Impact of Energy Storage Systems on Electricity Market Equilibrium

Transcription

1 Impact of Energy Storage Systems on Electrcty Market Equlbrum A. S. A. Awad, raduate Student Member, IEEE, J. Davd Fuller, T. H. M. EL-Fouly, Member, IEEE, and M. M. A. Salama, Fellow, IEEE Abstract Integraton of large-scale energy storage systems (s) s desrable nowadays to aeve hgher relablty and effcency for smart grds. Controllng operaton usually depends on electrcty market prces so as to arge when the prce s low and arge when the prce s hgh. On the other hand, the market-clearng prce tself s determned based on the net demand,.e., ncludng energy storage output, at every hour. Therefore, t s crucal to develop a mathematcal model to determne the optmal operaton as well as the marketclearng prces. The problem s formulated as a mxed complementarty problem (MCP) that allows the representaton of specal (ncentve) prces, wh cannot be represented n a sngle optmzaton model. The proposed model s useful for power system operators to determne the optmal storage pat smultaneously wth the market-clearng prce n addton to the conventonal generaton pat. The mpact of energy storage sze and locaton on market prce, total generaton cost, energy storage arbtrage beneft, and total consumer payment s further nvestgated n ths paper. The latter analyss provdes some gudelnes for power system planners to dentfy the optmal sze and locaton for nstallng large-scale s. Index Terms Energy storage systems; smart grds; mxed complementarty problem Sets and ndces I. OMECLATURE Set of system buses equpped wth generators Set of system buses equpped wth energy storage, j System bus ndces Hour ndex Varables P enerated actve power at bus durng hour The authors would lke to thank the overnment of Canada for fnancally supportng ths resear tough the Program on Energy Resear and Development. A. S. A. Awad s currently pursung hs Ph.D. at Electrcal and Computer Engneerng Department, Unversty of Waterloo, Ontaro, Canada (e-mal: asamr@uwaterloo.ca) J. Davd Fuller s a professor of Management Scences, n the Faculty of Engneerng at the Unversty of Waterloo, Ontaro, Canada (e-mal: dfuller@uwaterloo.ca) T. H. M. EL-Fouly s wth CanmetEERY, atural Resources Canada, Varennes, Québec, Canada (e-mal: telfouly@nrcan.gc.ca) M. M. A. Salama s a professor at Electrcal and Computer Engneerng Department, Unversty of Waterloo, Ontaro, Canada (e-mal: msalama@uwaterloo.ca) Q P P E Pflow, j, enerated reactve power at bus durng hour Energy storage argng actve power at bus durng hour Energy storage argng actve power at bus durng hour Total energy stored at bus at hour Power flow of the lne between buses and j durng hour V Voltage magntude of bus at hour, Phase angle of bus at hour j, Dfference n phase angles of buses and j at hour,.e., j, Parameters,, and C M Total number of system buses eneraton cost functon parameters at bus Energy storage operaton and mantenance cost P D Demand actve power at bus durng hour Demand reactve power at bus durng hour QD max flow, j P Rated power flow of the lne between buses and j Energy storage argng effcency P E, rated, rated, mn Energy storage argng effcency Rated energy storage actve power at bus Rated energy storage capacty at bus P Mnmum generated actve power at bus P Maxmum generated actve power at bus,max Q Mnmum generated reactve power at bus, mn Q Maxmum generated reactve power at bus mn,max V Mnmum voltage at ea bus V max Maxmum voltage at ea bus j Real part of bus admttance matrx element (,j) B j Imagnary part of bus admttance matrx element (,j)

2 2 C II. ITRODUCTIO LASSICAL power systems mply undrectonal flow of energy from generatng statons to trbuton systems tough transmsson and sub-transmsson networks. Ths scenaro has been anged after allowng for trbuted generaton to be connected at trbuton systems, and thus leadng to bdrectonal power flow wthn trbuton networks. As a result, trbuton systems become actve and hence they are referred to as actve trbuton networks. Further, renewable portfolo standards place oblgatons to have certan penetraton percentage from renewable energy sources (RESs), e.g., state of Calforna requres that 33% of the supply mx should be provded from RESs by 2020 []. From another pont of vew, customers become nterested to partcpate n electrcty market operatons to reduce ther energy blls. Ths s referred to as load management or demand response. Load management can be aeved by mplementng two-way communcaton nfrastructure between utltes and customers [2]. Consequently, t s crucal that the trbuton system be operated n a fundamentally dfferent manner. One of the ntatves that have been proposed to manage ths new envronment s the smart grd concept. Smart grd can be defned from dfferent perspectves; t s the two-way flow of electrcty and nformaton between supply and demand. Another defnton s the applcaton of ntellgent devces and communcaton tenologes n power systems [2]. enerally, smart grds ntend to facltate ntegraton of RESs and to satsfy the needs of hgher system relablty and effcency. An energy storage system () s one of the promsng tenologes that wll enable smart grd concepts. s can support RESs ntegraton by reducng the fluctuatons assocated wth ther power producton. s can further provde some ancllary servces, e.g., load followng, spnnng reserve, black start capablty, etc., and they can also be deployed to mprove system relablty. Moreover, s can be used to shave peak loads to avod the hgh cost assocated wth peak pck-up generators. Peak load shavng mples power exange between base generaton unts and storage devces n order to store some power durng off-peak perods and arge them durng peak load perods. Ths practce ncreases the capacty factor of base generaton unts. Ths s n addton to the fact that off-peak power can be stored or bought wth a low prce, and then arged or sold wth a hgh prce. Ths prce dfference, usually called arbtrage beneft, s benefcal for an owner, e.g., a utlty or a customer drven [3]. In Canada, the frst battery-energy storage projects have been recently mplemented by Brtsh Columba (BC) Hydro and Toronto Hydro wth ratngs of 2 MW and 500 kw-250 kwh, respectvely [4, 5]. Several resear works have addressed the problem of determnng the optmal operaton strategy of s,.e., when and how mu power s to be arged or arged, as n [6] [7] [8]. In these works, the storage devces were modeled as prce-taker frms knowng the electrcty prce at ea hour for some perod ahead. Su modelng s based on the assumpton that storage capactes are too small to affect the market prce. However, the ncreased potental of adoptng large central storage facltes n power systems would contradct that assumpton. Mathematcal models were further developed n [9] to fnd the optmal capacty and the optmal pat of a hybrd system comprsed of generaton and storage facltes. Ths was aeved by mnmzng the annual captal and operaton costs of the system. The mpact of adoptng large-scale energy storage on system prce has been also nvestgated, but snce the developed models dd not represent the power network, the mpact of storage locaton was not consdered. In [0], the authors evaluated the arbtrage beneft of small-sze energy storage by optmzng ts operaton durng two weeks perod and assumng perfect market prce foresght durng that perod. The mpact of large-scale energy storage was further cussed by representng the prce as an econometrcally estmated nondecreasng functon of the net power demand ncludng storage output, aggregated over the whole network. That representaton does not actually optmze the market prce at every hour nor s the storage locaton represented. evertheless, the results showed lower and hgher prces durng peak and off-peak perods, respectvely. As a result, the arbtrage value was found to be 0-20% less than that calculated consderng constant prces at every hour. The results further revealed an ncrease n consumer surplus wh was larger than the decrease n producer surplus, and thus resultng n a net ncrease n the socal welfare. Smlarly, the authors n [] nvestgated the mpact of large-scale energy storage operaton on the wholesale electrcty prce. However, no mathematcal models were descrbed for determnng ether the optmal operaton strategy of the storage unts or the market-clearng prce. The mpact on electrcty prce was nstead approxmated by observng the effect of storage unts on the generaton cost of margnal conventonal plants. Lke [9] [0], [] dd not model the power network, so locatonal effects were not consdered. From the aforementoned lterature survey, t can be concluded that suffcent work has addressed the problem of determnng the optmal operaton strategy of s assumng forecasted market prces for some perod ahead. The mpact of large-scale energy storage operaton on market prces and generaton costs has been further nvestgated assumng ether a hstorcal operaton as n [] or a prce functon of the net power demand, wthout modelng the network, as n [0]. These two problems of determnng the optmal energy storage pat and the market-clearng prce were de-coupled to mtgate the complexty of the analyss. Therefore, ths paper ams to develop a mathematcal model for determnng not only the optmal argng/argng strategy of s, but the optmal market prce as well n a perfectly compettve envronment, wth a physcal model for the power network. To the best of the author s knowledge, ths problem has not been tackled yet n the lterature; however, t s very useful for In ths paper, the term pat s used for determnng the optmal operaton n day-ahead markets, n wh unt commtment s usually performed, contrary to the usual meanng of pat that s typcally conducted n short-tme perods ahead of the actual operaton.

3 3 power system operators dealng wth large-scale s n ther networks. The mpact of energy storage sze and locaton on market prce, total generaton cost and beneft, arbtrage beneft, and total consumer payment s further nvestgated n ths paper. The latter analyss provdes some gudelnes for power system planners to allocate large-scale s. s are very expensve n captal, operaton, and mantenance costs. Therefore, governments may consder specal ncentves for s n order to encourage prvate nvestment. For some forms of specal ncentves, t s mpossble to represent market equlbrum as a sngle optmzaton model, e.g., f an s to receve a fxed multple (greater than one) of the ordnary market prce for ts arged output [2]. In su cases, however, a mxed complementarty problem (MCP) formulaton can be used. In ths paper, we consder one su specal ncentve whereby the would receve or pay the hghest locatonal margnal prce (LMP) among all the buses n the system, and we formulate market equlbrum as an MCP. The man contrbutons of ths paper can be summarzed as follows: Ths paper presents a novel mathematcal model for determnng the optmal operaton strategy of an and the market-clearng prce smultaneously n a perfectly compettve envronment, even f specal ncentves make t mpossble to formulate a sngle optmzaton model. The model proposed s used to address the mpact of the locaton and sze on electrcty market equlbrum. The rest of ths paper s organzed n four sectons. The problem formulaton s derved n Secton III. Secton IV presents the system under study. Several case studes and smulaton results are then cussed n Secton V. Fnally, Secton VI summarzes the conclusons of ths resear work. III. PROBLEM FORMULATIO The ratonale behnd ths resear work s to solve two dependent problems,.e., socal welfare maxmzaton, gven the energy storage operatonal decsons, and energy storage arbtrage beneft maxmzaton, gven the hghest LMP, durng argng and argng, as a specal ncentve for the. Therefore, the man focus of ths paper s to propose a jont optmzaton strategy that smultaneously solves the two dependent problems, together wth a thrd optmzaton model that determnes the hghest LMP. Before cussng how to solve the whole model as an MCP, the tee optmzaton models are defned n the followng paragraphs. The MCP s outlned at the end of ths secton, and t appears n detal n Appendx A. The sngle aucton market structure s consdered n ths paper n wh the electrcty prce s settled based on the net demands at buses,.e., after accountng for argng and argng, and the bds offered by the generators. Socal welfare maxmzaton under su a structure s aeved by mnmzng the total generaton cost functon as follows [3] [4] 24 2 () mnmze F P P It s worth mentonng that the above cost functon neglects startup costs snce the representaton of these costs requres bnary varables, wh cannot be consdered n the MCP formulaton used n ths paper. Therefore, we assume that unt commtment decsons have already been made n an earler stage, and the commtted generators are only consdered n F. When decdng on unt commtments, the system operator would requre an estmate of the argng and argng sedule of the, as the operaton could affect the need for some generaton unts. An estmate of the sedule could be based on experence, to start, and the estmate could be updated after runnng the MCP model descrbed n ths paper, n an teratve process. In ths paper, we focus on the MCP model only, and leave the extenson to the unt commtment process for future resear. Moreover, f the power ratng of the s less than or equal to the capacty of the smallest generator (.e., mnmum spnnng reserve), wh s usually the case snce the capactes of are small compared to those of bulky generators, the would be arged wthout the need for startng up another offlne generator. Consequently, consderng the startup costs would not affect the storage sedulng under the above condton. The amount of spnnng reserve would be further unanged, f we neglected the losses n the, snce a part of the reserve would be stored n the n ths case [5]. evertheless, F s mnmzed under system constrants su as power flow constrants, generaton lmts, and voltage lmts, as gven n (2-9). ote that the varables for argng and argng are treated as parameters n ths optmzaton model; dual varables are n parentheses. D j, j P P P P V V (2) j j, j j, cos B sn D j, j Q Q V V (3) j j, j j, P V V V, j, max j j, j, flow, j, j,,mn,max,,,mn,max,, mn, max,, t,,, sn B cos cos flow j j j, j, B V sn P w j, P P P a, b, (5) Q Q Q c, d, (6) V V V e, f, (7) V constan g, (8) k, l, (9) (4)

4 4 In ths work, all generators and customers receve and pay the LMPs at every hour,.e., the bus dual varables (λ, ), respectvely. However, the hourly electrcty prce (ρ ) that s pay or receve for the energy stored or delvered, respectvely, s set to be the hghest bus dual varable as n (0), as motvated by [3] [4] max (0) Takng the hghest bus dual varable s justfed as an ncentve for promotng energy storage mplementaton. There tends to be mu smaller dfferences among LMPs durng offpeak, low-prce, tmes when the would arge, and so the hghest prce s close to all LMPs. The specal ncentve occurs when the hghest prce s very hgh durng peak perods, and the sells ts arged output. Applyng ths proposed ncentve requres that the pays the hghest LMP durng off-peak tmes, whle the power authorty compensates the wth the dfference between ts LMP and the hghest LMP n the system durng peak perods. Ths proposed ncentve s bascally one of many other possble ncentves that may be offered to the storage owners. Other ncentves could be, for example, to use a weghted average of the LMP at the connecton, and the hghest LMP, or to use the LMP, but the government pays a constant subsdy as an added amount on the sellng prce durng argng. It s worthwhle to menton that f the LMP correspondng to the locaton were used nstead, then n the case study of Sectons IV and V, the energy storage would not be pated unless the s located at the bus correspondng to the hghest market-clearng prce. Ths phenomenon s attrbuted to the fact that the dfference between off-peak and peak prce should be large enough n order to justfy the operaton and mantenance cost, and thus to economcally operate the. Ths condton s not satsfed n the case when usng the LMP. However, ths concluson depends on the system data and parameters. In other words, utlzng the LMP mght lead to an economc pat wth other systems of dfferent data. Equaton (0) s mplemented va a mathematcal devce that fts nto the framework for developng an MCP: the system operator has a second objectve (n addton to socal welfare maxmzaton) to mnmze the electrcty prce (ρ ) at every hour, subject to the constrant that ρ exceeds or equals the dual varable at every bus as follows (note that λ, are treated as parameters n ths optmzaton model): mnmze F Subject to 2 24 m, () (2) The arbtrage beneft maxmzaton problem assocated wth the energy storage s mathematcally represented as mnmzng the followng objectve functon, where the electrcty prces at every hour are treated as parameters n ths model: 24 3 P P M (3) mnmze F P P C In the above objectve functon, the frst term represents the drect operaton and mantenance cost assocated wth the due to hourly argng and argng, whle the second term represents the arbtrage value. Indrect costs of losses are represented mplctly n (4) below, tough the argng and argng effcency parameters. Ths formulaton thus prevents patng the for a zero arbtrage beneft snce the arbtrage beneft should be at least equal to the cost of operatng and mantanng the. F 3 s to be mnmzed under the energy storage constrants as gven n (4-7) E E P P / n,,,, rated oh, r p,,, rated q,,,, rated s,, t, (4) 0 P P,, (5) 0 P P r (6) 0 E E, (7) If the was to pay and receve the LMP at ts bus (, nstead of ), then the optmal power flow (OPF) problem (- 9) could be combned wth (4-7) n a sngle OPF that mnmzes generaton costs n () plus costs n the frst term of (3). However, su a formulaton cannot be used to determne the optmal pat of the wth the specal (ncentve) prce n (0). In other words, conventonal market models cannot take nto consderaton the formulatons ntroduced n (-7) whle solvng for the 24-hour OPF problem (-9). Therefore, we propose a novel method that determnes the optmal operaton strategy of and the specal prce that wll pay or receve at ea hour, n addton to the conventonal pat varables,.e., the generaton power levels at ea hour. As a result, the man allenge of ths work s to solve the aforementoned tee dependent problems together. In order to solve the tee dependent problems smultaneously, for equlbrum, they are formulated as an MCP. In su a formulaton, the KKT condtons of all optmzaton problems are combned together to form a square set of equatons, nequaltes, and complementarty condtons, as gven n Appendx A. However, any soluton to those KKT condtons s not guaranteed to gve the optmal solutons to the tee problems unless certan suffcency condtons are met, e.g., the objectve functon s a contnuously dfferentable convex functon, and the constrants consttute a convex set [2]. By examnng the tee problems under study, we can conclude that the objectve functons are convex functons snce the frst one s a quadratc functon wth non-negatve parameters, whle the second and thrd objectves are lnear. However, all constrants are lnear functons,.e., convex, except the power

5 5 flow equatons wh are non-convex functons n most cases [6]. Consequently, the obtaned solutons are only guaranteed to be local optma IV. SYSTEM UDER STUDY In all case studes, the system under study conssts of a 6- bus transmsson system and a 3-bus trbuton system, as shown n Fg. [3]. The trbuton system s nterconnected to the transmsson system tough a 00-MVA transformer. Two generatng statons ( and 2) are connected at buses and 3; ther cost functon parameters, generaton lmts, and daly peak demand are gven n [3]. Ths system s smple enough to be solved n a short tme,.e., nearly one mnute on a personal computer. Therefore, the model can be run several tmes, n a good tmely manner, n order to provde a senstvty analyss for the mpact of the locaton and sze on market equlbrum. However, the IEEE 4 and 30 bus systems are also used n the frst case study n order to demonstrate the performance of the model developed n solvng larger real systems. The data of the IEEE 4 and 30 bus systems can be found n [7]. The demand profle at ea node s assumed to follow the IEEE-RTS summer load profle n [8] wh provdes the hourly load magntude as a percentage of the daly peak demand. However n real case studes, one day ahead forecasted load demand profle as n [9] can be utlzed n the developed model to set the market prce and determne the optmal operaton of allocated s. On the other hand, the sze and the locaton of the energy storage wll be vared as wll be cussed later on n secton V. The argng and argng effcences are assumed to be 90% (.e., 8% round trp effcency) n all case studes [9]. The operaton and mantenance cost of (C M ) s assumed to be 0.6 cents/kwh [20]. V. SIMULATIO RESULTS The aforementoned MCP s solved by means of the PATH solver n the eneral Algebrac Modelng System (AMS) envronment. Several case studes are presented n ths secton; the frst one shows the sgnfcance of the proposed MCP model to power system operators,.e., to determne the optmal pat and the hghest market-clearng prce n a perfectly compettve market. Afterwards, other case studes are cussed to show the mpact of sze and locaton on the hghest market-clearng prce, total generaton cost and beneft, energy storage arbtrage beneft, and total consumer payments. The smulaton results are cussed n the next subsectons. For all case studes, we report only the hghest market-clearng prce (ρ ), but not all nne LMPs, to save space. Case study : mpact of energy storage operaton Bascally, any energy storage conssts of an energy reservor and a power converson system (PCS). Therefore, the sze s defned by two parameters: rated argng/argng rate (n MW) and rated storage capacty (n number of arge hours at rated argng rate), wh correspond to PCS and energy reservor szes, respectvely. 4 5 Fg.. System under study In ths case study, the 9 bus system s utlzed frst, and t s assumed that one s allocated at the trbuton system (bus #7) wth a ratng of 00 MW and 2 hours arge,.e., P 00 MW, and E 200 MWh. The proposed rated rated MCP model s utlzed to determne the optmal pat and the hghest market-clearng prce for one day ahead. The hghest market-clearng prce s presented n Fg. 2 wth and wthout the ntegraton to the system. Wth the presence of the, the electrcty prces become almost leveled durng off-peak and peak perods. Furthermore, t s clear that the prces are ncreased durng off-peak tmes, whle they are reduced durng peak perods. Ths s because of the optmal argng and argng durng off-peak and peak tmes, respectvely, as shown n Fg. 3, wh shows the output power as a percentage of the rated argng/argng rate (.e., 00 MW n ths case study). Moreover, the model proposed s used to solve the IEEE 4 and 30 bus systems n order to assess the ncrease n computatonal tme as the model grows n sze. The run tmes correspondng to the systems used n ths paper are summarzed n Table I. Although t seems that the model developed could scale up to solve larger systems, we would lke to menton that for larger real-world systems, faster computer equpment and possbly specalzed algorthms su as decomposton, as cussed at apter 9 n [2], mght be needed, to be solvable wthn a reasonable amount of tme for day-ahead markets. Fg. 2. Hghest market-clearng prce wth and wthout ntegraton

6 Moreover, Fg. 9 and Fg. 0 show total consumer payments and total generaton beneft for the dfferent szes, respectvely, where total generaton beneft s calculated by subtractng total generaton cost from total generaton revenue. It can be notced that consumer payments and generaton benefts are reduced wth the ncrease of sze. 6 Fg. 3. Optmal pat Table I Complexty analyss of the MCP model developed System sze Run tme (n seconds) 9 bus 50 4 bus bus 206 Case study 2: mpact of energy storage sze Ths case study nvestgates the mpact of energy storage sze on the hghest market-clearng prce, total generaton cost and beneft, arbtrage beneft, and total consumer payments. Lke the prevous case study, one s assumed connected to bus #7. Frstly, the PCS sze s fxed at 40 MW, whle the reservor sze s vared between 2-6 arge hours n steps. Afterwards, the PCS sze s anged n steps between MW, whle the reservor sze s kept constant at 2 arge hours. Fg. 4 shows the hghest market-clearng prces for the dfferent energy reservor szes compared to the case of no energy storage n the system. Wth the ncrease of energy storage capacty, the can exange more power wth the generatng statons durng the day. Therefore, the market prces are settled at hgher prces durng low demand perods and at lower prces, on the other hand, when the demand s hgh. Smlar results are obtaned when the PCS sze s ncreased from 40 MW to 80 MW, as shown n Fg. 5. The total generaton cost profles are presented n Fg. 6 and Fg. 7 for the dfferent szes adopted n ths case study. Fg. 6 reveals that up to 20% hgher generaton costs are ncurred durng off-peak perods, whle generaton costs can be reduced by 0% durng peak tmes. Wth respect to the energy storage arbtrage beneft (n Fg. 8), t s clear that the arbtrage beneft ncreases wth an ncrement of the energy storage sze up to a certan sze. The arbtrage beneft then becomes steady at the maxmum value snce the optmal operaton does not ange beyond ths pont. The maxmum arbtrage beneft depcted s almost $3,00 per day, wh can be aeved wth dfferent combnatons between the PCS and reservor szes. For example, 80MW - 4 hours arge and 40 MW - 6 hours arge s result n the same (maxmum) arbtrage beneft. Therefore, the owner needs to calculate the economc sze to be nstalled that maxmzes the present value of the arbtrage beneft over the lfetme of the, mnus the nstallaton cost. Fg. 4. Hghest market-clearng prce for dfferent energy storage reservor szes Fg. 5. Hghest market-clearng prce for dfferent PCS szes Fg. 6. Total generaton cost for dfferent energy storage reservor szes Fg. 7. Total generaton cost for dfferent PCS szes

7 7 Fg. 8. Arbtrage beneft for dfferent szes nstallaton. As a result, t s more proftable for the owner to nstall the n the transmsson system n order to aeve hgher arbtrage beneft. On the other hand, Fg. 2 reveals that total generaton costs are larger wth transmsson system nstallaton durng off-peak tmes, whle they are smaller when the load s hgh, compared to nstallng the same n the trbuton system. Ths observaton can be explaned as generaton costs depend on the net system demand shown n Fg. 3. The net system demand s calculated takng nto consderaton the optmal operaton n ea case. Fg. 9. Total consumer payments for dfferent szes Fg.. Hghest market-clearng prce (case study 3) Fg. 0. Total generaton beneft for dfferent szes Case study 3: mpact of energy storage locaton The mpact of energy storage nstallaton locaton s analyzed n ths case study. Two possble locatons are consdered as follows: bus #5 (n the transmsson system) and bus #8 (n the trbuton system). In ths case study, the sze of nstalled s fxed at 40 MW - 4 hours arge. As shown n Fg., the energy storage locaton has an mpact on the hghest market-clearng prce. When the s nstalled n the transmsson system (bus #5), the dfferences between off-peak and peak market prces are hgher than those depcted when nstallng the same n the trbuton system (bus #8). Ths observaton s attrbuted to the fact that the market prces are hgher when more power losses are ncurred n the system and vce versa. Therefore, when unts are nstalled n the trbuton system, the system power losses are ncreased durng argng perods of, whle they are reduced durng argng perods of, thus ncreasng and decreasng the market prces durng off-peak and peak perods, respectvely. Furthermore, the arbtrage value assocated wth transmsson system nstallaton equals $2,947 (per day), wh s almost two tmes the value of the trbuton system Fg. 2. Total generaton cost (case study 3) Fg. 3. et system demand (case study 3) Moreover, the mpact of energy storage locaton s further studed durng congeston n the system. As an example, congeston n the transmsson system s smulated tough reducng the power-flow lmt of selected lnes that are shaded n Table II. Afterwards, the mpact of nstallng the same at buses #5 and #8 s nvestgated; the hghest market-clearng prces and total generaton costs are shown n Fg. 4 and Fg. 5. As observed, the locaton has the same mpact on the market prces and generaton costs even durng congeston n the transmsson system. Ths concluson s explaned by notng that the does not stress the system nfrastructure

8 8 snce t s arged durng off-peak perods, when the lnes are lghtly loaded, and arged durng peak tmes, thus relevng the congeston n the system. As shown n Table II, the lnes 3-4 and 3-5, for example, were congested before the was nstalled n the system; however, these congestons are allevated after connectng the at ether bus #5 or bus #8. Table II Power flow values durng congeston n the system Maxmum power flow Lne between Rated power buses flow (pu) * o at at bus 5 bus * Base power = 00 MVA storage locaton n the trbuton system. However, the arbtrage beneft assocated wth the trbuted storage s found to be slghtly hgher than that wth the central storage case. Therefore, t may be more desrable for the owner to nstall trbuted storage faclty than nstallng central energy storage. Smlarly, total generaton costs are found to be slghtly nfluenced by central/trbuted storage mplementaton, as shown n Fg. 7, snce the operaton s almost the same n both cases. Fg. 6. Hghest market-clearng prce (case study 4) Fg. 4 Hghest market-clearng prce (under congeston n the system) Fg. 7. Total generaton cost (case study 4) Fg. 5 Total generaton cost (under congeston n the system) Case study 4: central vs. trbuted storage Ths case study nvestgates the dfference between central and trbuted mplementaton of energy storage. The nstallaton of one (60 MW - 2 hours arge) at bus #8 s compared to the nstallaton of tee s (ea s 20 MW 2 hours arge) at buses #7, #8, and #9. It s shown n Fg. 6 that the hghest market-clearng prces are exactly the same wth both mplementatons snce the power losses n the transmsson network, consttutng the major part of total system losses, are ndependent of the VI. COCLUSIOS Ths paper develops a mathematcal model for determnng the optmal operaton strategy of s smultaneously wth the optmal market prces n a perfectly compettve envronment, modfed wth specal ncentve prcng for s based on the hghest LMP n the system. The problem formulaton solves two dependent problems, socal welfare and energy storage arbtrage beneft maxmzaton. Moreover, ths paper nvestgates the mpact of energy storage sze and locaton on market prce, total generaton cost and beneft, arbtrage beneft, and total consumer payments, tough several case studes. Due to operaton, the hghest market-clearng prce becomes almost leveled durng off-peak and peak ntervals. The larger the energy storage sze, the less dfference between off-peak and peak prces. The total generaton costs are also affected by the energy storage sze; for larger szes, hgher costs are observed durng low demand, whle lower costs are ncurred when the demand s hgh. Wth respect to the arbtrage beneft, t ncreases up to a certan maxmum value when t s plotted versus the storage capacty sze.

9 Furthermore, consumer payments and generaton benefts are reduced wth the ncrease of arbtrage beneft. Regardng the mpact of energy storage locaton, a hgher dfference between off-peak and peak prces s notced n the case of connectng the energy storage to the transmsson system compared to the case of nstallng the same n the trbuton system. Thus, the arbtrage beneft s hgher n the case of transmsson system nstallaton. Therefore, the owner s economcally encouraged to nstall the n the transmsson system. Moreover, central and trbuted energy storage mplementatons are compared n ths paper. The results show that the hghest market-clearng prce and the generaton costs are almost not nfluenced by central/trbuted mplementaton; however, the arbtrage beneft assocated wth trbuted storage s slghtly hgher than that found n the case of central storage. As a result, trbuted storage may be desrable to be mplemented n power systems, from the owner s perspectve. In concluson, energy storage sze and locaton have a drect mpact on electrcty market prces and arbtrage beneft. The conclusons are very useful for power system planners n allocatng large-scale s. Moreover, the proposed mathematcal model s helpful for power system operators to determne the optmal argng/argng strategy of s and the optmal market prces n a perfect competton. VII. APPEDIX A The KKT condtons can be derved by takng dervatves of Lagrangan functons, 2, and 3 that correspond to F, F 2, and F 3, respectvely, wth respect to the prmal varables and the Lagrangan multplers (dual varables) assocated wth equalty constrants, and settng those dervatves equal to zero. KKT condtons further nclude the complementarty condtons assocated wth nequalty constrants and ther dual varables. The complete MCP model s then gven as follows: P : 2 P a b 0, Q : c d 0, (A.) (A.2) j cosj, : V j, V B sn j j j, j, V j, V j, j cosj, j snj, j j Bj sn j, Bj cos j, j, V j, w j, V j, j snj, j cosj, j j Bj cos j, j Bj sn j, 2 j V V j, w, j, j cosj, j j Bj sn j, e f 0, j cosj, : V j, V B sn j j j, j, V j, V j, j cosj, j snj, j j Bj sn j, Bj cos j, j, V j, w j, V j, j snj, j cosj, j j Bj cos j, j Bj sn j, 2 j V V j, w, j, j cosj, j j Bj sn j, g 0, V j, : V j snj, j Bj cos j, j, V j, V j, j snj, j cosj, j j Bj cos j, Bj sn j, j, V j, w, j, V j, j cosj, j snj, j j Bj sn j, j Bj cos j, w V j, j, j snj, 0, j j Bj cos j, k l 9 (A.3) (A.4) (A.5)

10 0 j cosj, : V V j, B sn j j j, D P P P P 0 j snj, : V V j, B cos j j j, Q Q 0 g D 2 P 3 : V const ant, : m : C M n o p 0, P 3 M n : C / q r 0, E 3 : n n s t 0, n P 3 : E E P / 0, max flow, j flow, j,, j, (A.6) (A.7) (A.8) (A.9) (A.0) (A.) (A.2) (A.3) 0 P P w 0 j, (A.4) 0 P P a 0, (A.5), mn 0 P P b 0, (A.6),max 0 Q Q c 0, (A.7), mn 0 Q Q d 0, (A.8),max 0 V V e 0, (A.9) mn 0 V V f 0, (A.20) max 0 k 0 (A.2) 0 l 0 (A.22) 0 m 0, (A.23) 0 P o 0, (A.24),,, rated,,, rated 0 P P p 0, (A.25) 0 P q 0, (A.26) 0 P P r 0, (A.27) 0 E s 0, (A.28) 0 E E t 0, (A.29), rated VIII. REFERECES [] A. Ipak and F. Albuyeh, "rd of the future", IEEE Power and Energy Magazne, vol. 7, 2009, pp [2] K. Mosleh and R. Kumar, "A Relablty Perspectve of the Smart rd", IEEE Transactons on Smart rd, vol., 200, pp [3] R. B. Sanker, "Executve overvew: energy storage optons for a sustanable energy future", n IEEE Power Engneerng Socety eneral Meetng, 2004, pp Vol.2. [4] "BC Hydro breaks ground on nnovatve clean energy project", Avalable: project_golden_feld.html (20.) [5] "Introducng the frst urban communty energy storage project", Avalable: untyenergystorage.aspx (203.) [6] H. Lund,. Salg, B. Elmegaard, and A.. Andersen, "Optmal operaton strateges of compressed ar energy storage (CAES) on electrcty spot markets wth fluctuatng prces", Appled Thermal Engneerng, vol. 29, 2009, pp [7] J. Usaola, "Operaton of concentratng solar power plants wth storage n spot electrcty markets", IET Renewable Power eneraton, vol. 6, 202, pp [8] J. arca-onzalez, R. M. R. de la Muela, L. M. Santos, and A. M. onzalez, "Stoastc Jont Optmzaton of Wnd eneraton and Pumped-Storage Unts n an Electrcty Market", IEEE Transactons on Power Systems, vol. 23, 2008, pp [9] A. D. Lamont, "Assessng the economc value and optmal structure of large-scale electrcty storage", IEEE Transactons on Power Systems, vol. 28, 203, pp [0] R. Soshans, P. Denholm, T. Jenkn, and J. Wess, "Estmatng the value of electrcty storage n PJM: Arbtrage and some welfare effects", Energy Economcs, vol. 3, 2009, pp [] B. yamdash and E. Denny, "The mpact of electrcty storage on wholesale electrcty prces", Avalable: (20) [2] S. A. abrel, A. J. Conejo, J. D. Fuller, B. F. Hobbs, and C. Ruz, "Complementarty Modelng n Energy Markets ", Sprnger 203. [3] T. H. M. El-Fouly, H. H. Zeneldn, E. F. El-Saadany, and M. M. A. Salama, "Impact of wnd generaton control strateges, penetraton level and nstallaton locaton on electrcty market prces", IET Renewable Power eneraton, vol. 2, 2008, pp [4] H. H. Zeneldn, K. Bhattaarya, E. F. El-Saadany, and M. M. A. Salama, "Impact of ntentonal slandng of trbuted generaton on electrcty market prces", IEE Proceedngs, eneraton, Transmsson and Dstrbuton, vol. 53, 2006, pp [5] S. X. Chen, H. B. oo, and M. Q. Wang, "Szng of Energy Storage for Mcrogrds", IEEE Transactons on Smart rd, vol. 3, 202, pp [6] Y. V. Makarov, D. Zhao-Yang, and D. J. Hll, "On Convexty of Power Flow Feasblty Boundary", IEEE Transactons on Power Systems, vol. 23, 2008, pp [7] "Power system test case arve", Avalable: [8] Y. M. Atwa, E. F. El-Saadany, M. M. A. Salama, R. Seethapathy, M. Assam, and S. Cont, "Adequacy Evaluaton of Dstrbuton System Includng Wnd/Solar D Durng Dfferent Modes of Operaton", IEEE Transactons on Power Systems, vol. 26, 20, pp [9] "Market Summares", Avalable: [20] M. Kntner-Meyer, J. Chunlan, P. Balducc, M. Elzondo,. Xnxn, T. guyen, F. Tuffner, and V. Vswanathan, "Energy storage for varable renewable energy resource ntegraton A regonal assessment for the orthwest Power Pool (WPP)", n IEEE/PES Power Systems Conference and Exposton (PSCE), 20, pp. -7.

11 Ahmed S. A. Awad (S ) receved the B.Sc. and the M.Sc. degrees n electrcal engneerng from An Shams Unversty, Caro, Egypt, n 2007 and 200, respectvely. He s currently pursung the Ph.D. degree n the Department of Electrcal and Computer Engneerng, Unversty of Waterloo, Waterloo, O, Canada. In between September 2007 and 2009, he worked as an electrcal desgn engneer wth Dar El-Handasah (Shar and partners) and Alled Consultants Co. n Egypt. Snce 2008, he has been workng wth the Department of Electrcal Power and Manes Engneerng, An Shams Unversty, Caro, Egypt, where he s currently on a study leave untl he receves the Ph.D. degree. Hs resear nterests nclude applcaton of energy storage n smart grds, ntegraton of renewable energy resources, electrcty market equlbrum, as well as operaton and control of trbuton systems. Davd Fuller receved the B.Sc. degree n mathematcs n 973 from Queen s Unversty n Kngston, Ontaro, the M.Sc. n appled mathematcs n 975 from the Unversty of Brtsh Columba (UBC) n Vancouver, Brtsh Columba, and the Ph.D. n ntercplnary studes from UBC n 980. Hs resear has focused prmarly on models of markets for energy, and algorthms for ther soluton, wth a recent emphass on the desgn of electrcty markets. He s a professor of Management Scences, n the Faculty of Engneerng at the Unversty of Waterloo. Tarek H. M. EL-Fouly (M 02) receved the B.Sc. and M.Sc. degrees n electrcal engneerng from An Shams Unversty, Caro, Egypt, n 996 and 2002, respectvely, and the Ph.D. degree n electrcal engneerng from the Unversty Of Waterloo, Waterloo, O, Canada, n He joned CanmetEERY, atural Resources Canada, n 2008, as a Transmsson and Dstrbuton Resear Engneer, where he s conductng and managng resear actvtes related to actve trbuton networks, mcrogrds and remote communtes. In 200, he was apponted as Adjunct Assstant Professor at the Electrcal and Computer Engneerng Department, Unversty of Waterloo. Hs resear nterests nclude protecton and coordnaton studes, ntegraton of renewable energy resources, smart mcrogrds, smart remote communty applcatons, demand sde management, and forecastng. Magdy M. A. Salama (F 02) receved the B.Sc. and M.Sc. degrees n electrcal engneerng from Caro Unversty, Caro, Egypt, n 97 and 973, respectvely, and the Ph.D. degree n electrcal engneerng from the Unversty of Waterloo, Waterloo, O, Canada, n 977. Currently, he s a Professor n the Department of Electrcal and Computer Engneerng, Unversty of Waterloo, Waterloo, O, Canada. He has consulted wdely wth government agences and the electrcal ndustry. He s a regstered Professonal Engneer n the Provnce of Ontaro. Hs resear nterests nclude the operaton and control of trbuton systems, power-qualty montorng and mtgaton, asset management, and electromagnetcs.