using data from the Portuguese/Spanish generation system A long term generation expansion planning model using system dynamics –Casestudy Electric Power Systems Research

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Electric Power Systems Research

j o ur na l ho me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / e p s r

A long term generation expansion planning model using system dynamics – Case study using data from the Portuguese/Spanish generation system

Adelino J.C. Pereira

, João Tomé Saraiva

aDepartamentodeEngenhariaElectrotécnica,InstitutoSuperiordeEngenhariadeCoimbra,InstitutoPolitécnicodeCoimbra,RuaPedroNunes,3030-199Coimbra,Portugal

bINESCPortoandDepartamentodeEngenhariaElectrotécnicaeComputadores,FaculdadedeEngenhariadaUniversidadedoPorto,CampusdaFEUP,RuaDr.RobertoFrias,4200-465 Porto,Portugal

a r t i c l e i n f o

Articlehistory:

Received20June2012

Receivedinrevisedform12October2012 Accepted4December2012

Keywords:

Generationexpansionplanning Longtermanalysis

Systemdynamics Sensitivityanalysis Electricitymarkets

a b s t r a c t

Thispaperdescribesalongtermgenerationexpansionmodelthatusessystemdynamicstocapturethe interrelationsbetweendifferentvariablesandparameters.Usingthismodel,itispossibletoestimate thelongtermevolutionofthedemandandoftheelectricitypricethatarethenusedbygeneration agentstoprepareindividualexpansionplans.Theseplansaresubmittedtoacoordinationanalysisto checksomeglobalindicators,asthereservemarginandtheLOLE.Thedevelopedapproachisillustrated usingarealisticgenerationsystembasedonthePortuguese/Spanishsystemwithaninstalledcapacityof nearly120GWandanyearlydemandof312TWhin2010.Largeinvestmentsweredirectedinthelast20 yearstotheIberiangenerationsystembothregardingtraditionaltechnologiesanddispersedgeneration (namelywindparksandsolarsystems).Today,theexcessofinstalledcapacitytogetherwiththedemand reductionposesanumberofquestionsthatshouldbeaddressedcarefullynamelytoinvestigatethe impactofseveraloptions.Theplanningexerciseaimsatidentifyingthemostadequateexpansionplans inviewoftheincreasedrenewablegeneration(namelywindparks).Forillustrationpurposes,wealso conductedasensitivityanalysistoevaluatetheimpactofincreasingtheinstalledcapacityinwindparks, ofinternalizingCO2emissioncostsandofincorporatingacapacitypayment.Theseanalysesarerelevant inordertogetmoreinsightonthepossiblelongtermevolutionofthesystemandtoallowgeneration companiestotakemoresoundeddecisions.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Powersystemsrestructuringintroducednewchallengesboth inoperationandexpansionplanningactivities.Inparticular,the generationexpansionplanning,GEP,problemwasalreadyamat- terofconcernforverticallyintegratedutilitiesanditwastypically addressedinacombinedwaywithtransmissionexpansionplan- ning. Thiswasa complexproblemgiven thediscrete natureof possibleinvestments,aswellastheircapitalintensivenatureand theirone-stepandirreversiblecharacters,inthesensethatoncea decisionwastakenitcouldhardlybereversed.Finally,thesewere typicallylongpaybackinvestmentsthatrequiredalongtermanal- ysis.However,beforerestructuringtheriskoftheseinvestments wasmuchmorereducedthannowgiventhattheintroductionof marketmechanismsimposedashortertermaccent,thedemand isnowmoreuncertainandtheincreasingpresenceofrenewables (namelyusingvolatileresourcesaswindandsolarradiation)origi- natesnewchallengesnotonlyforoperationbutalsoforlongterm

∗Correspondingauthor.Tel.:+351222094230;fax:+351222094150.

E-mailaddresses:ajcp@isec.pt(A.J.C.Pereira),jsaraiva@fe.up.pt(J.T.Saraiva).

activities.Therestructuringleadtotheintroductionofcompeti- tivemechanismsingenerationandretailingwhileusuallykeeping transmission and distribution wiring as regulated activities. In generationthereare nowseveralcompaniesowning assetsand competingtosupply thedemandsothat theprofitofa partic- ularagentis affectedbythedemand andfuelprices evolution, by the incentives given to renewable stations and also by the decisionstaken byothercompanies.Asa result,thetraditional multiyearmixedintegerGEPproblemisnowmuchmorethanin thepastinfluencedbyuncertaintiesaffectingseveralparameters thatshouldbeinternalizedinthedecisionprocess.Finally,there areinterdependenciesthatshouldbeadequatelymodeledtocap- turetherealnatureoftheproblem.Infact,investmentdecisions aredrivenbytheexpectedprofitalongthehorizon,whichisinflu- encedbytheevolutionofthedemandandbythemarketprices.

However,thesetwoelementsareinterdependenttosomeextent andalsodependontheevolutionoffuelcosts.Thissuggeststhe adoptionofasystematicmodelingtooltoadequatelyrepresentall theseinteractions.

TheobjectiveofaGEPproblemistoidentifythemostadequate investmentscheduleofgenerationplantstogetherwiththeirsit- tingandtechnologytosupplythedemandconsideringitspossible 0378-7796/$–seefrontmatter© 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.epsr.2012.12.001

evolution alongthe planningperiodwhile enforcing somereli- abilityconstraints.TheGEPproblemwasusuallyaddressedinan integratedwaywithtransmissionexpansionplanning[1,2].Ref- erence[1]detailsanapproachusingStochasticProgrammingto model severaluncertain parameters and [2] describes a mixed integeroptimizationproblemthatusestheDCmodelofthetrans- missionsystem.References[2–4]useBendersdecompositionand [5,6]describemulti-objectiveapproachesconsideringinvestment, operationandtransmissioncosts,environmentalimpactsandthe riskofgettingaplanverymuchexposedtouncertainties.

Morerecently,metaheuristicsstartedtobeusedtosolvetheGEP problem,takingintoaccountitscombinatorialnature.Inthisscope, [7–10]report the useof genetic algorithms, simulated anneal- ing,expertsystems,antcoloniesand particleswarmalgorithms aswellascombinationsofthesetechniques[10].Thesemodels minimizeoperationplus investmentcostssubjected toa num- berofconstraints,forinstanceregardingthemaximumamount ofinvestmentthatcanbeaccommodatedineachplanningperiod.

Metaheuristics,bothusingasolutionineachiterationorpopula- tionbased,characterizetheinvestmentplansusinganevaluation functionthatcombinestheoptimizationfunctionoftheoriginal problempluspenaltiesontheviolatedconstraints.

The advent of restructuring created new concerns namely whetherexpansionplanspreparedbyindividualgenerationagents arecapableofensuringthesecurityofsupplyonthelongterm.In thisscope,[11]describesatwostepapproachinwhichindividual agentsprepareexpansionplansmaximizingtheirprofitthatare thensubmittedtoanupperlevelchecktoinvestigatethequalityof theglobalschedule,namelycomputingLOLPandthereservemar- ginalongthehorizon.Ontheotherhand,[12]comparescentralized andliberalizedGEPmodelsformulatinganoptimizationproblemto maximizetheprofitoftheinvestors.Thisproblemissolvedusing dynamicstochasticprogrammingtogetherwithdiscreteMarkov Chainstomodelthedemanduncertainty.

Finally,inrecentyearssystemdynamicsstartedtobeapplied totheGEPproblem.Systemdynamics[13]wascreatedbyJayFor- resterinthe60sandseveralapplicationstopowersystemsare reportedin[14].RegardingtheGEPproblem,[15,16]reportlong termelectricitymarketmodelsand[17]describestheapplication oftheseconceptstothegenerationsystemofNewZealand.

RecognizingthecomplexityoftheGEPproblem,theauthors developedaninitialapproach totheTEPproblemin whichthe demandand theelectricity priceevolution wereobtainedusing aCournotmodel[18].Thisapproachwasthenenhancedin[19]

inwhich thelongterm evolutionof theelectricity marketwas modeledusingsystemdynamics.In [19]itis usedageneration systemthatmirroredthemaincharacteristicsofthePortuguese generationsystemscaledby50%toillustratetheapproach.

Apartfromdescribing themaincharacteristicsandblocks of thelongtermdynamicmodelaswellastheprofitmaximization problems to be solved by each generation agent to schedule newgenerationinvestments,wearenowapplyingthisapproach to a larger system that incorporates the main features of the Portuguese/Spanish generation system having a total installed capacityofnearly120GWandanyearlydemandofabout312TWh in2010.Itisimportanttoanalyzebothsystemsinaglobalway given the common electricity market established between the two countriesand the increasing interconnectioncapacity that strongly contributed toreduce congestionsin thetransmission lines between them. The main motivation for using the Por- tuguese/Spanishgenerationsystemcomesfromthechallengesthat theIberiancountriesfaceinthenextyears.Infact,inrecentyearsa conjunctionoffactorsoccurrednamelyregardingthelargeamount ofinvestmentsthatweredirectedtonewgenerationstationsinthe last20years,therapidincreaseofdispersedgeneration(including renewabletechnologiesaswindparksandsolarsystems,aswell

a. positive cause effect relation b. negative cause effect relation.

x y

+

x y

-

Fig.1.Casualdiagramsillustratingapositiverelationintheleftandanegative dependencyintherightside.

asnonrenewablecogenerationsystems)andtherecentdecrease ofthedemandduetotheon-goingeconomiccrisis.Allthesesitu- ationsstronglysuggestedthatthepoliciesfollowedinthelast20 yearsshouldbelookedcloselyusinglongtermapproachestomore adequatelyevaluatethepossibleevolutionofthesystem.Onthe otherhand,asaresultofthemassiveintroductionofdispersedgen- eration,theliquiddemandavailabletobesuppliedbytraditional thermaltechnologiesisnowmuchmorereduced.Inthisscope,itis notrarethatinwinterwetvalleyperiodsthegenerationfromwind parksandhydrostationsbecomesenoughtosupplythedemandin Portugal,sothattheoutputoftraditionalthermalstationscomes tozeroaswellasthemarketprice.Asaconsequence,thenumber ofyearlyoperationhoursofseveralCCGTstationsismuchreduced andsogenerationcompaniesarenowcomplainingthattheirrev- enuesarenotenoughtopaythesestations.Asaresult,acapacity paymentwasawardedtosomePortuguesestationsin2009butit wasrecentlymuchreducedbythecurrentgovernment.Thiscor- respondstoanimportantissuethatalsodeservesattentionatthe Iberianlevel.Inordertoaddressthisissue,theGEPmodeldescribed in[19]nowincorporatesacapacitypaymentsothatwecanper- formsensitivitystudiesinordertoadequatelycalibratethevalueof thispayment,forinstanceasawaytoguaranteeaminimumreturn rateforsomelessusedthermalstations.

Considering these ideas,Section 2 provides an overview on system dynamics and Section 3 describes the overall adopted solutionapproach.Section4detailstheinvestmentplanningprob- lemsincorporatingthementionedcapacitypaymentandSection 5describesthelongtermdynamicmodeloftheelectricitymar- ket.Section6illustratesthisapproachwithacasestudyusingdata takenfromthePortuguese/Spanishgenerationsysteminthescope ofthecommonelectricitymarketestablishedbythetwocountries since2007andSection7drawsthemostrelevantconclusions.

2. Overviewonsystemdynamics

Systemdynamicsisamodelingtoolparticularlysuitedtorep- resentlongtermproblemsthatinvolvealargenumberofvariables andparametersaswellasloopsandinterdependencies.Inbrief, adoptingsystemdynamicstomodelaproblemimpliesdeveloping anin-depthunderstandingofthesystemtoidentifyitsboundaries, thetimehorizonandthemostrelevantvariables,parametersand interdependencies.Then,itisdevelopedaninitialdynamicmodel usingstandardbasicmodelsthatwillbebrieflydetailedbelow.The developedmodelisthen translatedintoa mathematicalformu- lation,thattypicallyincludesdifferentialequations.Finally,using thisformulation,themodelisvalidatedafterwhichmoreinvolving studiesandsimulationscanbedeveloped.

Therelationsanddependenciesbetweenvariables arerepre- sented using a number of standard sub-models. Figs. 1 and 2

Inflow Stock Outflow

Fig.2. Diagramofstocksandflows.

illustratepositiveandnegativecasualdiagramsandthediagram ofstocksandflows.Asthenamesuggests,apositivelooprepre- sentsapositivedependencybetweenxandy,inthesensethatifx increasesthenyalsoincreases,whileanegativelooprepresentsa negativerelationbetweenxandy.

Diagramsof stocksand flowsareintensivelyusedin system dynamics.Stockscharacterizethestateofthesystemandbased onthemwecanmodeldecisionsandactions.Theyrepresentthe memoryofthesystemandcanbeusedtomodeldelaysandto decoupleinflowsfromoutflows.Theflowsrepresenttheactivityof thesystemandareusedtoestablishrelationsbetweenthestocks.

ThediagramofFig.2istranslatedby(1)sothataftermodelingthe systemusingtheseelementarymodels,wecantranslatetheglobal casualdiagramintoamathematicalformulation.

∂Stock(t)

∂t =InputFlow(t)−OutputFlow(t) (1) 3. Structureofthelong-termexpansionplanningproblem

Thelong term evolution of thepowersystem wasmodeled bytheglobalcasualdiagramdisplayedinFig.3.Goingalongthis loopclockwise,thedecommissioningplansaffectnegativelythe installed capacity. On thecontrary,newadditions have a posi- tiveimpactinthereservesthat,ontheotherhand,arenegatively influencedbyanincreaseoftheelectricitydemand.Theevolution ofthedemandtogetherwithinformationabouttheevolutionof reserveswillthenbeusedtoestimatethelongtermevolutionof theelectricitypricethatisalsoaffectedbythelongtermevolution offuelprices.Theprofitsofthegenerationcompaniesaredeter- minedbythelevelofelectricitypricesaswellasbytheexpected maintenanceandinvestmentcosts.Finally,ifreservesdeclineand electricitypricesincrease,itistransmittedasignaltobuildnew powerstationssothatgenerationagentsprepareexpansionplans tomaximizetheirprofitsalongthehorizon,usingestimatesfor thedemandandtheelectricitypriceevolution.Thismeansthat eachgenerationagentsolvesitsownprofitmaximizationproblem toselectandschedulenewpowerstationinvestments.Thesetof newstations,thatis,thelongtermplannedevolutionofthegen- erationsystem,isthencheckedevaluatingsomereliabilityindices (astheLOLEandthereservemargin).Thisstepcanalsoinvolve checkingiftheinstalledcapacityinsometechnologiesdoesnot exceedmaximumvaluesifspecifiedinnationalenergystrategic plans.Accordingly,departingfromtheexistinggenerationmix,the dynamicmodelisusedtoestimatetheevolutionofthedemand, oftheelectricitypriceandofthecapacityfactorofeachtechnol- ogy,expressingthepercentageofhoursduringwhich,inaverage, eachtechnologyisused.Theseoutputsarethenusedbygeneration companiestopreparetheirownexpansionplans.Usingtheseplans, thedynamicmodelisrunagaintoupdatethementionedestimates thusdefininganiterativeprocedure.InSection4wewilldetailthe mentionedinvestmentproblemsandSection5describesthemain blocksofthedynamicmodeltogetthelongtermevolutionofthe powersystem.

4. Identificationofinvestmentplans 4.1. Individualinvestmentproblems

Admittingthat theevolution ofthedemand,of theelectric- itypriceandofthecapacityfactorofeachtechnologyalongthe horizonareknown,each generationcompany,Genco,solvesan optimizationproblemtomaximizeitsownprofitconsideringthe costsandtherevenuefromsellingelectricity.Whendoing this, a Genco can decideinvesting in new powerstations consider- ing a number of candidate technologies characterized by their

possibleinstalledcapacity,investmentandoperationandmainte- nancecosts.Thisinvestmentplanningproblemcanbemodeledby themixedintegeroptimizationformulationgivenby(2–8)inwhich thedecisionvariablesX_t^i,jrepresentthenewcapacityoftechnology jtobecommissionedinstagetbyGencoi.

max z=

⎡

⎣

j=1

^t·CC^ij_t ·t·˛^ij_t +

Pcap^j ·CC_t^ij·(1−˛^ij_t)

−

Cinv^j_t·Xt^ij₋

j=1

Cop^j_t·CC_t^ij·t·˛^ij_t

⎤

⎦

subj X_t^ij≤MIC_t^ij (3)

X_t^ij≤MIC_tⁱ (4)

X_t^ij·Cinv^j_t≤MXINVtⁱ (5)

X_t^ij·Cinv^j_t≤MXINVⁱ (6)

CC_t^ij=CC_t−^ij₁+X_t^ij (7) t=1,...,T; i=1,...,N; j=1,...,M (8) InthisformulationTisthenumberofstagesintheplanninghori- zon;tisthestageintheplanninghorizon;tisthedurationofeach stageintheplanninghorizon;Misthenumberofcandidatetech- nologies;jisthetypeofcandidateexpansiontechnology;iisthe indexassociatedtoaparticularGENCO;^tistheelectricitypricein staget(D/MWh);P_cap^j isthecapacitypaymentsetfortechnologyj (D/MW);˛^ij_t isthecapacityfactorinstagetforGENCOiandtech- nologyj(percentage);Cinv^j_tistheinvestmentcostfortechnologyj atstaget(D/MW);Cop^j_tisthevariableoperationandmaintenance costfortechnologyjatstaget(D/MWh);CC_t^ij isthecumulative capacityinstalledinstagetforGENCOi(MW);X_t^i,jisthecapacity additionoftechnologyjinstagetbyGENCOi(MW);MIC_t^ijisthe upperboundsetfortheinstalledcapacityoftechnologyjinstaget byGENCOi(MW);MICⁱ_tisthemaximumcapacityinstalledinstage tbyGENCOi(MW);MXINV_tⁱisthemaximumvaluespecifiedfor thecapitalinvestmentofGENCOiatstaget(D);MXINVⁱ isthe maximuminvestmentofGENCOialongthehorizonT(D).

Theobjectivefunction(2)containsfourterms.Thefirstonerep- resentstherevenuesobtainedbythegenerationagenti,Genco_i alongthehorizonTfromsellingelectricityatthemarketpricein each period tusing theinstalledcapacity and thecapacity fac- tor˛^i,j_t foreachtechnology. Thesecondtermmodelsacapacity paymenteventuallysetbyadministrativeorregulatoryagencies toremunerategenerationstationsduringtheperiodstheyarenot inoperation.AsmentionedinSection1,suchtermsalreadyexist insomecountriesandareunderdiscussioninseveralothers to copewiththereductionoftheoperationhoursofseveralthermal stationsdue,forinstance,totheincreaseoftheinjectionscoming fromdispersedgeneration,namelywindparksandsolarsystems.

Thethirdtermrepresentstheinvestmentcostineachperiodof thehorizonforeachtechnologyandthefourthonecorrespondsto theoperationandmaintenancecostsalongthehorizon.Itshould bementioned that when computingthevalue ofthis objective

+

+

+

+

_

+

+

+

+

+ _

_ _ +

Soluon of investment problems by individual generaon companies

Installed capacity

Reserve

Evoluon of the electricity price

Long-term evoluon of the electricity price

Forecast of expected profits along me

τ

Long-term evoluon of fuels and coal prices

Forecast of investment and maintenance costs

Evoluon of the electricity demand Decommission of

generaon units

Fig.3. Casualdiagrammodelingthelongtermpowersystemevolution.

functiontherevenuesand costsalongtheplanninghorizonare broughttotheinitialperiodusinganadequateactualizationrate.

Thisobjectivefunctionissubjectedtoconstraintsthatlimitthe newcapacitytobeaddedineachperiodtforeachtechnologyjfor Genco_i(3),thatenforcesthelimitonthenewcapacityadditions ofGenco_iineachperiodtofthehorizon(4)andthatlimitsinvest- mentcostseitherforeachperiodt(5)orfortheentirehorizonT (6)reflectingfinanciallimitationsofeachagent.Finally,(7)isused toupdatetheglobalinstalledcapacityofGenco_iastheplanning horizondevelops.

Thisisamixedintegerproblemthatwassolvedusingagenetic algorithmasbrieflydetailedbelow:

(i) Initialization – the initial population is randomly sampled consideringtheavailablecapacitiesthatitispossibletoinstall ofeachtechnology.Eachindividualisobtainedsamplingthe numberofstationsofeachtechnologyjtostartoperationin eachperiodtinT.

(ii)Evaluation–eachindividualcorrespondstoapossibleexpan- sion plan. The associated profit is given by (2) using the evolutionoftheelectricitypricesandofthecapacityfactors providedbythelongtermanalysis.Constraints(3)–(7)arealso checkedandifviolatedthenthefitnessfunctionisgivenby(2) minuspenaltiesovertheviolatedconstraints.

(iii)Convergencecheck–theconvergenceismonitoredchecking theaveragevalueand thestandard deviationofthefitness functionoftheindividualsinthecurrentpopulation.Thealgo- rithmconvergesiftheaveragevalueof thefitnessfunction issufficientlystableforaprespecifiednumberofiterations, thestandarddeviationissmallerthanaspecifiedthreshold andthefitnessfunctionofthebestindividual(theonehaving thelargestfitnessvalue)didnot changemore thanaspec- ified thresholdfora prespecifiednumberof iterations.We alsoimposedaminimumnumberofiterationstobecompleted independentlyoftheconvergencechecking.

(iv)Geneticoperators–iftheconvergencecriteriawerenotmet, thenthealgorithmproceedstoanewiterationapplyingthe selection,cross-overandmutationoperatorsoverthecurrent

population.Thenthealgorithmreturnstostep(ii)toanalyze theindividualsinthenewpopulation.

Whenthisiterativeprocessstops,theexpansionplanofthegen- erationcompanyi,Gencoi,willcorrespondtotheindividualinthe finalpopulationthatdisplaysthelargestprofit.

4.2. Coordinationanalysis

AsmentionedinSection3,eachgenerationagentshouldprepare itsownexpansionplan.ThisexercisecanalsobedonebyGenco_i that wantstodevelop itsown expansionplan while admitting pre-specifiedcommissioning schedulesforall otheragents.The expansionplanforGenco_icanthenbetestedagainstdifferentaddi- tionsoftheothercompetitorstoinvestigateitssensitivitytothe decisionsofotheragents.

Inanycase,thegenerationsystemshouldguaranteethesup- plyofthedemanddisplayinganadequatesecurityandreliability.

Toensurethatspecifiedstandardsaremetalongthehorizonwe submitthesetofdevelopedpartialplanstoacoordinationanalysis thatincludescalculating:

-thelossofloadexpectancymeasuringthenumberofhoursalong eachyearthatthegenerationsystemmaynotbeabletosupply thedemand.TheyearlyLOLEvaluesarecomparedwithamax- imumsetvalueandifsomeyearlyLOLEexceedsthemaximum, thentheglobalplanningexercisedidnotconvergeyet.

-The yearly valueof thereserve margin, correspondingtothe excess,inpercentage,oftheglobalinstalledcapacityregarding the peak power. The yearly values of this margin should be boundedbyaminimumvaluetocontributetoensurethesecu- rityofsupplyandeventuallybyamaximumvaluetopreventan excessiveinstalledcapacity.

Finally,itispossibletolimittheinstalledcapacityownedby eachgenerationcompanyagainsttheglobalcapacityinthesystem aswelllimiting,forinstance,theinstalledcapacityforaparticular technologyinthescopeofpublicnationalenergypolicies.

Volatility _dz

Regression

strength Regression velocity Long term growth rate

Gen_Ther_n Total

generation

Gen_HI _Res

Inst_cap_

HI_Res

Sim_est_cf HI_Res

Avail_HI _Res Inst_cap_

HI_RV

Avail_HI _RV

_

Avail_SRG

Avail_

Ther_n

Inst_cap_

Ther_n Sim_est_cf

_HI_RV Gen_SRG

Sim_est_cf SRG Inst_cap SRG

var_gen_

cost_Ther_n cf_Ther_n

Gen_HI _RV

Variations of price

Forecast of the prices along the horizon Adjustment time

Network losses

Average daily and annual prices

Demand/price elasticity Demand

Variation of the demand

Reference demand

Reference price Annual growth

rate

dx

Initial rate

FDP_normal

price

Fig.4.Dynamicmodeloftheelectricitymarket.

5. Longtermevolutionofthepowersystem 5.1. Globalstructureofthemodel

ThesolutionoftheinvestmentproblemsdetailedinSection4 requirestheknowledgeoftheevolutionoftheelectricitypriceand ofthecapacityfactorsofeachtechnology.Theseinputsareprovided bythelongtermmodeloftheelectricitymarketdevelopedusing systemdynamics.Fig.4presentsanaggregatedviewofthismodel toidentifythemainsubmodelsandtheirrelationstobedetailed inthenextsections.

5.2. Thesupplysystem

ThelowerpartofthediagramofFig.4containsthesubmodels representingthegenerationsystemtakingintoaccounttheirrele- vanttechnologies.Theleftsidecorrespondstothespecialregime generation,SRG,thelowercentralparttothehydrosystemandthe rightsidetothesetofthermalstations.

RegardingSRG,namelythewindparks,weadmittedthatthey arepaidfeedintariffs(asithappensforinstanceinPortugal)or thattheycanchoosebetweenfeedintariffsorreceivingthemarket priceplusapremium(asitoccursinSpain).Inanycase,windgener- ationhaspriorityoverothertechnologiessothatweusedhistorical valuesfortheircapacityfactorrangingfrom20%to25%.Theseval- uesreflectboththeavailabilityoftheprimaryresourceandofthe stationsthemselves.Usingthesehistoricalvalues,ineachrunof thesimulationwesampleavalueforthisindexusingastochastic process.

ThehydrosystemisrepresentedbytwonodesinFig.4cor- respondingtorunofriver,RV,andreservoirs,Res,and,foreach ofthem,wealsousedhistoricalvaluesofthecapacityfactorto obtainitsaveragevalueandstandarddeviation.Typically,forthe Portuguesehydrosystem,thecapacityfactorofrunofriversta- tionsisaround25%andforreservoirsitrangesfrom20%to25%

dependingontherainyordrynatureofeachyear.Ontheother hand,hydrostationswerenotsubjectedtoinvestmentdecisions inthescopeofthisproblem.Giventheirreducedoperationcosts, hydrostationsareveryattractiveandpossiblelocationsfornew stationshaverecentlybeensubjectedtotendersbyofficialenti- ties.So,weadmittedthatthereisinformationregardingadditions ofnewhydroadditionsalongtheplanninghorizoncomingfrom thesetenderingprocesses.

Finally,Fig.4includesanodeontherightlowersideforthermal stations,Ther.Thedevelopedmodelincludesanumberofsubnodes accordingtotheexistingtechnologiesinthemix.In thecaseof thePortuguese/Spanishsystemwemodeledcombinedcycles,coal (eventuallyfurthersubdividedindifferenttypesofcoal),fueland nuclearstations.Inthisapproachweadmittedthatnuclearisnot acandidatetechnologyandthattheexistingonesareinpractice mustrunstations,typicallyhavingalargecapacityfactor.

Thelongtermdynamicmodelusesanumberofinputsregarding thegenerationsystem(installedcapacityforeachtechnology,aver- agecapacityfactorsforwind,hydroandnuclearstations)andthen itestimatesthedemand,theelectricitypriceandthecapacityfac- torsof theremainingthermal stations.Using theinputand the computedcapacityfactorsplustheinstalledcapacityofeachtech- nologyitispossibletoobtainforeachperiodthegenerationper technologyusingthespecifiedoperationcosts.Thesepartialval- uesarethenaddedinthenode“TotalGeneration”andthisvalue ismultipliedbyafactorlargerthan1toconsidernetworklosses, typicallyintherangefrom1.08to1.10.

5.3. Evolutionofthedemand

Thedemandmodelisanothermajorblockinthedynamicmodel, givenitsimpactontheelectricityprice.Thedemandrateismodeled usinganOrneisten–Uhlenbeckmeanrevertingprocess[15]given thatthismodeliswellsuitedtoincorporatetheuncertaintythatcan affectavariableonthelongrun[20].Theevolutionofthedemand

rateisdeterminedbyalongtermtrendandbyashorttermcompo- nentdue,forinstance,tometeorologicalconditions.Thisshortterm componenttendstoattenuatesothatthedemandrevertsagainto thelongtermtrend.Thesetwotermsareincludedin(9).Thefirst one,FR,isgivenby(10)anditisinfluencedbythemeanvalueto whichthedemandraterevertsonthelongterm,drateLT,andbythe speedofreversion,,modelinghowfastvariationsdissipateand returnbacktoitsmeanvalue.Thesecondtermisgivenby(11)and itmodelstheshorttermcomponentusingaWienerprocessthat dependsonthevolatilityparameterı.Ifıincreases,thedemand tendstodisplaylargervariationsalthoughhavingthesamemean value.Startingatareferencedemandratedrate0itispossibleto obtaintheevolutionofthedemandrateinthestepsofthehorizon using(12).Intheseexpressionsεt representsarandomnumber extractedateachtimestepfromanormaldistribution(0,1).This demandmodelisrepresentedintheupperleftpartofFig.4.

dx=FR+dz (9)

FR=·(drateLT−dratet)·t (10) dz=εt·ı·

t (11)

drate=drate0+

dx·dt (12)

Usingthedemandrate,themodelestimatesthedemanditselfusing (13).Thedemandineach periodtdependsonthedemandrate andonthereferencedemandsetforthestartingyear.Finally,the demandgivenby(13)canbeaffectedbyanelasticitycoefficient using(14).Inthisexpression^t,⁰andEdrepresenttheelectric- itypriceinperiodt,theelectricitypriceinthestartingperiodand theelasticityofthedemandtotheprice.ThevalueofEdisspecified bytheplannerhavinginmindthatitistypicallyreducedincur- rentpowersystems.Thisblockislocatedintheupperrightsideof Fig.4.

dref,t=dref0+

dratet·dref0·dt (13)

delec,t=dref,t. ^{t 0}

(14)

5.4. Evolutionoftheelectricitymarketprice

Oncetheelectricitydemandisobtainedforeachperiodt,itis possibletoestimatetheevolutionoftheelectricitypriceasdis- playedinthecentralpartofFig.4.Thepriceevolutionisinfluenced bythepricesetattheinitialperiod,⁰,bythedemandevolution andbythegenerationmix,thatinternalizestheimpactoffueland coalpricestogetherwiththeavailabilityofwindresources.The priceinperiodtisgivenby(15)andthepricevariations^tare givenby(16).Thepriceevolutiondependsontherelationbetween thedemandinperiodtandthetotalinstalledcapacity.Forinstance, ifthedemandinperiodtexceedstheinstalledcapacity,thanthe outputof(16)ispositivethusinducingapriceincrease.Conversely, ademandvaluebelowtheinstalledcapacitywillleadtoaprice reduction.Thesepricevariationscanbesmoothedadoptingavalue largerthan1.0fortheattenuationfactor,AF.

^t=⁰+

^t·dt (15)

^t=⁰· delec,t−Gtotal

delec,t

· 1

AF (16)

5.5. Globalmodelandsolutionalgorithm

Using the dynamic model of the electricity market and the investmentplanningproblems tobesolvedby eachgeneration company,wecansummarizethesolutionalgorithmasfollows:

(i)inthefirstplace,thedynamicmodelisrunusingthereference demandrateandthegenerationmixavailableinthestarting periodassumingthatthismixisunchangedalongtheplanning horizon.Thisleadstotheevolutionoftheelectricityprice,of thedemandandofthecapacityfactorsofthetechnologiesin themix.

(ii) usingtheoutputof(i),thegenerationagentssolvetheirprofit maximizationproblemstoidentifytheirinvestmentschedules.

Thismeansthateachgenerationagentidentifiesanexpansion planwithnewcapacitiestobebuilt,theirtechnologiesand commissioningyears.

(iii) usingthedecommissioningscheduleofolderstations,theset ofplansobtainedin(ii)andtheexpecteddemandevolution,we computetheLOLEandthereservemarginalongthehorizonand checkotherglobalconstraintsastheonesmentionedinSection 4.2.

(iv)ifnoviolationsaredetectedin(iii)andiftheoutputsofstep (i)aresufficientlystablealongtwoconsecutiveiterations,then theiterativeprocessstops.Otherwise,weproceedtostepv).

(v)iftheproblemdidnotconvergeyet,thenthegenerationmixis updatedusingtheoutputsofstep(ii)andtheprocessreturns tostep(i)torunthedynamicmodelagain.

ThisapproachwasimplementedinMATLAB,POWERSYMand MicrosoftExcel.MATLABwasusedtosolvetheexpansionproblems detailedinSection4.1andtocomputetheLOLEalongthehorizon.It wasalsousedanacademicversionofPOWERSIMsoftwarepackage [21,22]todevelopthedynamicmodelusingtheRunge–Kutta4th ordernumericalintegrationmethodtosolvethedifferentialequa- tionswithatimestepof1h.FinallyExcelwasusedasaninterface withtheprevioustwomodulesandtoorganizeinputandoutput information,astablesandfigures.

6. CasestudyusingdatafromthePortuguese/Spanish generationsystem

6.1. Initialgenerationsystemanddata

Thedevelopedapproachwillnowbeillustratedusinga case studythatlargelymirrorsthePortuguese/Spanishgenerationsys- teminthescopeofthecommonelectricitymarketinvolvingthe twocountries.However,itisimportanttonoticethattheauthors arenotinthepossessionofinformationregardingtheinvestment strategiesofthemainplayersnoroflongtermforecastsofsev- eralparametersthatshouldbeusedifamorerealisticstudyonthe Iberiangenerationsystemwastobemade.Thisultimatelymeans thatweusedrealisticandpubliclyavailabledataregardingthecon- stitutionofthegenerationsystemsofbothPortugalandSpainand thentheremainingrequiredparametersweresetusingtheexpe- rienceoftheauthors.Theultimategoalofthisstudyisthereforeto illustratethedevelopedapplicationusingarealisticsizedsystem tohighlightthemainadvantagesandinsightsthatcanbeprovided bythistypeofstudies.

Bytheend of2010thePortugueseandtheSpanishsystems hadinstalledcapacitiesof18,000andof99,000MWandthetotal demand was 52,204GWh and 260,609 GWh. The transmission

Table1

CharacteristicsoftheexistinggenerationmixintheIberianPeninsula.

Technologies Inst.capacity(MW) FOR

Nuclear 7777.0 –

Coal 1 7500.0 0.02

Coal 2 5500.0 0.02

Fuel/gasturbine 4500.0 0.02

CCGT 1 20,000.0 0.02

CCGT2 10,000.0 0.02

Hydroreservoirs 15,000.0 –

Hydrorun-of-river 10,000.0 –

Windparks 23,800.0 –

Photovoltaic 3500.0 –

Biomass 800.0 –

Cogeneration 8600.0 –

systems are well developed and are interconnected by 7 lines at220kVand400kVandtheaveragemarketpricein2010was 55.3D/MWh.

TheexistinggenerationmixisdescribedinTable1.Apartfrom therespectiveinstalledcapacities,thistableindicatesthecorre- spondingFOR,exceptfor nuclearstations,hydro stations,wind parks,photovoltaic,biomassandcogeneration.Regardingnuclear stations, theytypically cover the basis of the diagram and the energyprovided bythem wasobtainedusinghistoric datathat alreadyreflectsoutagesandpreventivemaintenance.Asdetailed inSection5.2windparks,photovoltaic,biomassandcogeneration plantscorrespondtospecialregimestationsbothinPortugaland inSpain.Foroperationpurposes,thesespecialregimetechnologies cantypicallyinjectinthenetworksasmuchenergyasavailable giventhevolatilenatureoftheprimaryresource usedby some ofthem.Formodelingpurposeswealsousedhistoricdataindi- catingtheenergyprovidedbythesetechnologiesinrecentyears andderivingfromthesevaluesthecorrespondingcapacityfactors.

Thesevaluesreflectboththeavailabilityoftheprimaryresource andtheavailabilityofthegenerationstationsthemselves.

Thesimulationwasrunconsidering7generationcompanies, Genco1toGenco7, thatown thementionedinstalled capacity asfollows: Genco1 has16.5%, Genco2 has22.0%, Genco3 has 5.2%,Genco4has12.6%,Genco5has3.7%,Genco6has10.0%and Genco7has30%.Genco7representstheaggregatedshareofalarge numberofsmallgenerationagents.Furtherassumptionstomodel thegenerationsystemareasfollows:

-regardingthenuclearstations,weadmittedacapacityfactorof 85%withastandarddeviationof5%;

-theoperationoftheremainingthermalstationsdependsontheir operationcosts,ontheevolutionoftheelectricitypriceandofthe demandalongthesimulation.Inordertomodelinamorerefined waythetechnologiesinthegenerationmix,wedividedcoaland CCGTstationsintwosetseach,enablingspecifyingdifferentcosts foreachclass;

-hydrostationswerealsodividedintwosets–reservoirsandrun ofriverstations.Inthesimulation,weusedanaveragecapacity factorof20%forreservoirsand25%forrunofrivertogetherwith astandarddeviationof5%;

-forthewindparksandphotovoltaicsystemsweadmittedaverage capacityfactorsof25%andof20%basedonhistoricvaluesanda standarddeviationof5%;

-finallyforcogenerationandbiomasssystemsweusedaverage capacityfactorsof45%andof55%.

The planninghorizon wasset at 15 years and we admitted thereareanumberofstationstobedecommissionedasfollows:

1500MWofnucleargroupsinyear3,forCoal11000MWinyear 4and1000MWinyear8andfinally1000MWofCCGT1inyear 10.Giventhenatureofthespecialregimetechnologies,therearein

thetwocountriesspeciallicensingschemes,namelyusingtender mechanismsfornewwindcapacity.Therefore,weadmittedthere willbenewwindcapacityasfollows:200MWperyearfromyear1 to4and100MWfromyear5toyear10.Forphotovoltaicsystems weadmitted200MWinyear3,150MWinyear6and200MWin year9.Finally,newhydrocapacityhasalsobeensubjectedtoaten- derprocessinPortugalandsoweadmitted500MWofnewhydro capacityinyear6and300MWinyear10.

Thedemandin thedepartingyearofthehorizon wassetat 312.8TWh.Theyearlydemandwasmodeledusingaloadduration curvewith6stepsasfollows:100%ofthepeakpowerduring5%of theyear,90%for20%oftheyear,80%for45%oftheyear,70%for65%

oftheyear,60%for85%oftheyearand50%ofthepeakpowerdur- ing100%.Thelongtermdemandratewassetat2%andthenalong theplanninghorizonthedemandrateisadjustedbythedynamic modelbuttheabovediscretizationoftheloaddiagramremains unchanged.

Asforthetechnologiesusedintheexpansionplanningprob- lems,weconsideredthreeoptionsasindicatedinTable2.Wealso assumedthatthelifetimeofthesestationsis30yearsandthat theconstructionperiodis3yearsforTechs1and3and2years forTech 2.Theoperationcostsweremodeledusingacostfunc- tionorganizedinfivesegmentsandestablishedinfunctionofthe capacityfactor.Asanexample,forTech 1wespecifiedthefollow- ingpoints(0.0;0.0),(0.2;15.0),(0.4;30.0),(0.6;40.0),(0.8;65.0) and(1.0;80.0).Ineachofthesepairs,thefirstelementrepresents thecapacityfactorandthesecondisthevariableoperationcostin D/MWh.

Inordertopreventmarketpowerandtoincorporateenergy policyobjectiveswealsoadmittedthatineachyearofthehorizon eachagentcannotinstallmorethan800MWinTech1,400MW inTech2and400MWinTech3andthetotalnewcapacityinany ofthesetechnologiesshouldnotexceed50%.Asindicatedinthe beginningofthissectiontheselimitswereadoptedbytheauthors justforillustrationpurposesandhavenodirectconnectionwith theinvestmentpoliciesofthegenerationplayersinthesystem.

However,someexamplesofsuchlimitationswerealreadyputin practiceintherecentpast.Forinstance,inrecentyearsthePor- tuguesegovernmentusedpublicauctionstoallocatenewhydro capacityandthecurrentlargestPortuguesegenerationcompany wasforcedtoreduceitsgenerationassetsinordertobeallowed tobuildnewhydrocapacity.Asanotherexample,in2008itwas openedanauctiontoallocatenewCCGTstationsandamongthe rulessetforthisauctiontherewerelimitationsregardingthetotal amountofpowerthatcouldbeallocatedtothesameagent.The simulationsusedanumberofotherinputparametersasfollows:

theyearlyreservemarginshouldbelargerthan30%,themaximum valueallowedforLOLEis2h/year,anda7%actualizationratewas usedalongtheplanninghorizontobringrevenuesandcoststothe initialperiod.

Onceagaintoillustratethecapabilitiesofthedevelopedappli- cation,weadmittedthatGenco’s5,6and7arenotinterestedin expandingtheirgenerationcapacity.Ontheotherhand,Genco’s 1–4areavailabletoinvestinthesethreetechnologiesconsidering thefollowingfinanciallimitations:

-Genco1has1200MDavailablefortheperiodfromyear1toyear 10plus400MDinthefinal5years;

-Genco2has500MDavailableforthefirst5years,plus1200MD forthefinal10years;

-Genco3has500MD fromyear1to5,plus500MD fromyear6 to10,plus500MDforthefinal5years;

- Genco4hasnoresourcestoinvestfromyear1to3.Fromyear4 tillyear15ithas1200MDavailable.

Table2

Characterizationofthecandidatetechnologies.

Typeoftechnology Availablecapacities(MW) Investmentcost(D/MW) FixO&Mcost(D/MWyear) Costofcapitalwiththeloan(D/MWyear) FOR

Tech1 200or400 650,000 7050 52,380.40 0.02

Tech 2 200or300or400 500,000 6200 40,230.40 0.02

Tech 3 200or400 1,050,000 8600 82,300.10 0.02

Table3

GenerationexpansionplanobtainedforGenco 1.

Stage Tech1(MW) Tech2(MW) Tech3(MW)

2 400 – –

3 200 200 –

5 400 – –

6 – 200 200

9 – 200 –

12 200 – 200

Table4

GenerationexpansionplanobtainedforGenco2.

Stage Tech1(MW) Tech2(MW) Tech3(MW)

2 400 – –

3 – 200 –

6 400 200 200

10 – 200 –

11 200 200 200

Table5

GenerationexpansionplanobtainedforGenco 3.

Stage Tech1(MW) Tech2(MW) Tech3(MW)

3 400 – –

4 – 200 200

6 400 – –

7 – 200 –

11 200 – 200

6.2. Resultsofthegenerationexpansionstudy–basecase

Inthefirstplace,theapproachdescribedinSections3–5was usedtodeveloptheexpansionplansofGenco’s1–4usingtheabove dataandadmittingthatthecapacitypaymentincorporatedin(2) issettozero.Tables3–6detailtheobtainedfourexpansionplans indicatingtheyearinwhichinvestmentdecisionsaretaken.This means,forinstancethatGenco1decidedtobuilda400MWstation ofTech1inyear2butthisstationwillonlystartoperationatyear 5,givenitsconstructiontimeof3years.

Regardingthenewadditions,50%ofthenewinstalledcapacity isforTech1,28.94%forTech2and21.06%forTech3.Tech1isthe mostcompetitiveoneanditsshareisnotevenlargerbecauseitwas imposedthatthetotalnewcapacityinanytechnologyshouldnot exceed50%.ThedistributionofthenewcapacitybythefourGenco’s isasfollows:30.26%forGenco1,28.95%forGenco2,22.36%for Genco3 and 18.43% for Genco4. The maximum value of LOLE occurredinyear7,reaching0.88h/year.Fig.5displaystheevolu- tionoftheyearlyaverageelectricitypriceestimatedbythedynamic model.Inthebeginning,theaveragepricetendstoincreasebecause thefirstnewstationswillonlystartoperationatyear5,takinginto accountthe3yearconstructionperiod.Thepricedoesnotriseeven

Table6

GenerationexpansionplanobtainedforGenco4.

Stage Tech1(MW) Tech2(MW) Tech3(MW)

5 400 200 200

10 200 – 200

11 – 200 –

0,0 10,0 20,0 30,0 40,0 50,0 60,0

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11T12T13T14T15

(€/MWh)

Stage

Fig.5.Evolutionoftheaverageelectricitypricealongtheplanninghorizon.

morebecausetherearenewadditionsofwindparksandphoto- voltaicsystemsinthefirstyearsofthehorizon.Thepeakinyear3 isalsodeterminedbythedecommissioningof1500MWofnuclear groups.

Finally,Fig.6displaystheevolutionofthecapacityfactorsof thethreecandidatetechnologies.Thesevaluesarearesultofthe operationcostofeachtechnology,togetherwiththeevolutionof thedemand,thedecommissioningofexistingstationsandtheuse ofhydrostationsandthespecialregimestations.ForTech1the graphstartsinyear5giventheyearinwhichthefirstdecisionsare takenandtheconstructionperiod.Forsimilarreasons,thegraphs forTech2and3startinyear5andinyear7respectively.Inaverage, Tech1hasthelargestcapacityfactor,displayinganaveragevalue of0.69peryear,followedbyTech3(averagevalueof0.54peryear) andbyTech2(averagevalueof0.52peryear).

6.3. Sensitivityanalysis–impactofCO₂emissioncosts

Forillustrationpurposes,wealsoadmittedascenarioinwhich CO2emissioncosts wereinternalizedin themodel.We admit- tedthatTech1emits0.77CO₂ton/MWh,Tech2emits0.36CO₂ ton/MWhand forTech 3weused0.09 CO₂ ton/MWhreflecting theuseofcleanertechnologiesinthecaseofTech3.Ontheother hand,weusedacostof20.0D/tonofCO₂,consideringpricesonCO2 emissionmarkets,andthecapacitytermin(2)wasnotused.Using thesevalues,Tech2andTech3becomemoreattractiveregarding thebasecase.AsaresultoftheCO₂ emissioncosts,theaverage electricitypriceincreasedfrom51.1D/MWhinthebasecaseto 58.6D/MWh.Inthisnewscenariothenewcapacityadditionsareas follows:33.20%forTech1,26.80%forTech2and40.00%forTech3.

Regardingtheevolutionofthecapacityfactors,theaveragevalue obtainedforTech1decreasedfrom0.69to0.52peryearwhilefor

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15 Evolution of the Capacity factor (%)

Stage

Tech_1 Tech_2 Tech_3

Fig.6. Evolutionofthecapacityfactorofthethreecandidatetechnologies.

Tech’s2and3theyincreasedfrom0.52to0.57andfrom0.54to 0.71.

This type of studies shows that changes in legal, tariff or regulatoryprovisionscanoriginatesignificantalterationsonthe investmentplansconfirmingthatthegenerationactivityisnow moreriskythaninthepast.

6.4. Sensitivityanalysis–impactofincreasingwindparksby20%

Thegenerationsystemofbothcountriesalreadyhasaremark- ablepenetrationofrenewablestations,namelyhydroandwind parks.Inordertogetinsight ontheeventualimpactofa larger increase of the installed capacity in wind parks, we admitted thattheinstalledcapacityintheinitialyearwasincreasedfrom 23,800MWasindicatedinTable1to28,560MW, thatis,a20%

increase. Onceagainthe capacityterm in(2) wasnot used.As aresult ofthis windcapacity increase,theinstalledcapacity in the three candidate technologies got reduced when compared with the values reported in Section 6.2. Regarding Tech1 the installedcapacityreducedfrom3800MWto3200MW,forTech2 itreducedfrom2200MWto1900MWandforTech3itreduced from1600MWto1400MW.Thismeansthereisareductionofthe installedcapacityinthethreecandidatetechnologiesof14.5%.On theotherhand,theaveragevalueoftheelectricitypricealongthe planninghorizongotreducedfrom51.1D/MWhinthebasecase to48.9D/MWh,thatisareductionof4.3%.Itisimportanttonotice thatthismarketpricereductiondoesnotnecessarilymeanthatthe finalenduserswillalsoseeapricereduction.Infact,inPortugal forinstancerenewablestationsarepaidfeed-intariffsthatcur- rentlyhaveanaveragevalueof70.0D/MWhthatwillinanycase beincorporatedinthefinalendusertariffs.Adirectconsequence ofthisincreasedamountofrenewableinstalledcapacityisthepro- gressivereductionoftheincomeofgenerationcompanieshaving thermalstations,notonlybecausethemarketpricegetsreduced butalsobecausethenumberofhoursthesestationswillbeusedin eachyearalsogetsreduced.

6.5. Sensitivityanalysis–impactoftheimplementationofa capacitypaymentterm

AsmentionedinSection6.4,havingalargeamountofinstalled capacityusingrenewableresourceshasimportantconsequences fortheremaininggenerationagents, namelyfortheonesown- ingtraditionalthermalstations.Infact,themarketpricetendsto getreducedeitherbecausenewgenerationbidsatzeropriceare incorporatedintheaggregatedmarketsellingcurvesorbecausethe liquiddemandtobesuppliedbytraditionalstationsgetsreduced.

Inbothcases,theresultisthattheintersectionoftheaggregated buyingandsellingcurvesoccursformorereducedmarketprices.

Apartfromthat,thenumberofoperatinghoursalongeachyearof severalthermalstationstendstogetreduced,thatis,thecapacity factorsofseveralstationsarereduced.Thiseffectisalreadyvisi- bleinseveralstationsbothinPortugalandinSpain,wheresome recentlybuiltCCGTstationsoperatelessthan2000hayear,thus compromisingtheirprofitability.

Havinginmindthesefacts,westartedbycomputingtheaverage returnrateassociatedwiththethermalstationsfortheinvestment plansobtainedinthebasecasedescribedinSection6.2andalso whenadmittingthattheinstalledwindpowercapacityincreased by20%,asdescribedinSection6.4.Thisreturnratewascomputed asthequotientoftheprofitassociatedtoaspecificstationregarding itstotalinvestmentandoperationcostsalongtheentireplanning horizon.Ontheotherhandtheprofitcorrespondstothedifference betweentheincome obtainedfromsellingtheelectricityatthe marketpricesandthetotalinvestmentandoperationcosts.

Usingthisapproach,forthebasecaseweobtainedanaverage returnof11.3%andthisvaluegetsreducedto9.6%whenconsid- eringtheincrease of20%of thewindpower installedcapacity.

Thisreductioncanfreezetheinvestmentdecisionsinnewthermal capacityorcanultimatelyoriginatetheshutdownofsomealready existingthermalstations,asitisapparentlyunderconsiderationby somePortuguesegenerationagents,thuseventuallycompromising inthelongtermthesecurityofsupply.

Inothertocounteractthisimpactofrenewableinstalledcapac- ity,weusedthedevelopedGEPmodeltoestimatethevalueofthe capacitypaymenttermincludedin(2),Pcap^j ,thatshouldbecon- sideredinordertoobtainthe11.3%returnrateofSection6.2,but usingtheexpansionplansidentifiedinSection6.4whenadmit- tingthatthewindpowercapacityincreasedby20%.Afterrunning theGEPmodelseveraltimesusingdifferentvaluesforthecapacity paymentterm,weestimatedavalueof5.6D/MWforthecapacity terminordertoguaranteethe11.3%rateofreturn.

Thistypeofstudiescanbeusedinaprofitablewaybothby stateorregulatoryagenciestogetmoreinsightontheimpactof adoptingdifferentvaluesforPcap^j .Forinstance,theentireexpansion planningmodelincludingthelongtermdynamicsimulationwas runusingacapacitypaymentvalueof10.0D/MW.Inthiscase,the investmentplanswouldnowincludetheinstallationof3400MW ofTech1(more200MWregardingthesolutiondescribedinSec- tion6.4),2100MWofTech2(more200MWthanthesolutionin Section6.4)and1400MWofTech3(samevalueasobtainedinSec- tion6.4).Giventhattheinstalledcapacityisnowslightlyincreased, thecapacityfactorsofthethermalstations getslightlyreduced and,asaresult,thereturnratealongtheplanninghorizongets nowreducedfrom11.3%to10.8%.However,thissolutionisadvan- tageous regarding the immediate incorporation of a 5.6D/MW paymentusingthesameplansasobtainedinSection6.4because thetotalinstalledthermalcapacitybecomeslargerthusincreasing thesecurityofsupplyinfaceofthelargepresenceofgeneration usingvolatileprimaryresources.

7. Conclusions

Thispaperdescribesalongtermapproachtothegeneration expansion planningproblem combining the solutionof expan- sionprofitmaximizationproblemsbyindividualgenerationagents togetherwithalongtermdynamicsimulationtoestimatetheevo- lutionofthedemandandoftheelectricityprice.Thedeveloped approachwasillustratedusingagenerationsystemthatincorpo- ratesthemostrelevantcharacteristicsofthePortuguese/Spanish generationsystem.Thedevelopedapproachcanbeusedinaprof- itablewaybygenerationcompaniestohelpthempreparingtheir ownexpansionplans,simulatingpossiblebehaviorsofothercom- petitors,as wellas torun sensitivitystudies toinvestigate the impact,forinstance,ofchangesontheoperationorinvestment costsor onthelongterm evolutionof thedemand.It can also beusedbyregulatoryorstateagenciestoevaluatethelongterm impactregardingmarketorregulatorydesignchanges,sothatmore soundedandlessriskyoptionsareadopted.Asanexample,the developedapproachcanbeusedtoevaluatetheimpactofintroduc- ing a capacity term toremunerate stations that are becoming lessusedgiventhemassivedeploymentofdispersedgeneration, namelywindparksandsolarsystems,inPortugalandSpain.As aresultoftheselargeinvestments,thecapacityfactorsofseveral thermalstations,includingrecentlybuiltCCGT’s,areveryreduced thuseventuallyjustifyingtheintroductionofsuchcapacityterm.

Thedevelopedapproachcanbeusedtoinvestigatetheimpactof suchtermsandtohelpregulatoryandstateagentstoadequately setand calibratetheirvalues.In brief,this paperisan attempt tolookmorecloselyonrecentyearsandtoanticipatewhatmay

happeninseveralpowersystems till2030,taking asa realistic examplethegenerationsystemsofPortugalandSpain.

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AdelinoJ.C.PereirawasborninSanfins,Portugalin1975.Hereceivedhisdiploma andM.Sc.degreesinElectricalEngineeringandComputersfromtheFaculdadede EngenhariadaUniversidadedoPorto,FEUP,Portugal,in1998and2003.In1998 hejoinedtheCoimbraPolytechnicInstitute(ISEC)whereheiscurrentlyAdjunct Professor.InJuly2010heconcludedhisPh.D.atFEUPwithaThesisonlongterm generationexpansionplanningusingsystemdynamics.

JoãoToméSaraivawasborninPorto,Portugalin1962.In1987,1993and2002hegot hisM.Sc.,Ph.D.,andAgregadodegreesinElectricalandComputerEngineeringfrom theFaculdadedeEngenhariadaUniversidadedoPortowhereheiscurrentlyProfes- sor.In1985hejoinedINESCPortowherehewasheadresearcherorcollaboratedin severalprojectsrelatedwiththedevelopmentofDMSsystems,qualityinpowersys- tems,andtariffsduefortheuseoftransmissionanddistributionnetworks.Several oftheseprojectsweredevelopedunderconsultancycontractswiththePortuguese ElectricityRegulatoryAgency.