外文翻译原文-基于快速傅里叶变换的励磁涌流谐波分析

2013InternationalConferenceonPower,EnergyandControl(ICPEC)978-1-4673-6030-2/13/$31.002013IEEE520HarmonicAnalysisofInrushCurrentusingFastFourierTransformT.Sridevi,MIEEEPhDScholarJawaharlalNehruTechnologicalUniversityHyderabad,AndhraPradesh,INDIAsridi_K.RameshReddy,MIEEEDean&HOD,EEEGNarayanammaInstituteofTechnologyandSciencesHyderabad,AndhraPradesh,INDIAN.LeelaJayaSyamalaM.Tech.Student(EPS)AnnamacharyaInstituteofTechnologyandSciencesHyderabad,AndhraPradesh,INDIAAbstractThispaperpresents,analysisofmagnetizinginrushcurrentfordifferentvoltageanglesandharmonicanalysisofthatinrushcurrentusingdifferentFFTwindowingtechniques.Timedomainsimulationswereusedtosolvetheinrushphenomenon.Square,Welch,HanningandParzenwindowswereusedtotruncatetheobtainedinrushcurrentharmonicspectrumforinvestigationandwithparzenwindowingtheharmonicmagnitudeisgettingreducedduetoitsreducedsidelobes.InrushcurrentharmonicspectrumobtainedbyusingFFTalgorithminturndiscretefouriertransform.Outofdifferentsolverstosolvestateequation,ode23tsolverisused.Foranunloadedsinglephasetransformer,inrushcurrentintimedomainandharmoniccontentofinrushcurrentwerepresented.Theresultsarehelpfultoestimateharmonicseffectsinthetransformerinrushcurrents.Theresultsestablishaguidelineforharmoniceliminationduetoinrushcurrentandofferanimportantreferenceforsystemdesign.IndexTermsInrushcurrent,harmonicanalysis,windowingtechniques.I.INTRODUCTIONTransformeristhemostsensitivecomponentinresponsetopowersystemharmonics.Inrushcurrentisanimportantissuefortransformer.Duetotemporaryoverfluxinginthetransformercore,attheenergizationofthetransformer,itresultsmagnetizinginrushcurrent.Thesteadystatemagnetizingcurrentofatransformermaybeonly1or2%oftheratedcurrentbutitmayreach10-20timesratedcurrent.Whentransformerisswitchedontoasource,inrushcurrentexistsseveralsecondsbeforethesteadystateconditionisreachedandcauseunnecessarytrippingofprotectiverelays.Inrushcurrentmagnitudemainlydependsonswitchingparameterslikeresistanceofprimarywinding,voltageanglesetc.Inthispaper,inrushcurrentatdifferentvoltageangleswereobtainedinitially.Magnitudeoftheinrushcurrentdependsuponthemagnitudeandpolarityoftheremanentfluxdensitywithrespecttothoseofthesteadystatefluxdensityattheinstantofenergization.Inrushphenomenonisofnonlinearnatureandcanonlybereproducedbyactualtests&computersimulations.Duetothenon-linearnatureofinrushphenomenonitmustbesolvedbyiteration1Inmostcasesthemagnetizingcurrentofsinglephaseironcoreswillbesymmetricandtheharmoniccurrentspectrumjustconsistsofthefundamentalfrequencycomponentandoddharmonics,noevenharmonicandDCterms.Mostlyharmonictermsinthemagnetizingcurrentabove15thharmonicarenegligiblysmallandharmless.ButpracticallyifDCcomponentresultsfromanypowerelectroniccircuitfeddirectlyfromtransformer,finditswayintothemagneticcore,itwillcausethetransformertosaturateasymmetrically.Duetothis,theharmonicspectrumofthemagnetizingcurrentincreasesinmagnitudeandcontainsevenharmonicsandDCterminadditiontofundamentalfrequencycomponentandoddharmonics.Accordingtostrategiesofdevelopment&diffusionofenergyefficientdistributiontransformers(SEEDT),thelossescausedbyharmonicsandreactivepowerinEuropeanUnionDistributionTransformersareestimatedatabout5000GWh/year2.Thereforeharmonicanalysisplaysanimportantroleintransformerstoreduceharmonicsaffect.InthepresentworkwedevelopedaMATLABcodetogetthetimedomainwaveformsofthetransformerexcitationcurrentandthemagnitudeandphaseanglesoftheharmoniccomponentoftheinrushcurrentsatdifferentvoltageangleswithfourdifferentFFTwindowingtechniques.II.INRUSHCURRENTFORDIFFERENTVOLTAGEANGLESThecircuitmodelforcalculatingmagnetizinginrushcurrentofanunloadedsinglephasetransformerisshownintheFig.1.Fig.1Single-phasetransformerequivalentcircuit.2013InternationalConferenceonPower,EnergyandControl(ICPEC)521Thenonlinearcharacteristicequationinthiscasecanberepresentedbyapolynomialequationas3nullnullnullnullnullnull0.7576nullnullnullnullnullnull1.03null10nullnullnullnullnullnullnullnullKCLloopequationsofprimarysideofthetransformerarenullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullTherelationshipbetweentheappliedvoltageandthefluxinthetransformersmagneticcoreisnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullThereforevoltagedropacrosstheironcoreresistanceiswrittenasnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullFromtheaboveequations(1)and(2),stateequationobtainedisnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnull0nullnull0nullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnull1nullnullnullnullnullnullnullnull0nullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullWherer1=0.192,r0=612.86,l1=0.9mHarethetransformerparameters3Theenergizationofawindingatapointdifferentfromthevoltagepeakwillalsoresultinafluxwhichisequivalenttothefluxduetoremanence.Usingthisbasicpremisetheinrushcurrentiscalculated.Theattenuationofinrushcurrentisnotsignificantlyaffectedbyeddycurrentandhysteresislossesintheironcore.So,nodiscretizationofthelaminationshasbeenconsideredinthiswork3.Inthepresentwork,nullnullnullnullnullnull110nullnullnullnullnullnullnulltnullnullnullV,nullnullnull50nullnullisselectedand200cyclesofsimulationisdone.Outofdifferentsolversavailablelikeode23s,ode15s,ode113,etc.,ode23tsolverisusedtosolvetheinitialvalueproblemforordinarydifferentialequation.Figure2specifiestheflowchartforobtainingmagnetizingcurrentoftransformeratdifferentvoltageangles.Fig.2Flowchartforevaluatinginrushcurrentatspecifiedvoltageangles.(1)(2)NoYesStartEvaluateStateMatrix&InputMatrixInitializeflux,specifyIteration×panEntersomevoltageangleEndPVoltageAnglePlotInrushcurrentversusTimewithRedcolourSolveStateEquationforfindingInrushcurrent&FluxPlotInrushcurrentversusTimewithGreencolourPlotInrushcurrentversusTimewithBluecolourIncrementP=0P=nYesYesNoNo2013InternationalConferenceonPower,EnergyandControl(ICPEC)522Fig.3InrushCurrentwaveformfor43Fig.4InrushCurrentwaveformfor90Fig.5InrushCurrentwaveformfor150Figure3toFig.5showstheinrushcurrentphenomenonatdifferentvoltageangles.Itwasobservedthatthetimetakentoreachthesteadystatevalueofcurrentvariesforeachvoltageangle.Fromzeroto180degreestheslopeofthecurrentspectrumisdecreasingandforhigheranglestheslopeisincreasingduetonegativeremanentfluxdensity.III.HARMONICCONTENTOFINRUSHCURRENTAsthecurrentspectrumofinrushcurrenttakesmuchlargertimetoreachsteady-state,ithasbeenexploitedtoconductthesimulationusingharmonicdomaintechniques,arguingthattheinrushcurrentmaybeconsideredlikeanon-sinusoidalcurrentinaquasi-steady-stateconditionifoneonlylooksatareducednumberofcycles4.ForthepresentworkFFTalgorithmwaschosensincedirectevaluationofDFTusingnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullrequiresN2complexmultiplicationandN(N-1)complexadditions.ButforanN-pointDFT,thenumberofcomplexmultiplicationsrequiredusingFFTisnullnulllognullnull.FFTishighlyefficientprocedureforcomputingtheDFTofafiniteseriesandrequireslessnumberofcomputationthanthatofdirectevaluationofDFT.FFTreducesthecomputationtime.Abrupttruncationoftheseriesforanalysis,resultsinoscillationswhichareduetoslowconvergenceoftheseries.Toreducetheiroscillations,fouriercoefficientsofthefilteraremodifiedbymultiplyingtheinfiniteimpulseresponsewithafiniteweighingsequenceW(n)knownaswindow.Where,nullnullnullnullnullnullnullnullnullnullnull0nullnullnull|null|nullnullnullnull12nullnull0nullnullnull|null|nullnullnullnullnullnullnull.ThesequencesforSquare,Hanning,WelchandParzen(Ws,Wh,WwandWp)windowswhichareusedinharmonicanalysisforthepresentworkare,nullnullnullnullnullnull1nullnullnullnullnullnullnullnull12nullnullnullnullnull12null0nullnullnullnullnullnullnullnullnullnullnullnull12null1nullcos2nullnullnullnull1nullnullnullnull1nullnullnullnull12nullnullnull1null12nullnullnull1nullnullnullnullnullnull1nullnullnullnullnullnullnull12nullnullnull1null12nullnullnull1nullnullwithnumberofpointspercycles(T)as50andNvariesfrom1tonumberofpointspercycles(T)andtotalnumberofpointsaretakenas10000forcarryingoutthework.Figure6specifiestheflowchartforfindingharmoniccontentininrushcurrentusingdifferentFFTwindowingtechniques.FordifferentvoltageangleshowitisvaryingisshownfromFig.7toFig.9.TheCurvesrepresentsfundamental,second,third,DC,fourthtermsetc,.fromtoptodownintheFigs.2013InternationalConferenceonPower,EnergyandControl(ICPEC)523Fig.6Flowchartfordeterminingharmoniccontentofinrushcurrent.Fig.7HarmoniccontentofInrushCurrentwaveformfor30Fig.8HarmoniccontentofInrushCurrentwaveformfor43Fig.9HarmoniccontentofInrushCurrentwaveformfor90EndStartReadr1,r0,l,f&EvaluateStateMatrix&InputMatrixInitializeflux,specifyIteration×panEntersomevoltageanglenFFToftheInrushcurrentandshiftingthemaboutoriginandstoretheminresultSolveStateEquationforfindingInrushcurrent&FluxSwitchtoFFTwindowingtechniqueforanyspecificwindowfunctionK=1K(NP-T-1)Storeresultincomplexformofharmonics,harmonicmagnitude&angleK=K+(NP-T-1)YesNo2013InternationalConferenceonPower,EnergyandControl(ICPEC)524IV.RESULTS&CONCLUSIONTABLEI.COMPARISONOFDIFFERENTWINDOWINGTECHNIQUESParzenHanningWelchSquare30Im0.17230.36620.1820.3890.2200.4760.2630.554Ia0-112.000-114.570-108.580-101.6543Im0.98781.87471.0772.0541.1832.2461.2712.379Ia0-132.560-132.890-130.490-128.1560Im3.81647.13854.1107.6984.3068.0224.4458.233Ia0-149.160-148.770-147.570-146.6090Im7.411113.70837.92714.638.16614.998.32015.22Ia0-174.970-175.240-175.460-175.54TableI.representstwosamplevaluesofharmonicmagnitude(Im)andangle(Ia)forthefourwindowingtechniques.Elaborationoftheinrushcurrentwaveformfor43isexposedinFig.10.Figure11displaysbarrepresentationofharmoniccontent.Thedecayofthemagnetizinginrushcurrenthasbeenobserved.Itwasfoundthat,switchingat90ofthevoltagewavereducesthemagnitudeofthemagnetizinginrushcurrent.Switchingatlowerswitchinganglesproducesafirstcycleofrelativelylargemagnitudewhereasalowpeakcurrentappearedwhentheswitchingtookplaceat180.Thereasonforthiscanbeexplainedintermsofthelaggingnatureofthefluxdensitywaveformandthevalueofremenantfluxdensity.Duetotheasymmetricalnatureofthemagnetizinginrushcurrentevenharmonicsaremoredominantonesintheharmonicspectruminparticularthesecondharmonic.Parzenwindowsequenceisgivingbetterevaluationofharmonicmagnitudesasthecentrallobeofthefrequencyresponseofthewindowcontainsmostoftheene