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    TUTORIALSolarModulePhysicalModel

    OCTOBER2016

  • SolarModulePhysicalModel

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    Thephysicalmodelofthesolarmodulecantakeintoaccountvariationsofthelightintensityandambienttemperature.However,itrequiresmanyparameterinputs.Someoftheparameterscanbeobtainedfrommanufacturerdatasheets,whileotherparametersneedtobeobtainedbytrialanderror.

    Inordertomakeiteasierforuserstodefineparametersforaparticularsolarmodule,autilitytoolcalledSolarModule(physicalmodel)isprovidedinthePSIMsUtilitymenu.Thistutorialdescribeshowtousethistoolthroughexamples.

    Thesolarmodulephysicalmodelhasthefollowingparameters:

    NumberofCellsNs: NumberofsolarcellsinseriesinasolarmoduleStandardLightIntensityS0: Light intensityunderstandardtestconditions, inW/m2.This

    valueisnormally1000W/m2.Ref.TemperatureTref: Temperatureunderstandardtestconditions,inoC.SeriesResistanceRs: Seriesresistanceofeachsolarcell,inOhm.ShuntResistanceRsh: Shuntresistanceofeachsolarcell,inOhmShortCircuitCurrentIsc0: Short circuit current of the solar module at the reference

    temperature,inA.SaturationCurrentIs0: Saturationcurrentofthediodeinthemodel,inABandEnergyEg: Bandenergyofeachsolarcell,ineV.IdealityFactorA: Idealityfactor,alsocalledemissioncoefficient,ofthediodein

    themodel.TemperatureCoefficientCt: Temperaturecoefficient,inA/K.CoefficientKs: Coefficient that defines how light intensity affects the solar

    celltemperature

    ThesolarmoduleMSX60fromBPSolarisusedtoillustratehowtousetheutilitytooltoobtainthemodelparameters.Theprocessinvolvesthefollowingsteps:

    Entertheinformationfromthedatasheet;

    Makeaninitialguessofcertainparameters;

    ObtaintheIvandPvcurves,andthemaximumpowerpoint.Comparewiththedatasheetandexperimentaldatafordifferentoperatingconditions,andfinetunetheparameters.

    1. EnteringDatasheetInformationThefigurebelowshowsthemanufacturerdatasheetimage,andtheregionoftheutilitytooldialogwindowrelatedtomanufacturerdatasheet.

    Alltheinformationrequiredbythisregion,exceptthedv/divalueatVoc,canbereaddirectlyfromthedatasheet,ashighlightedbytheredrectangles.Inthedatasheet,thetemperaturecoefficientoftheopencircuitvoltageisexpressedinV/oC.Itneedstobeconvertedto%/oCfortheutilitytoolas:80mV/oC=0.08/21.1/oC=0.38%/oC.

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    Thevaluedv/di(slope)atVocreferstothedv/dislopeattheopencircuitvoltageVocof21.1V.FromthedatasheetIVcharacteristics,byreadingthevaluesfromthegraph(markedinreddottedlines),wecancalculateapproximatelytheslopeas:

    68.05.034.0

    iV

    didv

    IftheIVcurveisnotavailableonthedatasheet,leavethedv/divalueat0.

    2. EstimatingParameterValuesEg,A,Rsh,andKsThese fourparametersarenormallynotprovidedon thedatasheet,andoneneeds tocomeupwithagood initialguess,orobtainthemfrommanufacturers:bandenergyEg, ideality factorA,shuntresistanceRsh,andcoefficientKs.

    Manufacturerdatasheet

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    AgoodinitialguessofthebandenergyEgisaround1.12eVforcrystallinesilicon,andaround2eVforamorphoussilicon.

    AgoodinitialguessoftheidealityfactorAisaround2forcrystallinesilicon,andislessthan2foramorphoussilicon.

    AgoodinitialguessoftheshuntresistanceRshisseveralthousandOhm.

    Ifunknown,theinitialvalueofthecoefficientKscanbesetto0.

    Inthisexample,weset:

    Eg=1.12A=1.2Rsh=1000Ks=0.

    3. CalculatingParameterValuesRs,Isc0,Is0,andCtBased on the datasheet information and the initial guess of Eg, A, Rsh, and Ks, the rest of theparameters(seriesresistanceRs,shortcircuitcurrentIsc0,saturationcurrentIs0,andtemperaturecoefficient Ct) can be calculated by clicking on theCalculate Parameters button. The followingvalueswillbeobtained:

    Rs=0.0108Isc0=3.8Is0=2.16e8Ct=0.00247

    Notethatthecalculationisapproximate,andprovidesonlythebasevalues.Usersshouldfeelfreeto adjust these parameters to fit the calculated IV curve to the datasheet curve or theexperimentalresults.

    4. FineTuningtheParametersUndergiveoperatingconditionsofthelightintensitySandtheambienttemperatureTa,onecanobtain the IV and PV curves by clicking on the Calculate IV Curve button. The calculatedmaximumpowerpointwillalsobecalculated.

    IfwedefineS=1000W/m2andTa=25oC,wecanobtainthemaximumpowerpointas:Pmax=59.27W,Vmax=16.73V,and Imax=3.54A.Both themaximumpowerandthevoltageat themaximumpowerarelowerthanthedatasheetvaluesof60Wand17.1V.OneshouldadjusttheparametersEg,A,Rsh,Ks,Rs,Is0,andCttoobtainabetterfit.

    In this example, if we change the series resistance Rs to 0.008 Ohm, the calculatedmaximumpower point is: Pmax = 60.54 W, Vmax = 17.04V, and Imax = 3.55 A, which is closer to thedatasheetvalues.

    ThefinalparametervaluesandtheIVandPVcurvesareshownbelow.

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    Many iterations and trialanderror may be needed to obtain a good fit to the datasheet orexperimentaldata.Aftertheparametersarefinalized,clickontheCopyPSIMParametersbuttontocopythemodelparameterstothePSIMschematic.

    Tosavethedatasheetandparametervaluestoatext fileto lateruse,clickontheSavebutton,andsaveittoafile(forexampleSolarexMSX60.txt).Toloadthedataofaspecificsolarmoduleback,clickontheLoadbutton.

    5. MultipleModulesinSeriesOftenseveralidenticalsolarmodulesareconnectedinseriestoformasolararray.Onecanuseasolarmoduleblocktomodelthesolararray.

    The figure below shows 2 solarmodules SolarexMSX60 connected in series, and a combinedblockthatmodels2modules.Themodelparametersofthecombinedblockisthesameasforasinglesolarmodule,exceptthatthenumberofcellsNsis2timesofthesinglesolarmodulevalue.

    Notethatwhenmultiplemodulesareconnected inseries,abypassdiode isneededacrosseachmodule if the light intensity and ambient temperature inputs are different. Also, a very smallcapacitor(inthiscase30nF)isneededacrosseachmodulefornumericalconvergence.

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    To plot the IV curve of the combined block, change the following quantities from the singlemodulevalue:

    NumberofCellsNs*2MaximumPowerPmax*2VoltageatPmax*2OpenCircuitVoltageVoc*2dv/di(slope)atVoc*2

    The figurebelowshowsthesolarmoduleutility tooldialog forasinglemoduleandacombinedblock.Theparameterinputsintheredboxeshighlightthedifferences.

    2modulesinseries Acombinedblockrepresenting2modulesin

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    6.MultipleModulesinParallelInothercases,severalidenticalsolarmodulesareconnectedinparalleltoformasolararray.Onecanuseasolarmoduleblocktomodelthesolararray.

    The figurebelowshows2 solarmodulesSolarexMSX60connected inparallel, anda combinedblock thatmodels 2modules. Some of the parameters of the combined block are different ascomparedtotheparametersofasinglesolarmodule,ashighlightedintheredboxesbelow.

    Dataofonesinglesolarmodule Dataofthecombinedblock

    2modulesinparallel Acombinedblockrepresenting2modulesinparallel

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    To plot the IV curve of the combined block, change the following quantities from the singlemodulevalues:

    MaximumPowerPmax*2CurrentatPmax*2ShortCircuitCurrentIsc*2dv/di(slope)atVoc*0.5SeriesResistanceRs*0.5ShortCircuitCurrentIsc0*2SaturationCurrentIs0*2TemperatureCoefficientCt*2

    The figurebelowshowsthesolarmoduleutility tooldialog forasinglemoduleandacombinedblock.Theparameterinputsintheredboxeshighlightthedifferences.

    Dataofonesinglesolarmodule Dataofthecombinedblock