Solar Energy Generation Systems

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IEEETRANSACTIONSONCONTROLSYSTEMSTECHNOLOGY,VOL.19,NO.1,JANUARY2011199SupervisoryPredictiveControlofStandaloneWind/SolarEnergyGenerationSystemsWeiQi,JinfengLiu,XianzhongChen,andPanagiotisD.Christofides,Fellow,IEEEAbstract—Thisworkfocusesonthedevelopmentofasupervi-requiresaddressingkeyfundamentalchallengesintheopera-sorymodelpredictivecontrolmethodfortheoptimalmanagementtionandreliabilityofintermittent(variableoutput)renewableandoperationofhybridstandalonewind-solarenergygenerationresourceslikesolar-andwind-basedenergygenerationsystems.systems.Wedesignthesupervisorycontrolsystemviamodelpre-Specifically,unexpecteddropsinenergyproductionofasolardictivecontrolwhichcomputesthepowerreferencesforthewindandsolarsubsystemsateachsamplingtimewhileminimizingaorwindenergysystemmayrequirequickstartunitstocoverthesuitablecostfunction.Thepowerreferencesaresenttotwolocalshortfallwhileunexpectedincreasesrequiretheabilitytoabsorbcontrollerswhichdrivethetwosubsystemstotherequestedpowertheunscheduledgeneration.Onewaytodealwiththevariablereferences.Wediscusshowtoincorporatepracticalconsiderations,outputofwindandsolarenergygenerationsystemsisthroughforexample,howtoextendthelifetimeoftheequipmentbyre-theuseofintegratedenergygenerationsystemsusingbothwindducingthepeakvaluesofinrushorsurgecurrents,intotheformu-lationofthemodelpredictivecontroloptimizationproblem.Weandphotovoltaicenergy,whicharealsotightlyintegratedwithpresentseveralsimulationcasestudiesthatdemonstratetheap-distributedenergystoragesystems(batteries)andcontrollableplicabilityandeffectivenessoftheproposedsupervisorypredictiveenergyloadslike,forexample,awaterproductionsystemthatcontrolarchitecture.operatesatcontrollabletimeintervalstomeetspecificdemand.IndexTerms—Modelpredictivecontrol(MPC),solarenergy,Withrespecttopreviousresultsoncontrolofwindandsolarstandalonewindandsolarsystems,supervisorypredictivecontrol,systems,mostoftheeffortshavefocusedonstandalonewindorwindenergy.solarsystems.Specifically,thereisasignificantbodyofliter-aturedealingwithcontrolofwindenergygenerationsystems(see,forexample,[2]–[12]forresultsandreferencesinthisI.INTRODUCTIONarea),whileseveralcontributionshavebeenmadetothecon-trolofsolar-basedenergygenerationsystems(see,forexample,LTERNATIVEenergytechnologies,likewind-andsolar-[13]–[17]).However,therearefewworksthathavefocusedonAbasedenergygenerationsystems,arereceivingnationalthecontrolofstandalonehybridwind-solarenergygenerationandworldwideattentionowingtotherisingrateofconsumptionsystems.In[18],areduced-ordernonlinearmodelwasusedtoofnuclearandfossilfuels.Inparticular,driversforsolar/winddesignacontrollertoregulatethewindpowergenerationtorenewableenergysystemsaretheenvironmentalbenefits(re-complementthepowergeneratedbyaphotovoltaicsubsystemductionofcarbonemissionsduetotheuseofrenewableenergyandtosatisfyaspecificpowerdemand.In[19],slidingmodesourcesandtheefficientuseoffossilfuels),reducedinvestmentcontroltechniqueswereusedtocontrolthepowergeneratedbyrisk,fueldiversification,andenergyautonomy,increaseden-aphotovoltaicarrayinordertosatisfythetotalinstantaneousergyefficiency(lesslinelosses)aswellaspotentialincreasepowerdemandinahighlyuncertainoperatingenvironment.Inofpowerqualityandreliabilityandincertaincases,potential[20],asupervisorycontrolsystemwasdevelopedtosatisfythegridexpansiondeferralduetothepossibilityofgenerationcloseloadpowerdemandandtomaintainthestateofchargeofthetodemand.InarecentreportoftheCaliforniaEnergyCom-batterybanktopreventblackout.Inarecentwork[21],acost-ef-mission,forexample,thestate’stargetistogeneratefromre-fectivecontroltechniquewasproposedformaximumpowernewablesourcesthe33%oftheenergyneededbyyear2020,pointtrackingfromthephotovoltaicarrayandwindturbinewithabout70%ofthatenergybeingproducedbywindandundervaryingclimaticconditionswithoutmeasuringtheirra-solarsystems[1];manyotherstateshavesimilargoals.How-dianceofthephotovoltaicorthewindspeed.However,noat-ever,achievingsuchmajorrenewableenergyproductiongoalstentionhasbeengiventothedevelopmentofsupervisorycon-trolsystemsforstandalonehybridwind-solarenergygenerationManuscriptreceivedSeptember11,2009;revisedDecember04,2009andsystemsthattakeintoaccountoptimalallocationofgenerationJanuary18,2010.ManuscriptreceivedinfinalformJanuary25,2010.Firstassignmentbetweenthetwosubsystems.publishedFebruary25,2010;currentversionpublishedDecember22,2010.Theobjectiveofthepresentworkistodevelopasupervi-RecommendedbyAssociateEditorJ.Lee.W.Qi,J.Liu,andX.ChenarewiththeDepartmentofChemicalandsorypredictivecontrolmethodfortheoptimalmanagementandBiomolecularEngineering,UniversityofCalifornia,LosAngeles,CAoperationofhybridwind-solarenergysystems.Weproposeto90095-1592,USA(e-mail:qiwei.0216@gmail.com;jinfeng@ucla.edu;designthesupervisorycontrolsystemviamodelpredictivecon-xianzhongchen@gmail.com).P.D.ChristofidesiswiththeDepartmentofChemicalandBiomoleculartrol(MPC)whichcomputesthepowerreferencesforthewindEngineeringandtheDepartmentofElectricalEngineering,UniversityofCali-andsolarsubsystemsateachsamplingtimewhileminimizingafornia,LosAngeles,CA90095-1592,USA(e-mail:pdc@seas.ucla.edu).suitablecostfunction.ThepowerreferencesaresenttotwolocalColorversionsofoneormoreofthefiguresinthispaperareavailableonlineathttp://ieeexplore.ieee.org.controllerswhichdrivethewindandsolarsubsystemstothede-DigitalObjectIdentifier10.1109/TCST.2010.2041930siredpowerreferencevalues.MPCisapopularcontrolstrategy1063-6536/$26.00©2010IEEE 200IEEETRANSACTIONSONCONTROLSYSTEMSTECHNOLOGY,VOL.19,NO.1,JANUARY2011(dc/dcconverter1inFig.1)],isthePMSGnumberofpoles,istheinertialoftherotatingparts,andisthewindturbinetorque.Thewindturbinetorquecanbewrittenas(2)whereistheairdensity,istheturbine-sweptarea,istheturbineradius,isthewindspeed,andisanonlineartorquecoefficientwhichdependsonthetipspeedratio(Fig.1.Wind-solarenergygenerationsystem.withbeingtheangularshaftspeed).Basedon(1),wecanexpressthepowergeneratedbythewindbecauseofitsabilitytoaccountforstateandinputconstraintssubsystemandinjectedintothedcbusasfollows:aswellasoptimalityconsiderationsexplicitlyintheevaluation(3)ofcontrolactions.MPCusesamodelofthesystemtopredictateachsamplingtimethefutureevolutionofthesystemfromthecurrentstatealongagivenpredictionhorizon[22],[23].UsingThemodelofthewindsubsystemcanberewritteninthefol-thesepredictions,theinput/set-pointtrajectorythatminimizeslowingcompactform:agivenperformanceindexoverafinite-timehorizoniscom-(4)putedsolvingasuitableoptimizationproblemsubjecttocon-straints.Inthiswork,wediscusshowwecanincorporateprac-whereisthestatevectorofthewindsub-ticalconsiderations(forexample,howtoextendthelifetimeofsystemand,aretheequipmentsbyreducingthepeakvaluesofinrushorsurgenonlinearvectorfunctionswhoseexplicitformisomittedforcurrents)intotheformulationoftheMPCoptimizationproblembrevity.bydetermininganappropriatecostfunctionandconstraints.WeNext,wedescribethemodelingofthesolarsubsystem.Inthepresentseveralsimulationcasestudiesthatdemonstratetheap-solarsubsystem,thereisaphoto-voltaic(PV)panelarrayandplicabilityandeffectivenessoftheproposedsupervisorypredic-ahalf-bridgebuckdc/dcconverter.Thesolarsubsystemiscon-tivecontrolarchitecture.nectedtothedcbusviathedc/dcconverter.Inthissubsystem,similartothewindsubsystem,theconverterisusedtocontrolII.WIND-SOLARSYSTEMDESCRIPTIONtheoperatingpointofthePVpanels.Thewind-solarenergygenerationsystemconsideredinThemathematicdescriptionofthesolarsubsystemisasfol-thisworkisbasedonthemodelsdevelopedin[18]–[20].Alows[19]:schematicofthesystemisshowninFig.1.Inthishybridsystem,therearethreesubsystems:windsubsystem,solarsub-system,andalead-acidbatterybankwhichisusedtoovercomeperiodsofscarcegeneration.First,wedescribethemodelingofthewindsubsystem.Inthewindgenerationsubsystem,thereisawindmill,amultipolar(5)permanent-magnetsynchronousgenerator(PMSG),arectifier,andadc/dcconvertertointerfacethegeneratorwiththedcbus.whereisthevoltagelevelonthePVpanelarrayterminals,Theconverterisusedtocontrolindirectlytheoperatingpointisthecurrentinjectedintothedcbus,andareelectricalofthewindturbine(andconsequentlyitspowergeneration)byparametersofthebuckconverter(dc/dcconverter2inFig.1),commandingthevoltageonthePMSGterminals.isthecontrolsignal(dutycycle),isthecurrentgeneratedThemathematicaldescriptionofthewindsubsystemwrittenbythePVarray,isthenumberofPVcellsconnectedininarotorreferenceframeisasfollows[18]:series,isthenumberofseriesstringsinparallel,istheBoltzmanconstant,isthecelldeviationfromtheidealjunctioncharacteristic,isthephotocurrent,andisthereversesaturationcurrent.ThepowerinjectedbythePVsolarmoduleintothedcbuscanbecomputedby(6)(1)Notethatthispowerindirectlydependsonthecontrolsignal.whereandarethequadraturecurrentandthedirectcurrentThemodelofthesolarsubsystemcanberewritteninthefol-intherotorreferenceframe,respectively;andaretheperlowingcompactform:phaseresistanceandinductanceofthestatorwindings,respec-tively;istheelectricalangularspeed;isthefluxlinkedbythestatorwindings;isthevoltageonthebatterybanktermi-nals;isthecontrolsignal[dutycycleofthedc/dcconverter(7) QIetal.:SUPERVISORYPREDICTIVECONTROLOFSTANDALONEWIND/SOLARENERGYGENERATIONSYSTEMS201whereisthestatevectorofthesolarsubsystemandarenonlinearvectorfunc-tionsandisanonlinearscalarfunctionwhoseexplicitformisomittedforbrevity.Thedcbuscollectstheenergygeneratedbybothwindandsolarsubsystemsanddeliversittotheloadand,ifnecessary,tothebatterybank.Thevoltageofthedcbusisdeterminedbythebatterybankwhichcomprisesoflead-acidbatteries.Theloadcouldbeanacoradcload.InthecaseunderconsiderationinFig.2.Supervisorycontrolofawind-solarhybridenergysystem.thepresentwork,itisassumedtobeanacload;therefore,avoltageinverterisrequired.Wealsoassumethatthefutureloadofthesystemforcertainlengthoftimeisknown,thatisthetotalpowerdemandisknown.rechargethebatterybankandavoiddamages.Inthiswork,weBecauseallsubsystemsarelinkedtothedcbus,theirconcur-donotconsiderthepowerneededtochargethebatterybankrenteffectscanbeeasilyanalyzedbyconsideringtheircurrentsexplicitly.However,thispowercanbelumpedintothetotalinthecommondcside.Inthisway,assuminganidealvoltagepowerdemand.Inthereminderofthiswork,werefertotheinverter,theloadcurrentcanbereferredtothedcsideasantotalpowerdemandas.outputvariablecurrent.Therefore,thecurrentacrossthebat-terybankcanbewrittenasIII.CONTROLPROBLEMFORMULATIONAND(8)CONTROLLERSDESIGNwhereisassumedtobeaknowncurrent.A.ControlProblemFormulationThelead-acidbatterybankmaybemodeledasavoltagesourceconnectedinserieswitharesistanceandaWeconsidertwocontrolobjectivesofthewind-solarenergycapacitance.Basedonthissimplemodeland(8),thedcbusgenerationsystem.Thefirstandprimarycontrolobjectiveistovoltageexpressioncanbewrittenasfollows:computetheoperatingpointsofthewindsubsystemandofthesolarsubsystemtogethertogenerateenoughenergytosatisfytheloaddemand.Thesecondcontrolobjectiveistooptimize(9)theoperatingpointstoreducethepeakvalueofsurgecurrents.Withrespecttothesecondcontrolobjective,specifically,wewhereisthevoltageincapacitoranditsdynamicscanbeconsiderthattherearemaximumallowableincreasingratesofdescribedasfollows:thegeneratedpowerofthetwosubsystemsandthatfrequentdischargeandchargeofthebatterybankshouldbeavoidedto(10)maximizebatterylife.Notethattheconstraintsonthemaximumincreasingratesimposeindirectboundsonthepeakvaluesofinrushorsurgecurrentstothetwosubsystems.Themodelofthebatterybankcanalsoberewritteninthefol-TheproposedcontrolsystemisshowninFig.2inwhichlowingcompactform:thesupervisorycontrolsystemoptimizesthepowerreferencesand(operatingpoints)ofthewindandsolar(11)subsystems,respectively.Thetwolocalcontrollers(windsubsystemcontrollerandthesolarsubsystemcontroller)ma-whereisanonlinearscalarfunction.nipulateandtotrackthepowerreferences,respectively.ThedynamicsofthehybridgenerationsystemcanbewrittenRemark1:Notethat,inthiswork,weconsiderhybriden-inthefollowingcompactform:ergygenerationsystemsthatalreadyoperateinnormalgener-atingconditions,anddonotaddresstheissuesrelatedtosystem(12)startuporshutdown.Moreover,wefocusontheapplicationoftheproposedsupervisorycontrolsystemanddonotprovidewhereandaresuit-ablecompositionofand,and.specificconditions(anddetailedtheoreticalderivation)underTheexplicitformsofandareomittedforbrevity.whichthestabilityoftheclosed-loopsystemisguaranteed.WeNotethatthemaximumpowerthatcanbedrawnfromthealsonotethat,inthecaseofaenergygenerationsystemcon-windandsolarsubsystemsisdeterminedbythemaximumtainingseveralsolarandwindsubsystems,theproposedsuper-powerthatcanbegeneratedbythetwosubsystems.Whenthevisorycontrolapproachcanbeextendedtocontrolthesystemtwosubsystemsarenotsufficienttocomplementthegenerationinaconceptuallystraightforwardmannerbylettingthesupervi-tosatisfytheloadrequirements,thebatterybankcandis-sorycontrollerdeterminethepowerreferencesofallthesubsys-chargetoprovideextrapowertosatisfytheloadrequirements.temsoradistributedMPCapproach(inwhicheachMPCcon-However,whenthepowerlimitthatcanbeprovidedbythetrolsonlysomeofthesubsystems)canbeapplied.However,thebatterybankissurpassed,theloadmustbedisconnectedtodistributedMPCapproachisoutofthescopeofthiswork. 202IEEETRANSACTIONSONCONTROLSYSTEMSTECHNOLOGY,VOL.19,NO.1,JANUARY2011B.WindSubsystemControllerDesignInthepresentwork,themaximumsolarpowerprovided,,iscomputednumericallythroughdirectevaluationofForthewindsubsystemcontroller,theobjectiveistotrackthefollowingexpression[19]intheregionwhere(15)isclosethepowerreferencecomputedbythesupervisorypredictivetozerocontroller.Inordertoproceed,weintroducethemaximumpowerthatcanbeprovidedbyawindsubsystem,,first.de-(16)pendsonafewturbineparametersandonasimplemeasurementoftheangularshaftspeedasfollows[18]:Wefollowthecontrollerdesignproposedin[19]todesignthesolarsubsystemcontroller.Specifically,thiscontrollerisde-(13)signedasfollows:whereandisthetipififspeedratioatwhichthecoefficientreachesitsif(17)maximum[18],andisthetorquecoefficientofthewindififturbine.ifWefollowthecontrollerdesignproposedin[9].Specifically,thecontrollerisdesignedasfollows:whereand.if(14)D.SupervisoryControllerDesignifTheobjectiveofthesupervisorycontrolsystemistodeter-whereminethepowerreferencesofthewindandsolarsubsystems.WeproposetodesignthesupervisorycontrollerviaMPC.ByusingMPC,wecantakeoptimalityconsiderationsintoaccountaswellashandledifferentkindsofconstraints.AsstatedinSectionIII-A,theprimarycontrolobjectiveistomanipulatetheoperatingpointsofthewindsubsystemandofthesolarsub-systemtogethertogenerateenoughenergytosatisfytheloaddemand.ThiscontrolobjectivewillbeconsideredinthedesignofthecostfunctionfortheMPCoptimizationproblem(pleaseseeSectionIV).Thesecondcontrolobjectiveistooptimizetheoperatingpointstoreducethepeakvalueofsurgecurrents.Inwithandbeingdesignconstantsandordertotakeintoaccountthiscontrolobjective,wewillincor-poratehardconstraintsintheMPCoptimizationproblemtore-strictthemaximumincreasingratesofthegeneratedpowerofthetwosubsystemsaswellasaterminthecostfunctiontoavoidfrequentdischargeandchargeofthebatterybank.Weconsiderthecasewherethefutureloadofthesystemforcertainlengthoftimeisknown,thatisthetotalpowerdemand,,isknown.Themainimplementationelementofsupervi-Inthecontroldesignshownin(14),andsorypredictivecontrolisthatthesupervisorycontrollerisevalu-aretheslidingsurfaces.Whenthepowerrefer-atedatdiscretetimeinstants,withenceislessthanthemaximumpowerthatcanbeprovidedbytheinitialtimeandthesamplingtime,andtheoptimalfuturethewindsubsystem,thecontrollawwilloperatethesub-powerreferences,and,foratimeperiod(predic-systemtogeneratethedesiredpower;whenthepowerreferencetionhorizon)areobtainedandonlythefirstpartofthereferencesisgreaterthanthemaximumpowerthatcanbeprovidedbythearesenttothelocalcontrolsystemsandimplementedonthetwowindsubsystem,thecontrollawwilldrivethesubsystemunits.Inordertodesignthiscontroller,first,apropernumberoftooperateatpointsinwhichthesubsystemprovidesthemax-predictionstepsandasamplingtimearechosen.imumpower.TheproposedMPCdesignforthesupervisorycontrolsystemC.SolarSubsystemControllerDesignisdescribedasfollows:Theobjectiveofthesolarsubsystemcontrolleristoforcethe(18a)subsystemtotrackthepowerreferencecomputedbythesuper-visorycontroller.Themaximumpoweroperatingpoint(MPOP)s.t.ofthesolarsubsystemcanbecomputed,inprinciple,bythefol-lowingexpression[19]:(18b)(15)(18c) QIetal.:SUPERVISORYPREDICTIVECONTROLOFSTANDALONEWIND/SOLARENERGYGENERATIONSYSTEMS203arechosentobe1000Wand500W,(18d)respectively.Notethatthechoiceofthepredictionhorizonisbasedonthefastdynamicsofthehybridgenerationsystem,theuncertaintyassociatedwithlong-termfuturepowerdemandand(18e)isalsomadetoachieveabalancebetweentheevaluationtimeoftheoptimizationproblemofthesupervisoryMPCandthede-(18f)siredclosed-loopperformance.(18g)IV.SIMULATIONRESULTS(18h)Inthissection,wecarryoutseveralsetsofsimulationsto(18i)demonstratetheeffectivenessandapplicabilityofthedesigned(18j)MPCwhenthecontrolobjectivesstatedinSectionIIIaretakenintoaccount.Notethatinallthesimulations,standardnumericalwhereisthepredictedfuturestatetrajectoryofthehybridmethods,e.g.,Runge–Kutta,areusedtocarryoutthenumericalsystem,isapositivedefinitefunctionoftheintegrationoftheclosed-loopsystem.stateandthetwopowerreferencesthatdefinestheoptimiza-tioncost,andarethemaximumallowablein-A.ConstraintsontheMaximumIncreasingRatesofcreasingvalueofandintwoconsecutivepowerandreferences,isthepredictionhorizon,Inthissetofsimulations,thecontrolobjectiveistooperateandisthestatemeasurementobtainedattime.Wede-thehybridwind-solarenergygenerationsystemtosatisfythenotetheoptimalsolutiontotheoptimizationproblemof(18)totalpowerdemand,subjecttoconstraintsontherateofasandwhicharedefinedforchangeofand.Becausetheconstraintsonthemax-.imumincreasingratesofandareconsideredasThepowerreferencesofthetwosubsystemsgeneratedbythehardconstraintsintheformulationoftheMPC[i.e.,constraintssupervisorycontrollerof(18)aredefinedasfollows:of(18d)–(18e)],inthecostfunction,weonlypenalizethetotalpowerdemand.Thecostfunctiondesignedforthesecontrolob-jectivesisshownasfollows:(19)(20)Intheoptimizationproblemof(18),(18a)definestheop-whereandareconstantweightingfactors.timizationcostthatneedstobeminimized,whichwillbeThefirstterm,,inthecostfunctioncarefullydesignedinthesimulationsinSectionIV.BecausepenalizesthedifferencebetweenthepowergeneratedbythetheMPCoptimizesthetwopowerreferencesinadiscretetimewind-solarsystemandthetotalpowerdemand,whichdrivesfashionandthereferencesareconstantswithineachsamplingthewindandsolarsubsystemstosatisfythetotaldemandtointerval,theconstraintsof(18b)–(18c)requirethatthecom-themaximumextent.Becausethereareinfinitecombinationsputedpowerreferencesshouldbesmallerthantheminimalofofandthatcanminimizethefirstterm,inordertothemaximumavailablewithineachsamplinginterval,whichgetauniquesolutiontotheoptimizationproblem,wealsoputmeansthepowerreferencesshouldbeachievableforthewindasmallpenaltyon.Thisimpliesthatthewindsubsystemandsolarsubsystems.Constraintsof(18d)–(18e)imposecon-isoperatedastheprimarygenerationsystemandthesolarsub-straintsontheincreasingrateofthetwopowerreferences.Insystemisonlyactivatedwhenthewindsubsystemalonecannotordertoestimatethemaximumavailablepowerofthetwosub-satisfythepowerdemand.Inthesimulation,weassumethatthesystemsalongthepredictionhorizon,themodelofthesystemenvironmentalconditionsremainconstantwithwindspeed(18f),thecurrentstate(18g)andtheequationsexpressingthe12m/s,insolation90mW/cmandPVpaneltemperaturerelationbetweenthemaximumavailablepowerandthestate65C.ofeachsubsystem[(18i)and(18j)]areused.NotethatintheFig.3showstheresultsofthesimulations.FromFig.3,weMPCoptimizationproblem,inordertoestimatethefutureseethatat4sthereisademandpowerincreasefrom2100maximumavailablepowerofeachsubsystem,weassumethatto4000W[seeFig.3(a)],andthatbecauseoftheconstraintsontheenvironmentconditionssuchaswindspeed,insolationthemaximumincreasingratesofand,thewind-andtemperatureremainconstant.Whenthesamplingtimesolarsystemcannotsupplysufficientpower[seeFig.3(b)–(c)]issmallenoughandthepredictionhorizonisshortenough,andtheshortageofpowerismadeupbythebatterybank[seealongwithhigh-frequencywindvariationscausedbygustsandFig.3(a)].turbulencebeingreasonablyneglected,thisassumptionmakesNotethatweassumethatthefuturepowerdemandforashortphysicalsense[20].Theconstraintsof(18b)–(18e)areinspiredtimeperiodisknowntotheMPC.Becauseofthis,at8byresultsonthedesignofLyapunov-basedmodelpredictives,whentheMPCsupervisorycontrollerreceivesinformationcontrolsystems[24]–[27].aboutapowerdemandincreaseat9s,andhavinginforma-Intheremainderofthiswork,thesamplingtimeandthepre-tionofthelimitsonthepowergenerationofthetwosubsystems,dictionhorizonoftheMPCarechosentobe1sand.itcoordinatesthepowergenerationsofthewindandsolarsub-Themaximumincreasingvaluesofthetwopowerreferencessystemstobestsatisfythepowerdemandbyreducingthepower 204IEEETRANSACTIONSONCONTROLSYSTEMSTECHNOLOGY,VOL.19,NO.1,JANUARY2011Fig.3.Powertrajectorieswithconstraintsonthemaximumincreasingratesofand.(a)Generatedpower(solidline),totalpowerde-mand(dashedline)andpowerprovidedbybatterybank(dottedline).(b)Powergeneratedbywindsubsystem(solidline),windpowerreference(dashed-dottedline)andmaximumwindgeneration(dashedline).(c)Powergeneratedbysolarsubsystem(solidline),solarpowerrefer-ence(dashed-dottedline)andmaximumsolargeneration(dashedFig.4.Powertrajectoriestakingintoaccountsuppressionofbatterypowerline).fluctuation.(a)Generatedpower(solidline),totalpowerdemand(dashedline)andpowerprovidebybatterybank(dottedline).(b)Powergeneratedbywindsubsystem(solidline),windpowerreference(dashed-dottedline)andmaximumwindgeneration.(c)Powergen-eratedbysolarsubsystem(solidline),solarpowerreference(dashed-generationofthewindsubsystemandactivatingthesolarsub-dottedline)andmaximumsolargeneration.(d)Generatedpowersysteminadvanceat8s.Thiscoordinationrendersthetwo(solidline),totalpowerdemand(dashedline)andpowerprovidebybat-subsystemsabletoapproachasmuchaspossibletothetotalterybank(dottedline).powerdemandrequirementat9s(eventhoughtheycannotfullymeetthisrequirementduetooperationconstraintsofthewindandsolarsubsystems)byboostingtheirpowerproductiontoavoidfrequentbatterychargeanddischarge.Thecostfunc-atthemaximumpossiblerate,i.e.,about1500Wboostinpowertionismodifiedasfollows:productionfrom8sto9s.Ontheotherhand,ifthereisnoinformationofthefuturepowerdemandincreasethatisfedtotheMPC,thewind-solarsystemwouldnotincreaseits(21)productionasfasttoapproachthetotalpowerdemandrequire-mentbecausethesolarsubsystemwouldstaydormantupto9s(thepowerdemandrequirementat8scanbefullysat-whereisthechangeofthepowerprovidedbythebatteryisfiedbythewindsubsystemonly)andthepresenceofahardbankbetweentwoconsecutivestepsandisaweightingconstraintontherateofchangeofpowergeneratedbythesolarfactor.Notethatthisnewlyaddedtermrequiresthatwestoresubsystemwouldnotallowtoboostitsproductionenoughtothetrajectoryof.Inthissetofsimulations,theenvironmentalmeetthetotalpowerdemandrequirementat9s(inthisconditionsaresetwithwindspeed11m/s,insolationcase,thetotalpowerdemandrequirementcannotbeachieved90mW/cmandPVpaneltemperature65C.byoperationofthewindsubsystemonly);asaresulttheboostFig.4showsthesimulationresults.FromFig.4,weseethatintotalpowerproductioninthiscasewouldbeonly1200W.thereisapowerdemanddecreaseat3s,andthoughthewindandsolarsubsystemsareabletoprovideenoughpowertosatisfythedemand,thesupervisorycontrollerwillnotreduceB.SuppressionofBatteryPowerFluctuationthepowergeneratedbythebatteryto0immediatelyat3s;instead,thesupervisorycontrolleroperatesthesystemtoInthissetofsimulations,wemodifythecostfunctionof(20)makethepowerprovidedbythebatterybankdecreaseslowertotakeintoaccountthefluctuationofthebatterypowerinorderandreachitsrechargestateat5s[seeFig.4(a)].Fig.4(d) QIetal.:SUPERVISORYPREDICTIVECONTROLOFSTANDALONEWIND/SOLARENERGYGENERATIONSYSTEMS205Fig.6.Powertrajectoriesundervaryingenvironmentconditions.(a)Generatedpower(solidline),totalpowerdemand(dashedline),andpowerprovidedbybatterybank(dottedline).(b)Powergeneratedbywindsub-Fig.5.Environmentalconditionsandloadcurrent.(a)Windspeed.(b)Inso-system(solidline),windpowerreference(dashed-dottedline),andlation.(c)PVpaneltemperature.(d)Loadcurrent.maximumwindgeneration(dashedline).(c)Powergeneratedbysolarsubsystem(solidline),solarpowerreference(dashed-dottedline),andmaximumsolargeneration(dashedline).showsthepowertrajectoryofthebatterybankifnopenaltyonthechangeofthepowerprovidedbythebatterybankisapplied.C.VaryingEnvironmentalConditionsInthissubsection,wecarryoutsimulationsundervaryingen-vironmentalcondition.Timeevolutionofwindspeed,PVpaneltemperatureandinsolationareshowninFig.5(a)–(c).Fig.5(d)showsthetrajectoryoftotalpowerdemand.ItcanbeseenfromFig.6(a)thatthewind/solar/batterypowerscoordinatetheirbehaviortomeettheloaddemand.TimeevolutionofoutputpowerandmaximumavailablepowerfromthewindsubsystemandsolarsubsystemareplottedinFig.6(b)–(c).Whensufficientenergysupplycanbeextractedfromthetwosubsystemssuchasduring0–60s,100–140s,and160–173s,thebatteryisbeingrecharged.Inotherperiods,loaddemandisrelativelyhighandtheweathercondition,whichdeterminesthemaximumavailablegenerationcapacityofthetwosubsystems,cannotpermitsufficientenergysupply.Thus,thesupervisorycontrollerdriveswind/solarpartstotheirin-stantmaximumcapacityandcallsthebatterybankforshortagecompensation.D.ConsiderationofHigh-FrequencyDisturbanceofWeatherConditionIntheprecedingscenario,weassumedthatthevariationofweather-relatedparameters,likewindspeedandinsolation,withineachsamplingtimeintervalisnegligible.Whilethisassumptionisreasonableinmostcases,additionalattentionforrobustsystemoperationshouldbegivenunderevenharsherconditionswherehighfrequencydisturbancesthatinfluencetheFig.7.Environmentalconditionsandloadcurrent.(a)Windspeedwithhighvaluesofwindspeedandinsolationarepresent.Thisscenarioisfrequencydisturbance.(b)Insolationwithhighfrequencydisturbance.possiblewhenthewindturbineencountersturbulentflow[28],(c)PVpaneltemperature.(d)Loadcurrent. 206IEEETRANSACTIONSONCONTROLSYSTEMSTECHNOLOGY,VOL.19,NO.1,JANUARY2011V.CONCLUSIONInthiswork,wefocusedonthedevelopmentofasupervi-sorypredictivecontrolmethodfortheoptimalmanagementandoperationofhybridwind-solarenergygenerationsystems.WeproposedasupervisorycontrolsystemdesignedviaMPCwhichcomputesthepowerreferencesforthewindandsolarsubsys-temsateachsamplingtimewhileminimizingasuitablecostfunction.Thepowerreferencesaresenttotwolocalcontrollerswhichdrivethetwosubsystemstothepowerreferences.Wedis-cussedhowtoincorporatepracticalconsiderations,forexample,howtoreducethepeakvaluesofinrushorsurgecurrents,intotheformulationoftheMPCoptimizationproblem.Simulationresultsdemonstratedtheeffectivenessandapplicabilityoftheproposedapproach.Futureworkwillincludetheinvestigationoflargetimespanbehaviorofthehybridwind-solargenerationsystemtakingintoaccountinformationoffutureweatherfore-cast,andinvestigationoftheperformanceofthesystemundertheconditionthatthefuturepowerdemandisunknown.REFERENCES[1]CaliforniaEnergyCommission,“2008energypolicyreportupdate,”2008.[2]R.SpeeandJ.H.Enslin,“Novelcontrolstrategiesforvariable-speedFig.8.Powertrajectoriesundervaryingenvironmentconditionswithhighfre-doublyfedwindpowergenerationsystems,”RenewableEnergy,vol.quencydisturbance.(a)Generatedpower(solidline),totalpowerde-6,pp.907–915,1995.mand(dashedline),andpowerprovidedbybatterybank(dottedline).[3]P.Novak,T.Ekelund,Y.Jovik,andB.Schmidtbauer,“Modelingand(b)Powergeneratedbywindsubsystem(solidline),windpowerreferencecontrolofvariable-speedwind-turbinedrivesystemdynamics,”IEEE(dashed-dottedline)andmaximumwindgeneration(dashedControlSyst.Mag.,vol.15,no.4,pp.28–37,Aug.1995.line).(c)Powergeneratedbysolarsubsystem(solidline),solarpowerrefer-[4]T.ThiringerandJ.Linders,“Controlbyvariablerotorspeedofence(dashed-dottedline)andmaximumsolargeneration(dashedfixed-pitchwindturbineoperatinginspeedrange,”IEEETrans.line).EnergyConv.,vol.8,no.3,pp.520–526,Sep.1993.[5]M.G.Simoes,B.K.Bose,andR.J.Spiegel,“Fuzzylogicbasedintelli-orwheninsolationisaffectedbyabruptchangesinatmosphericgentcontrolofavariablespeedcagemachinewindgenerationsystem,”IEEETrans.PowerElectron.,vol.12,no.1,pp.87–95,Jan.1997.turbidity[29].[6]K.Uhlen,B.A.Foss,andO.B.Gjosaeter,“RobustcontrolandanalysisTostudythiscasefromacontrolpointofviewandevaluateofawind-dieselhybridpowerplant,”IEEETrans.EnergyConv.,vol.therobustnessoftheproposedcontrolsysteminthiscase,wein-9,no.4,pp.701–708,Dec.1994.[7]F.Valenciaga,P.F.Puleston,R.J.Mantz,andP.E.Battaiotto,“Antroducedisturbancesintwoparameters;specifically,10%vari-adaptivefeedbacklinearizationstrategyforvariablespeedwindenergyationinthewindspeedand5%variationintheinsolation.Theconversionsystems,”Int.J.EnergyRes.,vol.24,pp.151–161,2000.profilesofthewindspeedandinsolationareshowninFig.7(a)[8]K.TanandS.Islam,“Optimumcontrolstrategiesinenergyconver-sionofPMSGwindturbinesystemwithoutmechanicalsensors,”IEEEand(b).WehaveusedthesystemmodeltoestablishthattheTrans.EnergyConv.,vol.19,no.2,pp.392–399,Jun.2004.controlsystemoperatingonthewindsubsystemcantoleratethe[9]F.Valenciaga,P.F.Puleston,andP.E.Battaiotto,“Variablestruc-turesystemcontroldesignmethodbasedonadifferentialgeometricwinddisturbanceandnoadditionalmeasuresareneededtobeapproach:Applicationtoawindenergyconversionsubsystem,”IEEtakentosecureitsreliability.However,forthesolarsubsystem,Proc.—ControlTheoryAppl.,vol.151,pp.6–12,2004.whichischaracterizedbyfasterdynamics,inordertomaintain[10]M.Chinchilla,S.Arnaltes,andJ.C.Burgos,“Controlofperma-nent-magnetgenratorsappliedtovariable-speedwindenergysystemsitsclosed-loopstabilityweneedtouseamoreconservativees-connectedtothegrid,”IEEETrans.EnergyConv.,vol.21,no.1,pp.timateoftheinsolation(i.e.,95%ofthevalueofthemeasured130–135,Mar.2006.insolation)intheevaluationofthepowerreference.Thiscon-[11]F.ValenciagaandP.F.Puleston,“High-orderslidingcontrolforawindenergyconversionsystembasedonapermanentmagnetsynchronousservativeestimateofinsolationensuresthatthepredictedmax-generator,”IEEETrans.EnergyConv.,vol.23,no.3,pp.860–867,Sep.imumpowerdeliveredbythesolarsubsystemdoesnotexceed2008.[12]D.Q.Dang,Y.Wang,andW.Cai,“Nonlinearmodelpredictivecontrolwhattheweatherpermits.(NMPC)offixedpitchvariablespeedwindturbine,”inProc.IEEEInt.Theclosed-loopprofilesofpowergenerationaredisplayedinConf.SustainableEnergyTechnol.,Singapore,2008,pp.29–33.Fig.8(a)–(c).Again,theentireenergygenerationsystemoper-[13]T.A.JohansenandC.Storaa,“Energy-basedcontrolofadistributedsolarcollectorfield,”Automatica,vol.38,pp.1191–1199,2002.atesreliably,therebyyieldingpositiveresultsfortherobustness[14]F.Coito,J.M.Lemos,R.N.Silva,andE.Mosca,“Adaptivecontrolofofthecontrolsystemwithrespecttoabruptvariationsinwindasolarenergyplant:Exploitingaccessibledisturbances,”Int.J.Adapt.speedandinsolation.Bothmaximumpowergenerationcapa-ControlSignalProcess.,vol.11,pp.327–342,1997.[15]E.F.CamachoandM.Berenguel,“Robustadaptivemodelpredictivebilitiesofthetwosubsystemsareperturbedasaresultofthecontrolofasolarplantwithboundeduncertainties,”Int.J.Adapt.C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