外文翻译-使用时间保持控制反激式DC-DC变换器漏感效应的分析

英文原文AnalysisofLeakage-InductanceEffectinaFlybackDC-DCConverterUsingTimeKeepingControlHirotoTerashi,TarnotsuNinomiyaAbstract-FlybackDC-DCconverterisoftenusedaspowersupplyformanyelectronicsystemsbecauseofcircuitsimplicity.WehavealreadypresentednovelflybackDC-DCconverterwithimprovedstability(timekeepingcontrolledflybackconverter)byusingthetechniqueofkeepinginductorcurrentconstant3.ThisconverterbehavesaslikeforwardconverterwithoutRWZ(RightHalfPlaneZero),thereforethefrequencybandwidthofopen-looptransferfunctionfromdutyratiotooutputvoltageiswiderthanconventionalflybackconverterduetodisappearingofRHPZ.Inthispaperwereportthestaticanddynamicanalysisaboutthisnovelflybackconverterwitbleakageinductance,whichbecomelargerincaseofafewturn01secondarywindingespecially.Theanalysismethodisselectedwithstatespaceaveragingmethodbecauseofobtainingthesymbolicalsolution.Thenumberofstateis5includingtheperiodregardingleakageinductancesofprimaryandsecondarystages.Accordingtotheresultsthetheoreticaldatawithstatespaceaveragingmethodagreewiththeexperimentaloneandalsothetheoreticaldatewithsampled-datamethodwell.Anditisconfirmedthattheleakageinductancesactasanequivalentresistanceandthatstaticloadregulationisdeteriorated,hutthedynamicresponseissmoothedduetotheincreaseddumpingfactor.ICIRCUITTOPOLOGYANDBASICOPERATIONFig.1showsanovelflybackconvertertopology,whichhastheperiodofkeepingatransformercurrentconstant.BasicschematicsareinFig.1(a)andFig.1(b)thatwillbeexplainedtheoperationfromnowisusedastheexperimentalcircuit.Fig.2showsthekeywaveformsinthetimesequenceofgatedrivevoltagesformainswitches,primary,secondaryandmagnetizingcurrentsinthetransformer,andtransformervoltage.Q2D1Q1D2VinQ2VinCQ1D2D1D3CLLRLRLN:1(a)(b)Fig.1.Circuittopologyoftheproposedflybackconvert12345dydyDP=constaDutyRaioSeTransfomerVltgMgtizCuSecondaryutPrimayCuetQ1GateVolg2tlTFig.2.KeywaveformsoftheproposedflybackconverterInstate1,atfirstthebothswitchesQ1,andQ2areturnedON.Then,theremainingsecondarycurrentdecreasesgraduallyandprimarycurrentincreaseatthesametimeandthesamerateduetoleakageinductance.Instate2,whensecondarycurrentreachestozero,primarycurrentcontinuestoincreasewithsmallerslopethanState1.Instate3,onlyswitchQ2isturnedOFFandtheenergyiskepttobethesamevaluejustbeforetheswitchQ2wasturnedOFF.Instate4,theswitchQ1isturnedOFF,thentheprimarycurrentdecreasesgraduallyandsecondarycurrentinthetransformerincreasesoppositetoState1.Finally,theprimarycurrentbecomeszero.Instate5,thestoredenergyinprimaryinductanceoftransformeristransferredtosecondaryside.Thesumofdutycycleinstate4and5canbedefinedasP.ThePhassomeconstantvaluelessthan1andisselectedas0.5inFig.2,whichrepresentsthekeywaveformsinthisschematics.Thedutyratioofeachstateisshownbydy1,dy2,dy3,dy4,dy5.ThedutyratioDisthesumofdutyinstate1and2,whichshouldbecontrolled.IIANALYSISOFCHARACTERISTICSFig.3showseachstateofequivalentcircuitsinFig.1.ItisnotedthatthepolarityofinputvoltageVinisoppositeforstate1and4.Thereforetherisingandfallingslopesofprimarycurrentaredifferentinbothcommutationperiods.Thecomponentsymbolsandparameters,whicharerepresentedinFig.1and3,aredefinedasfollows;LMagnetizinginductanceRLLoadresistanceRReflectedRLfromprimarytosecondaryCOOutputcapacitorCReflectedCOfromprimarytosecondaryKCouplingcoefficientofthetransformerTSwitchingperiod(1-k)L(1-k)LVinkLimCRvoState1Q1,Q2,D3ONState2Q1,Q2ONVinkLCRvo(1-k)LimState3Q1OND1,D2,D3ONState4State5D3ONkLCRvo(1-k)Lim(1-k)L(1-k)LVinkLimCRCRvoim(1-k)LkLvoFig.3.TheequivalentcircuitofEachstateATransformerwithLeakageInductanceA-1.AverageStateSpaceEquationThemagnetizingcurrentim,andoutputvoltagevoisselectedastwostatespacevariables.Thedy1,anddy4arethedutyratiocalledcommutationperiodinstate1and4respectively.AndthedutyratioofPwhichisconstantandthatofDwhichshouldbecontrolledareshowninexpression(1)asyoucanseeinFig.2.TheuseofbothPandDallowsthedutyratioofdy5,anddy2,tobeeliminated.(1)4512,PdyDdyThestatespaceequationsregardingimandvoisderivedfromsumof“volt-secondproduct”and“current-secondproduct”respectivelyasin(2).Regardingdy1,dy4,theexpression(3)canheobtainedusingthecharacteristicofstatespaceaveragingmethod.Thehatmarkoverthesymbollikeandmeans“averaging”.TheP,whichissumofdutyinstate4and5,istheperiodofmi0venergytransferringtosecondaryside.Anditischosenaslessthan1.Pisselectedas0.5inFig.2.(2)011040400401mmdikkLVinvdykinDdyVinvdykdytvvCiiR(3)2214001,kLkLdyidyiVinvTVinvTIfthecouplingcoefficientkisclosetounity,theequations(11)and(12)canbesimplifiedasin(4)and(5).(4)01140400122mmivdydLkinDdytVnPdvvyCitR(5)1400,mmHdyidyiVnvVnvwhereHmeanstheimpedanceofleakageinductancedividedbyatswitchingfrequency(1/T):(6)2kLTSummarizing(13)-(15),thestatespaceequationincludingsystemmatrixarederivedasin(7).(7)0414141,220midxAbVinxtvdyPLdyPCRDbLTosimplify(7),andaredefinedasin(6)and(9).(8)04124120mHvidyVnii(9)0,iPDvAsshownin(9).thedutyratiochangesfromP(withoutleakageinductance)toP-(withleakageinductance).alsochangessameway.Thismeansthereductionofeffectivedutyratiotocontributetheenergytransferring.Theapproximateandaveragingsystemmatrixandwithdutyratioofdy1,anddy4,in(1)Abareobtainedusingexpression(10).(10)0,10LCRA-1-1.StaticAnalysisThesolutionofsteadystatecanbeobtainedbyputtingin(7)tobezero.LetthestatedxtvariablesinsteadystatebeXo.(11)20,ommoooVRIXinHIPViDWhereIm,Vo.D.o,o,oarethefixedvaluesinsteadystate.A-1-2.DynamicAnalysisThedynamicequationsin(12)areobtainedtogivetheperturbation,andxDVinlinearizationaroundfixedvaluesofXotothestatespaceaveragingequation(7).(12)0000000ududxVintAbxxinDbbViwherethenotationstandsforthevaluesontheDCfixedpointofXo.Asaresulttheexpression(12)canbewrittenasin(13).(13)222211111,0oomodumVininPLILVPCCRiLVinLinIVThetransferfunctionfrom,tocanbesolvedasin(13).Dix(14)11,duxssinThecontroldutyratiotooutputvoltagetransferfunctionisespeciallywrittenasin(15)and(16).(15)2ovgsef(16)22020220220111ooooooheCRLhfPPhgVinWherethesymbols,aredefinedasinexpression(16)and(17).Thesymbols,handhavenodimension.(17)21,ookhTLC(18),moomoiVinvIiLVThenaturalangularfrequencyindenominatoroftransferfunctionin(15)ispresentedastanddampingfactoris.f2efWhencouplingcoefficientkbecomessmaller,hbecomeslargerasyoucanseein(16).Andobecomesover1,becauseDisbelow0.5,whenthePisselectedas0.5(referFig.5).Thetermoffin(7)becomesgreaterthan(incaseofk=1)becauseincreaseasdecreasingkor2oPocontroldutyratioD.Astheresult,thetermeandfinexpression(16)increasecomparewithnoleakageinductance(k=1)asmakingksmall.Thereforetheandareslightlyincreased.Howeverthetermg1representedDCgaindecreasestothecontrary.Incaseofnoleakageinductancek=1,thenhbecomeszero.Sothisfollowingidealtransferfunctionin(19)accordwiththetransferfunctionin(9)asmentionedinsection-(A).(19)211ooovVinDPsLsRCPA-2.Sampled-DataMerhodThesampled-datamethodisnumericalanalysisandhaveaprecisesolutionduetomoreinformationwhichithaveinoneperiodthanstatespaceaveragingmethod.Thequantityofinformationisproportionaltothenumberofsamplingpointcomeoutfromthebeginningofeachstateinonecycle.Intheresultthebettersolutioncomparertostatespaceaveragingmethodcanbeobtainedespeciallyaroundhigherfrequencyneartoonesecondofswitchingfrequency.Theprocedureinthesolutionofthismethodhavealreadymentionedbefore6.ThereforeonlytheresultisshownasinFig.4inthispaper.1.0dutyratioDVoltageconversionratiok=1k=0.98k=0.94Fig.4.Vo/VinvoltageconversionratiocharactensticsIIICOMPARISONOFTHEORETICALANDEXPERIMENTALRESULTSA.StaticAnalysisResultsTheswitchingfrequencyissetto300KHztoreducethetransformersize,andthemagnetizinginductanceLisaround57Handcouplingcoefficientisk=0.98and0.94intheexperiment.Thevaluesofotherparametersareshownasfollows.OutputcapacitanceC=1F,loadresistanceR=0.37,inputvoltageVin=60V,andturnratioN=9.Figs.4,5and6showthetheoreticalandexperimentalresults.Theleftsideofthiseachfigureshowstheresultwiththestatespaceaveragingmethodandrightsideisthatwithsample-datamethod.Theboxandcircularsymbolsinthesefiguresillustratetheexperimentalresult,thedottedandsolidlinesshowtheoreticalresultsincaseofk=0.94andk=0.98respectively.Bothresultarewellagreed.0.50dutyratioDDutyratiody1,dy4k=0.98k=0.94k=0.98k=0.94dy4dy1k=0.98k=0.9110L/(RT)VoltageconversionratioFig.5.Commutationperioddylanddy4Fig.6.CurrentlimitationcharacteristicsFig.4,whichshowsthevoltageconversionratio,inputvoltageVintooutputvoltageVowithrespecttodutyratioD.Itcanbeobtainedbysolving(11)anditdisplaysassolidanddottedlinesinFig.4.Thischaracteristicsmakeitsslopeloweratalargedutyratioandthesmallercouplingcoefficientk.Thereforethishasanoperationofoutputcurrentlimitationbyitselfduetothelowslope.Fig.5showstherelationofcontroldutyratiowithbothcommutationperiod.Thecontroldutyratiobecomesgreater,thenthecommutationperiodalsobecomebigger.WhenthecontroldutyratioDis0.5,thecommutationperioddy4becomes0.5.Thismeanstheenergyistransferredfromprimarytosecondarysidebyonlytheleakageinductance.Fig.6representsthecurrentlimitationcharacteristicswhichshowsthatoutputvoltagegoesdownastheoutputcurrentincrease.TheconditionD=0.25inFig.6ismaximumdutyratiowhichisusedincaseofovercurrentprotection.X-axisisdefinedastomakenodimension.ThevoltageconversionratioLRTconvergestonear0.5inasmalloutputcurrent.Itcanbefoundbyexpression(8)(D=0.25,P=0.5).B.DynamicAnalysisResultThetheoreticaltransferfunctionto,whenthecouplingcoefficientkisvariedbyovusing(15)to(18),isshowninFig.7incaseofk=1,0.98and0.94.ThetoplineintheFig.7showsideallinewithk=1.ItisobviousfortheincreaseofleakageinductancetogettheDCgaindecreased,thedumpingfactordecreasedandnaturalfrequencyincreased.Fig.8isobtainedwithsampled-datamethod.ThebothFig.7and8havingtheoreticalresultagreewell.TheexperimentalresultisrepresentedasFig.9incaseofk=0.98and0.94.Frequeency(Hz)PhaseGain1*1031*1041*105-180-120-600-200204060Fig.7.TheoreticalFrequencyresponsewithstatespaceaveragingmethodFrequeency(Hz)01020304050-100-50-100-150-200-250Magnitude(dB)Magnitude(dB)Fig.8.TheoreticalFrequencyresponsewithsampled-datamethodFrequeency(Hz)Magnitude(dB)104103105-2002040600-90-180-270GainPhasek=0.98k=0.98k=0.94k=0.94Fig.9.ExperimentalFrequencyresponseThismattercanprobablyheseentheeffectasthesameasthatofequivalentinternallosses.TheboththeoreticalandexperimentaldataagreeswellasinFig.7,8and9.Thereforethetheoreticalanalysisisconfirmedbytheexperiment.IVCONCLUSIONSThenovelflybackconverterproposedbeforewasanalyzedincaseofthetightcouplingtransformer,anditwasclarifiedthattheright-half-planezerointhecontroltransferfunctionisdeletedandthisconverterisalwaysstable3.Furthermore,theeffectoftransformersleakageinductancesonthestaticanddynamiccharacteristicswasconsideredthroughanalysisandexperiment.Asaresult,itisconfirmedthattheleakageinductancesactasanequivalentresistanceandthatthestaticloadregulationisdeteriorated,butthedynamicresponseissmoothedduetotheincreaseddumpingfactor.Sothisaffectofleakageinductanceisthoughtasanequivalentinternalresistance.VREFERENCES1T.Ninomiya,M.Nakaham.T.Higashi,K.Hmda“AUnifiedAnalysisofResonantConvenen”IEEETrans.onPowerElecuonics,vol.PE6,No2,April1991,pp.260-2702T.Ninomiya,K.Harada.M.Nakahm“StabilityAnalysisofBoostandBuck-BoostConvetten”,Thetrans.OfIEEE.vol.J66C,Nol,Jan.1983.pp.1-83H.Terashi,I.Cohen.T.Ninomiya“NovelFlybackDC-DCconvenerwithimprovedStabilityandDynamicResponse”ICPE01pp.208-211,Oct15-19.Seoul4KoreaK.viswanathan,R.Oruganti,DSrinivasan,“Tn-StateBoostConvenerwithNoRightHalfPlaneZero”IEEEPEDS2001,proceeding,pp687-693,Oct22-25Bali,lndonesia5H.Terashi.I.Cohen,T.Ninamiya“StabiliiyandDynamicResponseImprovementofFlybackDC-DCConvenerbyaNovelControlScheme”APEC02proceeding,pp.389-394(March2002)6H.Terashi,T.NinoMya,“AnalysisofLeakage-InductanceEffectonCharactensticsofFlybackConvenerwithoutRightHalfPlaneZero”,lntelec03Proceedings,pp.463-469(October2003)7K.HaradqT.Ninomiya,B.Gu“TheFundamentalsofSwitchedModeConverters”.Coronapub.,19928SoumitroBanerjee,GeorgeC.Verghese“NonlinearPhenomenainPowerElectronics”,IEEEPRESS中文译文使用时间保持控制反激式DC-DC变换器漏感效应的分析HirotoTerashi，TarnotsuNinomiya摘要：因为电路简单，所以反激式DC-DC转换器通常用于许多电子系统的电源供应。我们已经推出了利用该技术保持电感电流恒定，提高稳定性的新颖的反激式DC-DC转换器（时间保持控制的反激式转换器）。这个转换器的运转像没有RHPZ（右半平面零点）的正向转换器。因此，由于没有RHPZ开环传递函数的频率带宽占空比的输出电压比传统的反激式转换器的宽。在本文中，我们报告有关此新型有漏感的反激变换器的静态和动态分析，特别是几个二次绕组的情况下漏感会大。为了获得象征性的解决方案选中了状态空间平均法作为分析方法。状态的数目是5包括了一级和二级阶段的泄漏电感期间。根据研究结果状态空间平均法的理论数据和实验相符合，采样数据的方法与理论的数据也符合。它证实，泄漏电感充当一个等效电阻而且静态负载调节恶化，但由于增加的反倾销因素动态响应平滑。I电路拓扑结构和基本操作图1显示了一种新型反激变换器的拓扑结构，其中有变压器的电流不变的时期。在图1（a）和图1（b）将解释从现在开始操作实验电路的基本原理图。图2显示在主开关管，初级，中级和变压器中，变压器的电压栅极驱动电压的时间序列的关键波形。Q2D1Q1D2VinQ2VinCQ1D2D1D3CLLRLRLN:1(a)(b)图1提出的反激式转换器电路拓扑结构图在状态1，首先打开两个开关Q1和Q2。然后，由于漏感，剩下的二次电流的降低逐渐，同时初级电流以同样的速度增。在状态2，当二次电流达到零，初级电流继续增加小于状态L的斜率。在状态3，只有开关Q2关闭而且关闭开关Q2之前电源被保持相同的值。在状态4，开关Q，关闭，然后在变压器的初级电流减小逐步二次电流增加相反的状态1。最后，初级电流变为零。在状态5，在变压器初级电感储存的能量被转移到二次侧。在状态4和第5占空比的总和可以被定义为P。P有一些恒定值小于1和图2中被选定为0.5，这代表在这个原理图的关键波形。每个状态占空比由dyl，dy2，dy3，dy4，dy5表示。占空比D是状态l和2的总和，应加以控制。12345dydydyDP=二二二二二二二二二二二Q1二2二T图2提出的反激式变换器的关键波形图II特征分析图3显示了如图1每个状态的等效电路。我们注意到输入电压Vin的极性是和状态l和4相反的。因此，初级电流上升和下降斜坡在两个换相时期都不同。代表图1和3中组件符号和参数，定义如下：L磁化电感RL负载电阻R反应RL，从初级到高级CO输出电容器C反应CO，从初级到高级k变压器耦合系数的影响T切换时间(1-k)L(1-k)LVinkLimCRvoState1Q1,Q2,D3ONState2Q1,Q2ONVinkLCRvo(1-k)LimState3Q1OND1,D2,D3ONState4State5D3ONkLCRvo(1-k)Lim(1-k)L(1-k)LVinkLimCRCRvoim(1-k)LkLvo图3不同状态等效电路A变压器漏电感A-1平均状态空间方程励磁电流im，输出电压vo被选定为两个状态空间变量。和dy4分别称为换相期间状态l和4的占空比。和占空比的P不变一样，D也应有式（1）所示公式控制，图2中可以看到。P和D的使用允许的占空比dy5和dy2被剔除。(1)4512,dydy状态空间方程中的im，vo是分别来自“伏秒产品”和“流秒产品”总和如式（2）。由dy1，dy4使用状态空间平均法的特点可以得到表达式（3）。像和头顶上的符号表示平mi0v均。状态4和5占空比总和P，是能量转移到二次侧的时期。它被选为小于1。P被选定为0.5如图2。(2)011040400401mmmdikkLVinvdykinDdyVinvdykdytvvCPiiR(3)2214001,mkLkLdyidyiVinvTVinvT如果耦合系数k是接近统一，方程（2）和（3）可简化为式（4）和式（5）。(4)01140400122mmVinvdydkLkinDdytPdvvyCitR(5)1400,mmHdyidyiVnvVnv其中，在开关频率（1/T）下，H表示泄漏电感的阻抗除以：(6)2kLT通过总结式（4）式（6），状态空间方程包括的系统矩阵如式（7）。(7)0414141,220midxAbVinxtvdyPLdyPCRDbL为了简化式（7），、和定义如式(8)和式(9)，(8)04124120mHvidyVnii(9)0,iPDv如式（9）所示，占空比从P(有漏感)到P-(没有漏感)变化，的变化也一样。这意味着减少有效占空比，可以促进能源转移。利用式（10）近似和平均系统矩阵和式（1）中占空比dy1和dy4可以得到。Ab(10)0,10LAbCRA-1-1。静态分析通过把式（7）中设为0可以得到的稳态解Xo：dxt(11)20,ommoooVRIXinHIPViD其中：Im，Vo，D，o，o，o是稳态中的固定值。A-1-2动态分析通过给定x，D，Vin的扰动和固定值XO的状态空间平均方程式（7）附近线性化得到的动力学方程式（12）。(12)00000000ududxVintAbixxinDAbbVii在符号代表着不动点Xo上的直流值，作为一个结果表达式(12)可以写成式(13)。(13)222211111,0oomooodumVininPLILVPiCCRLVinLVinI如式（14）从D，Vin到x的传递函数可以解决(14)11,duxxssDVin控制占空比输出电压传递函数尤其是写在式（15）和（16）。(15)2ovgsef(16)20220220220111oooooooheCRLhfPPhgVin式（17）和（18）中定义了符号，。符号，和没有位数。oh(17)1,okhTLC(18),moomoiVinvIiLVC自然角频率在传递函数（15）的分母中为和阻尼因子为。tf2ef当耦合系数k变小，h变大，可以看到在式（16）。当P被选为0.5时，的值超过了o1，因为D小于0.5。由于增加，k和控制占空比D减少，式（7）中的f比大很o2P多作为结果，与比较无泄漏电感（k=1）表达式（16）中字母e和f的增加，而使k小。因此和是稍微增大。然而这个词代表直流增益减少相反的情况。1在没有漏感（k=1）时，然后h变成0。所以这后在理想传递函数(18)符合如II-(A)内所述的传递函数(9)。(19)211ooovVinDPsLsRCPA-2采样方法抽样数据的方法是数值分析，由于更多的信息，它有一个周期状态空间平均比的方法，并有一个精确的解决方案。信息的数量是与来自在一个周期内每个状态开始的采样点的数量成正比。结果比较可以得到状态空间平均法更好的解决方案的，特别是围绕一秒钟开关频率附近的频率较高。程序中的解决这一方法已经前面的6提到。所以只有结果表现为图4进行了论述。1.0占空比D电压转化比k=1k=0.98k=0.94图4Vo/Vin电压转换比特征III理论分析与实验结果的比较A静态分析结果在开关频率设置为300千赫至降低是实验设备变压器尺寸和周围磁化电感L是57H和耦合系数k=0.98和0.94。其他参数的值显示如下。输出电容C=1F，负载电阻R=0.37，输入电压Vin=60V，匝数比N=9。图4、5、6表示理论和实验结果。左边的这各图与状态空间平均法结果和右边的是随着采样方法的结果。这些数字的方块和圆形符号说明实验结果，虚线和实线显示在k=0.94和k=0.98的情况下的理论结果。这两种结果都相符。图4显示的电压转换比，输入电压Vin，输出电压Vo与占空比D。求解式（11）可以得到，它显示在图4为固体和虚线。这个特性使得它在大占空比较小的耦合系数k的斜率。因此，由于低的斜率，这本身的输出电流限制的操作。图5显示了控制占空比既换向期间的关系。控制占空比变大，然后换向期间也变得更大。当控制占空比D为0.5，dy4变换时期，就变成0.5了。这意味着，只有漏感的能量从初级到次级侧转移。图6代表显示输出电流增加，输出电压下降，电流限制特性。条件D=0.25在图6是最大占空比，这是过电流保护的情况下使用。义为X轴t没有维度。收敛的电压转换比接近0.5在一个小的输LRT出电流。可以在式（8）中得到(D=0.25，P=0.5)。0.50占空比D占空比dy1,dy4k=0.98k=0.94k=0.98k=0.94dy4dy1图5dyl和dy4期间的整流交换k=0.98k=0.9110L/(RT)电压转换率图6限流特征B动态分析结果D理论对V传递函数，当耦合系数k是多样的利用式(15)、(18)，被显示在图7如分别