1Chapter5：Line-FrequencyDiodeRectifiers5-1Introduction5-2Single-phasehalf-waverectifier

5-3Single-PhaseDiodeBridgeRectifiers5-4Voltage-Doubler(Single-Phase)Rectifiers5-5EffectofSingle-PhaseRectifiersonNeutralCurrentsinThree-Phase,Four-WireSystems5-6Three-Phase,Full-BridgeRectifiers25-7ComparisonofSingle-PhaseandThree-PhaseRectifiers5-8InrushCurrentandOvervoltagesatTurn-on5-9ConcernsandRemediesforLine-CurrentHarmonicsandLowPowerFactor35-1-1RectifierPowerelectronicsystems,suchasSwitchingdcpowersupplies,acmotordrives,dcservodrivesgenerallygettheirpowerfromtheutilitysource,Dioderectifiers,thesimplestandinexpensiverectifiers,commonlybeusedastheirFront-Ends.5-1IntroductionTheroleofarectifieristoconvertacpowerintodcpower.rectifier4Thepowerisdrownbymeansofhighlydistortedcurrents,whichhaveadeleteriouseffectonthepowerqualityoftheutilitysource.vsisidvdFig.5-1dioderectifier5Toquantitydistortioninthecurrentdrawnbypowerelectronicsystems,itisnecessarytodefinecertainindices.5-1-2

PerformanceParameters

6Example1:Supposeweplugaresistorloadintothewallsocket.Thefuseisratedforaspecifiedrmscurrent,abovethat,itwillblowsothatdissipationinRwiredoesnotstartafire.Witha220V,15Afuse,weget3.3kWmax.fromwallsocket(neglectingRwire).Asabasecase,wefirstconsiderlinearload.RwireFuseR+V-7Example2:Supposeinsteadweplugainductorloadintothewallsocket.neglectingRwireWhilewedrawnorealpower,westilldrawcurrent.220V,50Hz,L=40mH→Irms=17.5A>15A.So,thefusewillstillblow(toprotectthewallwire).Inthiscase,wearenotutilizingthesourcewell.RwireFuseL+V-8Fromexample1andexample2,wecanseethatdifferentloadgetsdifferentutilizationofthesource.Toprovideameasureoftheutilizationofthesource,wedefine

PowerFactorP---realaveragepower

VsIs---apparentpowerFortheresistorPF=1,bestutilization.Fortheinductor,PF=0,worstutilization.9IsandPFareinverselyproportional,unitypowerloadsthatdrawpowerattheminimumrmscurrent.☆

LinearLoads:Thesinusoidalcurrentdrawnbylinearloadhaszerodistortion.10NonlinearLoads11Definingthe

TotalHarmonicDistortion

(orharmonicfactorHF):idistortion(t)consistsofcomponentsatfrequenciesthataremultiplesof1/T1.WhereIshisthermsvalueoftheharmoniccomponent“h”.12Definingthe

DisplacementPowerFactor

(or

DisplacementFactor)Nonlinearloadsreducepowerfactor.☆Definingthe

DistortionFactor

13DefiningtheCrestfactor:Is,peak----thepeakvalueofis.14HarmonicCurrentsLowerPowerFactorRatioofactualpowerfactortodisplacementpowerfactordecreaseswithincreasingTHD153DeleteriouseffectsofharmonicdistortionandapoorPowerFactorIncreasingpowerlossintransmissionlines,transformers,generators.Overloadingtheshuntcapacitorsusedbyutilitiesforvoltagesupport.Maycausingresonanceconditionsbetweenthecapacitivereactanceoftheshuntcapacitorsandtheinductivereactanceofthetransmissionlines.Theutilityvoltagewaveformwillalsobecomedistorted,adverselyaffectingotherlinearloads.1617Example5-A

AcurrentisofsquarewaveformisshowninfollowingFigure.Calculateandplotitsfundamentalfrequencycomponentanditsdistortioncomponent.WhatistheTHDassociatedwiththiswaveform?Solution18Solution

FromFourieranalysis,BychoosingthetimeoriginasshowninFigure,is(t)canbeexpressedas:

194ImportantCalculatingEquations(1)Ifm≠n→Sinusoidalsofdifferentfrequencyareorthogonal.(3)Ingeneral(2)→Sin.andcosineareorthogonal.TheseEquationswillbeusefulforcalculatingpower,etc.20Example5-BThevoltagevacrossaloadandthecurrentiintothepositive-polarityterminalareasfollows(whereω1andω3arenotequal):Calculatethefollowing:(a)TheaveragepowerPsuppliedtotheload(b)Thermsvalueofv(t)andi(t)(c)ThepowerfactoratwhichtheloadisoperatingSolution21Solution225-2Single-phasehalf-waverectifier

1Pureresistiveload:Duringthepositivehalf-cycleoftheinputvoltage,Dconductsandinputvoltageappearsacrosstheload.Duringthenegativehalf-cycle,Disablockingconditionandtheloadvoltageiszero.Becauseofthelargerippleinvdandi,thiscircuitisoflittlepracticalsignificance.232InductiveloadIncomparisontothecaseofpurelyresistiveload,theaverageloadvoltageisless.Subsequenttot=0,Dbecomesforwardbiasedandacurrentbeginsflow.243LoadwithaninternalvoltageCurrentbeginstoflowwhentheinputvoltageexceedsthedcback-emf.Currentcontinuestoflowsforawhileevenaftertheinputvoltagehasgonebelowthedcback-emf.25Lsisthesumoftheinductanceinternaltotheutilitysupplyandanexternalinductance(forimprovingtheline-currentwaveform).5-3Single-PhaseDiodeBridgeRectifiersFigure5-5Single-phasediodebridge+Vd-26RectifiermodelwithapurelyresistiveloadRectifiermodelwithlargeinductorload(R-Lload),theinductorcurrentcanbeconsideredconstant.5-3-1IdealizedcircuitwithLs=027Note:Inbothcircuits,whenvsispositive,D1andD2conductandvd=vsandis=id;whenvsgoesnegative,D3andD4conductandvd=-vsandis=-id.Therefore,28Inbothcases,thedc-sidevoltagewaveformisthesameCurrentcommutationisfinishedinstantaneouslyduetotheassumptionofzeroLs29Diode-Rectifierwithlargeinductorload30315-3-2EffectofLsonCurrentCommutationPreviously,weassumethattheac-sideinductanceLs=0,sothecurrentcommutationisfinishedinstantaneously.NowweconsidertheexistenceofLs.Insuchcase,theinputcurrentneedsafiniteamountoftimetoreverseitsdirection.Intheconditionofdc-currentidflowscontinuous.321CurrentCommutationProcess:Priortoωt=0,D3andD4conduct,is=-Id.Whenωt>0,D1/D2becomeforwardbiasedandthereforeconduct.However,withafiniteLs,thecurrentthroughthemdoesn’tjumpinstantaneously,andD3/D4remainconductingmodeforashortintervalcalledthecommutation(overlap)angleμ,thusresultinginvd=0andapplyingvsacrossLs.33Duringthecommutationintervalμ:Atωt=μ,Figure5-15RedrawncircuitofFig.5-14aduringcurrentcommutation.Circulatingcurrent

iμ:from0→Id342Calculatingcommutationvoltage-integral:

Theeffectoftheoverlapistoreducetheaverageoutputvoltageofconverters.353Calculatingcommutationangleμ(orγ).CommutationangleμincreasewithLsandIdincreasinganddecreasewithvoltageVsincreasing.☆Duringthecommutationinterval,vL=vs,therefore:364Calculatingvoltagedrop

ΔVd.Voltagedrop

ΔVd

increasewithLsandIdincreasing.☆Note:voltagedropinthepresenceofLsdoesn’tmeanapowerlossinLs;itsimplymeansareductioninthevoltageavailableonthedc-side.37Example5-CConsiderthebasiccommutationcircuitasfollowwithId=10A.(a)WithVs=120Vat60HzandLs=0,calculateVdandtheaveragepowerPd.(b)WithVs=120Vat60HzandLs=5mH,calculateμ,Vd,andPd.(c)Herevshasa60Hzsquarewaveformwithanamplitudeof200V,andLs=5mH.Plotitswaveformandcalculateμ,Vd,andPd.38SolutionWaveformsassumeLs=039Solution40Solution200V2πμVd10Ais415-3-3Rectifierwithadc-sidevoltagevd(t)=VdWhenvsexceedsVdatθb,D1/D2begintoconduct.Thecurrentreachesitspeakatθp,beyondwhichvLbecomesnegative.Thecurrentbecomeszeroatθfandremainszerountilπ+θb.42WithagivenVd,Idcanbecalculatedasfollows:43Obviously,forgivencircuitparametersIdwilldependonVdandviceversa.44Defining:1DC-SideVoltageVdandCurrentIdRelationshipZerocurrentcorrespondstodcvoltageequaltothepeakoftheinputacvoltage5-3-3-1RectifierCharacteristic

☆45

VeryhighTHDandlowpowerfactoratlowcurrentvalues.☆2EffectofDC-SideCurrentonTHD,PFandDPF46

TheCrestFactorisveryhighatlowvaluesofcurrent.☆3CrestFactorversustheCurrentLoading47IncreasingLsresultsinimprovediswaveformwithalowerTHD,abetterpowerfactorandalowercrestfactor.☆48Rsrepresentsacsidelosses.EquivalentresistanceRloadrepresentsdcsideload.5-3-4Diode-RectifierwithaCapacitorFilter☆ConclusionsaboutRectifierCharacteristics

inRectifierwithadc-sidevoltagearesuitableforthiscondition.491Line-CurrentDistortionAnalysisusingPSpice50CurrentpulseswidenasLsisincreased,andthereforeimprovediswaveformwithalowerTHD,abetterpowerfactorandalowercrestfactor.☆→sometimes,anexternalinductorLsmustbeintroducedtoimprovediswaveform.

51

TheeffectofintroduceanexternalLsonthecharacteristicsofdioderectifierwithacapacitor:☆Thepowerfactorisimprovedfromverypoortosomewhatacceptable.Harmonicsaredecreased.TheoutputvoltageVdislowercomparedwiththeno-inductancecase.Theoverallenergyefficiencyremainsessentiallythesame;thereareadditionallossesintheinductor,buttheconductionlossesinthediodesarelower.52Someotherconclusions:

☆Onlyoddorderharmonicsexistinsingle-phasecircuit.Magnitudeofharmonicsdecreasesasharmonicorderincreases.Harmonicsincreasesandpowerfactordecreasesascapacitorincreases.HarmonicsdecreasesandpowerfactorincreasesasinductorLsincreases.532Line-VoltageDistortionDistortedcurrentsdrawnbyloadscanresultindistortioninutilityvoltagewaveform.

Distortioninvoltagesuppliedtootherloads.54555-6Three-Phase,Full-BridgeRectifiersInindustrialapplications,itispreferabletousethree-phaserectifier,comparedtosingle-phaserectifier,becauseoftheirlowerripple

contentinthewaveformsandahigherpower-handingcapability.

Commonlyused56Thecircuitconsistsofatopgroup(positive)andabottomgrope(negative).Fourtypesofload:575-6-1IdealizedcircuitwithLs=0Considerrectifiermodelwithlargeinductorload(R-Lload)58VoltageandCurrentWaveformsThewaveformsforthevoltagesvPnandvNn,consistof120°segmentsofthephasevoltages;WhenD1conductingWhenD4conductingneitherD1orD4conducting59Thewaveformofthedc-sidevoltagevd(=vPn-vNn)consistsof60°segmentsoftheline-linevoltages.Hence,thisrectifierisoftentermedasix-pulserectifier.Conductionsequence:ab→ac→bc→ba→ca→cb→ab60InputLine-Current61

Theinputpowerfactorishigherthanthatofsingle-phaserectifier.625-6-2EffectofLsoncurrentcommutationPreviously,weassumethattheac-sideinductanceLs=0,sothecurrentcommutationisfinishedinstantaneously.NowweconsidertheexistenceofLs.Insuchcase,theinputcurrentneedsafiniteamountoftimetoreverseitsdirection.631CurrentCommutationConsiderthecommutationofcurrentfromD5/D6toD6/D1.Duringcommutationinterval:642CalculatingvoltagedropΔVd.Voltagedrop

ΔVd

increasewithLsandIdincreasing.☆653Calculatingcommutationangleμ(orγ)CommutationangleμincreasewithLsandIdincreasinganddecreasewithvoltageVsincreasing.☆665-6-3Rectifierwithadc-sidevoltagevd(t)=Vd67

VeryhighTHDandlowpowerfactoratlowcurrentvalues.☆1EffectofDC-SideCurrentonTHD,PFandDPF68

TheCrestFactorisveryhighatlowvaluesofcurrent.☆2CrestFactorversustheCurrentLoading69IncreasingLsresultsinimprovediswaveformwithalowerTHD,abetterpowerfactorandalowercrestfactor.☆705-6-4Diode-RectifierwithaCapacitorFilter☆A(yù)pplications:AC-DC-ACfrequencyconverterUninterruptiblepowersupplySwitchingpowersupplyConclusionsaboutRectifierCharacteristics

inRectifierwithadc-sidevoltagearesuitableforthiscondition.71PSpice-basedanalysis72SimulationResults73CurrentpulseswidenasLsisincreased,andthereforeimprovediswaveformwithalowerTHD,abetterpowerfactorandalowercrestfactor.☆→sometimes,anexternalinductorLsmustbeintroducedtoimprovediswaveform.74

TheeffectofintroduceanexternalLsonthecharacteristicsofdioderectifierwithacapacitor:☆Thepowerfactorisimprovedfromverypoortosomewhatacceptable.Harmonicsaredecreased.TheoutputvoltageVdislowercomparedwiththeno-inductancecase.Theoverallenergyefficiencyremainsessentiallythesame;thereareadditionallossesintheinductor,buttheconductionlossesinthediodesarelower.75Someotherconclusions:

☆Only6k1(kispositiveinteger)orderharmonicsexistinthree-phasecircuit.Magnitudeofharmonicsdecreasesasharmonicorderincreases.Harmonicsincreasesandpowerfactordecreasesascapacitorincreases.HarmonicsdecreasesandpowerfactorincreasesasinductorLsincreases.765-7ComparisonofSingle-PhaseandThree-PhaseRectifiers☆

1Comparisonofisandvdwaveforms:Three-phaserectificationresultsinsixidentical“pulses”percycleinthedc-sidevoltage,whereassingle-phaserectificationintwosuchpulses.Therefore,three-phaserectifiersaresuperiorintermsofminimizingdistortioninlinecurrentsisandrippleacrossthedc-busvoltageVd.772Comparisonofidwaveforms:

Therippleinidinathree-phaserectifierissmallerthanthatinsingle-phaserectifier,thereforerequiremuchsmallerfiltercapacitor.783ComparisonofthemaximumregulationintheVd:

Inathree-phaserectifier,