Auction-based allocation of shared electricity storage resources through physical storage rights

Auction-based allocation of shared electricity storage resources through physical storage rights

Tom Brijs

^a,b,d,

*, Daniel Huppmann

^c,d

, Sauleh Siddiqui

^d,e

, Ronnie Belmans

^a,b

aDepartmentofElectricalEngineering,UniversityofLeuven(KULeuven),Heverlee,Belgium

bEnergyVilleResearchInstitute,Genk,Belgium

cInternationalInstituteofAppliedSystemsAnalysis(IIASA),Laxenburg,Austria

dDepartmentofCivilEngineering,TheJohnsHopkinsUniversity,Baltimore,MD,USA

eDepartmentofAppliedMathematicsandStatistics,TheJohnsHopkinsUniversity,Baltimore,MD,USA

1. Introduction

Theintegrationofvariablerenewableenergysources(RES)isa major challenge for the operation of the power system. Their limitedcontrollability andpredictability resultsinan increased need for power system flexibility, while flexible conventional power plants currently experience decreasing profitability as a resultoflowelectricitypricesandalimitednumberofoperating hours[1].Flexibilityistheabilitytoprovideup-anddownward poweradjustmentstodealwithtemporaryimbalancesbetween generationandconsumptionofelectricenergy[2,3].Thisflexibility can be provided by flexible generation and consumption, and

electricitystorage,butcanalsobeactivatedinneighboringregions throughinterconnectioncapacity and thefurther integrationof adjacent markets (Fig. 1). Electricity storage hasthe ability to compensate temporary power surpluses and shortages by decouplingthegenerationofelectricenergyfromitsconsumption overtime.Theextentofthiscompensationislimitedbyitsstorage capacity.

Althoughthereisaneedforflexibilitybecauseofitsincreasing demand and decreasing supply, market participants are only incentivizedtointegratenewflexibleresourcesiftheinvestmentis profitable.Inaddition,thevalueofstorageisoftenunderestimated due tothefocuson operation strategiesbasedon onlya single application,usuallypricearbitragebetweenoff-peakandon-peak hours.However,determiningthetruevalueofelectricitystorage willlikelyrequiretheaggregationofmultipleapplicationswhile accounting for theinterdependence between potentialrevenue streams[4–6].Thevalueofindividualapplicationscannotsimply beadded together, butneed tobeco-optimizedsince different storageservicescanconflictwitheachother[7].

ARTICLE INFO

Articlehistory:

Received12March2016

Receivedinrevisedform13May2016 Accepted17May2016

Availableonline

Keywords:

Electricitystorage Sharedstorageresources Auction-basedallocation (Generalized)Nashequilibrium Mixedcomplementarityproblem

ABSTRACT

This articleproposes anew electricity storagebusiness model based onmultiple simultaneously consideredrevenuestreams,whichcanbeattributedtodifferentmarketactivitiesandplayers.These playersthusshareelectricitystorageresourcesandcompetetoobtaintherighttousetheminadynamic allocationmechanism.Itisbasedonthedesignofanewperiodicallyorganizedauctiontoallocateshared storageresourcesthroughphysicalstoragerightsbetweendifferentmarketplayersandaccompanying applications.Throughsuchaflexibilityplatformownersofflexibleresourcescancommercializetheir flexiblecapacityoverdifferentapplications,whilemarketplayerslookingforadditionalflexibilitycan obtain this through a pay-per-use principle and thus not having to make long-term investment commitments. As such,they can quicklyadapt theirportfolio according to the market situation.

Alternatively,throughsuchanallocationmechanismplayerscaneffectivelysharestorageresources.

Playersmaybeincentivizedtoparticipateastheycansharetheinvestmentcost,mitigaterisk,exploit economies of scale, overcomeregulatory barriers, and merge time-varying and player-dependent flexibilityneeds.Themechanismallocatesthelimitedstorageresourcestothemostvaluableapplication foreachmarket-clearing,basedonthecompetingplayers’willingness-to-pay.Anillustrativecasestudy isprovidedinwhichthreeplayerssharestorageresourcesthatareallocatedthroughadailyauctionwith hourlymarket-clearings.

ß2016ElsevierLtd.Allrightsreserved.

* Correspondingauthorat:DepartmentofElectricalEngineering,Universityof Leuven(KULeuven),Heverlee,Belgium.Tel.:+32485826161.

E-mailaddresses:tom.brijs@esat.kuleuven.be(T.Brijs),

huppmann@iiasa.ac.at(D.Huppmann),siddiqui@jhu.edu(S.Siddiqui), ronnie.belmans@esat.kuleuven.be(R.Belmans).

ContentslistsavailableatScienceDirect

Journal of Energy Storage

j o urn a lhom e pa g e :ww w . e l se v i e r. c om / l oca t e / e st

http://dx.doi.org/10.1016/j.est.2016.05.009 2352-152X/ß2016ElsevierLtd.Allrightsreserved.

Therefore,thisarticleconsidersanewstoragebusinessmodel based on multiple simultaneously considered revenue streams, whichcanbeattributedtodifferentactivitiesinthemarketand canthusbethefocusofdifferentmarketplayers.Assuch,these marketplayersshareelectricitystorageresourcesandcompeteto usetheshared storageresources.Theallocationis basedon the designofaperiodicallyorganizedauctionwithsequentialmarket- clearings,in which therightto usestorageresourcesis traded betweendifferentplayers.

1.1. Electricitystorageapplications

Electricity storage refers tosystems, bidirectionally coupled withthepowersystem,whichbufferenergy.Thisincludesboth systemsinwhichthecharginganddischargingsideisphysically locatedat one location, e.g., pumped-hydro storage plants and batterystoragesystems,oratmultiplelocations,i.e.,power-to-gas systems in combination with a gas turbine. This definition distinguishes electricity storage from the broader concept of energystorage,whichmay,e.g.,alsoincludestock-pilingfuelatthe supplysideofthepowersystem.¹

Historically,electricity storageplants wereconsidered asan alternative for investing in peak-load generation, by charging during off-peak and discharging during on-peak moments.

However,duetotheliberalizationofelectricitymarketsandthe integration of RES, distinct valorization paths for different applicationsofstorageemerged[8–11].Thesecanbecategorized inenergy,network,andreliabilityservices.

Energyservicesincludearbitrageandportfoliooptimizationof marketparticipants.Arbitrageisbasedonpricedifferencesover time:electricityisboughtandstoredwhenthepriceislow,andis sold and generated again when the price is higher. Portfolio optimizationisperformedatdifferenttimescales,i.e.,investment, scheduling, and operation, and covers generation investment deferral, inter-temporal energy shifting, and capacity firming, respectively.Through inter-temporal energyshiftinggenerators optimizethevalueof generationbydecoupling generationand physical injection, while consumers optimize the cost of con- sumptionbydecoupling consumptionand physicalwithdrawal.

Capacity firming can indicate the ability to smoothen the generationorconsumptionoutput,resultinginlessvolatilepower profiles,ortofollow predeterminedoutputschedulestoreduce imbalancedpositions in real-time. Network services include the provisionoffrequencycontrol(i.e.,primary,secondary,tertiary),²

voltagesupport,congestionmanagement,andblack-startcapabil- itiestothetransmissionsystemoperator(TSO).Inthefuture,some ofthesewilllikelybeprovidedtothedistributionsystemoperator (DSO)aswell.Reliabilityservicesincludetheprovisionofreliability onboththelocalandsystemlevel.

Thismultitudeofapplicationsmakeselectricitystorageplants an interesting asset for a wide range of market participants.

However,operatingastorageplanttoprovidejustoneorafewof theseservicesmightnotalwaysresultinapositivebusinesscase;

profitabilitymayrequiretheaggregationofmultipleapplications.

1.2. Motivation

Althoughsomestudiesfocusontheco-optimizationofdifferent storageapplications(e.g.,[5,7,12]),mostexistingworkfocuseson only a single application or allocates the available storage resourcesa-prioriwhenconsideringmultipleapplications,instead of applying a periodically performed optimization process. In addition, the sharing and operation of storage resources by differentplayershasonlybeenstudiedtoalimitedextent,except fortheworkdoneby[4].Assuch,thecontributionoftheauction- basedallocationdescribedinthisarticleisthatitdoesnota-priori definetheapplicationsoreventhemarketplayerthatthestorage resources will serve at a certain moment in time. This can be accomplishedbythedevelopmentofacentralizedplatformwhere periodicalauctionswithsequentialmarket-clearingstakeplaceto allocatetherighttouse(dis)chargepowercapacitiesandenergy storagecapacity.Theseauctionscanservebothsettingswhere(1) multipleplayerssharecommon storageplantsand (2)multiple suppliersofstorageresourcesandprospectiveconsumersmeetto trade physical storagerights. Whereas thepresented allocation mechanism allows tosimultaneously includemultiple resource suppliersandplayerscompetingfortherighttousethem,andto simultaneouslyconsidertheiroffers,themethoddiscussedin[4]

considers asequential allocationtoplayerswhichexpresstheir needforflexibleresourcesatdifferenttimescales.Inaddition,the presented allocation mechanism auctions physical (dis)charge powerrightsandstoragecapacityrights,whereastheallocationin [4]isbasedonactualutilizationprofiles.

Marketplayerscanhavemultipleincentivestoshare,contract, or offerstorageresourcesbymeansof a periodicallyorganized auction.First,thismayallowthemtoexploiteconomiesofscale, i.e.,increasingtheplantsizeatareducedcostperunitofpowerand energy.Second,theycansharetheinvestmentcostandassociated risk,especiallywhenconsideringlarge-scalestorageplants.Third, asflexibilityneedsvarythroughouttheyearandeventhroughout the day, and across market players, they may have different (possiblycomplementary)storageutilizationpatterns,providing anincentivetoshareresources.

Fromasystempointofview,thereareadditionalreasonsto share storage resources. First, as storage resources are usually limitedduetogeographicalrequirements,theyshouldbeallocated tothemostvaluableservicesateachpointintime.Second,dueto the introduced competition to use storage resources strategic under-oroverusage[13]islikelytooccurlessfrequently.Third, although pumped-hydro storage is currently the most mature storage technology, rapidly decreasing costs and technological advancements aremaking battery storage systems increasingly competitive [14]. To overcome barriers for such small-scale storageresourcestoparticipateinthemarket,thedevelopment ofacentralizedplatformallowsownersoftheseresourcestooffer flexibility to market players that aggregate them. Finally, regulatory barriersmight prevent storage operatorsto provide certainservicessimultaneously.IntheUnitedStatesstorageplants can either provide market-based or regulated services (e.g., congestion management to avoid grid upgrades), but they are Fig.1.Overviewofpowersystemflexibilitysources.

1Powerplantsmayhavesignificantfuelreserves,e.g.,thenaturalgasgridwith itsstoragecapabilitiesforgas-firedpowerplants,coalpilesatclassicthermalpower plants,andnuclearfuelatnuclearpowerplants.

2IntheENTSO-E synchronouszoneoperatingreservesare categorizedinto frequencycontainmentreserves(FCR),frequencyrestorationreserves(FRR),both automatic(aFRR)andmanual(mFRR),andrestorationreserves(RR).

notallowed tocombine both ina singlebusinesscase [15]. An auctionsuchastheoneproposedinthisarticlecanovercomethis regulatorybarrierbyallocatingstoragerightstodifferentplayers toprovideeithermarket-basedorregulatedservices.

Thisdecouplingoftheownershipofstorageresourceswithits physicaloperationhassimilarcharacteristicstothetreatmentof transmissioncapacity,asbothhavetheabilitytomovepower,the formerintimewhilethelatterinspace.In Europeanelectricity marketscross-bordertransmissioncapacityisauctionedexplicitly orimplicitly[16,17].Theformerindicatesthatmarketplayerscan obtaintherighttouseinterconnectorcapacity,afterwhichthey canusethesecapacitiestocapturepricedifferencesinneighboring markets.Inthelatter,thesecapacitiesarenotauctionedtomarket playersbut allocated to thepower exchange toinclude in the market-clearing algorithm to maximize social welfare. The allocationmechanismdiscussedinthisarticleisbasedonexplicit auctioning,asfirsttherighttousestorageresourcesisauctioned, after which players can use these resources in the electricity market.Furthermore,Refs.[18,19]considerasituationwherethe surpluscollectedbythesystemoperatororpowerexchange(i.e., storagecongestionrent),followingacentraloperationofstorage resources to maximize social welfare, is allocated to players holdingfinancialstoragerights.Thesearebasedonthedesignof financialtransmissionrights[20,21],andthusremuneratestorage investorsbyeithertherevenuesoftheauctionoffinancialstorage rightsorthevalueofthestoragecongestionrentitself.Similarto the proposed auction-based allocation mechanism, this allows themtorecovertheinvestmentcostwithoutparticipatinginthe electricitymarketthemselves.

1.3. Contributions

Themaincontributionofthisarticleisthepresentationofan alternative approach for electricity storage plants toaggregate multipleapplications.Thisisbasedonanewmarketforflexibility, namelyaperiodicallyorganizedauctiontoallocatesharedstorage resources through physical storage rights between different market players and accompanying applications. Through this allocationmechanism(1) marketparticipantscansharestorage resourcestoexploiteconomies of scale, reducetheinvestment cost,mitigate risk, matchcomplementary flexibilityneeds, and overcomeregulatorybarriers,and(2)ownersofflexibleresources cancommercializetheir flexiblecapacityoverdifferentapplica- tionswhilemarketplayerslookingforadditionalflexibilityhave accesstotheseresourcesonashort-termbasis.Assuch,thelatter donothavetomakelong-terminvestmentcommitmentsandcan adapttheirportfolioaccordingtochangingmarketsituations.

The article is structured as follows. Section 2 discusses (Generalized) Nash games, mixed complementarity problems, andthe designedstorage allocation mechanismin more detail.

Section3illustratesthisauction-basedallocationthroughacase studyinwhichthreemarketplayerssharestorageresources,by providingthemathematicalformulationoftheplayers’individual optimizationproblemsandresultingmarketequilibriumproblem.

While Section 4 discusses the case study’s results, Section 5 providestheconclusionsofthisarticle.

2. Methodology

2.1. (Generalized)Nashequilibriumproblems

Theinteractionbetweenseveralmarketplayers,inwhicheach playeraimstooptimizethevalueofitsobjectivefunctiongiventhe decisionsbyall rivals,canbemathematically formulatedasan equilibrium problem. We first introduce Nash equilibrium problems (NEP) [22] before discussing the concept of a

Generalized Nash equilibrium problem (GNEP) [23]. Assume a marketwithafiniteamountofplayers,inwhicheachplayeri2I facesthefollowingoptimizationproblem:

maxx_i f_iðxi;xiÞ; (1a)

s:t: xi2Xi: (1b)

Eachplayer’svectorofdecisionvariablesxi,hastobechosen fromitssetoffeasiblestrategiesXi,whilethevectorofdecision variablesofitsrivalsxiisconsideredasgiven.ANashequilibrium x_i isthenreachedwhenthefollowingconditionholds:

fiðx_i;x_iÞfiðyi;x_iÞ; 8i2I; yi2X_i: (2) Thisequilibriummeansthatgiventhedecisionsbyallrivals,no playerhasan incentivetodeviatefromits chosenstrategy. An implicitassumptionoftheNEPisthatthestrategieschosenbythe competingplayersonlyaffecttheplayers’objectivefunctionand not their feasible set of strategies. In contrast, in a GNEP this assumptionisrelaxed[23–27],aseachplayer’svectorofdecision variablesxihastobechosenfromasetoffeasiblestrategiesXiðxiÞ thatisaffectedbythestrategieschosenbythecompetingplayers.

A Generalized Nash equilibrium x_i is then reached when the followingconditionholds:

f_iðx_i;x_iÞf_iðy_i;x_iÞ; 8i2I;y_i2Xiðx_iÞ: (3) ThegeneralstructureofbothaNEPandGNEP,consistingofaset ofinterrelatedoptimizationproblems,isillustratedinFig.2.Ina GNEP, each player’s objective function may be subject toboth individualandsharedconstraints.Whileeachindividualoptimi- zationproblemrepresentsthedecisionprocessofoneplayer,the equilibrium problem represents the interactions in a market environmentofmultipleinterrelatedplayers.

2.2. Mixedcomplementarityproblems

TheNEPandGNEPcanbesolvedbyformulatingtheproblemas amixedcomplementarityproblem(MCP).Thisisdonebyderiving thefirst-orderoptimality,orKarush–Kuhn–Tucker(KKT),condi- tions of each player’s optimization problem and solving them simultaneously. In the MCP formulation, the complementarity conditions enforce that the inner product of an inequality constraint and the primal or dual variable³ is zero, and the nonnegativityofboththeinequalityconstraintandtheprimalor dual variable. This means that either theinequality constraint holdsasanequality,i.e.,isbinding,ortheprimalordualvariableis

Fig.2.Illustrationof(Generalized)Nashequilibriumproblems.

3Aconstraint’sdualvariablerepresentstheincrementalimprovementofthe player’sobjectivevaluewhenmarginallyrelaxingtherespectiveconstraint,andcan beinterpretedasthemarginalpriceoftheresourcesubjecttotheconstraint.

zero.Mathematically,thisisexpressedbyusingtheperpendicular operator?,whichindicatescomplementarity.

AnMCPisthusanarrayofequalitiesandinequalitieswhichis obtained by aggregating all players’ KKT conditions. However, when tacklinga GNEP, aggregating theindividual players’ KKT conditionsintoanMCPresultsinanonsquaresystem:theshared constraintsareidenticalforeachplayer,whiletheassociateddual variablesofeachinvolvedplayermayholddifferentvalues.This

‘squareness’ issuecan besolved by assigningan identicaldual variableforeachplayertothesharedconstraint[23],meaningthat eachplayervaluesthesharedresourceidentically,whichleadstoa single‘price’forthesharedresource[24,25].

Thisapproachcanbeinterpretedasanauctioneerallocatingthe shared resource to theplayers accordingto theprice theyare willingtopaytoobtaintherighttouseit.Theirwillingness-to-pay directlyrelatestotheimprovementoftheirobjectivevaluefroma marginalrelaxationofthesharedresource.

2.3. Auction-basedallocationofsharedstorageresources

The shared storage resources’ allocation problem can be formulated as both a NEP and GNEP. In the former case, the suppliersof storageresources aremodeled explicitly,while the consumers and suppliers in the market for storage resources interactbymeansofmarket-clearingconditionsrepresentingthe auctioneer.Thisformulationrelatestothesituationwheremultiple suppliers and consumers of storage resources compete in a centralizedmarket.Inthelattercase,thesuppliersarenotmodeled explicitlybutareincludedimplicitlythroughthestorageresources’

sharedconstraints.Throughthesesharedconstraintsanauctioneer isassumedtoallocatethestoragerightsoverthedifferentplayers.

Thisformulationis particularlyusefultorepresent thesituation wheremultiple marketplayers sharethe storageresourcesand allocatethemperiodicallyamongeachother.

Itiswellknownfrom[23]thataNEPwheretheauctioneeris modeledexplicitlyyieldsthesamesolutionasaGNEPwherethe dual variables of each player for the shared constraints are assumed to beidentical. If the solutionis nonunique,the two solutionsmaydifferintermsoftheprimalvariables(i.e.,operation decisions),but theobjectivevalue(i.e.,pay-off)for eachplayer mustbeidentical.Inthisarticle,weusetheGNEPformulationtoa casestudyinSection3asitillustratesacaseinwhichthreeplayers sharestorageresources.Forillustrativepurposes,theremainderof thediscussionassumesasinglestorageplant.

Inboth formulationstheauctioneerthusactsasa facilitator betweenthesupplyofsharedstorageresources(i.e.,chargepower P^c,max,dischargepowerP^d,max,energystoragecapacityE^max)⁴anda

number ofplayersjIjwhich competetoobtaintherighttouse them.Aperiodicalauctionisorganized,inwhichforeachmarket periodt2Tthesupplierofthestorageresourcessubmitssupply bidss^c_t,s^d_t,s^e_t andeachmarketplayeri2Ihastheopportunityto submitdemandbidsd^c_i;t,d^d_i;t,d^e_i;tforeachstorageresource(Fig.3, left).The supplieris assumed toprovide a supply bid foreach sharedresourceequaltoitsmaximumcapacity,tobesoldatany pricedefinedbythemarket.Eachplayeribidsthemaximumprice heiswillingtopaytoobtaintherighttouseaspecifiedvolumeof eachstorageresource.Thismaximumpriceequalsitsincremental pay-off.Theauctioneerthenaggregatesthedemandbidsforeach storageresource,i.e.,thedemandcurve,andmatchesthemwith eachresource’ssupplybid,i.e.,thesupplycurve,whichresultsina market-clearingfor each timestept (Fig.3, right).Thisyieldsa clearedvolumeforthechargepowerrightsp^c;max_i;t ,dischargepower rightsp^d;max_i;t ,andstoragecapacityrightse^max_i;t foreachplayeri,and uniformmarket-clearingprices

m

^c_t,

m

^d_t,

m

^e_t.Inequilibrium,these pricesequalthemarginalwillingness-to-payforeachrespective resource.

Similar to the case in current electricity markets, the allocation process may be iterated at different timeframes (e.g., week-ahead, day-ahead, intra-day, real-time) to allow playerstoadjusttheirobtainedphysicalstoragerights,basedon updatedmarketinformation.Inafirstauction(e.g.,day-ahead) the shared resources are allocated to the different players according to their willingness-to-pay, which is dependent on their market expectations and risk aversion, while in a consecutiveallocationclosertoreal-time(e.g.,intra-day)players can trade and reallocate the obtained resources among each other:playersthatcontractedtoomuchcanoffer partoftheir obtained rights again to the platform, while players that contractedtoolittlecanbidtoobtainadditionalstoragerights.

Asisthecaseinelectricitymarkets,thesesequentialmarketsfor storageresourcesmayalsoallowforarbitrageopportunitiesas price spreads can be captured over the different sequential markets.Arbitrageurscould,e.g.,obtainadditionalstoragerights attheday-aheadstagetoafterwardssellintheintra-daymarket tootherplayersiftheyexpecttheintra-daypricetoclearata higher price. Alternatively, players could, e.g., postpone the reservationofphysicalstoragerightsintheday-aheadmarketto theintra-daymarketiftheyexpecttheintra-daymarkettoclear atalowerprice.Althoughthevalueofthisarbitrageisrelatedto the presenceof pricespreads,italso dependsonthe effect of additional/fewerrequestedstoragerightsonprices,asarbitrage may reduce price spreads by increasing low prices when requestingadditionalstoragerightsanddecreasinghighprices whenrequestingfewerstoragerights.

3. Casestudy

To illustrate the presented auction-based allocation mecha- nism, a case study is shown for a daily auction with hourly Fig.3.Illustrationofthemarket-clearingmechanismtoallocatestorageresources.

4Table1providesanoverviewofthesymbolsforsets,primalvariables,dual variables,andparametersusedinthisarticle.FormulasareprovidedassumingSIor base units, while input data and results follow typical units in electrical engineering.

market-clearings in which three market players compete for constrained storage resources, i.e., I¼fa;p;rg, with index a representing a player arbitraging day-ahead market prices, indexpaplayerfocusingonportfoliomanagement,andindexr aplayerthataimstousestorageresourcestocaptureimbalance price differences in the real-time market.First, the individual optimization problems are presented as if electricity storage resources would be readily available to them. Second, we discusswhichchangeshavetotakeplaceinorderfortheplayers to share storage resources and compete in an auction-based allocationmechanism,i.e.,equilibriumproblem.Third,theMCP formulationoftheequilibriumproblemisdiscussedwhileitis providedinfullinAppendixA.

The model formulationsof theprovided case study include discretized hourly time periods h2H, with jHj¼24 and T^h representingthelengthofonetimeperiod,i.e.,onehour.Variables in parentheses denote the dual variables of the respective constraints.Inaddition,allplayersareassumedtobeprice-takers withperfectforesightforthenextoptimizationhorizon,i.e.,the nextdayinthiscasestudy.Thestorageplantisassumedtohave sufficiently fast ramp rates for the considered hourly time resolution, with no restrictions regarding simultaneous charge anddischargeactions,andasufficientlylargecycle-lifesuchthat its impact on the operation is negligible. These storage plant assumptionsmightservetomodeltypicalpumped-hydrostorage plants.

3.1. Individualoptimizationproblems

First a storage operator is consideredthat aims tocapture price differences in the day-ahead market. This player is indicated by index a, and its optimization problem, in which the pay-offis maximized over a timehorizon jHjT^h,reads as follows:

max

ea;h;p^c_a;h;p^d_a;h

X

h2H

l

^dah ½T^hðp^d_a;hp^c_a;hÞ=ðjHjT^hÞ; (4a)

e_a;h¼e_a;h1þT^hðp^c_a;h

h

^cp^d_a;h=

h

^dÞ; ð

g

^e_a;hÞ; 8h2H; (4b)

p^c_a;hP^c;max; ð

m

^ca;hÞ; 8h2H; (4c)

p^d_a;hP^d;max; ð

m

^d_a;hÞ; 8h2H; (4d)

ea;hE^max; ð

m

^ea;hÞ; 8h2H; (4e) ea;h;p^c_a;h;p^d_a;h2Rþ; h2N; 8h2H

with p^c_a;h the charge power, p^d_a;h the discharge power, ea,h the stored energy,

l

^da_h the day-ahead market price,

h

^c the charge efficiency, and

h

^d the discharge efficiency. Constraint (4b) expresses the intertemporal character of electricity storage, Table1

Tableofsymbols.

Type Symbol Quantity Unit(SI) Typicalunit

Sets h2H Timesteps – –

i2I Players – –

t2T Timestamps – –

Primalvariables ei,h Storedenergy J MWh

e^max_i ,e^max_i;h ,e^max_i;t Storagecapacityrights J MWh

p^c_i;h Chargepower W MW

p^c;max_i ,p^c;max_i;h ,p^c;max_i;t Chargepowerrights W MW

p^d_i;h Dischargepower W MW

p^d;max_i ,p^d;max_i;h ,p^d;max_i;t Dischargepowerrights W MW

p^g_i;h Powergeneration W MW

p^l_i;h Powercurtailment W MW

bi Cost s_/s s_/year

pi Profit s_/s s_/year

p^op_i Operatingprofit s_/s s_/year

Dualvariables m^c_i;h Dualtochargepowerconstraints s_/s/W s_/h/MW

m^c_h,m^c_t Priceofchargepowerrights s_/s/W s_/h/MW

m^c Priceofchargepowerrights s_/s/W s_/day/MW

m^d_i;h Dualtodischargepowerconstraints s_/s/W s_/h/MW

m^d_h,m^d_t Priceofdischargepowerrights s_/s/W s_/h/MW

m^d Priceofdischargepowerrights s_/s/W s_/day/MW

m^e_i;h Dualtostoragecapacityconstraints s_/s/J s_/h/MWh

m^e_h,m^e_t Priceofstoragecapacityrights s_/s/J s_/h/MWh

m^e Priceofstoragecapacityrights s_/s/J s_/day/MWh

g^e_i;h Dualtoenergybufferconstraints s_/s/J s_/h/MWh

g^g_i;h Dualtoavailablerenewablepowerconstraints s_/s/W s_/h/MW

g^l_i;h Dualtoimbalancedpositionconstraints s_/s/W s_/h/MW

t^c_i;h Dualtochargepowerrightsconstraints s_/s/W s_/h/MW

t^d_i;h Dualtodischargepowerrightsconstraints s_/s/W s_/h/MW

t^e_i;h Dualtostoragecapacityrightsconstraints s_/s/J s_/h/MWh

Parameters E^max Storagecapacity J MWh

Gp,h Availablerenewablepower W MW

L^max_r Imbalancedpositionupperbound W MW

P^c,max Chargepowerrating W MW

P^d,max Dischargepowerrating W MW

T^h Timesteplength s h

h^c,h^d (Dis)chargeefficiency % %

l^da_h Day-aheadprice s_/J s_/MWh

l^rt_h Real-timeimbalanceprice s_/J s_/MWh

while (4c)–(4e) represent capacity bounds on the electricity storageresources.

Next,aRESgeneratoroperatingaportfolioofbothwindand photovoltaic(PV)capacityisconsidered.Thisplayerusesstorage resourcestoincreasethemarketvalueofitsRESgeneration.This canbedonebyeitherdirectlysellingitsRESpoweroutputtothe marketor temporarilystoring it during lowpriceperiods. This applicationofelectricitystorageresultsfromthefactthatperiods experiencinghighRESgenerationoftencoincidewithlowerprice periods[1].Thisplayerisindicatedbyindexp,anditsoptimization problemis:

max e_p;h;p^c_p;h;p^d_p;h;

p^g_p;h;p^l_p;h X

h2H

l

^dah ½T^hðp^g_p;hþp^d_p;hÞ=ðjHjT^hÞ; (5a)

p^c_p;hþp^g_p;hþp^l_p;h¼G_p;h; ð

g

^g_p;hÞ; 8h2H; (5b)

ep;h¼ep;h1þT^hðp^c_p;h

h

^cp^d_p;h=

h

^dÞ; ð

g

^ep;hÞ; 8h2H; (5c)

p^c_p;hP^c;max; ð

m

^cp;hÞ; 8h2H; (5d)

p^d_p;hP^d;max; ð

m

^d_p;hÞ; 8h2H; (5e)

ep;hE^max; ð

m

^ep;hÞ; 8h2H; (5f)

e_p;h;p^c_p;h;p^d_p;h;p^g_p;h;p^l_p;h2Rþ; h2N; 8h2H

with Gp,h the available RES power output, p^g_p;h theRES output directly sold tothe market, and p^l_p;h thecurtailed RES output.

Constraint(5b)denotesthattheRESpoweroutputcaneitherbe stored,sold,orcurtailed.

Unforeseenimbalancesbetweengenerationandconsumption are dealt with in real-time on the balancing market, which is coordinatedbytheTSO.Attheprocurementsideofthebalancing markettheTSOcontractsandactivatesreservecapacitytocover systemimbalances,whileatthesettlementsideofthebalancing markettheTSOsettlesindividualimbalancedpositionsofmarket participantsbymeansofanimbalancepricethatisbasedonthe activationcostofreserves[1].Thethirdconsidered playerisan arbitrageurthatisactiveonthesettlementsideofthereal-time balancingmarkettocaptureimbalancepricedifferencesovertime.

As the real-time balancing market is characterized by a small volume compared to the day-ahead market, the imbalanced positionsthisplayercantakewhilenotdiminishingtheexpected pricespreadsareassumedtobeboundedbyL^max_r (6b).Assuch,the price-takingassumptionassumed in this illustrative casestudy holds.Althoughthebalancingmarketisusuallycharacterizedby quarter-hourly or semi-hourly market periods, for illustrative purposes hourly market periods are assumed. This player is indicatedbyindexr,anditsoptimizationproblemreadsasfollows:

max

e_r;h;p^c r;h;p^d

r;h

X

h2H

l

^rth½T^hðp^d_r;hp^c_r;hÞ=ðjHjT^hÞ; (6a)

p^c_r;hþp^d_r;hL^max_r ; ð

g

^l_r;hÞ; 8h2H; (6b)

er;h¼er;h1þT^hðp^c_r;h

h

^cp^d_r;h=

h

^dÞ; ð

g

^er;hÞ; 8h2H; (6c)

p^c_r;hP^c;max; ð

m

^cr;hÞ; 8h2H; (6d)

p^d_r;hP^d;max; ð

m

^dr;hÞ; 8h2H; (6e)

e_r;hE^max; ð

m

^e_r;hÞ; 8h2H; (6f) er;h;p^c_r;h;p^d_r;h2Rþ; h2N; 8h2H

with

l

^rt_h thereal-timeimbalanceprice.

3.2. GeneralizedNashequilibriumproblem

When formulatingthepresentedoptimizationproblemsasa GNEP,twochangestakeplace.First,astheycompetefortheshared electricity storage resources, the constraints representing the limitedchargepower(4c),(5d),(6d),dischargepower(4d),(5e), (6e),andenergystoragecapacity(4e),(5f),(6f)arereplacedby:

p^c_i;hp^c;max_i;h ; ð

t

^ci;hÞ; 8i2I; h2H; (7a)

p^d_i;hp^d;max_i;h ; ð

t

^di;hÞ; 8i2I; h2H; (7b)

ei;he^max_i;h ; ð

t

^e_i;hÞ; 8i2I; h2H; (7c) with p^c;max_i;h , p^d;max_i;h ,and e^max_i;h theallocated charge power rights, dischargepowerrights,andstoragecapacityrights,respectively.

These physical rights are bounded by the supplied storage resources, whichareassumed toequal theinstalled (dis)charge powerratingandenergystoragecapacityinthisillustrativecase study:

X

i2I

p^c;max_i;h P^c;max; ð

m

^c_hÞ; 8h2H; (8a)

X

i2I

p^d;max_i;h P^d;max; ð

m

^d_hÞ; 8h2H; (8b)

X

i2I

e^max_i;h E^max; ð

m

^e_hÞ; 8h2H: (8c)

Alternatively, when considering a centralized market for storage resourcesrather thana situation whereplayers share them,thesupplyischaracterizedbyindexhaswellasitwillbe time-varying. Second, a cost term is subtracted ex-post from eachplayer’sobjectivevalue,sincetherighttousethelimited storageresourcesisnowallocatedthroughanauctioninsteadof beingreadilyavailabletothem.Theuniformpriceoftheshared resources

m

^c_h (8a),

m

^d_h (8b),

m

^e_h (8c) at each hourly market- clearingisdeterminedbythewillingness-to-payoftheplayers’

marginally cleared demand bid to obtain the right to use them. The ex-post calculation of the profit

p

i as opposed to the operating profit

p

^op_i is done by considering the objective value resulting from (4a), (5a), (6a) and subtracting a cost term

b

i:

b

i¼X

h2H

ðp^c;max_i;h

m

^chþp^d;max_i;h

m

^dhþe^max_i;h

m

^ehÞ; 8i2I; (9a)

p

^op_i

b

i¼

p

i; 8i2I: (9b) TheMCP comprisedofeach player’sKKTconditions andthe sharedconstraintsissolvedinGAMSusingthePATHsolver[28], andisprovidedinAppendixAforbothadailyauctionwithhourly market-clearings, and a less dynamic periodically organized (e.g., daily, weekly)auction including a singlemarket-clearing, i.e.,allocation,foreachofthesharedresourcesfortheentireperiod (e.g.,day,week).Sincetheconsideredoptimizationproblemsare

convex and the players only face linear constraints, the KKT conditionsarebothnecessary(i.e.,anoptimalsolutionsatisfiesthe KKTconditions)andsufficient(i.e.,eachKKTpointisanoptimal solution)[27].

4. Results

TheBelgianday-aheadmarketprice[29],real-timeimbalance price[30],andRESgenerationprofiles[30]for2014areusedfor the illustrative case study. The hourly imbalance price

l

^rth is calculated asthe average of thefourquarter-hourly imbalance pricesinhourh.TheRESportfolioofplayerpisassumedtoconsist ofbothPVsystemsandoffshorewindturbines,bothaccountingfor 50%oftheportfolio.Thetime-varyingavailableRESpoweroutput Gp,h isdetermined bymultiplying thehourlyavailabilityof the respectivesourcesbytheinstalledcapacityG^max_p .Thestorageplant characteristicsusedforthecasestudy,alongwithotherinputdata, aredisplayedinTable2.

Fig. 4 shows the individual operating profit

p

^op_i and total operatingprofitP

i2I

p

^op_i for2014asaresultoftheuseofstorage resources⁵ fordifferentallocations,either fixeda-priori defined allocations(i.e.,columns 1–4) orallocations resultingfrom the

proposedallocationmechanism(i.e.,columns5and6).Inthefirst threecolumns,

p

^op_i isshownforthecasewheretheplayersareeach allocated100%ofthestorageresources.Columnfourindicates

p

^op_i

incaseeachplayerisawardedafixedshareequaltoone-thirdof thestorage resourcesfor theentire year.Since theplayers are assumedtobeprice-takersintheirrespectivemarkets(i.e.,day- aheadelectricityandreal-timebalancingmarket),onemayexpect that

p

^op_i isequaltoone-thirdof

p

^op_i followinga100%allocationto therespectiveplayer.Althoughthisisthecaseforplayera,thisis not the case for player p(42.5%) and player r (61.5%)as their actionsarelimitedby Gp,hand L^max_r intheprovidedcase study.

Columnfiveshows

p

^op_i whenassumingadailyorganizedauction with a single market-clearing, i.e., daily allocated (dis)charge powerandstoragecapacityrights,whilecolumnsixisbasedona dailyorganizedauctionwithhourlymarket-clearings.Fig.4shows thattheauction-basedallocationsleadtoahighertotalrealized operatingprofitP

i2I

p

^op_i ,withshortertimeframesforthemarket- clearings performingbetter.Thelatter ensuresthat thelimited storageresourcesareallocatedtothemostvaluable servicesat eachpointintime.

Table 3 shows

p

^op_i ,

b

i,and

p

ifor the differentplayers. The revenuecollectedthroughtheauctioningofthe(dis)chargepower andstoragecapacityrightsisindicatedbyP

i2I

b

i.Thepriceofan auctionedright(i.e.,

m

^c_h,

m

^d_h,

m

^e_hforhourlyallocationsand

m

^c,

m

^d,

m

^e

forsingleallocationsperauction)onlytakesonanonzerovalue whentheinequalityconstraintrepresentingthelimitedavailabili- tyofthestorageresourcesubjecttotheconstraintisbinding(i.e., (A.4a)–(A.4c) forhourly allocationsand (A.8a)–(A.8c) for single allocationsperauction).Incasethepriceisnonzero,ittakesonthe willingness-to-payofthedemandbidofthemarginallycleared playerfortherespectiveresource.Assuch,thezeroprofit

p

dand close-to-zeroprofit

p

pindicatethatwhentheseplayers’bidsto obtainstoragerightsareacceptedtheyrepresentthemarginally cleared bids. This is similar to the situation in electricity markets,wheretheplayerofthemarginallycleareddemandbid paysas muchas hevalues theconsumptionof electric power during that market period. Contrarily, the positive profit

p

r

showsthatitsbidstoobtainstoragerightsnotalwaysrepresent themarginally clearedbid.This canbeexplained bythe large price spreads at the real-time market compared to the day- aheadmarket,throughwhichplayerrvaluestheuseofstorage resourceshigher,andbecausetheinequalityconstraintsarenot binding when he is the only player that contracts storage resourcesas its (dis)charge actionsare limitedby L^max_r . Inthe formercaseplayerrpaysthelowerwillingness-to-payofoneof theotherclearedplayers,whileinthelattercasethepriceofthe right of thestorageresource subject totheconstraint is zero.

Table2

Tableofinputparameters.

E^max 200MWh L^max_c 25MW P^d,max 50MW h^c 86.6%

G^max_p 75MW+75MW P^c,max 50MW T^h 1h h^d 86.6%

Table3

Yearlyoperatingprofit,costtoobtainstoragerights,andprofit,2014.

Dailyauctionswithhourlyallocations Dailyauctionswithdailyallocations

Operatingprofit Cost Profit Operatingprofit Cost Profit

p^op_i bi pi p^op_i bi pi

[Ms_{/year] [M}s_{/year] [M}s_{/year] [M}s_{/year] [M}s_{/year] [M}s_/year]

Playera 0.445 0.445 0.000 0.365 0.365 0.000

Playerp 0.369 0.336 0.033 0.230 0.197 0.033

Playerr 1.934 0.367 1.567 1.958 0.584 1.374

P

i2I 2.748 1.148 1.600 2.553 1.146 1.407

Fig.4.Totalandindividualoperatingprofitfordifferentallocationsoftheshared storageresources,2014.

5Thismeansthatforplayerpthevaluethatwouldhavebeenrealizedwithout useofthestorageresourcesduetotheRESgenerationissubtracted.

Contrary to this illustrative case study, as more players participate in such an auction, and more applications are considered,thesesituationswilloccurlessfrequently.Assuch, therevenuecollectedthroughtheauctioning ofstoragerights will converge to the total captured value in the electricity marketmoreclosely.

Fig. 5 illustrates the allocation of the auctioned(dis)charge powerandstoragecapacityrightsforadailyauctionwithdaily(a,c ande)andhourly(b,dandf)market-clearingsfor2014.Asfor price-takingplayerswithperfectforesighttheoveralldailyvalue ofstorageresourcesislikelytobehigherforarbitragingreal-time imbalancepricesthanarbitragingday-aheadelectricityprices,due tothelargerandmorefrequentpricespreads,playeraandplayerp donotoftengettheopportunitytousemorethan25MWinthe dailyallocation case. However, for somehoursof thedaythey might actually have a higher willingness-to-pay and thus the storageresourceswouldbevalorizedatahighervalue.Therefore, when using more frequent market-clearings (i.e., with shorter durations),thestorageresourcesareallocatedmoreefficientlyto thetime-varyingmostvaluableservices,resultinginahighertotal storagevalue.

5. Conclusions

Electricity storage has the ability tocompensate temporary power surplusesand shortagesbydecouplingthegenerationof electricenergyfromitsconsumptionovertime,therebymeeting increasedflexibilityneeds.However,marketparticipantsareonly incentivized to invest in new flexible resources when the investmentisprofitable.Asthismaynotbethecasewhenonly considering a single or a few storage services, maximizing the valueof electricitystorage requirestheaggregationofmultiple valuestreamsinasingleoperatingstrategy.

Assuch, this articleproposes a newstoragebusiness model basedonmultiplesimultaneouslyconsideredrevenuestreams,in which the applications or even the player that the storage resources will serve at a certain moment in time are not predefined. Thiscanbe accomplishedby thedevelopment ofa platform where periodical auctions with sequential market- clearings take place to allocate physical storage rights to use (dis)chargepower capacitiesandenergystoragecapacity.These auctions allowstorageownerstocommercializetheirresources over differentapplications, while playerslookingfor additional Fig.5.Allocationofphysicalstoragerightsinadailyauctionwithdaily(a),(c),(e),andhourly(b),(d),(f)market-clearings,2014.

flexibility can obtain this on a short-term basis. Alternatively, through such an allocation mechanism players can effectively sharestorageresources.Themechanismallocatestheresourcesto themostvaluableapplicationforeachmarket-clearing,basedon the players’ willingness-to-pay, which directly relates to the improvementoftheir objectivevaluefromamarginalimprove- mentoftherespectivestorageresource.

Playersmaybeincentivizedtoparticipateinsuchamechanism tosharetheinvestmentcost,mitigatetheassociatedrisk,exploit economiesofscale,overcomeregulatorybarriers,andmergetime- varyingandplayer-dependentflexibilityneeds.In addition,this mayinclude positive effects for thesystem as well, as limited storageresourcesareallocatedtothemostvaluableservicesat eachpointintimeandthestrategicoperationofstorageresources islikelytooccurlessfrequentlyduetotheintroducedcompetition.

Futureworkincludesthecomparisonoftheexplicitauctioning of storage resources through physical storage rights to a centralizedoperationof storagewithimplicitauctioningand to financialstoragerights.Inaddition,futureresearchincludesthe analysisofdifferentdesignparameters(e.g.,leadtimesbetween theauctionandphysicaldelivery,allocationhorizon),aswellas the accommodation of flexible consumption processes in this flexibility platform because of the similarities with electricity storageplants(e.g.,limitedduration).

Acknowledgments

The authors would like tothank Benjamin F. Hobbs for his feedbackonapreliminaryversionofthiswork,andtoco-hostTom BrijsatTheJohnsHopkinsUniversity.Theauthorswouldalsolike to thank Cedric De Jonghe and Frederik Geth for valuable comments,andResearchFoundationFlanders(FWO)forproviding TomBrijswithatravelgrantforanextendedresearchvisitatThe JohnsHopkinsUniversity.

AppendixA

FirsttheMCPformulationforaperiodicallyorganizedauction withhourlymarket-clearingsforthesharedstorageresourcesis presented.TheKKTconditionsofplayeraare(A.1a)–(A.1j),while thoseofplayerpare(A.2a)–(A.2m),andfinallytheKKTconditions ofplayer r are(A.3a)–(A.3k). The shared constraintsare repre- sentedby(A.4a)–(A.4c)intheMCPformulation:

0

l

^dah =jHjþT^h

g

^ea;h

h

^cþ

t

^ca;h ? p^c_a;h0; 8h2H; (A.1a)

0

l

^da_h=jHjT^h

g

^e_a;h=

h

^dþ

t

^d_a;h ?p^d_a;h0; 8h2H; (A.1b)

0

g

^e_a;hþ

g

^e_a;hþ1þ

t

^e_a;h ?ea;h0; 8h2H; (A.1c)

0

t

^c_a;hþ

m

^c_h ?p^c;max_a;h 0; 8h2H; (A.1d)

0

t

^d_a;hþ

m

^d_h ? p^d;max_a;h 0; 8h2H; (A.1e)

0

t

^e_a;hþ

m

^e_h ?e^max_a;h 0; 8h2H; (A.1f)

0¼ea;hþea;h1þT^hðp^c_a;h

h

^cp^d_a;h=

h

^dÞ;

g

^e_a;h2R; 8h2H; (A.1g)

0p^c;max_a;h p^c_a;h ?

t

^ca;h0; 8h2H; (A.1h)

0p^d;max_a;h p^d_a;h ?

t

^d_a;h0; 8h2H; (A.1i)

0e^max_a;h ea;h ?

t

^ea;h0; 8h2H; (A.1j)

0

g

^g_p;hþT^h

g

^ep;h

h

^cþ

t

^cp;h ? p^c_p;h0; 8h2H; (A.2a)

0

l

^dah=jHjT^h

g

^ep;h=

h

^dþ

t

^dp;h ? p^d_p;h0; 8h2H; (A.2b)

0

g

^e_p;hþ

g

^e_p;hþ1þ

t

^e_p;h ?ep;h0; 8h2H; (A.2c)

0

l

^da_h=jHjþ

g

^g_p;h ?p^g_p;h0; 8h2H; (A.2d)

0

g

^g_p;h ? p^l_p;h0; 8h2H; (A.2e)

0

t

^c_p;hþ

m

^c_h ? p^c;max_p;h 0; 8h2H; (A.2f)

0

t

^dp;hþ

m

^dh ?p^d;max_p;h 0; 8h2H; (A.2g) 0

t

^e_p;hþ

m

^e_h ? e^max_p;h 0; 8h2H; (A.2h)

0¼G_p;hþp^c_p;hþp^g_p;hþp^l_p;h;

g

^g_p;h2R; 8h2H; (A.2i)

0¼e_p;hþe_p;h1þT^hðp^c_p;h

h

^cp^d_p;h=

h

^dÞ;

g

^e_p;h2R; 8h2H; (A.2j)

0p^c;max_p;h p^c_p;h ?

t

^c_p;h0; 8h2H; (A.2k)

0p^d;max_p;h p^d_p;h ?

t

^d_p;h0; 8h2H; (A.2l) 0e^max_p;h e_p;h ?

t

^e_p;h0; 8h2H; (A.2m)

0

l

^rt_h=jHjþT^h

g

^e_r;h

h

^cþ

g

^l_r;hþ

t

^c_r;h ?p^c_r;h0; 8h2H; (A.3a)

0

l

^dah=jHjT^h

g

^e_r;h=

h

^dþ

g

^l_r;hþ

t

^d_r;h ? p^d_r;h0; 8h2H; (A.3b) 0

g

^er;hþ

g

^er;hþ1þ

t

^er;h ? er;h0; 8h2H; (A.3c) 0

t

^c_r;hþ

m

^c_h ? p^c;max_r;h 0; 8h2H; (A.3d)

0

t

^d_r;hþ

m

^d_h ? p^d;max_r;h 0; 8h2H; (A.3e)

0

t

^er;hþ

m

^eh ? e^max_r;h 0; 8h2H; (A.3f)

0L^max_r p^c_r;hp^d_r;h ?

g

^l_r;h0; 8h2H; (A.3g)

0¼er;hþer;h1þT^hðp^c_r;h

h

^cp^d_r;h=

h

^dÞ;

g

^e_r;h2R; 8h2H; (A.3h)

0p^c;max_r;h p^c_r;h ?

t

^c_r;h0; 8h2H; (A.3i)

0p^d;max_r;h p^d_r;h ?

t

^d_r;h0; 8h2H; (A.3j)

0e^max_r;h er;h ?

t

^er;h0; 8h2H; (A.3k)

0P^c;maxp^c;max_a;h p^c;max_p;h p^c;max_r;h ?

m

^c_h0; 8h2H; (A.4a)

0P^d;maxp^d;max_a;h p^d;max_p;h p^d;max_r;h ?

m

^dh0; 8h2H; (A.4b)