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Power
Electronics整流電路ACtoDCConverters(Rectifiers)Outline3.1Single-phasecontrolledrectifier3.2Three-phasecontrolledrectifier3.3Effectoftransformerleakageinductanceon
rectifiercircuits3.4Capacitor-filtereduncontrolledrectifier3.5Harmonicsandpowerfactorofrectifiercircuits3.6Highpowercontrolledrectifier3.7Invertermodeoperationofrectifiercircuit3.8Realizationofphase-controlinrectifiercircuits3.1Single-phasecontrolled
(controllable)rectifier3.1.1Single-phasehalf-wavecontrolledrectifier3.1.2Single-phasebridgefully-controlledrectifier3.1.3Single-phasefull-wavecontrolledrectifier3.1.4Single-phasebridgehalf-controlledrectifier3.1.1Single-phasehalf-wave
controlledrectifierHalf-wave,single-pulseTriggeringdelayangle,delayangle,firingangleResistiveload(3-1)3.1.1Single-phasehalf-wave
controlledrectifierInductive(resistor-inductor)loadBasicthoughtprocessoftime-domainanalysisforpowerelectroniccircuitsThetime-domainbehaviorofapowerelectroniccircuitisactuallythecombinationofconsecutivetransientsofthedifferentlinearcircuitswhenthepowersemiconductordevicesareindifferentstates.ωt=
a
,id=0(3-3)(3-2)Single-phasehalf-wavecontrolledrectifierwithfreewheelingdiodeMaximumforwardvoltage,maximumreversevoltageDisadvantages:OnlysinglepulseinonelinecycleDCcomponentinthetransformercurrentInductiveload(Lislargeenough)VTia)Tu1u2uVTLRdudVDiRVDR(3-5)(3-6)(3-7)(3-8)3.1.2Single-phasebridge
fully-controlledrectifierForthyristor:maximumforwardvoltage,maximumreversevoltageAdvantages:2pulsesinonelinecycleNoDCcomponentinthetransformercurrentResistiveloaddRTu1u2i2abVT1VT3VT2VT4udia)3.1.2Single-phasebridgefully-
controlledrectifierResistiveloadAverageoutput(rectified)voltage (3-9)Averageoutputcurrent(3-10)Forthyristor(3-11)(3-12)Fortransformer(3-13)3.1.2Single-phasebridge
fully-controlledrectifierCommutationThyristorvoltagesandcurrentsTransformercurrentInductiveload
(Lislargeenough)(3-15)Electro-motive-force(EMF)loadDiscontinuouscurrentidWithresistorElectro-motive-force(EMF)loadWithresistorandinductorWhenLislargeenough,theoutputvoltageandcurrentwaveformsarethesameasordinaryinductiveload.WhenLisatacriticalvalue(3-17)3.1.3Single-phasefull-wave
controlledrectifierTransformerwithcentertapComparisonwithsingle-phasebridgefully-controlledrectifier3.1.4Single-phasebridge
half-controlledrectifierHalf-controlComparisonwithfully-controlledrectifierAdditionalfreewheelingdiodeabRLu2i2udidVT1VT2VD3VD4VDRTAnothersingle-phasebridge
half-controlledrectifierComparisonwithpreviouscircuit:NoneedforadditionalfreewheelingdiodeIsolationisnecessarybetweenthedrivecircuitsofthetwothyristorsSummaryofsomeimportantpointsinanalysisWhenanalyzingathyristorcircuit,startfromadiodecircuitwiththesametopology.Thebehaviorofthediodecircuitisexactlythesameasthethyristorcircuitwhenfiringangleis0.Apowerelectroniccircuitcanbeconsideredasdifferentlinearcircuitswhenthepowersemiconductordevicesareindifferentstates.Thetime-domainbehaviorofthepowerelectroniccircuitisactuallythecombinationofconsecutivetransientsofthedifferentlinearcircuits.TakedifferentprinciplewhendealingwithdifferentloadForresistiveload:currentwaveformofaresistoristhesameasthevoltagewaveformForinductiveloadwithalargeinductor:theinductorcurrentcanbeconsideredconstant3.2Three-phasecontrolled
(controllable)rectifier3.2.1Three-phasehalf-wavecontrolledrectifier(thebasiccircuitamongthree-phaserectifiers)3.2.2Three-phasebridgefully-controlledrectifier(themostwidelyusedcircuitamongthree-phase
rectifiers)3.2.1Three-phasehalf-wave
controlledrectifierCommon-cathodeconnectionNaturalcommutationpointResistiveload,a=0oResistiveload,a=30oResistiveload,a=60oResistiveload,quantitativeanalysisWhena
30o,loadcurrentidiscontinuous.
Whena>30o,loadcurrentidisdiscontinuous.
(3-18)(3-19)AverageloadcurrentThyristorvoltages(3-20)1-resistorload2-inductorload3-resistor-inductorloadInductiveload,LislargeenoughLoadcurrentidisalwayscontinuous.Thyristorvoltageandcurrents,transformercurrent(3-18)(3-23)(3-24)(3-25)3.2.2Three-phasebridge
fully-controlledrectifierCommon-cathodegroupandcommon-anodegroupofthyristorsNumberingofthe6thyristorsindicatesthetriggersequence.
CircuitdiagramddbacidudVT1VT3VT5VT4VT6VT221TnialoadResistiveload,a=0oResistiveload,a=30oResistiveload,a=60oResistiveload,a=90oInductiveload,a=0oInductiveload,a=30oInductiveload,a=90oPowerElectronics31QuantitativeanalysisAverageoutputvoltageForresistiveload,Whena>60o,loadcurrentidisdiscontinuous.Averageoutputcurrent(loadcurrent)TransformercurrentThyristorvoltageandcurrentSameasthree-phasehalf-waverectifierEMFload,LislargeenoughAllthesameasinductiveloadexceptthecalculationofaverageoutputcurrent(3-26)(3-20)(3-27)(3-28)(3-29)3.3Effectoftransformerleakage
inductanceonrectifiercircuitsInpractical,thetransformerleakageinductancehastobetakenintoaccount.Commutationbetweenthyristorsthuscannothappeninstantly,butwithacommutationprocess.CommutationprocessanalysisCirculatingcurrentikduringcommutationCommutationangleOutputvoltageduringcommutationub-ua=2·LB·dia/dtik:0Idia=Id-ik:Id0ib=ik:0Id(3-30)ReductionofaverageoutputvoltageduetothecommutationprocessCalculationofcommutationangleId,gXB,gFora
90o,a,gQuantitativecalculation(3-31)(3-36)SummaryoftheeffectonrectifiercircuitsConclusionsCommutationprocessactuallyprovidesadditionalworkingstatesofthecircuit.di/dtofthethyristorcurrentisreduced.Theaverageoutputvoltageisreduced.Positivedu/dtNotchingintheACsidevoltage
Single-phasefullwaveSingle-phasebridgeThree-phasehalf-waveThree-phasebridgem-pulserecfifier①②Circuits3.4Capacitor-filtereduncontrolled
(uncontrollable)rectifierEmphasisofprevioussectionsControlledrectifier,inductiveloadUncontrolledrectifier:diodesinsteadofthyristorsWideapplicationsofcapacitor-filtereduncontrolledrectifierAC-DC-ACfrequencyconverterUninterruptiblepowersupplySwitchingpowersupply3.4.1Capacitor-filteredsingle-phaseuncontrolled
rectifier3.4.2Capacitor-filteredthree-phaseuncontrolled
rectifier3.4.1Capacitor-filteredsingle-phase
uncontrolledrectifierSingle-phasebridge,RCload3.4.1Capacitor-filteredsingle-phase
uncontrolledrectifierSingle-phasebridge,RLCload3.4.2Capacitor-filteredthree-phase
uncontrolledrectifierThree-phasebridge,RCload3.4.2Capacitor-filteredthree-phase
uncontrolledrectifierThree-phasebridge,RCloadWaveformwhenwRC
1.732a)wRC=
b)wRC<
3.4.2Capacitor-filteredthree-phase
uncontrolledrectifierThree-phasebridge,RLCload3.5HarmonicsandpowerfactorofrectifiercircuitsOriginatingofharmonicsandpowerfactorissuesinrectifiercircuitsHarmonics:workinginswitchingstates—nonlinearPowerfactor:firingdelayanglecausesphasedelayHarmfuleffectsofharmonicsandlowpowerfactorStandardstolimitharmonicsandpowerfactor3.5.1Basicconceptsofharmonicsandreactivepower3.5.2ACsideharmonicsandpowerfactorof
controlledrectifierswithinductiveload3.5.3ACsideharmonicsandpowerfactorof
capacitor-filtereduncontrolledrectifiers3.5.4HarmonicanalysisofoutputvoltageandcurrentForpuresinusoidalwaveformForperiodicnon-sinusoidalwaveformorwhereFundamentalcomponentHarmoniccomponents(harmonics)3.5.1Basicconceptsofharmonics
andreactivepower(3-54)(3-55)(3-56)Harmonics-relatedspecificationsTakecurrentharmonicsasexamplesContentofnthharmonicsInistheeffective(RMS)valueofnthharmonics.I1istheeffective(RMS)valueoffundamentalcomponent.Totalharmonicdistortion
Ihisthetotaleffective(RMS)valueofalltheharmoniccomponents.(3-57)(3-58)DefinitionofpowerandpowerfactorForsinusoidalcircuitsActivepowerReactivepower
Q=UI
sinjApparentpower
S=UIPowerfactor
l=cos
j(3-59)(3-60)(3-61)(3-63)(3-62)(3-64)DefinitionofpowerandpowerfactorFornon-sinusoidalcircuitsActivepowerP=UI1
cosj1PowerfactorDistortionfactor(fundamental-componentfactor)
n=I1/IDisplacementfactor(powerfactoroffundamentalcomponent)l1=cos
1Definitionofreactivepowerisstillindispute.(3-65)(3-66)ReviewofthereactivepowerconceptThereactivepowerQdoesnotleadtonettransmissionofenergybetweenthesourceandload.WhenQ10,thermscurrentandapparentpoweraregreaterthantheminimumamountnecessarytotransmittheaveragepowerP.Inductor:currentlagsvoltageby90°,hencedisplacementfactoriszero.Thealternatestoringandreleasingofenergyinaninductorleadstocurrentflowandnonzeroapparentpower,butP=0.Justasresistorsconsumereal(average)powerP,inductorscanbeviewedasconsumersofreactivepowerQ.Capacitor:currentleadsvoltageby90°,hencedisplacementfactoriszero.CapacitorssupplyreactivepowerQ.Theyareoftenplacedintheutilitypowerdistributionsystemnearinductiveloads.IfQsuppliedbycapacitorisequaltoQconsumedbyinductor,thenthenetcurrent(flowingfromthesourceintothecapacitor-inductive-loadcombination)isinphasewiththevoltage,leadingtounitypowerfactorandminimumrmscurrentmagnitude.PowerElectronics473.5.2ACsideharmonicsandpowerfactorof
controlledrectifierswithinductiveloadSingle-phasebridgefully-controlledrectifierACsidecurrentharmonicsofsingle-phasebridgefully-controlledrectifierwithinductiveloadConclusionsOnlyoddorderharmonicsexistIn
1/nIn/I1=1/nwheren=1,3,5,…(3-72)(3-73)Powerfactorofsingle-phasebridgefully-controlledrectifierwithinductiveloadDistortionfactorDisplacementfactorPowerfactor(3-75)(3-76)(3-77)Three-phasebridgefully-controlledrectifierACsidecurrentharmonicsofthree-phasebridgefully-controlledrectifierwithinductiveloadConclusionsOnly6k
1orderharmonicsexist(kispositiveinteger)In
1/nIn/I1=1/n(3-79)where(3-80)Powerfactorofthree-phasebridgefully-controlledrectifierwithinductiveloadDistortionfactorDisplacementfactorPowerfactor(3-81)(3-82)(3-83)3.5.3ACsideharmonicsandpowerfactorof
capacitor-filtereduncontrolledrectifiersSituationisalittlecomplicatedthanrectifierswithinductiveload.Someconclusionsthatareeasytoremember:Onlyoddorderharmonicsexistinsingle-phasecircuit,andonly6k
1(kispositiveinteger)orderharmonicsexistinthree-phasecircuit.Magnitudeofharmonicsdecreasesasharmonicorderincreases.Harmonicsincreasesandpowerfactordecreasesascapacitorincreases.Harmonicsdecreasesandpowerfactorincreasesasinductorincreases.3.5.4Harmonicanalysisofoutputvoltage
andcurrentwhereOutputvoltageofm-pulserectifierwhena=0o(3-85)(3-86)(3-87)RipplefactorintheoutputvoltageOutputvoltageripplefactorwhereURisthetotalRMSvalueofalltheharmoniccomponentsintheoutputvoltage
andUisthetotalRMSvalueoftheoutputvoltageRipplefactorsforrectifierswithdifferentnumberofpulses(3-88)(3-89)m23612∞gu(%)48.218.274.180.9940Harmonicsintheoutputcurrentwhere(3-92)(3-93)(3-94)(3-95)Conclusionsfora=0oOnlymk(kispositiveinteger)orderharmonicsexistintheoutputvoltageandcurrentofm-pulserectifiersMagnitudeofharmonicsdecreasesasharmonicorderincreaseswhenmisconstant.Theordernumberofthelowestharmonicsincreasesasmincreases.Thecorrespondingmagnitudeofthelowestharmonicsdecreasesaccordingly.Fora10oQuantitativeharmonicanalysisofoutputvoltageandcurrentisverycomplicatedfora10o.Asanexample,
for3-phasebridge
fully-controlledrectifier(3-96)3.6Highpowercontrolledrectifier3.6.1Double-starcontrolledrectifier
3.6.2Connectionofmultiplerectifiers3.6.1Double-starcontrolledrectifierDifferencefrom6-phasehalf-waverectifierCircuitWaveformsWhena=0oEffectofinterphasereactor(inductor,transformer)(3-97)(3-98)Quantitativeanalysiswhena=0o(3-99)(3-100)(3-101)(3-102)Waveforms
whena>0oComparisonwith3-phasehalf-wave
rectifierand3-phasebridgerectifierVoltageoutputcapabilitySameas3-phasehalf-waverectifierHalfof3-phasebridgerectifierCurrentoutputcapabilityTwiceof3-phasehalf-waverectifierTwiceof3-phasebridgerectifierApplicationsLowvoltageandhighcurrentsituations3.6.2ConnectionofmultiplerectifiersElectronicsPowerLargeroutputcurrent:
parallelconnectionConnection
ofmultiplerectifiersToincreasethe
outputcapacityToimprovetheACsidecurrentwaveformandDCsidevoltagewaveformLargeroutputvoltage:
seriesconnectionPhase-shiftconnectionofmultiplerectifiersParallelconnection12-pulserectifierrealizedbyparalleled3-phasebridgerectifiersPhase-shiftconnectionofmultiplerectifiers12-pulserectifierrealizedbyseries3-phasebridgerectifiersSeriesconnectionVoltageAverageoutputvoltageParallelconnection:
Seriesconnection:OutputvoltageharmonicsOnly12mharmonicsexistInput(ACside)currentharmonicsOnly12k±1harmonicsexistConnectionofmore3-phasebridgerectifiersThree:18-pulserectifier(20ophasedifference)Four:24-pulserectifier(15ophasedifference)Quantitativeanalysisof12-pulserectifierSequentialcontrolofmultiple
series-connectedrectifiersCircuitandwaveformsofseries-connectedthreesingle-phasebridgerectifiers3.7InvertermodeoperationofrectifiersReviewofDCgenerator-motorsystemshouldbeavoid
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