Stochastic Framework for Strategic Decision-making of Load-serving Entities for Day-ahead Market

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1 Stochastc Framewor for Strategc Decson-mang of Load-servng Enttes for Day-ahead Maret Mohammad Al Fotouh Ghazvn, Pedro Fara, Hugo Moras, Zta Vale, Sérgo Ramos GECAD - Knowledge Engneerng and Decson Support Research Center IPP - Polytechnc of Porto Porto, Portugal mafgh@sep.pp.pt, pnfar@sep.pp.pt, hugvm@sep.pp.pt, zav@sep.pp.pt, scr@sep.pp.pt Abstract The deregulaton of electrcty marets has dversfed the range of fnancal transacton modes between ndependent system operator (ISO), generaton companes (GENCO) and load-servng enttes (LSE) as the man nteractng players of a day-ahead maret (DAM). LSEs sell electrcty to end-users and retal customers. The LSE that owns dstrbuted generaton (DG) or energy storage unts can supply part of ts servng loads when the nodal prce of electrcty rses. Ths opportunty stmulates them to have storage or generaton facltes at the buses wth hgher locatonal margnal prces (LMP). The short-term advantage of ths model s reducng the rs of fnancal losses for LSEs n DAMs and ts long-term beneft for the LSEs and the whole system s maret power mtgaton by vrtually ncreasng the prce elastcty of demand. Ths model also enables the LSEs to manage the fnancal rss wth a stochastc programmng framewor. Index Terms Demand-sde, load-servng enttes, locatonal margnal prce, maret power, stochastc programmng. I. NOMENCLATURE Indces: LSEs. t Hours. s Scenaros. b Buses. c Consumers. DG unts. Storage unts. Parameters: LMP Locatonal margnal prce at bus b ( /MWh). R c N s s b Utlty rate that the consumer c s charged by the LSE for electrcal energy consumpton ( /MWh). Number of scenaros. Weght of scenaro s. F C Fxed cost of DG ( /h). P C Producton cost of DG ( /MWh). start C Start-up cost of DG ( ). Max/Mn E Maxmum/mnmum storage level of storage unt (MWh). Max/Mn G Maxmum/mnmum power generaton of DG (MW). IN/OUT Chargng/dschargng effcency of storage unt. IN/OUT R Chargng/dschargng rate of storage unt (MW/h). l Real energy consumpton forecast for consumer c c (MWh). T Number of tme perods. Varables: 1 P Expected payoff of LSE n the DAM ( ). g D Real power generaton of DG (MWh). IN/OUT p Chargng/dschargng power of storage unt (MW/h). stored E Energy storage level of storage unt at the end d b of each tme perod (MWh). Amount of energy that s bought from the wholesale maret by the LSE (MWh). u Bnary decson varable showng the commtment status of DG unt (1 f the unt s onlne and 0 otherwse). v w x y Bnary decson varable for start-up status of DG (1 f the unt starts up at the begnnng of perod t and 0 otherwse). Bnary decson varable for shut-down status of DG (1 f the unt shuts down at the begnnng of perod t and 0 otherwse). Bnary decson varable for dschargng status of storage unt (1 f t s dschargng and 0 otherwse). Bnary decson varable for chargng status of storage unt (1 f t s chargng and 0 otherwse). Ths wor s supported by FEDER Funds through Programa Operaconal Factores de Compettvdade COMPETE program and by Natonal Funds through FCT Fundação para a Cênca e a Tecnologa under the proects FCOMP FEDER: PEst-OE/EEI/UI0760/2011, PTDC/EEA-EEL/099832/2008, and PTDC/SEN-ENR/122174/2010.

2 Sets: bc Buses that the LSE s servng loads n them or possesses DGs or storage unts n them. Consumers served by LSE at bus b. DGs owned by LSE at bus b. bdg storage unts owned by LSE at bus b. bess II. INTRODUCTION The welfare of LSEs s the proft acheved from resellng the purchased power at wholesale marets to retal customers [1]. Retal end-users do not receve sgnals from the changes n the electrcty prce, and almost never react to the short-term prce rses. Although the two-sded aucton structure of wholesale marets provdes the potentals for electrcty buyers to neutralze the maret power [2], the wllngness of retal customers n payng regulated electrcty rates wthout beng nfluenced by hourly wholesale LMPs s a barrer for ths purpose. The LSEs buy bul power from DAM at volatle maret prces and sell at fxed prces. They face uncertanty and rsy operaton le other players of electrcty marets, but ther rs for fnancal losses s hgher than other partcpants. In ths paper, we am to model a framewor that lmts the potental for maret power and asssts the LSEs n fnancal rs management durng DAM. The proposed stochastc framewor gves LSEs the possblty of managng the fnancal rss by consderng the mpact of uncertan loads and maret prces. It s also assumed that these LSEs possess several DGs and storage unts to lmt the potental for maret power by submttng more prce elastc demand bds. The supplers cannot sgnfcantly ncrease the prce above ther actual costs, and by repeatedly playng n ths maret, they wll learn over tme to compete less aggressvely [3]. Demand bdng of LSEs n a DAM wth a non-proft ISO and prce-senstve demand-sde s studed n [1]. It has been proved that n absence of actve demand-sde bddng, the supplers have the potental for maret power and can push up the prces [2]. Smulaton results n [3] show how the GENCOs facltated by Q-learnng can explot the maret flaws and acheve hgher profts relatve to the compettve benchmar n the absence of maret power mtgaton strateges. The problem of energy tradng for a LSE that owns generatng unts and coordnates the vehcle-to-grd servces s formulated as a mxed-nteger stochastc lnear program n [4]. The LSE n ths model also acts as an electrc vehcle aggregator. Blateral contracts between the GENCOs and the LSEs have been nvestgated n [5-7] as a means to manage and lmt the fnancal rss of both sdes. Strategc bddng of GENCOs, facng an nelastc load n a DAM wth a snglesded unform prce aucton s modeled n [8]. We have made the followng contrbutons n our proposed model compared to the state of the art: () The LSEs manage ther fnancal rss wth a stochastc programmng model. () K-means clusterng s used to partton the scenaros and reduce the sze of the stochastc problem. () The expected ncrease n the payoff of LSEs when they use DGs or the storage unts to supply ther loads and submt more prce elastc demand bds s analyzed through a case study. The DAM operatons and the maret power experence n ths envronment are ntroduced n secton III. In secton IV, the reasons for LSEs fnancal rss are descrbed. The stochastc programmng model n secton V s appled on a test system n secton VI. The fnal secton s assgned to the conclusons and the future wors. III. DAY-AHEAD MARKET OPERATIONS The LSE obtan the electrcal energy needs of the end users from forward maret, day-ahead maret, real-tme maret and the blateral contracts wth GENCOs [7, 9]. It sells electrcty and other ancllary servces that are provded from the wholesale maret to the end-users n a retal maret [10, 11]. Although n real-world marets a large part of electrcty consumpton s traded through long-term contracts, DAM eeps ganng mportance because of ts role n determnng the long-run electrcty costs [12]. In a DAM the LMPs are determned based on a securty-constraned optmal power flow, consderng the lmtatons of the generaton sector and the load specfcatons. The LSEs procure the day-ahead capacty on wholesale marets, even so the consumptons of the retal customers should be adapted n real tme [10]. The ISO/Maret Operator of a deregulated electrcty maret matches sellers quanttyprce supply offers and buyers demand bds for day-ahead power exchange wth an aucton based mechansm [8]. The bddng strateges are affected wth the aucton rules, protocols and the electrcty maret structure [8]. The bdders submt the bds to the ISO/Maret Operator wthout nowledge of the submtted bds of other maret partcpants. The aucton also runs n one round and the partcpants do not have the opportunty of recevng any feedbac on ther agents bddng behavor [12]. Fg. 1 shows the procedure of bddng and maret clearance n a DAM. One day pror to the start of a DAM, load predcton data s gathered from LSEs and the ISO publshes the forecasted zonal load data for the followng day [3]. The hourly demand bd of LSEs ncludes an nverse demand functon, showng the wllngness to pay for each MWh based on antcpatons of the energy consumpton of the end-users wth varable-prce retal contracts and a fxed load level for customers wth fxed-prce retal contracts [1, 5]. The demand functons are obtaned after curve-fttng dfferent prces for each year and the correspondng optmal energy usages. Once the demand functon of each ndvdual consumer s determned, the LSE can aggregate them to obtan the demand bd [13]. The ISO bulds the demand and supply functon after aggregatng the submtted curves of maret players [12]. The specfc features of deregulated electrcty marets,.e., open competton; unbundlng electrcty servces and open access to the networ allow the GENCOs to experence maret power by tenderng optmal offers [8]. Maret power causes prce rse n DAM when the few frms that own most of the generaton capacty unlaterally alter the prces away from

3 the compettve levels [14]. More elastc demand bds n a DAM can lmt the rs of maret power. A great proporton of ongong debates on electrcty maret desgn are focused on desgnng the maret power mtgaton rules [6]. The uncertanty of parameters plays an mportant role when the fnancal schedulng s based on future events [16]. The stochastc programmng s used n ths model to manage the fnancal rss of LSEs n DAMs by allowng the uncertanty to be taen nto account [16]. It s mplemented n ths model to characterze the strateges of a rs-averse LSE to avod fnancal losses. A bg assumpton n stochastc programmng s that the probablty dstrbutons of random parameters are nown [16]. The man challenge n stochastc programmng s the sze of the model that wll be dealt wth by reducng the number of scenaros. V. PROBLEM FORMULATION Fgure 1. Bddng and clearnace procedure n a DAM [1]. IV. FINANCIAL RISKS OF LSES Fnancal rss often ndcate downsde rss n a maret, meanng the uncertanty of a payoff and the potental for fnancal loss [15]. The LSEs sell the electrcty at fxed prces, but ther return s uncertan n DAM [16]. The LSEs partcpatng n the electrcty marets face rss due to volatlty of the pool prces and the loads energy consumpton [6]. In DAMs the MCP can be estmated wth a hgh uncertanty and the LSEs are drected to base ther plannng on the estmated MCPs n order to acheve hgher ncomes. The LSE also faces the volume rs for the optmal resource and load schedulng, because the amount that each customer wll use n a day-ahead cannot be forecasted wth hgh accuracy. The contracts of retal customers wth the LSEs sheld them from even the smallest prce fluctuatons n short-term perspectve, and the LSE has to face the fnancal rss of wholesale maret [7]. However, the proft-seeng LSEs of compettve electrcty marets should accordngly react to system condtons to gan more fnancal payoff or avod the fnancal loss. Buyng electrcty at a fxed prce through forward contracts allows LSEs to hedge aganst the rss of prce varablty [6]. Involvng n hedge contracts wth the producers s an opton for LSEs to overcome the hgh rs of attendng the aucton for the loads that buy electrcty at a regulated rate. A. Stochastc model The goal of ths model s to precsely characterze how the LSEs that own DGs/storage unts obtan the optmal demand bd. Durng day D, the LSEs submt ther demand bds that nclude a 24-hour load profle at the buses that they serve loads. The retal customers wll pay LSEs a regulated rate ( /MWh) for each hour. But at the end of day D, the LSEs are charged the maret clearng prce for each bus at tme perod t ( LMPb () t ). The devaton between cleared demand and actual demand s resolved n the real-tme balancng marets. The maret operator or the ISO determnes the maret clearng prce at each bus through runnng optmal power flow [5]. The obectve of the LSE s to obtan the optmal demand bd that ensures the maxmum payoff for them. The LSE controls the output of the storage unts/dgs to gan hgher proft. The optmal demand bds are determned wth regard to the optmal schedules of the commtment and generaton of the DGS/storage unts owned by the LSEs. Supplers and customers submt hourly supply and demand bds to the ISO. The hourly maret clearng prce and the cleared energy volume of each partcpant s determned for the followng day by the ISO after ntersectng the aggregated supply and demand bds [4]. Several plausble scenaros wth ther assgned probabltes represent the stochastc processes and the uncertan varables n the stochastc programmng model. The uncertanty of LMPs s a notable determnant for the LSEs schedulng procedure, due to ts sgnfcant nfluence on the total payoff. LMPs at each bus depend on the prce elastcty of the loads beng suppled at that node. The obectve of the LSE s to maxmze ts expected payoff (1) n the DAM. Ns 24 D1 s s s P s Rc ( t) lc ( t) LMPb ( t) db ( t) s1 b 1 b c t c F s P s Start s C u ( t) C ( t) g ( t) C. v ( t) bdg n, s s P ( t) LMPb ( t) bess LSE procures the loads wth the energy bought n the wholesale maret and uses the storage unts/dgs that are owned or managed by t (2) [17]. It needs the schedules of ts (1)

4 storage unts/dgs to determne the optmal demand bd to submt to the ISO. s s s OUT, s lc ( t) d b ( t) g ( t) p ( t) s, t, b. bc bdg bess c The generaton of each DG should be wthn the range of mnmum power generaton and the capacty of the DG (3). The logc between the start-up, shut-down and the commtment of the DG unts s shown n (4) and (5), and DG starts up or shuts down once durng each tme perod (6). G u ( t) g (t) G u ( t) s,, t. (3) Mn s s Max s s s s s v ( t) w ( t) u ( t) u ( t 1) s,, t 2,..., T. (4) s s s ntal ( ) ( ) ( ),, 1. (2) v t w t u t u s t (5) s s v ( t) w ( t) 1 s,, t. (6) The energy storage level at the end of each tme perod depends on the storage level of the begnnng of the tme perod n addton to the chargng and dschargng hourly power (7) [18]. The effect of ntal energy storage level of storage unts for the frst tme perod s characterzed n (8). The level of storage n each storage unt s wthn a certan range represented by ts mnmum allowed storage and the capacty (9). E ( t) p ( t) 1 p ( t) stored, s IN IN, s OUT, s K OUT stored, s + E ( t 1) s,, t 2,..., T. E ( t) p ( t) 1 p ( t) stored, s IN IN, s OUT, s K OUT ntal + E s,, t 1. Mn stored, s Max (7) (8) E E ( t) E s, t,. (9) The storage unts are scheduled to ust charge or dscharge durng each perod (10). The constrants (11) and (12) establsh an addtonal lmtaton on the operaton of storage unts that the charge and dscharge rate should also be wthn the nomnal rates. s s x ( t) y ( t) 1 s,, t. (10) 1 OUT, s OUT s OUT p ( t) R x ( t) s, t,. (11) p ( t) R y ( t) s, t,. (12) IN IN, s IN s B. Scenaros The uncertanty of the nput data n a stochastc programmng model s ntroduced wth a set of scenaros. The selecton of these scenaros s an mportant tas that profoundly mpacts the procedure of decson mang. If the number of scenaros s large and the nput data s not processed before mplementaton, the sze of the problem and the tme needed for the executon of the optmzaton problem can be a great challenge for decson-maers. In ths paper, scenaros are generated from the hstorcal data and the K-means clusterng technque s used to reduce the data set by groupng smlar scenaros. The number of observatons n each group gves the probablty of occurrence for these scenaros [19]. Hstorcal data have been used for the prce and load data. In order to acheve a tractable data set from the orgnal nformaton, the K-means clusterng algorthm teratvely computes the dstance between each scenaro and the cluster centrod [20]. The number of clusters should be frstly set for the algorthm. VI. NUMERICAL RESULTS The proposed model s tested on the modfed IEEE 24-bus test system (Fgure 2) [21] to assess ts applcablty and performance n fnancal rs management of LSEs. As shown n the test system, 5 LSEs are partcpatng n the DAM as load aggregators. There are also a few loads that drectly enter the maret ndependent of the LSEs. The LSEs own several storage unts/dgs at the nodes that they are servng the retal customers (Tables I and II). The LSEs use these sources to reduce the rs of fnancal loss and submt more prce elastc demand bds to the ISO/maret operator. Each LSE supply one or more customer groups at each node. The LSEs have offered specfed fxed or hourly varable tarffs for electrcty consumpton to the retal customers. The tarffs of the customer groups depend on the type of the contracts sgned wth the LSEs. The electrcty consumpton tarffs for each customer group are shown n Fgure 3. The red lnes n ths fgure show the maxmum and mnmum amount of the regulated rates. It s assumed that the LSEs have consdered 100 dfferent hourly LMP realzatons for each bus wth equal probablty of occurrence. The number of scenaros s then reduced to 10 clusters for each LSE wth the K-means clusterng technque. The hourly average of LMPs n each cluster represents the LMP profle for that scenaro, and the number of scenaros assgned to each cluster relatve to the number of total scenaros gves the weght for that scenaro. All the mxed nteger optmzaton problems of LSEs are mplemented n GAMS [22] and solved wth the CPLEX solver. The expected profts of LSEs n both cases show how the LSEs are expectng more payoffs by usng ther own DGs or storage unts (Table III). LSE 2 expects of proft nstead of expectng of fnancal loss n the DAM by consderng ts DGs or storage unts and changng the demand bds that t s submttng for the DAM. Other LSEs also expect more payoffs by usng ther DGs or storage unts. In Fgure 4 the dfference between the forecasted demand and the demand bds that the LSEs are submttng to the DAM s llustrated.

5 TABLE I. SPECIFICATION OF THE STORAGE UNITS OWNED BY LSES. Storage Unts Chargng Effcency Dschargng Effcency Capacty (MWh) Mnmum Energy Level (MWh) Chargng Rate (MW/h) Dschargng Rate (MW/h) LSE Bus TABLE II. SPECIFICATION OF THE DGS OWNED BY LSES. DGs Fxed Cost ( /h) Producton Cost ( /MWh) Start-up Cost ( ) Capacty (MW) Mnmum Power (MW) LSE Bus Fgure 2. IEEE 24-bus test system. Fgure 3. Regulated electrcty rates for the customer groups.

6 TABLE III. EXPECTED PAYOFF OF LSES. Wthout DGs/storage unts ( ) Wth DGs/storage unts ( ) LSE LSE LSE LSE LSE Fgure 4. The forecasted demand and the demand bds of LSEs n DAM. VII. CONCLUSION The LSEs at any level of partcpaton n the electrcty maret are encouraged to supply ther loads wth ther storage unts or DG unts when prces rse. Through ths mechansm, they can ncrease the prce elastcty of the demand that they are submttng to the ISO for the DAM and reduce the rs of maret power for GENCOs. The advantage of ths mechansm n reducng the rs of fnancal loss n a short-term horzon s analyzed n ths paper. If the LSEs expect hgher LMPs durng pea load perods, they wll partally supply ther loads wth ther own sources and consequently the total pea consumpton reduces. In our proposed model, the LSE owns several storage unts/dgs and the schedulng of these sources for the optmal operaton s ts man ssue before enterng the DAM. Besdes ths, we are gong one step forward n our future wors by shftng the problem to calculatng the storage unts/dgs optmal ratng n order to reduce the fnancal rss of LSEs n a long-term horzon. REFERENCES [1] L. Hongyan and L. Tesfatson, "ISO Net Surplus Collecton and Allocaton n Wholesale Power Marets Under LMP," Power Systems, IEEE Transactons on, vol. 26, pp , [2] S. J. Rassent, V. L. Smth, and B. J. Wlson, "Demand-sde bddng wll control maret power, and decrease the level and volatlty of prces," Economc Scence Laboratory, Unversty of Arzona2001. [3] Y. Nan-Peng, L. Chen-Chng, and J. Prce, "Evaluaton of Maret Rules Usng a Mult-Agent System Method," Power Systems, IEEE Transactons on, vol. 25, pp , [4] A. T. Al-Awam and E. Sortomme, "Coordnatng Vehcle-to-Grd Servces Wth Energy Tradng," Smart Grd, IEEE Transactons on, vol. 3, pp , [5] Y. Nanpeng, L. Tesfatson, and L. Chen-Chng, "Fnancal Blateral Contract Negotaton n Wholesale Electrcty Marets Usng Nash Barganng Theory," Power Systems, IEEE Transactons on, vol. 27, pp , [6] S. Pneda and A. J. Coneo, "Managng the fnancal rss of electrcty producers usng optons," Energy Economcs, vol. 34, pp , [7] R. C. Leou and J. H. Teng, "The optmal portfolo of the day-ahead maret and real-tme maret for the load servng enttes," n Industral Informatcs (INDIN), 8th IEEE Internatonal Conference on, 2010, pp [8] G. L and J. Sh, "Agent-based modelng for tradng wnd power wth uncertanty n the day-ahead wholesale electrcty marets of snglesded auctons," Appled Energy, vol. 99, pp , [9] Z. Vale, T. Pnto, I. Praça, and H. Moras, "MASCEM: Electrcty Marets Smulaton wth Strategc Agents," Intellgent Systems, IEEE, vol. 26, pp. 9-17, [10] J. Lbn and S. Low, "Mult-perod optmal energy procurement and demand response n smart grd wth uncertan supply," n Decson and Control and European Control Conference (CDC-ECC), 50th IEEE Conference on, 2011, pp [11] H. M. Ghadolae, E. Ta, J. Aghae, and M. Charwand, "Integrated day-ahead and hour-ahead operaton model of dscos n retal electrcty marets consderng DGs and CO2 emsson penalty cost," Appled Energy, vol. 95, pp , [12] N. S. María, "Day-ahead electrcty maret: proposals to adapt complex condtons n OMEL," M.Sc. thess, ICAI School of Engneerng, Comllas Pontfcal Unversty, Madrd, [13] J.-Y. Joo and M. D. Ilc, "A mult-layered adaptve load management (ALM) system: Informaton exchange between maret partcpants for effcent and relable energy use," n Transmsson and Dstrbuton Conference and Exposton, IEEE PES, 2010, pp [14] U. K. Shula and A. Thampy, "Analyss of competton and maret power n the wholesale electrcty maret n Inda," Energy Polcy, vol. 39, pp , [15] A. J. McNel, R. Frey, and P. Embrechts, Quanttatve rs management: concepts, technques, and tools: Prnceton unversty press, [16] X. Yang, "Applyng Stochastc Programmng Models n Fnancal Rs Management," Ph. D. dssertaton, Unv. Ednburgh, Ednburgh, UK, [17] M. A. Fotouh Ghazvn, H. Moras, and Z. Vale, "Coordnaton between md-term mantenance outage decsons and short-term securty-constraned schedulng n smart dstrbuton systems," Appled Energy, vol. 96, pp , 8// [18] T. Sousa, H. Moras, J. Soares, and Z. Vale, "Day-ahead resource schedulng n smart grds consderng Vehcle-to-Grd and networ constrants," Appled Energy, vol. 96, pp , [19] M. A. Fotouh Ghazvn, B. Canzes, Z. Vale, and H. Moras, "Stochastc short-term mantenance schedulng of GENCOs n an olgopolstc electrcty maret," Appled Energy, vol. 101, pp , [20] L. Barngo and A. J. Coneo, "Rs-Constraned Mult-Stage Wnd Power Investment," Power Systems, IEEE Transactons on, vol. 28, pp , [21] P. Subcommttee, "IEEE relablty test system," Power Apparatus and Systems, IEEE Transactons on, pp , [22] General Algebrac Modelng System (GAMS). Avalable: