外文翻译-三相高功率因数PWM整流器的模型与仿真

英文原文ModelingandSimulationofThreePhaseHighPowerFactorPWMRectifierYuFang*,YongXie*andYanXing*CollegeofInformationEngineeringofYangzhouUniversity,Yangzhou,P.R.China*Aero-PowerSic-techCenter,NanjingUniversityofAeronauticsandastronauticsNanjing210016,P.R.ChinaAbstract-NumericalsimulationmethodologybasedonhighfrequencymathematicalmodelofhighpowerfactorPWMrectifierisproposedinthispaper.Andinputtooutputtransformfunctionisdeduced.Withthehelpofinputtooutputtransformfunction,thedesignmethodofvoltageregulatorhasbeenpresented.Thesimulationforthree-phasePWMrectifierisimplementedwithRunge-kutta,thuscomprehensivesimulationcanbeachievedwithMfileinMATLAB.Finally,thesimulationresultsandexperimentalresultsaregiven.Thecompleteagreementwiththeresultsofsimulationandexperimentmanifeststhattheproposedsimulationmethodinthispaperiseffective.Ofcourse,thedesignperiodofthree-phasehighpowerfactorPWMrectifiercanbeshortenedbyvirtueofproposedsimulationmethodology.Keywordspowerfactorcorrection;SVPWM;NumericalsimulationI.INTRODUCTIONPWMrectifierismaintechniqueappliedinlargeunitpowerfactor.ThreephasePWMrectifiercanbecatalogedinvoltageandcurrenttypes,inwhichcurrenttyperectifiermayemploymanykindsofconventionalPWMtechniques,however,inputlinecurrentisdiscontinuousandoutputvoltagerippleismuchlarger.Whilevoltagetypetopologynotonlyadoptmanyappropriatecontrolstrategiesbutalsoimplementsbidirectionalenergyflow,anditsmainmeritisthatfardynamicresponseandsimpleconfigure.AndsmallerinputfiltercanachievelowerEMI.Consequently,thevoltagetypePWMrectifierisusuallyservedaspowerfactorcorrection.SVPWMisthebestwaytosuppressharmonics1-4,andusedtoadjustmotorvelocity.Especiallyitcanattainlowharmonicseveninloweroperatingfrequency.SVMcanshapetheinputvoltagesofthreephasebridgeconverterintorotatingcircularvoltagevector.WiththedevelopmentofDSP,SVPWMhavebeeneasilyimplementedsofar.AndanothermeritemployingSVPWMinPWMinvertercanachieve15%morefundamentalcomponentamongoutputvoltage.Hence,ifemployedSVPWMtechniqueinPWMrectifier,theuseefficiencyofDCvoltagewillbehigherclosetounit.Astheresultthatthevoltagestressesacrossswitchesisdecreased.ThebestwaytoimplementSVPWMisdigitalcontrol.DuetothatDSPhavebeencommercialized,highperformancedigitalizedSMPScometotrue.However,itishardtoprogramtoimplementcontrollerinDSP,whichresultinlongerdevelopmentperiod.Thiscaseisremarkableinthedesignofthreephasepowerfactorcorrection;becauseinthiscasemanycontrolvariablesneedtocontrolanddoubleclosedloopsmustbeaccomplished.Infaceofthispoint,thenumericalsimulationmethodologybasedonhighfrequencymathematicalmodelofhighpowerfactorPWMrectifierisproposedinthispaper.Thesimulationprogramcontainsthevoltageregulator,currentcontrollerandtheSVPWM,sowecancallitcomprehensivesystemsimulationforPFC.ThetotalsimulationisimplementedwithMfileinMATLAB,henceweonlytranslatetheMfileintotheDSPlanguagetoachievedigitalizedthreephasepowerfactorcorrection.Consequentlythecompensationparameterscanbeoptimizedinsimulationandthedesignperiodwillbegreatlyshorteneddesigncostcut.Itisclearthattheproposedsimulationmethodologyisvaluableforfastdesignofthree-phasePFCandmaybeusedforreferencetootherdigitalizedSMPSdesign.Inthispaper,thehighfrequencymathematicalmodelisdevelopedfirstly,andthenthecontroltooutputtransformationfunctionisdeducedbasedoninstantaneouspowertheory.ItisnaturethatthevoltageregulatorisgivenandthePIregulatoristestifiedtoworkhere.Inthisway,wewritethesemathematicmodelsintoprograminMfile.Andfinallythesimulationresultsandexperimentalresultsaregiven.Thecompleteagreementwiththeresultsofsimulationandexperimentverifythattheproposedsimulationmethodinthispaperiseffective.II.MODELINGFORPWMRECTIFIERThemodelisimportantwaytoanalyzetheoperationbasic,dynamicandstablestateofPWMrectifier.Thestudiedtopologyisshowninfig.1.Assumingthat:(1)ideaswitches(2)ballancedinputvoltagesource(3)withoutswitchingdeadtimeFig.1Three-phasePWMVRCtopology(1)3/2costEUtmsbsa/cstImsbawhereEm(Im)andCoareamplitudeofthephasevoltage(current)andangularfrequencyrespectively.A.HighfrequencymathematicalmodelinABCfixedcoordinateAsshowninfig.1,Usa、Usb、Usc、areinputphaselinevoltages,isa、isb、isc、inputlinecurrents,Rsisresistenceofinputrail,Lsboostinductor,Csfitercapacitor;Ud,outputvoltage,ReffectiveloadresistenceandIloadcurrent.Duetothatthecomplmentarycharacteristicofswitchesinthesamebridgeleg,thefollowingswitchingfunctioncanbedefined.Hencewecangetthemodel:(3)BUAxX.Where,(4)0/0/*scsbsaassCSCSSLRLRATSSdigB11TdscbsaIU0Eq.(3)showsthateachlinecurrentiscomposedofThreephaseswitchfunction,soPWMrectifieriscouplednonlineartimevariationsystem.Itcanbeconcludedthattheneutralpointvoltagelevelofoutputcapacitordiffersfromlinegridneutraloneinthree-phasePWMrectifierwithoutneutralconnection.Asfarasthehighfrequencyisconcerned,PWMrectifieriscoupledwitheachphase.Eqs.(2)-(4)arethemathematicmodeforthree-phasePWMrectifierinhighfrequencystate.Fig.1canbeemployedinvariablefrequencyconverter,three-phaseUPS,APF,SVGandsoon.Fig.2showstheequivalentelectricalcircuit.Fig.2PWMrectifierhighfrequencyequivalentcircuitB.Highfrequencymathematicmodelina-ffixedcoordinateTheabovegivesthehighfrequencyPWMrectifiermathematicalmodelinABCfixedcoordinate,whilethissectionpresentscorrespondingmodelin-fixedcoordinate.Expression(5)istranslationmatrixfromthreedimensioncoordinatetotwodimensions.Hence,themathematicalmodelscoordinateareasfollows:(6)UBXA*0/0/SLRss（7）TTssdcuUCBViX/1/1scbsaabciiTi/Asseenfromexpression(7),therelatedvariableshavebeendecoupled.ia、ibareonlyeffectedbycorrespondingswitchingfunctionS,SBrespectivelyinu-Pfixedcoordinate.However,voltageandcurrentarestillsinusoidal.Whenswitchingfrequencyfarmorethanthatoflinegrid,(4)and(7)theswitchingfunctioncanbereplacedwithdutycycleofupperswitchinoneswitchingperioddk(k=a,b,c),hence,theaveragemodelinoneswitchingperiodcanbegotten,i.e.lowfrequencymathematicalmodelforPWMrectifier.TheaveragemodelneglectsswitchingprocessandsimplifiesPWMrectifiermodel.(8)presentstherelationsbetweencontrolvoltagesandaverageswitchingfunctionFrom(6),theoutputcurrentisshownin(9).(9)isii0From(6)and(9),highfrequencymodelforPWMrectifierinu-Pfixedcoordinateisdrawninfig.3.Andoutputcurrentcontainsripplecurrentinu-Pfixedcoordinate.Fig.3highfrequencyequivalentcircuitin-BfixedcoordinateIII.CONTROL-TO-OUTPUTSIMULATIONMODELInordertofacilitateanalysis,thecontrolschematicblockdiagramisshowninfig.4,andtheclosedloopsystemblockdiagraminfig.5.Controlvariableistheamplitudeofinputcurrentim*,controlledvariableisoutputvoltageudc.Wheninsteadystate,im*andudcareconstantvaluesImandUdcrespectively.im,UdcarecorrespondingsmallsignaldisturbanceofIm*andUdcrespectively.Udcrefisoutputdisturbance.Infig.5G(s)iscontrol-to-outputtransferfunction,andGC(s)isvoltageregulatormodel.Fig.4Three-phaseHPFPWMrectifiercontrolblockdiagramFig.5ClosedloopsystemblockdiagramA.smallsignalmodelforControltooutputIfneglectingharmoniccomponentsinphaselinecurrents,andassumingphaselinecurrentsinphasewithphaselinevoltage,thefollowingexpressioncanbegotten.WithassumptionthatboostinductiveisLs,Rsisinpurailresistance,outputcapacitorisCs,andoutputloadisR.Assumingtheoutputofvoltageregulatorim2Rk6,sotheitem2Rs6mcanbeomittedandexpression(26)gotten:WhereRiisequivalentinputresistanceofthree-phaserectifier.Asseenintheexpression(26)thereexistsonezeropoint(1/Tz)onRHPofG(S),andthiszeropolecannotbeneglectedusually.HenceHPFBoostPWMrectifierbelongstonon-minimum-phasesystem.B.ThedesignofvoltageregulatorGc(s)Simulationparametersareasfollows:Rs=0.002Q,Ls=7.8mH,Cs=2200piF,inputphaselinevoltageamplitudeis,outputDCvoltageUd,=150V,VEm250outputpowerPo=1KW,andswitchingfrequencyfs=10KHz.BasedoncharacteristicofG(s)thedesiredopenloopmodelisspecifiedasfollows:(27)1()()(STmSGSQppCHenceGc(s)is:(28)(/)(KppCToguaranteeinputlinecurrentscantrackdownthelinevoltagescompletely,thebandwidthofvoltageloopmustbefarlowerthanthatofcurrentloop.Hence115ofswitchingfrequencyisspecifiedasthebandwidthofvoltagehereby160rad/s,andequalstom/Tzasseeninexpression(28),sowegetm=0.16.duetoselectedoutputcapacitorCsmuchlargerinthisdesignandpowersmaller,TzTp,Tzcanbeneglected,asaresult,voltageregulatordesignissimplifiedasshowninexpression(29).(29)SKTSGpC16.0)(ThisistypicalPIregulator.From(29)wecangetPandI:Substitutingthesimulationparametersgiveninto(30),get:Kp=0.479,K=19.34.Asshowninfig.6phasemarginis80.79degreeandgainmargin6.25dB,hencethesystemissteady.Fig6AmplitudeandphaseversusfrequencyIV.SIMULATIONANDEXPERIMENTVoltageregular,predictivecurrentcontrollerandSVPWMfastalgorithmareallimplementedinDSPinthisexperimentalprototype.Tosimulatephysicalprofileauthentically,MfileinMATLAB6.5isemployedtoimplementthecontrollogicinwhichallcontrolalgorithmsandpowerconvertermodelareincluded.InMfilethree-phasePWMrectifiermodelisaccomplishedwithaidofRunge-kuttamethodandthesamplefrequencyisjustswitchingfrequency.Simulationflowblockdiagramisshowninfig.7.Fig.7three-phasePWMrectifiersimulationflowdiagramA.SVPWMwaveformsFig.8showsthesimulationwaveformsofthePWMoutputswhichisachievedafterthecarrierhasbeentakenoutwithalow-passfilter.Theupperandthebottomwaveformsinfig.8aretwoofthethreePWMoutputs.Thewaveforminthemiddleisthedeferencebetweenthetwo,representingtheline-to-lineinputvoltageappliedtothree-phase-bridgerectifier.ItisclearthatthelinetolinevoltageisstillsinusoidandSVPWMwaveformscanbeequivalenttothesinusoidalwaveformsplusthe3thdharmonic.Henceover-modulationcannotoccuruntilmodulationrateishighby1.15.SVPWMisindeedthebestmodulationmethodtosuppressharmonicsandefficientuseofDCsupplyishigh,ascloseto1canattained.Fig.8SVPWMsimulationoutputswithcarrierfilteredoutB.WaveformsinsteadystateSimulationwaveformsinsteadystateareseeninfig.9.Ifweletthree-phasePWMrectifierstartupfromDCoutputvoltageatzero,thesmallnegativeoutputvoltagecanbeobservedandthentheoutputvoltageturnpositiveuptonominaloutputvoltage.Thiscaseprovesthecontrolloopofthree-phaseHPFPWMrectifierreallyexistszeroinRHP.Seenfromfig.9(a)andfig.1O(a),inputlinecurrentsachievesinusoidinphasewithphaselinevoltage.Itcanbeverifiedthatcurrentcontrolleriseffective.Fig.10(b)givestheexperimentalinputlinecurrentswaveformsofphaseAandB.Fig.9(b)andfig.1O(c)arethesimulationwaveformsandtheexperimentalwaveformsrespectively,theyarestable,hence,thevoltageregulatordesigniseffective.(a)Inputvoltageandcurrentwaveforms（b）OutputdirectvoltagewaveformFig9.Mainwaveformsinsteadystate(a)CH1ThevoltagewaveformofPhaseA(25V/div)CH2ThecurrentwaveformofPhaseA(1OA/div)(b)CH1ThecurrentwaveformofPhaseA(1OA/div)CH2ThecurrentwaveformofPhaseB(lOA/div)V.CONCLUSIONSimulationandexperimentalresultstellushattheunitpowerfactorcanbeaccomplishedbasedonSVPWMandPIvoltageregulator.SimulationwaveformsverifylowfrequencysmallsignalmodelofVSRPWMrectifier.ThecompleteagreementsbetweensimulationandexperimentalwaveformsprovethattheproposedsimulationalgorithminMATLABiseffectiveinthispaperandthissimulationfilecombinedpowercircuitmodelwithcontrolschemecangreatlyworktoinstructthedesignofthree-phaseHPFrectifier.EspeciallythecontrolalgorithminMfilecaneasilybetransplanttotheDSPprogramsothatwecanpromptlyimplementcontrolstrategyinDSP.Furthermore,thesesimulationpointscanworkinothersdigitalizedSMPSdesign.REFERENCES1ThomasG.Habetler,ASpaceVector-BasedRectifierRegulatorforAC/DC/ACConverters,IEEETransactionsonPowerElectronics,Vol.8,No.1,pp.30-36,1993.2LuigiMalesani,PaoloTomasin,andVanniToigo,SpaceVectorControlandCurrentHarmonicsinQuasi-ResonantSoft-SwitchingPWMConversion,IEEETransactionsonIndustryApplications,Vol.32,No.2,pp.269-277,1996.3K.Yamamoto,K.Shinohara,Comparisonbetweenspacevectormodulationandsub-harmonicmethodsforcurrentharmonicsofDSP-basedpermanent-magnetACservomotordrivesystem,IEEEProc.Electr.PowerAppl.,Vol.143,No.2,pp.151156,1996.4YuFangandYanXing,AFastAlgorithmforSVPWMinThreePhasePowerFactorCorrectionApplication,IEEEPESC2004.5YangDegang,LiuRunshengandZhaoLiangbing,Currentcontrollerdesignofathree-phasehigh-power-factorrectifier,TransactionsofChinaelectrotechnicalsociety,Vol.15,No.2,pp.83-87,2000.中文译文三相高功率因数PWM整流器的模型与仿真摘要：在这个论文中建议用数值仿真方法，此方法是基于高功率因数PWM整流器的高频率数学模型。演示了从输入到输出的转变功能。由于它的功能的改变，使电压调节器的设计方法随之出现，三相PWM整流器的仿真也得以实现。随后综合的仿真能够在MATLAB中的M文件夹里完成。最终给出了仿真的结果和实验的结果。通过比较仿真的结果与实验的结果得出两者完全一致，这就得出了本论文中所建议的模拟方法是有效的。当然，借助于仿真方法就能够缩短三相高功率因数PWM整流器的设计时期。关键词：功率因数校正；SVPWM；数字仿真1简介PWM整流器是应用于大单位功率因数的重要方法，三相PWM整流器分为电流型和电压型，电流型整流器可以用于多种传统的PWM技术，然而，输入线电流不连续，输出电压脉动非常大。电压型拓扑结构不仅采用了许多合适的控制策略，而且实现了能量的双向流动，它的重要优点是简单配置和动态响应。较小的输入滤波器能够完成低电磁干扰。因此，电压型PWM整流器被用于功率因数校正。SVPWM是抑制谐波的最好方法，常常用来调整电动机速度。尤其它能够在低操作频率下获得低谐波。SVM可以塑造三相桥式的输入电压换成圆形旋转电压矢量。由于DSP的发展，目前SVPWM已经轻松实现。另一个值得使用SVPWM的技术是由于PWM逆变器基本组成部分之间的输出电压可以达到15以上。然而，如果在PWM整流器中使用SVPWM技术，直流电压的效率会更接近于1。经过开关时电压值下降。实现SVPWM的最好方法是数字式时钟控制。由于DSP已经过于商业化，高性能数字化开关电源即将实现。然而，DSP中实现控制器这一计划非常难，导致了开关电源长期的发展。三相功率因数校正器的设计是十分杰出的；因为在这种情况下，许多控制变量需要控制和双闭环。面对这样的问题，本论文中建议用数值模拟方法，此方法基于高功率因数PWM整流器的高频率数学的模型。此仿真方案包含电压调节器，电流控制器，SVPWM，所以我们可以称之为功率因数校正的系统仿真。结果在MATLAB中的M文件下实现，因而我们仅仅需要把M文件翻译成DSP语言，来实现三相功率因数校正。因此，在仿真中补偿参数可以进行优化设计，设计周期将大大缩短并设计成本也削减了。仿真方法的这种提议对三相功率因数校正的设计是非常有价值的，并且参考这种方法设计其它的数字型开关电源。在本论文中，首先开发基于瞬时功率理论的高频率数学模型，演绎了输出转变功能的控制理论。给出了电压调节器的自然特性，并且验证了PI调节器的工作特性。用这种方法，我们把这些数学模型写入M文件中的程序中。最后给出实验结果和仿真结果。仿真结果于实验结果完全一致，验证在本文中建议的模拟方法是有效的。2PWM整流器模型这个模型是分析PWM整流器基本的，动态的，固定的几种操作的最重要的方法。拓扑结构如图1所示。假设：（1）理念开关（2）无死区开关图1三相PWMVRC拓扑结构3/2costEUtmsbsa（1）/cstImsba这里的Em()和w分别是相电压（电流和角频率的振幅）。mI如图1所示，、是输入相电压，是输入线电流aSUsbscscbsaii、是电阻，是升压电感，是滤波电容器；是输出电压，R是负载阻抗，SRLSCdcU是负载电流。由于相同桥臂上的开关有互补的特点，开关功能定义如下。0I（2）ii,01下桥臂道通上桥臂导通因此我们得到模型BUAxX.（3）0/0/*scsbsaassCSCSSLRLRA（4TSSdigB11）TbcsaUiXdssI03/*cbaSS式（3）所示三相开关功能由每一线电流组成，所以PWM整流器是耦合的非线性时变系统。它可以得出结论认为，输出电容器的中性点电压等级不同于线网格中三相PWM整流器无中性点的连接。目前，每一相耦合的高频率PWM整流器被广泛应用。式（2）-（4）是三相PWM整流器在高频率状态下的数学模型。图1是可以被用在各种频率下的转换器，如三相UPS,APF,SVG等等。图2展示了等值电路。图2高频率PWM整流器等值电路B.在-坐标下的高频率数学模型上述给出了在（a,b,c）坐标下的高频率PWM整流器的数学模型，这节介绍了在-坐标下相应的模型。表达式(5)是把三维坐标翻译成两维。（5）2/3/01132/abcT因而，在-坐标下的数学模型如下：（6）UBXA*其中0/0/SLRss（7）TTssdcuUCLBViX/1/1scbsaabciii/表达式（7）中可以看出，有关变量已经被解耦。只受相应的开关功、能的影响，分别在-坐标系中。然而，电压和电流还仍然是正弦的。S、当开关频率远高于线网络，（4）-（7）的开关功能被一个在转换周期的开关的占空比所替代，因而，得到了一个转换时期的平均模型，例如.PWM整流器的低频率数学模型。平均模型忽略切换过程，并简化PWM整流器模型。(8)介绍了控制电压和平均转换功能之间的关系。（8）0usr根据式（6），输出电流如（9）所示（9）iii0从式（6）和式（9）可以得出，在-坐标系下，PWM整流器的高频率模型可以等效为图三所示。输出电流包括了在-固定坐标下的载纹电流。图3-坐标系下的高频率等效电路3控制至输出仿真模型为了便于分析，控制方框图如图4所示，其闭环系统框图如图5所示。控制变量是输入电流IM的振幅，被控量是输出电压。当处于稳态时期，和分别为横值。dcUmI*dcU分别是and相应的小信号干扰。是输出干扰。dcui、*mI*dcdcrefu在图5中，G（s）控制直输出转换功能，是电压调节器模型。)(sG图4三相HPFPWM整流器控制方框图图5闭环系统方框图控制输出的小信号模型如果忽略谐波成分的相线电流，假设在相线电流的相线电压，能够得出如下表达式。（10）3/2costItmba假设提升电感是Ls,Rs是输入电阻，输出电容是Cs，输出负载是R。假设电压调节器的输出，因而，控制电流如下：*mIi（11）*mconIi从式（10）中可以得到：（12）2225.1cbaIii由于输入暂态功率等于输出之一，可以得到式（13）：（13）01PPCRLD为输出功率，和分别是和的功率。0PRL，CS，所以能够得到如下表达式：（14）)()()(id5.00,2,2k1tiutitdccbakScbaSD是输出电流，它包括流经CS和负载R的电流。从输入中可得到式（15）（15）mconkbaksDIEtiuP5.1)(,1在表达式中，我们可以得知。与表达式(12)联立，我们可以出式mconkIi（16），是提升电感的功率。1P（16）dtILdtiLmScbakS5.1)(5.0,2Rs的功率是：（17）2,2.)(mScbaKkSRIRtiP把表达式（17）带入表达式（14）和（15）中，我们可以得到表达式（18）20)(5.1conLconSconmdcidtiLiEtui（18）由于：（19）RtudtCtidccS)()()(0如果在稳态下考虑小干扰，可以得到表达式（20）：（20）tiItiuUutitimcowdcd0.0.0其中和是稳定值，和是低频率小干扰。如果把dcUI,0mI)(0dc、tm表达式（20）代人表达式（18）和（19），从表达式中我们除去小信号量得到式子（21）（21）RuiIdtiILiEtidcmSmSmdc025.1)(（22）ttuCtidcdcS0)()()(把表达式（22）代人（21）中，得到：（23）25.1.0)()(dtiILiIREUCRtudtmSmSmdcSdcc表达式（23）是三相HPFPWM整流器的小信号线性时域模型，控制变量是，输出变量是。表达式（23）经过拉普拉斯变换得到式（