Elecric Vehicle Baery Swapping Saion: Business Case and Opimizaion Model Mushfiqur R. Sarker, Hrvoje Pandžić, Miguel A. Orega-Vazquez Universiy of Washingon Seale, Washingon Email: {sarkermu, hpandzic, maov}@uw.edu Absrac In order o increase he adopion rae of elecric vehicles, hey need o appeal o cusomers as much as heir fossil fuel equivalens. However, major concerns include long baery charging imes and range anxiey. These concerns can be miigaed if cusomers have access o baery swapping saions, where hey can mee heir moion energy requiremens by swapping baeries for charged ones, in as much ime as i akes o fill he gasoline reservoir of a convenional vehicle. Besides benefiing he cusomers, he baery swapping saion is beneficial o he power sysem because i emulaes an energy sorage saion capable of paricipaing in elecriciy markes. In his saion, he baeries can be scheduled o charge in grid-o-baery mode, injec power o he grid in baery-o-grid mode, and ransfer energy beween baeries in baery-o-baery mode, if here are economic advanages in doing so. This paper discusses how hese various modes can be opimized and he resuls ranslaed ino a business case for baery swapping saions. Keywords Baery Swapping Saion, Elecric Vehicles, Energy Sorage, Elecriciy Marke. I. INTRODUCTION CUSTOMER accepance of elecric vehicles (EVs) is saring o be eviden. However, here are sill concerns hindering he wide spread adopion of hese devices, chiefly relaed o limied mileage range, long charging imes, and large baery replacemen coss. Alhough he number of baery charging locaions is increasing, he charging ime a hese saions is eiher oo long or reduce baery life by forcing hem o undergo fas charging processes. An alernaive o hese charging saions is he deploymen of Baery Swapping Saions (BSS), which swap a cusomer s discharged baery wih a fully charged one of he same ype. These saions could reduce he cusomers concerns abou long charging imes or having enough sored energy o finish a rip. By using elecrical energy for moion, EVs are expeced o increase he overall demand for elecrical energy [1]. For his reason, i is crucial o examine he impac of EVs and BSSs on he power sysem. Since EVs are equipped wih baeries, hey can ac as boh a load or a power source [2]. This feaure has been he focus of a number of research papers because he sream of services ha can be caered by EVs is highly aracive o several power sysem sakeholders. However, in order o have a noiceable effec on he sysem, a significan number of vehicles mus be aggregaed and operaed as an ensemble. In his sense, a BSS acs as a baery aggregaor and has, on is own, enough capaciy o paricipae in markes for elecrical energy and reserve. This work was suppored in par by he Naional Science Foundaion (NSF) under Gran No. 1239408. Alhough he BSS concep is no new, here are few works ha analyze he operaion and business model for hese eniies. In [3], he risks associaed o boh cusomers and BSS, upfron invesmen classificaion, and commodiies ha could be sold are briefly discussed. A BSS business model of a subscripionbased pricing srucure and infrasrucure coss are discussed in [4]. However, none of hese business models include he ineracions beween he cusomer, he BSS, and he wholesale elecriciy markes. In [5], an economic dispach model ha sabilizes and compensaes wind energy inermiency using a BSS is presened. However, his model is simplified, up o he degree where he benefis ha could be derived from BSSs are no included. In [6], a basic dynamic programming model is developed o deermine he number of baeries o be purchased by he BSS for operaion and he opimal baery charging schedule. However, he model does no consider he individual baery characerisics and no marke ineracion is considered. Some commercial businesses have developed BSSs o ake advanage of he marke opporuniies. One such company, Beer Place, insalled numerous saions handling cerain ypes of EVs [7]. Tesla Moors inroduced proprieary saions for heir lineup of EVs [8]. Though, in hese case i is assumed ha he BSS does no paricipae in elecriciy markes and hus, heir profis are solely based on service fees neglecing he sream of revenues ha can be colleced by operaing he BSS as a sorage saion. The BSS can maximize is profis by providing services o he sysem, such as volage suppor, regulaion reserves, or energy arbirage. Volage suppor and frequency regulaion operae a shor ime scales and are beyond he scope of his paper. This work presens he case where he BSS explois he difference in wholesale elecriciy marke prices a differen periods of ime [9]. To ake advanage of such differences, a wo-sage acion is required. Firs, i mus forecas he dayahead (DA) marke prices and he demand for baery charging. Second, i mus opimize is bids and offers in he DA energy marke. The demand for baeries hroughou he day may be esimaed based on hisorical daa. DA marke prices can be forecased using echniques similar o hose discussed in [10]. The opimal bidding and offering sraegy for BSS in he energy markes can be implemened using he echniques described in [11]. For he BSS o operae in an opimal manner, i needs o ake advanage of he low elecriciy prices o charge is baery sock in Grid-o-Baery (G2B) mode and sell energy when he price is high in Baery-o-Grid (B2G) mode. However, baeries should be discharged only if hey are no o be swapped in he near fuure. Similar modes of operaion,
bu from an EV perspecive, known as Grid-o-Vehicle (G2V) and Vehicle-o-Grid (V2G) are sudied in he recen lieraure, see for example [12] and [13]. Therefore, G2B and B2G are he counerpars of G2V and V2G bu for he baeries raher han he vehicles. The BSS business model presened in his paper models explicily he ineracions beween he cusomer and he BSS. This model also accouns for he benefis o he cusomer as well as he benefis o he power sysem. The opimizaion model operaes on a day-ahead basis and deermines he BSS s opimal charging schedules for he baery sock and is opimal bidding sraegy in he elecriciy markes. The BSS model considers he wholesale marke prices, EV characerisics, cusomer behavior, and relaed baery swapping fees. In addiion o he G2B and B2G operaing modes, Baeryo-Baery (B2B) mode is allowed o ake place wihin he BSS. B2B mode enables he BSS o ransfer energy beween baeries, hus minimizing elecriciy purchases during highprice periods. The remainder of his paper is organized as follows. Secion II describes he BSS business model. Secion III explains he BSS opimizaion model. Secion IV discusses he resuls. Finally, Secion V concludes he paper. II. BUSINESS MODEL A. Cusomer benefis Owning an EV will allow he cusomer o use elecriciy for moion raher han fossil fuels. However, poenial EV owners are concerned abou he long charging imes, inabiliy o insall chargers, limied range, and limied number of public charging saions. These concerns can be alleviaed bu require infrasrucure invesmens. For example, a he household level high-power chargers can minimize wai-ime for charging bu a a considerable moneary expense o he cusomer. These high-power chargers migh also no be allowed in renal housing or in places where he curren elecrical supply canno accommodae an increased power demand. Anoher major concern is he limied range of he average EV, i.e. he infamous range anxiey. In order o relieve his concern, cusomers require access o public charging saions ha provide a service equivalen o gasoline saions. The BSS could eliminae hese concerns. Typical EVs are equipped wih a sandard 1.6 kw Level I chargers ha connec direcly o household oules [14]. A maximum power (i.e. 1.6 kw), he wai-ime unil a 24 kwh baery is fully charged is approximaely 15 hours. A Level II charging insallaion (charging a 3.3 kw) reduces he charging ime o approximaely 7 hours, bu his would come a an exra cos o he cusomers (approximaely $2150 wih iemizaion of he coss given in [15]). Moreover, chargers are available only o cusomers ha reside in deached single-uni housing. Cusomers residing in aached muli-uni housing, e.g. aparmens, may have difficulies charging heir EV due o he inabiliy o insall chargers. These reasons provide a business opporuniy for BSSs, because he cusomers do no need o make an upfron invesmen in a high-power charger and will ge he expeced service in a shor-ime. B. Power sysem benefis From he power sysem s perspecive, he BSS could operae as a sorage faciliy and help avoid or defer invesmens in he disribuion nework. A BSS emulaes an energy sorage saion ha has he abiliy o reshape is demand so ha peaks are shaved raher han increased if he BSS injecs elecriciy back o he power sysem. This sorage capabiliy enables he BSS o perform arbirage in he elecriciy marke and hence increase is profi. Addiionally, as he EV peneraion increases, more cusomers will insall chargers wih large power requiremens. This rend may require upgrades in he disribuion nework. On he oher hand, if enough cusomers uilize baery swapping as an alernaive o residenial charging, less invesmen in he disribuion nework will be required. However, upgrades o he sysem may be required a he locaion of he BSS which should be refleced in he business model. Lasly, he energy sorage capabiliies of he BSS can provide services o a microgrid by supporing he ransmission sysem in cases of a coningency [16]. C. BSS operaions Figure 1 illusraes he main feaures of he operaion of a BSS. I shows ha he BSS communicaes bidirecionally wih he power sysem o paricipae in marke aciviies [17]. The BSS opimally schedules baeries o discharge energy o he grid (B2G), charge energy from he grid (G2B), or discharge/charge energy o and from oher baeries (B2B). These feaures will pose he BSS as an ideal candidae o paricipae in elecriciy markes by submiing bids/offers and hus exploiing he ime-dependency of wholesale elecriciy prices, while saisfying he energy needs of is baery sock. The BSS also incorporaes several replacemen plaforms for differen groups of baeries. Fig. 1. BSS ineracions wih cusomers, marke, and power sysem. The BSS is assumed o own baeries ha i leases o he EV owners [3]. Baery degradaion due o charging/discharging, mainenance, and labor coss are hus incurred by he BSS. In reurn for he swapping service, cusomers pay a fixed service fee. From he cusomers perspecive, hey would no incur he baery replacemens coss which range from $12,000 o $14,400 (500-600 $/kwh) for a 24 kwh baery as of 2012 [18] and are hus he mos expensive componen of EVs. A lease-based approach would allow cusomers o purchase an EV wihou facoring in he cos of baery replacemens. The only cos o cusomers, in erms of he EV baery is he cos of household elecriciy, in case of residenial charging or he service fee for baery replacemens when hey use he BSS services. III.OPTIMIZATION MODEL The following nomenclaure is uilized for clariy. The se of ime-periods is denoed by T wih index. Baeries are par of he se I wih index i. The se of baery group is denoed G wih index g.
A. Model assumpions The BSS model relies on several assumpions. Firs, i relies on he DA elecriciy marke o derive he opimal offering/bidding schedule. Second, he BSS forecass he number of baery replacemens and he DA wholesale marke prices for each period of he following day. Addiionally, i is designed o manage muliple groups of baeries. Cusomers expec a 100% charged baery, and if he BSS canno mee his requiremen, he cusomers receive a discoun as compensaion. B. Model formulaion A he DA sage, he BSS derives opimal charging/discharging schedules for baeries, idenifies he baeries ha should be replaced o mach he baery demand, N g,, in each hour, and deermines he amouns of elecriciy ha should be purchased or sold in he DA marke. The model is formulaed as follows: Maximize BSR ( T ) (i I) ( T ) λ DA x i, V olc ( em buy em sell ( T ) (g G) ) BSR ba shor g, ( T ) (i I) subjec o: ( ) soc i, = soc i, 1 + ba chg i, ηchg ba dsg i, (1 x i, ) β i, (1) + SoCi, ini x i, i I, T (2) soc i, 1 + soc shor i, BC g S i,g x i, i I, g G, T (3) (i I) em buy S i,g x i, + ba shor g, = N g, g G, T (4) em sell = (i I) ( ) ba chg i, badsg i, T (5) 0 ba chg i, (1 x i,) Pi max i I, T (6) 0 ba dsg i, (1 x i,) Pi max i I, T (7) 0 soc i, BC g S i,g i I, T (8) (g G) ba dsg i, P i max a i, i I, T (9) ba chg i, P i max (1 a i, ) i I, T (10) em sell Mb i, i I, T (11) em buy M (1 b i, ) i I, T (12) Equaion (1) shows ha he objecive is o maximize he BSS profis. The firs erm in (1) is he revenue colleced from service fees priced a he Baery Swap Revenue, BSR ($/baery). The second erm accouns for he inabiliy o supply baery demand, ba shor g,, and is priced a he Value-of- Los-Cusomer, VoLC ($). This value should be derived from surveys o deermine wha value cusomers place on a charged baery. The hird erm is he cos of purchasing em buy (kwh) elecriciy or profi of selling em sell (kwh) elecriciy in he DA marke wih wholesale forecased prices, λ DA ($/kwh). The las erm in (1) is he discouns given o cusomers and is discussed in subsecion III.C. This opimizaion problem is subjec o consrains (2)-(12). The binary variable, x i,, is equal o 1 if baery i is replaced a ime period, and 0 oherwise. Consrains (2) monior he energy sae of charge (esoc), soc i, (kwh), of each baery a every ime period, accouning for charging power, ba chg i, (kw), and discharging power, ba dsg i, (kw). Baery charging efficiency, η chg, is accouned for in (2). If x i, is equal o 1, equaions (2) does no updae esoc a his period. Insead, he esoc of baery i is se o he iniial esoc, soc ini i, (kwh), of he cusomer baery ha has jus been swapped. If a baery is being swapped, he esoc mus be a he nominal baery capaciy, BC g (kwh). Oherwise, a shorage, soc shor i, (kwh), is capured in equaions (3). Each baery belongs o a group, classified by is capaciy (kwh), and denoed by binary parameer, S i,g. The overall cusomer baery demand should be me for each group of baeries as in (4). The unme demand is capured in variable ba shor g,. To mee he demand, BSS submis offers/bids for elecriciy o he marke, which is enforced by equaions (5). Addiional consrains are needed o ensure baeries are operaed wihin he esablished limis. Baery charge/discharge power is limied o Pi max (kw) in (6)-(7), and he esoc is limied o BC g by consrain (8). Finally, consrains (9)-(10) ensure ha charging/discharging of baeries do no occur simulaneously, and consrains (11)- (12) ensure ha purchasing/selling in he marke do no occur simulaneously. In (2) and (4), he produc of binary variable x i, and real variables are presen. These non-linear consrain are replaced by linear equivalens as explained in [19]. Fig. 2. Piecewise linear discoun funcion. C. Discouns The las erm in he objecive funcion, (1), represens he discouns given o cusomers for acceping less han 100% charged baeries. The BSS has a radeoff of swapping baeries a less han nominal charge, e.g. 80% esoc, a a discouned price versus no selling he baery and hus, incurring he VoLC. The discoun given o cusomers progressively increases as he baery esoc shorage increases following a piecewise linear curve shown in Fig. 2. The piecewise curve is modeled using consrains (13)-(16), where D is he se of discoun blocks wih index d. In (13), he esoc shorage is limied o he baery capaciy. Equaions (14) forces he sum of esoc shorage block variable, L d, o be equal o he normalized esoc shorage of a specific baery. In (15), β i, is he discoun percenage for each baery ha could no be replaced a 100% esoc. This percenage is calculaed wih muliplicaion of he discoun slope parameer, k d, and he respecive esoc shorage block as shown in (15). Lasly, equaions (16) limis he esoc shorage block o he parameer L max d. The BSS can prese parameers k d and L max d dependen upon is business model.
0 soc shor i, S i,g BC g i I, T (13) (g G) soc shor i, (g G) S = L d i I, T (14) i,gbc g (d D) β i, = k d L d i I, T (15) (d D) L d L max d d D (16) IV. RESULTS The proposed model is applied o a small and a large case sudy. The small case sudy illusraes he feaures of he proposed BSS model, while he large case simulaes a largescale BSS sysem. From he marke perspecive, he BSS is a price-aker. Parameers for boh case sudies are as follows. The BSR is assumed o be $70 as used by [8], while he VoLC is se o $200. The discoun curve (Fig. 2) is designed wih four piecewise approximaions: 1) k 1 = 1.1 and L max 1 = 10%, 2) k 2 = 3.0 and L max 2 = 30%, 3) k 3 = 5.0 and L max 3 = 50%, and 4) k 4 = 10 and L max 4 = 100%. The charge/discharge maximum power of baeries is 3.3 kw. The model was implemened in GAMS 24.0 [20] and solved using CPLEX 12.1 [21]. A. Small case sudy In his sudy, for illusraion purposes, he EV baeries have nominal esoc of 12 kwh wih a single baery group, zero kwh of iniial esoc, and efficiencies of 100%. As for he BSS, i is equipped wih a sock of wo baeries. For he sock of baeries, he demand in hours 5 and 11 are one baery and hour 19 of wo baeries. Fig. 3 displays he resuls of he sudy. Fig. 3a shows DA marke purchasing/selling acions agains he forecased marke prices. Figs. 3b and 3c show he esoc of baery 1 and 2 and heir corresponding charging/discharging profiles where posiive power indicaes charging and negaive power indicaes discharging. The demand profile shown in Fig. 3d is iemized by which baery performs he swapping. This figure shows ha he BSS purchases elecriciy during low-cos periods o charge baeries (G2B) and sells energy during high-cos periods by discharging baeries (B2G). Afer a baery from he BSS is replaced wih a cusomer s baery, he received baery can sar charging or discharging afer idenifying is iniial esoc, as shown in Fig. 3c and 3d. Since baery 2 is no scheduled for swapping again unil he hour 19, i discharges in hours 12-14 from pre-charged energy in G2B mode performed in prior hours. Specifically, in hours 12 and 14, baery 2 performs in B2B o supply baery 1 due o he high cos of elecriciy in he marke. This mode occurs since boh baeries are required o be replaced a hour 19 requiring full esoc. Alogeher, 55.8 kwh is purchased in he marke in G2B mode, 7.8 kwh is sold in he marke in B2G mode, and 5.4 kwh is ransferred from baery o baery in B2B mode. The required elecriciy for supplying he baery demand is 48 kwh. Therefore, excess G2B charging akes place because here is a perceived benefi in erms of energy arbirage in fuure high-cos periods. B2B mode allows for furher profi maximizaion since he energy is ransferred beween baeries prevening he BSS of having o buy elecriciy during periods in which he elecriciy price is high. This case depics no discouns or VoLC since baery demand is me. The revenue colleced from BSR fees is $280, and wihin ha -$2.20 is elecriciy purchase loss in G2B mode, and $0.374 is elecriciy selling profi in B2G mode. The overall profi aained by he BSS is $278.17. Fig. 3. (a) DA marke purchasing/selling acions, (b) baery 1 esoc and charge/discharge profiles, (c) baery 2 esoc and charge/discharge profiles, and (d) baery demand profile iemized by each baery s replacemen saus. B. Large case sudy The large case sudy assumes a baery sock of 550 baeries for he BSS, of which 150 are 16 kwh and 400 are 24 kwh capaciy baeries. The EV and he BSS parameers are he same as in he small case sudy excep he baery charging and discharging efficiencies are 90%, and he iniial esoc for all baeries uniformly randomized beween 10% and 50% of he nominal baery esoc. The vehicular ravel daa is aken from [22], and i is used o derive a disribuion funcion of he cusomer arrival imes for replacemen as shown in Fig. 4a. Furhermore, wih he disribuion funcion, baery demand profiles were creaed for wo groups of baeries, 16 and 24 kwh, as shown in Fig. 4b. Typical marke prices were obained by averaging DA LMP prices for every Thursday from he period January-March 2013 in he PJM marke [23], as shown in Fig. 5a. Thursday was chosen in order o show he effecs on a ypical weekday. The model derives marke offers, during high-cos periods, and bids, during low-cos periods, as illusraed in Fig. 5b. Fig. 6 displays he power ransfer in differen modes of operaion. In Fig. 6a, he baeries discharge in B2G mode during highcos periods, whereas hey charge in low-cos periods in G2B mode. The B2G mode is enabled since he baeries charge in excess o ransporaion energy requiremens. The BSS uses B2B mode as well, as shown in Fig. 6b. In B2B, sand-by baeries discharge and supply baeries due for swapping. In paricular, in hours 7-11 and 18-22, baeries perform B2B for
wo reasons. Firs, he marke prices are high which resuls in reduced elecriciy purchases, as shown in Fig. 5b. Secondly, he demand (Fig. 4b) is high in hese periods. If B2B was no an opion, he elecriciy would have been purchased in he DA marke. more crucial for he BSS as compared o radiional gasoline saions. Wih he opimal schedule, he BSS needs o ensure i generaes sufficien profis o mainain is business. In Fig. 7a, he profis are shown periodically and cumulaively. The cumulaive profi is $44,033 wih revenue of $48,510. The oal losses accrued are $4,477. The iemizaion of he losses is shown in Fig. 7b. When baeries perform B2G, he BSS is selling elecriciy and hence, obains a cumulaive profi in he marke of $107.37. Though, when performing G2B, he BSS profi is reduced by $632.08 due o purchased elecriciy. Fig. 4. (a) Disribuion funcion of cusomer arrival a BSS. (b) Demand profiles for wo groups of baeries. Fig. 7. BSS. (a) Cumulaive and periodical profi, and (b) iemized coss for he Fig. 5. Fig. 6. (a) Marke prices for PJM [23]. (b) DA marke offers and bids. (a) G2B and B2G, and (b) B2B acions scheduled by he BSS. Unlike radiional gasoline saions, which receive weekly (or even daily) gasoline refills, occurring in a maer of hours or less, he BSS is limied by he baeries maximum charging/discharging power raing. The opimal schedule is Mos of he economic losses of he BSS are due o discouns for no meeing he nominal esoc of swapped baeries. Due o high VoLC value, he model favors discouns over losing cusomers. Ideally, afer replacemen of a large number of baeries in a high-demand hour, he BSS should have enough capaciy in baeries o manage he subsequen high-demand hours. However, afer replacemen, he iniial esoc of baeries are low and require several hours of charging o be available for anoher replacemen. This enails discouns o be given o cusomers which are visualized in Fig. 7b, indicaing large discouns being given a high-demand hours. The cos due o discouns for he BSS is $3,952.50. Furhermore, he VoLC loss is no amassed in his siuaion since i is perceived as he wors-case siuaion of no providing a baery o cusomers. From a cusomers perspecive, a decision needs o be made, as o ake he baery replacemen wih he discoun and lower esoc or uilizing residenial charging. From he BSS perspecive, i can inves in more baeries o minimize discouns or coninue using a firs-come firs-serve business model. As he cos of baeries decrease, he former approach for he BSS will be beneficial. Noneheless, i is crucial for he BSS o decide which group of baeries o inves in. This can be idenified by visualizing he frequency of discouns given per baery group as displayed in Fig. 8. Group 2 (24 kwh) has higher frequency of discouns as compared o Group 1 (16 kwh). This is caused by he larger demand (Fig. 4b) of Group 2 baeries. As for he value of discouns iemized by baery group, Group 2 (24 kwh) incurs cos of $2,735.40, whereas Group 1 (16 kwh) incurs cos of $1,217.08. Therefore, invesing in Group 2 baeries will allow for reducion in discouns accrued by he BSS.
Addiional benefi of invesing in Group 2 baeries is for B2G and B2B mode since larger sorage capaciy is available. Fig. 8. Frequency of discouns iemized by group of baeries. V. CONCLUSION This paper presens a business case and an opimizaion model for a baery swapping saion. The BSS can alleviae cusomer concerns relaed o long charging imes and range anxiey. No only does he BSS benefi cusomers financially bu also benefis he power sysem by paricipaing in elecriciy markes and by avoiding or deferring expensive infrasrucure upgrades. To be profiable, he BSS needs o ensure ha he fees i charges, he risk i akes of no saisfying is cusomers, and he discouns i offers are properly designed. Resuls show ha he uilizaion of marke prices allows baeries o pre-charge during low price periods (G2B), parially discharge during high price periods (B2G), and ransfer elecriciy beween baeries when purchasing energy from he elecriciy marke should be avoided (B2B). REFERENCES [1] Technology Roadmap: Elecric and Plug-in Hybrid Elecric Vehicles, Inernaional Energy Agency, Tech. Rep., 2011. [2] J. A. P. Lopes, F. J. Soares, and P. M. R. Almeida, Inegraion of elecric vehicles in he elecric power sysem, Proceedings of he IEEE, vol. 99, pp. 168-183, 2011. [3] Basic Business Conceps: Elecric Vehicle, G4V: Grid for Vehicles, Tech. Rep., 2011. [4] J. Lidicker, T. Lipman, and B. Williams, Business model for subscripion service for elecric vehicles including baery swapping for San Francisco bay area, California, Transporaion Research Record: Journal of he Transporaion Research Board, vol. 2252, no. -1, pp. 8390, 2011. [5] G. Ya-jing, Z. Kai-xuan, and W. Chen, Economic dispach conaining wind power and elecric vehicle baery swap saion, in Proceedings of Transmission and Disribuion Conference and Exposiion (T&D), 2012 IEEE PES, 2012, pp. 17. [6] O. Worley and D. Klabjan, Opimizaion of baery charging an purchasing a elecric vehicle baery swap saions, in Proceedings of Vehicle Power and Propulsion Conference (VPPC), 2011 IEEE, 2011, pp. 14. [7] Beer Place: Baery Swapping Saions (BSS). [Online]. Available: www.beerplace.com. [8] Tesla Moors: Baery Swap. [Online]. Available: www.eslamoors.com/baeryswap. [9] S. Borensein, The long-run efficiency of real-ime elecriciy pricing, The Energy Journal, vol. 26, no. 3, pp. 93116, 2005. [10] F. J. Nogales, J. Conreras, A. J. Conejo, and R. Espinola, Forecasing nex-day elecriciy prices by ime series models, IEEE Transacions on Power Sysems, vol. 17, no. 2, pp. 342348, 2002. [11] H. Pandzic, J. M. Morales, A. J. Conejo, and I. Kuzle, Offering model for a virual power plan based on sochasic programming, Applied Energy, vol. 105, no. 0, pp. 282292, 2013. [12] M. A. Orega-Vazquez, F. Bouffard, and V. Silva, Elecric vehicle aggregaor/sysem operaor coordinaion for charging scheduling and services procuremen, IEEE Transacions on Power Sysems, vol. 28, no. 2, pp. 18061815, 2013. [13] H. Sekyung, H. Soohee, and K. Sezaki, Developmen of an opimal vehicle-o-grid aggregaor for frequency regulaion, IEEE Transacions on Smar Grid, vol. 1, no. 1, pp. 6572, 2010. [14] Elecric-Drive Vehicle Basics, Deparmen of Energy, Tech. Rep., 2011. [15] K. Morrowa, D. Karnerb, and J. Francfor, Plug-in hybrid elecric vehicle charging infrasrucure review, U.S. Dep. Energy Veh. Technol. Program, Tech. Rep. Final Rep., 58517, Nov. 2008. [16] R. H. Lasseer, Smar disribuion: coupled microgrids, Proceedings of he IEEE, vol. 99, no. 6, pp. 10741082, 2011. [17] A. Vojdani, Smar inegraion, IEEE Power and Energy Magazine, vol. 6, no. 6, pp. 7179, 2008. [18] Baery echnology charges ahead. [Online]. Available: www.mckinsey.com/insighs/energy resources maerials/baery echnology charges ahead. [19] C. Gure, C. Prins, and M. Sevaux, Applicaions of opimizaion wih Xpress-MP. Dash Opimizaion Ld., 2000. [20] GAMS - A User s Guide. [Online]. Available: www.gams.com/dd/docs/bigdocs/gamsusersguide.pdf. [21] CPLEX 12 - Gams. [Online]. Available: www.gams.com/dd/docs/solvers/cplex.pdf. [22] Naional Household Travel Survey (NHTS) daa. [Online]. Available: nhs.ornl.gov. [23] Day-ahead LMP prices. [Online]. Available: www.pjm.com/markesand-operaions/energy/day-ahead/lmpda.aspx.