Table Of ContentHIGH-ORDERLINEARIZINGPULSEWIDTHMODULATOR
FORTHREE-PHASEPOWERCONVERTERS
BY
JUNCHEN
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
2000
ACKNOWLEDGMENTS
Iwouldliketoexpressmydeepestgratitudetomyresearchcommittee
chairman,Dr.KhaiD.T.Ngo,forwelcomingmetothepowerelectronicsgroup
attheUniversityofFlorida. Heprovided constantsupportandencourage-
mentformystudyandresearch.Ilearnednotonlytheknowledgeofpower
electronics,butalsoaworkattitudethathasgreatlyreshapedmycareer.I
alsowishtothankDr.DennisP.Carroll,Dr.AlexanderDomijan,Dr.Vladimir
A.Rakov,andDr.LocVu-Quocfortheirparticipationonmyresearchcommit-
tee.
IamverygratefultoAmericanResearchCorporationforitsfinancial
supportandprojects,andalsoTexasInstrumentsforaTIfellowship.
Myspecialthanksgotomycolleagues,JunXuandPaiboonNakmah-
achal,fortheirhelpfuldiscussionsandsuggestionsinmyprojectanddisserta-
tion.
Thereisnowordformetodescribemygratitudetomywife,YinXie,
whospenthertimetakingcareofourfamilywhenIwasworkingatthelab
dayandnight.Withoutherhelpandpatience,Iwouldnotknowhowtofinish
myresearchanddissertation.
ii
TABLEOFCONTENTS
pages
ACKNOWLEDGMENTS
ii
ABSTRACT v
CHAPTERS
1 INTRODUCTION 1
2 MODELINGANDANALYSISOFTHREE-PHASECONVERTERS 10
2.1 DerivationofState-SpaceEquationsofPWMConverters 11
2.2 EquivalentCircuitintheABCCoordinates 20
2.3 ABC-OFBTransformation 26
2.4 EquivalentCircuitintheOFBCoordinates 28
2.5 GraphicalSteady-StateAnalysis 36
2.6 GraphicalSmall-SignalAnalysis 38
3 REVIEWOFPULSEWIDTHMODULATION 44
3.1 PulsewidthModulationforDCConverters 44
3.2 PulsewidthModulationforThree-PhaseConverters 48
3.3 SynthesisofContinuousSinusoidalPulsewidthModulation 55
3.4 SynthesisofSpace-VectorModulation 57
4 HIGH-ORDERLINEARIZINGPULSEWIDTHMODULATOR 62
4.1 First-OrderLinearizingPulsewidthModulator 63
4.2 NonlinearProbleminThree-PhaseConverters 66
4.3 Large-SignalLinearizationofPWMConverters 69
4.4 LinearizationbyFirst-OrderLPWM 72
4.5 LinearizationbyHigh-OrderLPWM 80
5 ANALYSISOFHIGH-ORDERLINEARIZING
PULSEWIDTHMODULATOR 97
5.1 AnalysisofHigh-OrderLinearizingPWM 98
5.2 SamplingEffectsinHigh-OrderLPWM 107
iii
6 IMPLEMENTATIONANDEXPERIMENTALRESULTSOF
HIGH-ORDERLINEARIZINGPULSEWIDTHMODULATOR 116
6.1 AnalogImplementationofHigh-OrderLPWM 118
6.2 ExperimentalResults 135
6.3 PracticalIssuesinExperiment 145
7 SUMMARYANDCONCLUSION 151
REFERENCES 155
BIOGRAPHICALSKETCH 162
iv
AbstractofDissertationPresentedtotheGraduateSchool
oftheUniversityofFloridainPartialFulfillmentofthe
RequirementsfortheDegreeofDoctorofPhilosophy
HIGH-ORDERLINEARIZINGPULSEWIDTHMODULATOR
FORTHREE-PHASEPOWERCONVERTERS
By
JunChen
August2000
Chairman:Dr.KhaiD.T.Ngo
MajorDepartment:ElectricalandComputerEngineering
Thefeasibilityofusingananalogpulsewidthmodulator(PWM)tolin-
earize balanced three-phase converters is investigated in this dissertation.
Prototypecircuits,models,andanalysistechniquesaredeveloped.
Mostbalancedthree-phasePWMconvertersthatarecontrolledbythe
conventionalanalogPWMshavenonlinearrelationshipsbetweenthecontrol
andoutputvoltages/currents.Thisstudyshowsthatthesenonlinearrelation-
shipscanbelinearizedbyananaloghigh-orderlinearizingpulsewidthmodu-
lator(LPWM)thatmakestheoutputvoltagetrackthecontrolvoltagelinearly.
Insteadofmultipliers/dividers, thehigh-orderLPWMusesonlyintegrators
withthereset, andsample/holdstocomputetheswitchinginstantsforthe
switchesintheconverter.TheinputstotheintegratorsoftheLPWMarejust
linearfunctionsofthecontrolandstatevariables,butarenonlinearfunctions
whenotheranalogPWMs,suchasfeed-forwardPWMsandone-cyclecontrol-
lers,areused.
Theanaloghigh-orderLPWMis synthesizedfromswitching-function
averaging(SFA)equationsofthethree-phasePWMconverter.Thankstothe
SFAmodelofthePWMswitch,thederivationofSFAstate-spaceequationsof
theconverterissimplydonebyinspectionandapplicationofdefinitionofcir-
cuitelements,KirchhofTslaw,andotherelectricalprincipleswithoutprobing
intotopologicaldetailsoftheconverter.ThesetofSFAequationscanbetrans-
formedintoanequivalentcircuitinthestationarycoordinatestomakesimu-
lationmoreefficient.
Inordertoanalyzethree-phaseconvertersthatarecontrolledbythe
LPWMorotherpulsewidthmodulationtechniques,allthree-phasecomponent
modelsintherotatingcoordinates,includingPWMswitches,sources,andpas-
sivecomponents, aredeveloped.Afterthree-phasecomponentsarereplaced
bytheirmodelsintherotatingcoordinates,thetime-variantthree-phasecir-
cuitistransformedintoatime-invariantequivalentcircuitthatmakesanaly-
sis and design much easier. The model of the high-order PWM is also
developed.ItisusefultoanalyzetheLPWM-controUedconverterandevaluate
timedelaycausedbysamplingeffects.
Thesynthesisandanalysistheoriesofthehigh-orderLPWMareveri-
fiedbya1KWprototypeofathree-phaseboostinverter.Bothsimulationand
experimentalresultsagreewiththeanalysis.Theexperimentalresultsshow
thatthecontrolcircuitissimple,andtheoutputvoltagesoftheinvertercan
vi
trackthe controlvoltages linearly, and theyhave low-distortion sinusoidal
waveforms.
Insummary,theS5nithesisandanalysistechniquesaredevelopedfor
linearizationofathree-phaseboostinverterinthedissertation.Asgeneral
methods,theycanbeappliedtootherthree-phasetopologies,multi-phaseor
multi-levelconverters.
vii
CHAPTER1
INTRODUCTION
Withthe developmentofhigh-speed,high-powersemiconductors, the
switchingpowerconverterhasgraduallyreplacedlinearpoweramplifiersto
become the main power conversion product on the market. The switching
powerconverternotonlyprovidesmoreefficientpowerconversionthanthe
linear power converter, but also has more flexible control capability that
allows the converter to meet various power demands and requirements.
Therefore,researchonswitchingpowerconvertershasreceivedmuchatten-
tion.Amajorresearchissueisthelinearizationofswitchingpowerconverters
thatmakesthecontrolledvariabletrackthecontrolsignalandimprovethe
performanceoftheconverter
Abasicswitchingpowerconverterconsistsoftwosections,asshownin
Figure1-1.Thefirstsectioniscalledthepowerstagethatusuallyconsistsof
semiconductor switches and energy storage components. The power stage
receivestheunregulatedenergyfromtheutilitypowerlineorpowerconvert-
ersandprovidestheregulatedenergytocustomerloads.Thesecondsectionis
themodulatorthatprovidescontrolsignalstothepowerstage.
1
2
UTILITYLINES POWERSTAGE CUSTOMER
OCORNVERTERS (switches,inductors, ^— LOADS
andcapacitors)
HIGH-FREQUENCY MODULATOR CONTROL
CARRIER (analog,orDSP SIGNALS
circuits)
Figure1-1 Abasicswitchingpowerconverter.
The modulator can be implemented by analog and digital means,
dependingontherequirements,complexity,andcostsinconverterdesign.The
digitalmodulatorisusedmostlyinthree-phaseconverterssinceithasmore
computationcapability.However,whentheswitchingfrequencyisincreased
bysizeandweightrequirements,thedigitalmodulatorwillbelimitedbyits
clockspeed.Meanwhile,whenthereferencevoltagedoesnotchangesmoothly,
thesample/holdcircuitwiththedigitalmodulatorwouldberestrainedbyres-
olution.Incontrast,theanalogmodulatorismuchfaster,anditcanhandle
anyfrequency,limitedonlybythecapabilityofpowerstage[1].
Aconventionalpulsewidthmodulator(PWM),asshowninFigure1-2,
consistsofacomparator,arampcarriersignalv^^ip,andacontrolsignalv^.
Thecarriersignalprovideshigh-switchingfrequencytothecontrolsignaland
totheswitches intheconverter. The control signalisfollowedbythecon-
trolledvariables,suchasoutputvoltages.IntheconventionalPWM,thecar-
rier signal has a constant slope. The control signal is compared with the
3
Figure1-2 AconventionalPWM.
carriersignalthroughthecomparator.TheoutputpulseVp(alsocalledswitch-
ingfunction),generatedbythecomparator,isusedtodrivetheswitchinthe
converter.Ithasthedutyratioof
(1.1)
whereVj^istheamplitudeoftherampVj^up.
The output signal Vp determines the switchingpatterns ofthe con-
verter.Thecontrolledvariableoftheconverter,suchastheoutputvoltage,is
thefunctionoftheconverterinputanddutyratioofVpthatisdeterminedby
Equation(1.1).Therefore,thecontrolledvariableoftheconvertercanberegu-
latedbyadjustingthecontrolsignal.
ThepowerstageinFigure 1-1couldbethedc-dcconverterinthedc
powerconversionorthethree-phaseconverterinthree-phaseacpowercon-
version.ThemostpopulardcconvertersareshowninFigure1-3.Theconver-
sionratiosbetweentheoutputandinputvoltagesarelistedinTable1.1.The
single-phaseconvertersanddcconverterswiththetransformerisolationare
