Photovoltaic Sources Modeling PDF
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PhotovoltaicSourcesModeling Photovoltaic Sources Modeling GiovanniPetrone UniversityofSalerno,Italy CarlosAndrésRamos-Paja NationalUniversityofColombia GiovanniSpagnuolo UniversityofSalerno,Italy Thiseditionfirstpublished2017 ©2017JohnWiley&SonsLtd Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or transmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise, exceptaspermittedbylaw.Adviceonhowtoobtainpermissiontoreusematerialfromthistitleisavailable athttp://www.wiley.com/go/permissions. TherightofGiovanniPetrone,CarlosAndrésRamos-PajaandGiovanniSpagnuolotobeidentifiedasthe authorsofthisworkhasbeenassertedinaccordancewithlaw. 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LibraryofCongressCataloging-in-PublicationData Names:Petrone,Giovanni,author.|Ramos-Paja,CarlosAndrés,author.|Spagnuolo,Giovanni,author. Title:Photovoltaicsourcesmodeling/GiovanniPetrone,UniversityofSalerno,Italy,CarlosAndrés Ramos-Paja,UniversidadNacionaldeColombia,GiovanniSpagnuolo,UniversityofSalerno,Italy. Description:Chichester,WestSussex,UnitedKingdom:JohnWiley&Sons,Inc.,[2017]| Includesbibliographicalreferencesandindex. Identifiers:LCCN2016038240(print)|LCCN2016054257(ebook)|ISBN9781118679036(cloth)| ISBN9781118756126(pdf)|ISBN9781118756492(epub) Subjects:LCSH:Photovoltaicpowergeneration–Mathematicalmodels. Classification:LCCTK1087.P432017(print)|LCCTK1087(ebook)|DDC621.31/244011–dc23 LCrecordavailableathttps://lccn.loc.gov/2016038240 Coverimage:TetraImages/Gettyimages CoverdesignbyWiley Setin10/12ptWarnockbySPiGlobal,Pondicherry,India 10 9 8 7 6 5 4 3 2 1 ToPatrizia,NicolaandMarcoAndrea GiovanniPetrone ToClaudiaPatriciaandAlejandro CarlosAndrésRamos-Paja ToSimonettaandValeria GiovanniSpagnuolo vii Contents Acknowledgements xi Introduction xiii TablesofSymbolsandAcronyms xv 1 PVModels 1 1.1 Introduction 1 1.2 Modeling:GranularityandAccuracy 1 1.3 TheDouble-diodeModel 2 1.4 TheSingle-diodeModel 4 1.4.1 EffectoftheSDMParametersontheI–VCurve 5 1.5 ModelsofPVArrayforCircuitSimulator 6 1.5.1 TheSingle-diodeModelbasedontheLambertW-function 10 1.6 PVDynamicModels 11 1.7 PVSmall-signalModelsandDynamic-resistanceModelling 14 References 17 2 Single-diodeModelParameterIdentification 21 2.1 Introduction 21 2.2 PVParameterIdentificationfromDatasheetInformation 21 2.2.1 ExactNumericalMethods 21 2.2.2 ApproximateExplicitSolutionforCalculatingSDMParameters 24 2.2.3 ValidationoftheApproximateExplicitSolution 27 2.3 Single-diodeModelSimplification 30 2.3.1 Five-parameterversusFour-parameterSimplification 32 2.3.2 ExplicitEquationsforCalculatingtheFourSDMParameters 34 2.4 ImprovedModelsforAmorphousandOrganicPVTechnologies 37 2.4.1 ModifiedSDMforAmorphousPVCells 37 2.4.2 Five-parameterCalculationforAmorphousSiliconPVPanels 38 2.4.3 ModifiedModelforOrganicPVCells 40 References 43 3 PVSimulationunderHomogeneousConditions 45 3.1 Introduction 45 3.2 Irradiance-andTemperature-dependenceofthePVModel 45 viii Contents 3.2.1 DirectEffectsofIrradianceandTemperature 45 3.2.2 Equationsfor“Translating”SDMParameters 49 3.2.3 IterativeProcedureproposedbyVillalvaetal. 51 3.2.4 ModifiedPVModelproposedbyLoBranoetal. 52 3.2.5 TranslatingEquationsproposedbyMarionetal. 53 3.2.6 ModifiedTranslationalEquationproposedbyPicaultetal. 53 3.2.7 PVElectricalModelproposedbyKingetal. 56 3.2.8 UsingtheKingEquationforEstimatingtheSDMParameterDrift 59 3.3 SimplifiedPVModelsforLong-termSimulations 61 3.3.1 KingEquationsforLong-termSimulations 63 3.3.2 PerformancePredictionModelbasedontheFillFactor 68 3.3.3 PVModelingbasedonArtificialNeuralNetworks 69 3.4 Real-timeSimulationofPVArrays 71 3.4.1 SimplifiedModelsincludingthePowerConversionStage 72 3.5 SummaryofPVModels 75 References 77 4 PVArraysinNon-homogeneousConditions 81 4.1 MismatchingEffects:SourcesandConsequences 81 4.1.1 ManufacturingTolerances 81 4.1.2 Aging 82 4.1.3 SoilingandSnow 83 4.1.4 Shadowing 83 4.1.5 ModuleTemperature 86 4.2 BypassDiodeFailure 87 4.3 HotSpotsandBypassDiodes 89 4.4 EffectofAgingFailuresandMalfunctioningonthePVEnergyYield 90 References 94 5 ModelsofPVArraysunderNon-homogeneousConditions 97 5.1 TheuseoftheLambertW-Function 98 5.2 ApplicationExamples 102 5.2.1 TheEntireI–VCurveofaMismatchedPVString 102 5.2.2 TheOperatingPointofaMismatchedPVString 104 5.3 GuessSolutionbyInflection-pointDetection 106 5.4 Real-timeSimulationofMismatchedPVArrays 108 5.5 EstimationoftheEnergyProductionofMismatchedPVArrays 109 References 111 6 PVArrayModelingatCellLevelunderNon-homogeneous Conditions 113 6.1 PVCellModelingatNegativeVoltageValues 113 6.1.1 TheBishopTerm 113 6.1.2 SiliconCellsTypeandReverseBehavior 115 6.2 CellandSubcellModeling:OccurrenceofHotSpots 116 6.2.1 CellModeling 117 6.3 SimulationExample 121 Contents ix 6.4 SubcellPVModel 123 6.5 ConcludingRemarksonPVStringModeling 124 References 124 7 ModelingthePVPowerConversionChain 127 7.1 Introduction 127 7.2 ReviewofBasicConceptsforModelingPowerConverters 129 7.2.1 Steady-stateAnalysis 132 7.2.1.1 Steady-stateValues 133 7.2.1.2 RippleMagnitudes 133 7.2.2 ConverterDynamicsAnalysis 134 7.3 EffectsoftheConverterinthePowerConversionChain 136 7.3.1 Steady-stateModelofthePowerConversionChain 136 7.3.2 AnalysisandSimulationusingtheSteady-stateModel 139 7.3.3 VoltageRippleattheGeneratorTerminals 143 7.3.4 I–VCurveofthePowerConversionChain 148 7.4 ModellingtheDynamicsofthePowerConversionChain 151 7.5 AdditionalExamples 159 7.5.1 MIUbasedonaBuckConverter 159 7.5.2 MIUbasedonaBuck–BoostConverter 161 7.6 Summary 162 References 163 8 ControlofthePowerConversionChain 165 8.1 Introduction 165 8.2 LinearController 166 8.3 Sliding-modeController 172 8.3.1 InductorCurrentControl 173 8.3.2 CapacitorCurrentControl 179 8.4 Summary 183 References 184 Index 185 xi Acknowledgements Theauthorswishtoacknowledgetheresearchgroupstheybelongto,theUniversityof SalernoandtheUniversidadNacionaldeColombia,forthemoralandtechnicalsupport inachievingtheresearchresultsandthebookwriting. G. Petrone and G. Spagnuolo also acknowledge the University of Salerno and the Italian Ministry of Education for having funded, through many projects, the research activitiestheresultsofwhichareoutlinedinthisbook. C.A. Ramos-Paja also acknowledges the Universidad Nacional de Colombia and Colciencias (Fondo Nacional de Financiamiento para Ciencia, la Tecnología y la Innovación Francisco José de Caldas) for having funded project MicroRENIZ-25439 (Code1118-669-46197)theresultsofwhichareoutlinedinthisbook. G.PetroneandG.SpagnuoloacknowledgeProf.N.FemiaandProf.L.Egiziano,fromthe UniversityofSalerno,forthejointresearchactivityinphotovoltaicsoverthelastsixteen yearsandfortheirsupportsincethePhDcoursestudies. SolarTechLab1 of Politecnico di Milano (Italy) is acknowledged for some photos in Chapter4. ThecontributionofDr.MarthaLuciaOrozcoGutierrezoftheUniversidaddelValle (Colombia)iswarmlyacknowledgedforhercontributionstoChapters5and6. 1 http://www.solartech.polimi.it. xiii Introduction The idea of writing this book was born ten years ago, when the authors, who before then used the simple electrical models that had been reported in the – very scant – literatureatthattime,publishedtheirfirstpaperonthistopic.Atthattime,thevalues of the parameters of the widely used single-diode circuit model (SDM) were identi- fied through approximate procedures, often consisting of two steps, the first neglect- ing the loss mechanisms and the following one introducing them by fixing the values of the other parameters. Mismatching phenomena, and especially partial shadowing, wereaccountedforbysimplemultiplicationofthearraypowerproductioninstandard test conditions by a loss factor. Events producing degradation of the cells and bypass diodeswereonlyobservedorsimulatedinsimplifiedcases.Also,theneedtosimulate the array, including bypass and blocking diodes, in unconventional operating condi- tionsandinrealtimeusinganembeddedsystem,didnotariseatthattime,sothatthe problemofhavingafast,accurate,efficientandreliablesimulationofevenlargearrays was treated in literature only marginally. Ten years later, the authors have gained an improvedknowledgeofthesematters,whichhasbeencondensedinthisbookwiththe mainaimofdrivingthereadertowardsthebestandmoresuitablearraymodelforagiven application. The SDM is used first, in Chapter 1, for fast simulations of even large arrays work- inginstandardconditionsthroughasuitablesymbolicmanipulationofthenon-linear equationdescribingitattheterminalsthroughthecurrentandvoltagevariables.This chapter gives the background for understanding almost all the advanced approaches presentedinthebook.Inordertousetheaforementionedmodelinpractice,andalsothe othersinthebook,thereaderhastoturnthedataavailableinthedatasheetprovidedby anypanelmanufacturerintotheparametersinvolvedintothecircuitmodel.Thisprob- lemisaddressedinthesecondchapterofthebook,wheremethods–bothapproxima- tionsusingexplicitformulaeandaccurateones–requiringthesolutionofanon-linear system of equations, are compared. The SDM presented in the first chapter and the parameters values determined by the methods described in Chapter 2 are thus ready forsimulatingarraysworkingintheso-called“standardtestconditions”thedatasheet measurementsreferto.Chapter3allowsthereadertoextendthesimulationcapabilities oftheSDMbysuggestinganumberofadditionalequationsallowingsimulationofthe arrayinanyoperatingconditions,bothintermsofirradianceandtemperaturevalues, undertheassumptionthatallthecellsinthearrayworkinexactlythesameoperating conditionsandaredescribedbytheSDMwiththesameparametervalues. xiv Introduction Mismatched conditions, and especially the presence of the partial shadowing phe- nomenon affecting the array, need more sophisticated simulation models and tools. Chapter4givesanoverviewofthemainsourcesofdegradationandmismatching,point- ingoutthatinmanycasestheeffectisatcelllevel,andsothemodelingofsuchconditions mayrequiremodelswithdifferentlevelsofdetailandgranularity.Chapter5introduces afirstpossibility,describingacomputationallyefficientsimulationmodelthatworksat thegranularitylevelofthemodule.Thuseachpanelcanbesimulatedbyaccountingfor uptotwoorthreedifferentoperatingconditionsaffectingthemodulesfromwhichitis made.Theproposedapproachallowsforveryfastsimulationofthemismatchedarray, with more accuracy than when introducing a simple power reduction. Nevertheless, cell-levelphenomenasuchashotspotsandadetailedstringbehaviorcanbeachieved onlybymodelingthearrayatcelllevel.Forfastsimulationofarraysconsistingofthou- sandsofcells,thisrequiresmoredetailedmodelsandtheuseofalgorithmicapproaches, andalsotheconsiderationofcellreversebiasing. Chapter6givesthemodelingandalgorithmicrecipesforapproachingthistaskina properway:someexamplesandcomparisonsarepresentedinordertoshowthereader thatasuitableorganizationoftheequationsintheoverallnon-linearmodelallowsfora savingofhoursofsimulationtimecomparedtotheuseofthestandardalgorithmsthat arebuiltintocommercialmathematicalsoftwarepackages.Oncethereaderhaschosen therightarraymodelfortheanalysisthatheorshehastoperform,itismergedwith themodelofthepowerprocessingsystemthatallowsharvestingofthemaximumPV poweratanygivenoperatingcondition.Indeed,theliteratureandmarkettrendsclearly indicate that, in the near future, electronics will be embedded into PV modules with theaimofmaximizingthepoweroutputandtomakeitsoperatingpointindependent ofothermodulesconnectedinseriesorinparalleltoit.Thusthemoduleanditsdedi- catedelectronicswillnolongerbedistinguishableandtheirintegratedmodelingwillbe required. Chapter7showsthatasuitablearraymodelisneededforthedesignoftheswitching converter that controls the power flux. Static and dynamic performance can be opti- mizedprovidedthatasuitablesimulationofthewholesystem,includingboththearray andthepower-processingsystem,isperformed.Oncethishasbeenachieved,different controltechniquescanbeused,assummarizedinChapter8.
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