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Topic5:Two-levelvoltagesourceinverter1VDM5000Two-levelVSITopic5:Two-levelvoltagesourceinverter2•SinusoidalPWM•SpacevectormodulationLectureContentsBipolarSPWMforFullBridgeInverters3Topic5:Two-levelvoltagesourceinverter4WhyUsePWMTechniques?•Tocontrolinverteroutputfrequency(fundamental)•Tocontrolinverteroutputvoltage(fundamental)•TominimizeharmonicdistortionSinusoidalPWM5InverterConfigurationAssumption:dccapacitorverylargedcvoltageripplefreeSinusoidalPWM6ModulatingandCarrierWaves•vcr–Carrierwave(triangle)•vm–Modulatingwave(sine)•Amplitudemodulationindex•FrequencymodulationindexSinusoidalPWM7GateSignalGenerationvg1andvg4arecomplementary.SinusoidalPWM8Line-to-LineVoltagevABSinusoidalPWM9WaveformsandFFT•ma=0.8,mf=15,fm=60Hz,fcr=900Hz•Switchingfrequencyfsw=fcr=900HzSinusoidalPWM10HarmonicContent•Loworderharmonicsn<(mf-2)areeliminated•VAB1versusmaislinear•VAB1,max=0.612

VdSinusoidalPWM11Over-Modulation•Fundamentalvoltage↑•Low-orderharmonics↑SinusoidalPWM12ThirdHarmonicInjectionPWM•-Fundamentalvoltageincreased•-Noloworderharmonicsproduced•3rdharmonic–zerosequence(toappearinvANandvBN)•NotriplenharmonicsinvAB(vAB=vAN-vBN)SpaceVectorModulation13SwitchingStatesSpaceVectorModulation14SwitchingStates(Three-Phase)•EightswitchingstatesSpaceVectorModulation15SpaceVectorDiagram•Activevectors:to(6,stationary,notrotating)•Zerovector:(2)•Sixsectors:ItoVISpaceVectorModulation16SpaceVectors•Three-phasevoltages(1)•Two-phasevoltages(2)•Spacevectorrepresentation(3)

(2)(3)(4)whereSpaceVectorModulation17SpaceVectors(example)•Switchingstate[POO]S1,S6andS2

ON

and(5)(5)(4)(6)Similarly,

(7)

SpaceVectorModulation18ActiveandZeroVectors•ZeroVector:1•Redundantswitchingstates:[PPP]and[OOO]SpaceVectorModulation19ReferenceVectorVref•Definition

•Rotatinginspaceatω(8)•Angulardisplacement

(9)

SpaceVectorModulation20RelationshipBetweenVrefandVAB•Vrefisapproximatedbytwoactiveandazerovectors•Vrefrotatesonerevolution,VABcompletesonecycle•LengthofVrefcorrespondstomagnitudeofVABSpaceVectorModulation21DwellTimeCalculation•Volt-SecondBalancing

(10)•Ta,TbandT0–dwelltimesforand•Ts–samplingperiod•Spacevectors

and(11)(11)(10)(12)

SpaceVectorModulation22DwellTimeSolve(12)

(13)

SpaceVectorModulation23VrefLocationversusDwellTimesSpaceVectorModulation24ModulationIndex(15)

(16)

SpaceVectorModulation25ModulationRange•Vref,max

(17)(17)(16)•ma,max=1

•Modulationrange:

0

≤ma≤

1(18)SpaceVectorModulation26SwitchingSequenceDesign•BasicRequirement:Minimizethenumberofswitchings

persamplingperiodTs•Implementation:Transitionfromoneswitchingstatetothenextinvolvesonlytwoswitchesinthesameinverterleg.SpaceVectorModulation27Seven-segmentSwitchingSequence•Selectedvectors:

V0,V1andV2•Dwelltimes:

Ts=T0+Ta+Tb•Totalnumberofswitchings:6SpaceVectorModulation28UndesirableSwitchingSequence•VectorsV1andV2

swapped•Totalnumberofswitchings:10SpaceVectorModulation29SwitchingSequenceSummary(7–segments)Note:Theswitchingsequencesfortheoddandevensectorsaredifferent.SpaceVectorModulation30SimulatedWaveformsf1=60Hz,fsw=900Hz,ma=0.696,Ts=1.1msSpaceVectorModulation31WaveformsandFFTSpaceVectorModulation32WaveformsandFFT(Measured)SpaceVectorModulation33WaveformsandFFT(Measured)(f1=60Hzand

Ts=1/720sec)SpaceVectorModulation34Even-OrderHarmonicEliminationType-Asequence(startsandendswith[OOO])Type-Bsequence(startsandend

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