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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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