheconventionalboostrecti erandtheboost-buckrecti erduringthein-tervalsinwhichactivevoltagespacevectorsareusedasdenotedasintervalxandy.

Themostsigni cantdi erencefromtheconventionalboostrecti erisinintervalzduringwhichzerovoltagespacevectorsareapplied.Byturningonbothoftheupperandlowerswitchesinaphaseleg,acouplingcapacitordis-chargingcurrentpathisestablished,therebypowertrans-ferfromthecouplingcapacitorstothedcloadisrealized.SincediodeD7isnaturallyturnedo ,shoot-throughfail-

滑膜控制

vcarrier*=vaca*=vacbvacc*=

1vccmcos(ωe t - δ)

2π)vccmcos(ωe t - δπ)vccmcos(ωe t - δHa_bst=g1bst=4bstconventional

boost rectifier

Hb_bst=g3bst=6bst

switching functions

Hc_bst=g5bst=2bstand gate pulsesH1=g1H4=g4H3=g3H6=g6H5=g5H2=g2

g7

intervalx

yzy

x

z

Ha=H1-HzHb=H3-HzHc=H5-HzHza_bstHc_bst

boost-buck rectifiergate pulses

(phase b and c leg short zero voltage space vector)

boost-buck rectifierswitching functions

(a)PWMschemeforrecti cation

(b)Powertransferillustration

+´´Fig.5.PWMschemeandpowertransferillustrationofCuk-Cukac-dcconverterforrecti cation-vcarrier*=vaca*=vacbvacc*=

1vccmcos(ωe t - δ)

2π)vccmcos(ωe t - δπ)vccmcos(ωe t - δHa_bst=g1bst=4bstconventional

voltage stiff converter

Hb_bst=g3bst=6bst

switching functions

==Hc_bstg5bstand gate pulsesH1=g1H4=g4H3=g3H6=g6H5=g5H2=g2H7=g7

intervalxyz7yx

z0

Ha=H1-H5Hb=H3-H5Hc=H5-H5Hza_bstHc_bst

boost-buck invertergate pulses

boost-buck inverterswitching functions

(a)PWMschemeforinversion(b)Powertransferillustration

´´Fig.6.PWMschemeandpowertransferillustrationofCuk-Cukac-dcconverterforinversion

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uredoesnotoccurinthephaseleg.ThecorrespondingcurrentpathsaredepictedatthebottomillustrationofFig.5(b).Sincethetwo-leg-shortzerovoltagespacevec-torischosenhere,twophasescarryingnegativecurrents,phasebandc,aretheleg-shortphases.Iftheaccur-rentrelationisia>ib>0>ic,phaseaandb,arethe

¯2=0inphasec.Thatis,leg-shortphasesandg5=g

twophasessharingthesameaccurrentsignaretheleg-shortphasesforthezerovoltagespacevectorintervalandtheupperswitchintheremainingphaselegstayson(o )andthelowerswitchstayso (on)throughoutthecarrierperiodifitsaccurrentispositive(negative).B.InverterOperation

Ininverteroperation,thenecessaryphase-leg-shortisnaturallyrealizedthroughanti-paralleldiodesinthethreephasebridge.Accordingly,thesamegatepulsesasintheconventionalVSCcanbeapplied.Ontheotherhand,theswitchonthedclink,S7,mustactivelyoperate.Fig.6illustratesthemodulationschemeandpowertransferfromthedcsourcetoacloadduringonetrianglecarrierperiod,

>vacb>vaccisassumedinthethreephasewherevaca

bridgeacterminalvoltagecommandandia<ib<0<icisassumedinthethreephaseaccurrent.Inaddition,|iLdc|>|ic|=|ia|+|ib|isassumed.

Duringtheintervalsinwhichactivevoltagespacevec-torsareused,asinintervalxandyinFig.6,thesituationisbasicallythesameasintherecti eroperationexceptthedirectionsoftheloadcurrent,dcinductorcurrent,andpowertransfer.Duringtheseintervals,theenergystoredinthecouplingcapacitorisdischargedthroughthethreephasebridgetotheacload.

Duringtheintervalsinwhichzerovoltagespacevec-torsareused,asinintervalzoandz7inFig.6,theactiveswitchonthedclinkisturnedo ,andthecouplingca-pacitorischargedwithiLdc.Since|iLdc|>|ic|=|ia|+|ib|isassumed,theamountof|ic|iniLdc owsthroughtheacloadandtheextraamount,|iLdc| |ic|, owsthroughnaturallyshortedphaselegsviatheiranti-paralleldiodesasillustratedatthetopandbottomofFig.6(b).If|iLdc|islessthanthecurrent owingthroughtheacload,theextraamountofaccurrent owsthroughanactivedeviceinthebridgeandthecontinuityofcurrent owismain-tained.Suchanactivedeviceisoneofthelowerdevicesforintervalz0oroftheupperdevicesforintervalz7.Itmaybenotedthat,althoughthegatepulsesinthethreephasebridgearethesameasthoseoftheconven-tionalVSC,thezerovoltagespacevectorrealizedhereareagainunconventionalonesbecauseofthephase-leg-shortthroughanti-paralleldiodes.

IV.ModelingandAnalysisforControllerDesignTheanalyticalmodelderivationisbasedonthepowerstageschematicshowninFig.4wheretheidealswitchesandzeroEquivalentSeriesResistance(ESR)intheca-pacitorsareassumed.Thefollowingmatrix-vectorformofequationcanbederivedfromasetofdi erentialequa-tionswiththeassumptionofthebalancedthreephasesetofacsourceandthreewiresystem,andapplyingthe

synchronousframed-qtransformation.

dx

=Ax+Bu(1)dt

(2)x=[iqidvcciLdcvdc]Tandu=vq

Rdqac

Lac ωe Lac00

ω Rac dd

00 eLacLac

3dq3dddz(3)A= 2C2C 0 0Cccc Rdcdz

0 L10Ldc Ldcdc

11

000Cdc CdcRLoad

T

0000(4)B=L1ac

wherethearbitrarycoe cientandtheaxesdirectioninthesynchronousframed-qtransformationusedherearefollowingthosein[21]andvd=0duetotheassumptionthataaxisandqaxiscoincide.Inaddition,bytakingthelocaltimeaverage,theswitchingfunctionsarereplacedwiththecorrespondingdutyratio.AsinFig.5,when

>vacb>therecti erisintheoperatingsectorofvaca

vacc,thedutyratiointhesynchronousd-qframecanbeexpressedas

11

(5)dq=mcosδ,dd=msinδ

22√

3

msin(ωet δ)dz= (1 Habst) Hcbst =1 2(6)wheremandδarethemodulationindexandmodulation

displacementangle,orpowerangle,respectively.

Thesametreatmentcanbeappliedtoalltheotherop-eratingsectorsoverafullfundamentalfrequencyperiod.Fig.7showsdutyratio,dq,ddanddzover0≤ωet≤2πforarepresentativevalueofmandδ.Unlikethewell-knownboostorbuckrecti er,evenafterthesynchronousframed-qtransformationandlocaltimeaveraging,thesystemisstilltimedependentfora xedvalueofmandδbecauseofdz,whichcontainsintegermultiplesofthesixthharmonic.TheFourierseriesexpansionofdzis√

dz=1 32π3m

√ ∞1

331(8)[00000]=AoX+BU

滑膜控制

T

dx6nILdcVcc

=Aox6n+00 CcLdc0dz6n(9)dt

(10)Ao=A|dq=Dq,dd=Dd,dz=Dz

wherethecapitallettersofthestatevariablesanddutyra-tiodenotetheirdccomponentandsubscript6ndenotestheirsextuplenharmoniccomponents.Itmaybeseenthatthesteadystatecircuitbehaviorin(9)looksthatofalineartimeinvariantsystemexcitedwithsextuplenfre-quencies.Thisimpliesthatthereactivecomponentselec-tionmustbedonesuchthattheresonancewithsextuplenfrequenciesisavoided.Thisispossiblebysolvingequa-tions(8)and(9).Oncethecircuitparametersandtheoperatingpointaresetup,dcalgebraicequation(8)canreadilybesolvedandacequation(9)canbesolvedwiththephasorcomputationforeachsextuplenfrequencyas

(11)x6n=[j6nωeI Adc] 1Bdz6n

Fig.8showsasolutionexampleof|vcc6n|for360[Hz](n=1)asafunctionofCc.Alltheotherparame-tersarepresentedinthecaption.Itcanbeseenfromthe gurethat30～40[µF]ofCcmustbeavoided.Takingintoaccounthigherfrequencyexcitation(n=2,3,...)andoper-atingpointdependentproperty,itisreasonabletotakea

smallsignalanalysisisnowapplicabletothedcsidemod-elingandthefollowingequationsareobtained.

d xdc

=Adc xdc+Bdc udq(12)dt(15)

whereAdcandBdcareshownatthetopofthenextpage.ThecomplexityinAdcandBdccomesfromthenonlin-earitybetweendq,ddanddzexpressedinequations(5)and(6),andthatindqandddasfunctionsofiqandvccembeddedinequations(1)～(3).Althoughthisdcsidemodelisnotquitephysicallyinsightful,itcanbeutilizedtoobtainthedcvoltagecontrollooptransferfunctionwithanumericaltoolsuchasMatlab.

Fig.9showsrepresentativeopenlooptransferfunc-tionsoftheaccurrentanddcvoltagecontrolforthecon-trolstructureshowninFig.10withoutLoad .Theyareobtainedwithequations(1)～(15)andMatlab.Proportional-Integral(PI)controllersareassumedforboththeaccurrentandthedcvoltagecontrolandtheircontrollergainsaregivenalongwiththeplots.Sincethecross-couplingbetweendandqaxesintheacsideisde-coupled,thebodeplotsofaccurrentcontrolisatypicaloneofthosecomposedofPIanda rstorderphysicalsys-tem.ALowPassFilter(LPF)isassumedtobeonthedcvoltagefeedbackpath,whosecuto frequencyis40[Hz]Thevoltagecontrolbandwidthisabout20[Hz].Thislowbandwidthisnecessarytoavoidunwantedaccurrentam-

xdc=[ vcc iLdc vdc], udq=[ iq id]

TT

Thewell-separatedpolesbetweentheacsideandthedcside,however,makeaquasi-staticdynamicanalysisap-proximationapplicable,namely,theuppertwoandthelowerthreedi erentialequationsexpressedin(1)～(4)canbedealtwithseparately,providedaproperchoiceofthereactivecomponentsbasedonthesteady-stateanaly-sispresentedintheabove.Therefore,thewell-developedaccurrentcontroltechniquesforVSCcandirectlybeap-pliedbecausethedclinkvoltageseenbythethreephasebridge,vcc,canbetreatedasaconstant,Vcc.Thesyn-chronousframecurrentcontroller[22],[23]withd-qde-coupling[7]isusedhereasshownlaterinacontrolblockdiagram.

Thedcoutputvoltagecontrolbandwidthmustbeevenlowerthanthe6thharmonicfrequencyinordertoavoidinputcurrentwaveformdegradationinsteady-state.Not-ingthisrequirement,itbecomesreasonabletoneglectthesextuplenharmonictermsindzwhichexpressthetimedependencyevenwitha xedoperatingpoint.Theusual

Fig.9.Representativebodeplotsofaccurrentcontrol(up-pertrace)anddcvoltagecontrol(lowertrace)open-looptransferfunctions(circuitparametersandoperatingpointaregiveninFig.8andCc=470[µF])

V.CircuitSimulations

AseriesofcircuitsimulationshavebeencarriedoutwithSabersimulationpackage.Thepowerstagecompo-nentparametersandcontrollergainsarethesameasthoseinFig.8andFig.9.Aratedoperationof5[kW]outputpowerand300[V]ofdcoutputvoltagewith230[V]ofacline-to-linevoltageinrmsareassumed.

Fig.10showsacontrolblockdiagramforthesimu-lation.Twophasecurrentsanddcvoltagearesensed

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Adc

=

RacIq Vq

2

Vcc

√

ωeLacIq33qILdcILdc3Iqd√D√D+ 22+D2Cc2+D2Cc2CcVccπDqDqd√d√

RacIq VqωeLacIq133√Dq33√Dd

2+D22+D2VccLdcLdcDz πVccLdc+πDqDq

dd

√

33π

+

3Id2Cc

1

Dz Cc

dc

RLdc

0 L1

dc

(13)

Bdc

2CcDq =

ii31

RacVcc

√33π

√

ILdcILdcqωeLac33√Dd3Iq

√D++2+D2Cc2+D2Cc2CcVccπDqDqdd√√

RacωeLac33√Dd33√Dq

π2+D2Ldc2+D2πLdcDqDq

dd

1

CdcR

Load

Id21+32Cc2CcDd

0 0

1Cdc

(14)

i1

436527

Fig.10.Controlblockdiagramforcircuitsimulation

80.040.0 (A)

(V)

0.0 40.0 80.080.040.0 (A)

(V)

0.0 40.0 80.0

100.050.00.0 50.0 100.0100.050.00.0 50.0 100.0

0.770.775

0.780.785

t(s)

0.790.795

(A)

inversioni_a (A)

rectification

20.010.00.0 10.0 20.020.010.00.0 10.0 20.0

(V) (V)

200.0100.00.0 100.0 200.0200.0100.00.0 100.0 200.0

0.370.375

0.380.385

t(s)

0.390.395

0.4

inversion

rectification

Fig.

11.Simulationresultsforstep-uprecti cation(up-pertrace)andstep-downinversion(lowertrace)withac115[V]line-to-lineinrms,dc300[V]andiLoad=16.7[A],phaseavoltageandcurrentFig.12.Simulationresultsforstep-downrecti cation(upper

trace)andstep-upinversion(lowertrace)withac230[V]line-to-lineinrms,dc150[V]andiLoad=8.4[A],phaseavoltageandcurrent

forthefeedbackcontrolpurposes.Inaddition,inordertoimprovedynamicresponseinthedcvoltagecontrol,loadcurrentiLoadisalsosensedandaddedtotheaccur-rentamplitudereferenceasloadfeedforward.Thecor-nerfrequencyoftheLPFontheloadfeedforwardpathis180[Hz].Changeoverofrecti er/inverteroperationisdeterminedbythesignofi q.Inordertochoosepropertwo-leg-shortphasesforzerovoltagespacevectorsinitsrecti eroperation,threephasecurrentinformationispro-videdtotheregularsampledPWMblock.ThetrianglecarrierfrequencyfortheregularsampledPWMis9[kHz].Strictlyspeaking,thetrianglecarrieramplitudeshouldbeadjusteddependingonthecouplingcapacitorvolt-agevcc,whichisthedcbusvoltageseenbythethreephaseVSCbridge.Thiswouldhoweverintroduceextracomplexityintothecontrolblock,thereforea xedtrian-glecarrieramplitudefortheratedoperatingpoint,i.e.610[V],isusedhere.

Fig.11andFig.12showsteady-statesimulationresultsoffourdi erentoperatingconditions,namelystep-upandstep-downforeachrecti cationandinversion.Itcanbeseenfromthese guresthatalmostunitypowerfactorandnearlysinusoidalaccurrentoperationispossible.ItmaybenotedthattheaccurrentwaveformqualityunderthelightlyloadedconditionofFig.12isdegraded.Thisisbecauseswitchingfrequencyripplecomponentandthelowordernontriplenharmoniccomponentsareincreasedwithrespecttothefundamentalcomponent.Thelatteriscausedbythesextuplenexcitationdescribedinthepre-vioussection.

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M

g1g4

g7

360.0330.0 (V)

300.0270.0240.020.010.0

(A)

0.0 10.0 20.0300.0200.0100.00.0 100.0 200.0 300.030.020.010.00.0 10.0 20.0

v_av_bi_Load

v_dc

i_a (A)

Fig.14.Hardwareexperimentalresultsofsteady-staterec-ti eroperation(uppertrace:step-uprecti cation,A:line-to-linevoltagevac(phaseanglereferencepurposeonly),uppertraceB:phaseBcurrentib10[A/div]withvcdc=150[V],iLoad=9.2[A]andacsourcevoltage58[V]line-to-lineinrms,lowertrace:step-downrecti cationC:line-to-linevoltagevac(phaseanglereference

purpose

(V)

0.280.290.30.31 t(s)

0.320.33

Fig.13.Simulationresultsforsuddenchangefromfullrecti -cationtofullinversion

Asadynamicresponseexample,Fig.13showssimu-lationresultsofasuddenloadchangerequiringchangingoverfromfullratedrecti cationtofullratedinversion.Theloadcurrentdirectionisreversedatabout0.3[sec].Byutilizingloadfeedfoward,thelowbandwidthofthevoltagecontrolloopiswellcompensatedandthedclinkvoltageishardlydisturbed.Alongwiththewaveformsareshownthegatepulsesforswitchesofphasealegandthedclink.Itcanbeseeninthe gurethattheactiveswitchonthedclinkoperatesonlyforinverteroperation.

VI.HardwareExperiments

´´AhardwareprototypeoftheCuk-Cukconverterhas

beenbuiltwiththesamecomponentvaluesasshowninFig.8andFig.9.TheintegratorgainsinthePIcompen-satorforbothaccurrentanddcvoltagecontrolcontrollersarethesameasthoseobtainedfromtheanalysisandusedinthesimulations,i.e.Kii=300andKiv=7asshowninFig.9.Theproportionalgainshavebeen,ontheotherhand,decreasedtoaquarteroftheoriginalvaluesob-tainedfromtheanalysistoreducenoisesusceptibilityinthe netuningprocess.

Fig.14andFig.15showsteady-stateaccurrentwave-formibinfourdi erentoperatingconditions,namelystep-upandstep-downforeachrecti cationand

inver-

Fig.

15.Hardwareexperimentalresultsofsteady-statein-verteroperation(uppertrace:step-downinversion,A:line-to-linevoltagevac(phaseanglereferencepurposeonly),uppertraceB:phaseBcurrentib10[A/div]withvcdc=150[V],iLoad=10.2[A]andacsourcevoltage57[V]line-to-lineinrms,lowertrace:step-upinversionC:line-to-linevoltagevac(phaseanglereferencepurpose

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sion.Sincetheneutralpointisnotaccessible,line-to-linevoltagevac(phaseanglereferencepurposeonly)isover-laid.Themaximumpointofvaccorrespondsto0oofvb.Itcanthenbeseenfromthe guresthatalmostunitypowerfactoroperationhasbeenrealizedinalltheoperat-ingconditions.Aspredictedfromtheprecedingsections,theaccurrentwaveformisrelativelydegradedinlightlyloadedoperations,i.e.step-downrecti cationinFig.14andstep-upinversioninFig.15.

Fig.16showsdynamicresponseinasuddenchangefromrecti cationtoinversion.AlthoughtheoperatingpointisnotthesameasthatinFig.13,asimilardynamicresponseisobserved.Inparticular,dcoutputvoltagevcdcisbarelydisturbedinspiteofthelowbandwidthofthedcvoltagecontrolloopthankstotheload

feedforward.

Fig.16.Hardwareexperimentalresultsofsuddenchangeover

fromrecti cationtopowerregeneration(traceA:gatepulseforS35[V/div],traceB:gatepulseforS75[V/div],traceC:dcoutputvoltagevcdc50[V/div],traceD:phaseBcurrentib5[A/div]withacsourcevoltage116[V]line-to-lineinrms)

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