A multi-layer market for vehicle-to-grid energy trading in the smart grid

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1 A mult-layer market for vehcle-to-grd eergy tradg the smart grd Albert Y.S. Lam, Logbo Huag, Aloso Slva, Wald Saad To cte ths verso: Albert Y.S. Lam, Logbo Huag, Aloso Slva, Wald Saad. A mult-layer market for vehcleto-grd eergy tradg the smart grd. IEEE INFOCOM Workshop o Gree Networkg ad Smart Grds (CCSES), Mar, Orlado, Florda, Uted States. pp.85-9,, <.9/INFCOMW >. <hal-7657> HAL Id: hal Submtted o Oct HAL s a mult-dscplary ope access archve for the depost ad dssemato of scetfc research documets, whether they are publshed or ot. The documets may come from teachg ad research sttutos Frace or abroad, or from publc or prvate research ceters. L archve ouverte plurdscplare HAL, est destée au dépôt et à la dffuso de documets scetfques de veau recherche, publés ou o, émaat des établssemets d esegemet et de recherche fraças ou étragers, des laboratores publcs ou prvés. Copyrght

2 A Mult-Layer Market for Vehcle-to-Grd Eergy Tradg the Smart Grd Albert Y.S. Lam, Logbo Huag, Aloso Slva Uversty of Calfora, Berkeley Emal: Wald Saad Uversty of Mam Abstract I ths work, we propose a mult-layer market for vehcle-to-grd eergy tradg. I the macro layer, we cosder a double aucto mechasm, uder whch the utlty compay act as a auctoeer ad eergy buyers ad sellers teract. Ths double aucto mechasm s strategy-proof ad coverges asymptotcally. I the mcro layer, the aggregators, whch are the sellers the macro layer, are pad wth commssos to sell the eergy of plug hybrd electrc vehcles (PHEVs) ad to maxmze ther utltes. We aalyze the teracto betwee the macro ad mcro layers ad study some smplfed cases. Depedg o the elastcty of supply ad demad, the utlty s aalyzed uder dfferet scearos. Smulato results show that our approach ca sgfcatly crease the utlty of PHEVs. I. INTRODUCTION The rsg ol prces combed wth the ogog tred for developg evrometal-fredly techologcal solutos, mples that electrcally-operated vehcles wll le at the heart of future trasportato systems. I partcular, t s evsoed that plug- hybrd electrc vehcles (PHEVs), whch are essetally electrc vehcles equpped wth storage devces, wll costtute oe key compoet towards realzg the vso of gree, evrometfredly trasportato etworks. For stace, t s forecast that up to.7 mllo electrc vehcles wll be put o the road the Uted States, by []. The presece of eergy storage devces mples that PHEVs ca ot oly serve as a gree meas of trasportato, but also, f properly cofgured, they ca fucto as a movg eergy reservor that ca store ad, possbly, supply power back to the power grd. Whle curret PHEV deploymet are mostly cocered wth grd-to-vehcle teractos, eablg two-way vehcle-to-grd (VG) teractos betwee the grd ad PHEVs, has recetly started to receve cosderable atteto both research ad stadardzato ageces [], [3], [], [5], [6] ad s expected to le at the heart of the emergg smart grd system. Eablg VG teractos has several advatages such as servg as backup power sources durg outages or supplyg acllary servces back to the grd for regulato servces. However, order to fully reap the beefts of VG systems, several key challeges must be addressed at dfferet level such as cotrol, commucatos, chargg behavor, mplemetato, ad market mechasms. I [7], the authors propose a scheme that uses PHEV batteres to absorb the radomess termttet wd power geerato. The authors [8] study the use of game theory for provdg frequecy regulato through VG operato. Usg the PHEVs as storage uts s studed ad aalyzed [9] whle commucato archtectures sutable for VG systems are dscussed []. Further, the authors [] cosders the problem of optmally provdg eergy ad acllary servces usg electrc vehcles. Clearly, most exstg work are focused o mplemetato, commucato, ad eergy trasfer VG systems. However, the eed for eergy trasfer ad exchage from PHEVs to the grd has also a ecoomcal aspect that must be addressed. I ths respect, the work [] sheds a lght o ths aspect by vestgatg the prce ad quattes exchaged f the PHEVs ad the grd elemets form a eergy trade market. Beyod [], lttle work seems to have bee focused o the ecoomcs of VG exchages whch are essetal for a better uderstadg o the potetal of usg VG future power grd systems. The ma cotrbuto of ths paper s to propose a geeral framework ad algorthm for studyg the ecoomcs of the market emergg betwee PHEVs, aggregators, ad the smart grd elemets. To address ths problem, we propose a mult-layered market mechasms whch the agreggators, the PHEVs, ad the grd elemets ca decde o the quatty ad prces at whch they wsh to trade eergy whle optmzg the tradeoff betwee the beefts (e.g., reveues) ad costs from ths eergy exchage. I ths proposed market, frst, the aggregators ad the smart grd elemets (e.g., substatos) submt ther reservato prces ad bds so as to agree o a prce ad eergy tradg mechasm. These teractos are modeled usg a double aucto whose result s the fed back to the secod layer, whch deals wth the maagemet of PHEV resources at each aggregator. I ths layer, wth each PHEV group, the aggregator egotates wth the PHEVs to settle for a agreemet o the resource usage. I partcular, the aggregator wll aouce ts eergy buyg prce to the PHEVs, ad each PHEV determes how much eergy t s wllg to supply to the aggregator. The outcome of ths layer s drectly lked to the prevous market due to the fact that the aggregator has to carefully balace ts eargs from the eergy market ad ts paymets to the PHEVs wth ts group. Hece, ulke exstg work such as [], the proposed scheme depeds, ot oly o prcg ssues, but also o modelg the PHEVs-to-aggregator teractos (from a ecoomcal perspectve) as well as o provdg cetves for the PHEVs to partcpate the foresee market ad, hece, t ca leverage VG, for mprovg the overall smart grd performace. We characterze the equlbra resultg from the proposed multlayered market ad we show ther exstece. Further, usg lear

3 (X k,b k ) (A,S ) p Buyer k Auctoeer 5 8 Aggregator 6 7 PHEV (P,Q ) a Macro layer Mcro layer Fg.. The two-layer market model. The umbers the fgure correspod to the step umbers Algorthm. approxmato techques we provde a large-system aalyss o the ecoomcs of VG eergy tradg. Usg smulatos, we assess the propertes ad performace of the eergy tradg mechasms resultg from proposed scheme ad we show that our approach ca sgfcatly crease the utlty of PHEVs. The paper s orgazed as follows: I Secto II, we preset the proposed system model. I Secto III, we aalyze the system for dfferet PHEV eergy supply costs. Smulato results are dscussed ad aalyzed Secto IV whle coclusos are draw Secto V. II. THE MODEL AND THE MARKET MECHANISM Cosder a smart grd system cosstg of K grd elemets (e.g., substatos) wth K = {,..., K} deotg the set of all such elemets. I ths grd, N electrc vehcles aggregators are deployed. We let N = {,...,N} deote the set of all aggregators. Each aggregator N maages a group of PHEVs deoted by I = {,...,I }. I ths model, we are partcularly terested smart grd elemets that are uable to meet ther demad ad, hece, eed to buy eergy from alteratve sources such as the PHEV aggregators. Hece, hereafter, all grd elemets are referred to as buyers whle the aggregators are referred to as sellers. The eergy exchage process betwee the aggregators ad the grd elemets s modeled usg a two-layered market model as show Fg. wth the utlty compay s cotrol ceter actg as a mddlema that hadles the prospectve eergy tradg mechasms. O the oe had, at the frst layer, referred to as the macro layer, the aggregators ad the grd elemets teract so as to trade eergy. At ths layer, the buyers wsh to optmze ther performace ad meet ther demad by buyg eergy from the PHEVs through the aggregators whle the aggregators wsh to strategcally choose ther prce ad quatty to trade so as to optmze ther reveues. O the other had, at the secod layer, referred to as the mcro layer, the aggregators must teract wth the PHEVs so as to optmze the eergy resources ad provde cetves for the PHEVs to actually partcpate the trade. Clearly, the outcomes of these two layers are coupled ad, thus, ay market soluto must take to accout ths terlayer depedece. Below, we dscuss ad aalyze, detals, the market operato at each layer. A. Macro Layer A aucto s a mechasm for buyg or sellg goods or servces by takg bds ad the sellg them to the hghest bdders. The ma approach to study ths mechasm s game theory by cosderg the bdders as the players of ths game, ad ther bds as ther strateges. For more detals o aucto theory see [3]. For the completeess of ths work, here we gve a overvew of the double aucto mechasm [], [5], []. I ths layer, each potetal seller or aggregator N seds the quatty of eergy A that t teds to supply ad ts reservato prce S to the auctoeer. The reservato prce set by the potetal sellers correspods to the mmum prce at whch the seller s wllg to sell ts offered amout of eergy. Each buyer k K proposes a bd B k ad the quatty t requests, deoted byx k, to the auctoeer. Here, we are maly focused o the teractos betwee buyers ad sellers a certa wdow of tme durg whch the bds ad reservato prces do ot vary. Ths ca correspod to a eergy tradg market whch decsos are based o medum or log-term eergy eeds such as a day-ahead market. I each roud, each aggregator decdes ts ow A wth the fxed S. After recevg all A s, the auctoeer determes the prce P(A) of the eergy, where A = (A, N), ad Q (A), whch correspods to the total quatty sold by aggregator, N, by a double aucto. I ths work, we adopt a double aucto mechasm based o [], [], [6], [5]. I ths aucto: we order the sellers a creasg order of ther reservato prce. W.l.o.g. we cosder S < S <... < S N. () we order the buyers a decreasg order of ther reservato bds. W.l.o.g. we cosder B > B >... > B K. () f two sellers (respectvely, buyers) have equal reservato prces (bds), they are aggregated to oe sgle vrtual seller (or buyer). we geerate the supply curve (sellg reservato prce S versus the amout of eergy put out for sale A ) we geerate the demad curve (offered bds B k versus quatty eeded X k ). we fd a tersecto pot. Ths tersecto s at the level of a certa seller L ad buyer M, such that B M S L ad B M+ < S L+. We fd seller L ad buyer M ad the double aucto dctates that the frstl adm buyers wll partcpate the eergy tradg. We do t cosder seller L ad buyer M ths trade sce t s a ecessary codto for matchg the total supply ad demad whle matag a strategy-proof mechasm [5]. Thus all sellers wth dex < L ad all buyers wth dex k < M become the partcpats the double aucto so as to clear the market. I cosequece, the tradg prces for the sellers ad the buyers ca be chose wth ay pot the rage [S L,B M ] [6]. I ths work, for ay strategy choce A (or

4 A, N ) by the sellers (.e. aggregators), gve seller L ad buyer M at the tersecto, we cosder all sellers < L ad buyers k < M trade at a prce P(A), gve by P(A) = S L(A)+B M (A), (3) where the depedece o A s due to the fact that each A ca gve dfferet teracto pots wth the demad ad supply curves, ad thus we ca have dfferet L ad M. At the ed of the aucto, umerous crtera ca be used for determg the amout of traded eergy betwee each oe of the L sellers ad M buyers. We adopt the approach of [5] whch the volume s dvded such a way as to esure a strategy-proof aucto. Usg the method [5] the total quatty Q (A) sold by ay PHEV group, for a gve choce A s: A f M k= X k j= A j, Q (A) = (A Ψ) + f = L, () f > L, where (x) + = max{,x} ad Ψ s the oversupply,.e., Ψ = L j= A j M k= X k. B. Mcro Layer I ths layer, each aggregator aouces a prce p to ts PHEVs by p = γ P(A), N, (5) where < γ < s the commsso rate. The prce dfferece, P(A) p, s the commsso (.e., cost of maagemet) eared by aggregator from ts maaged PHEVs. Each aggregator ca make a proft ths way ad thus t has a cetve to help ts PHEVS partcpate the market. Ths provdes a cetve for a aggregator to maxmze ts PHEVs profts. By utlty maxmzato, each PHEV I determes ts avalable supply a [, ] accordg to ts utlty where characterzes the amout of eergy the ower of PHEV ca afford to sell,.e., after reservg eough for ts ow use. For the same type of vehcle, a PHEV whch eeds more reservato for ts proper operato has a lower. We have A = I = a, N. (6) Let a = (a, I ) be the strategy of the PHEVs group. Aggregator determes the actual quatty q (a,q (A)) allocated to PHEV group proportoal to a by ad thus a q (a,q (A)) = Q (A), (7) I a Q (A) = I = q (a,q (A)), N. (8) Cosder that each PHEV I mposes a cost of dschargg ts battery to supply eergy to ts aggregator. We deote ths cost by c (a), where a s the amout of eergy sold by PHEV. We assume that durg each trasacto, each PHEV wll try to maxmze ts proft by choosg the amout of eergy a to be a = argmax a {p (a ) c (a )}. C. Market Mechasm The teracto betwee the macro ad mcro layers ca be see as a market mechasm or a algorthm, show Algorthm, whch s used to fd the market equlbrum P,A. It termates whe a pre-determed umber of teratos t max has bee reached or the percetage chage of the market prce s less tha a certa threshold ξ. Algorthm Market Mechasm : For all k, buyer k submts ts bd B k ad ts requested amout X k to the auctoeer : t 3: repeat : For all, aggregator submts ts reservato prce S ad ts proposed supply A to the auctoeer 5: The auctoeer mplemets a double aucto ad determes the market prce P(t) ad the allocated quatty Q for aggregator for all 6: For each aggregator, the sellg prce p s aouced to ts PHEVs 7: For each PHEV, t determes ts proposed sellg amout a by maxmzg ts utlty accordg to p ad returs a back to ts aggregator 8: Each aggregator sums up all a s from ts PHEVs 9: t t+ : utl t > t max or P(t) P (t ) < ξ P (t) As we ca see smulato later, Algorthm performs very effcetly ad coverges wth a few steps. III. LINEAR APPROXIMATION FOR LARGE SYSTEMS I a practcal smart grd, both the umber of PHEVs ad smart grd elemet are expected to be large. I ths respect, t s of terest to aalyze the mpact of the presece of large umbers of buyers ad aggregators o the overall proposed market mechasm. Therefore, here, we cosder the stuatos whe N ad M are suffcetly large such that the correspodg supply ad demad curves ca be approxmated by a lear fucto, depedg o the dstrbuto of aggregators reservato prce (buyers bds). We assume that the reservato prces S from each oe ca be ordered cely to a le wth each pot beg oe ut apart. Fg. shows oe example of the supply ad demad curves, each of whch s approxmated by oe sgle lear fucto. I the followg, sce the focus of ths paper s o the supply sde, we study dfferet types of supply curves whle always keepg the demad curve of the same type. A. Lear Cost Fucto wth Homogeeous PHEVs I ths subsecto, we cosder that the cost fucto of PHEV s a lear fucto wth respect to the amout of eergy t provdes,.e., c (a) = η a, wth a certa terval [, ]. If the amout of eergy to be sold exceeds, the cost wll become fte. Note that ths case also takes to accout the coveece cost (e.g., whe the PHEV does ot have eough eergy to operate ormally). The ts utlty fucto s gve by

5 p demad q (a) Real stuato Fg.. supply p q d = q βp Supply ad demad curves (b) Lear approxmato q q s = αp u (a) = (γ P η )a. The problem PHEV eeds to address s the followg: u = maxmzeu (a ). (9) a [, ] We ote that, a PHEV ca always decde ot to partcpate the market whch case t maxmum utlty wll be u =. As a result, the maxmum utlty (9) s always oegatve. I ths case, the soluto { a of (9) s a a max = f η p, () else. We ca the subdvde the set of PHEVs I two dsjot sets I () ad I (), such that I () I () = I, where a =, I(), ad a = amax, I (). Thus, we obta A = a = a + a. () I I () I () Sce for all I (), a =, the a I () =, ad cosequece A = a =. () I () I () ) Lear Approxmato: Cosder the lear case as Fg. (b). The PHEVs are prce takers ad the supply ad demad curves are gve by Supply(P, Q) = αp, (3) Demad(P,Q) = Q βp. () Here Q s the total demad from all the buyers ad P s the prce determed from the double aucto the macro layer. Also, α wll deped o I () for all aggregator. I that case, the equlbrum prce P ad the quatty sold Q ca be determed whe the supply meets the demad,.e., Supply(P,Q ) = Demad(P,Q ) αp = Q βp, or equvaletly, whe P = Q α+β. (5) The utlty for each PHEV group wll be thus gve by ) If η γq (α+β) the a = ad u =. ) If η < γq (α+β) the a = amax ad ( ) u = (γ P η )a γ Q = (α+β) η. (6) The total utlty U of aggregator s gve by U = ( ) γ Q (α+β) η I (). (7) From ths smple example, we ca deduce the followg propertes: ) If the supply slope of a market s hgher tha that of a market,.e., α > α, the the utlty gaed market s smaller tha that market. ) If the demad slope of a market s hgher tha that of a market,.e., β > β, the the utlty gaed market s smaller tha that market. 3) If the total possble demad of a market s hgher tha that of a market,.e., Q > Q, the the utlty gaed market s greater tha that market. B. Quadratc Cost Fucto We frst recall that uder the quadratc cost model, each PHEV wll supply the followg amout of eergy: [ ] a max a p (a ) η =. (8) υ I order to make the aalyss easer, below we assume that a for all. The, we have: where a = p (a ) η υ, ad A = C p (a ) d, (9) C = υ ad d = η υ. () I ths case, A s the supply from oe aggregator ad A s the slope of the supply curve,.e., α = A. Thus, we have by (5) that: P = Q A +β. () Hece, we see that there s a terato process of the market prce, whch approxmates the actual prce terato: I terato t, wth A (t) computed, we obta the optmal prce P (t) = Q A (t)+β. I terato t+, we compute the ew supply quatty by (9),.e., A (t+) = C γ P (t) d. Based o the above observato, we have the followg smple lemma characterzg the ecessary codtos uder whch there exsts market equlbrums,.e., (9) ad () both hold. Lemma : The followg codtos are ecessary for the above terato process coverges to a market equlbrum (P,A ): (β +d ) (d β C Q ), N () (β d ) +C Q, N. (3) Proof: I equlbrum, ths prce must result a supply that s exactly equal to the resultg A,.e., A = C Q γ A +β d. () Ths gves rse to the followg codto o A : A +(β +d )A +βd C γ Q =. (5)

6 Note that the above argumet also shows a terestg fact that there s a mplct terato for the market prce P as follows: P Q = C γ P d +β. (6) Ths smlarly mples that the fxed pot should be: C γ P +(β d )P Q =. (7) Sce both (5) ad (7) are quadratc fuctos, we see that the oly way there exsts a market equlbrum s whe () ad (3) hold. I the ext secto, we wll show how the algorthm evolves through smulato ad demostrate the tuto behd the terato process. IV. SIMULATION RESULTS For smulatos, we cosder a smart grd etwork whch a umber of aggregators sell ther eergy surplus to smart grd elemets (buyers) through a utlty compay. The smulato settg s as follows. Each aggregator maages a certa umber of PHEVs, radomly geerated the rage of [5, ]. Each PHEV has mum battery capacty of 5 mles wth power cosumpto kwh per mles [7], [8] out of whch a arbtrary amout of eergy, betwee 3 ad mles, s reserved for the PHEV s prvate use. The reservato prces of the aggregators are uformly selected [,5] dollars/mwh whle the buyers bds are radomly chose from[5,6] dollars/mwh. Each buyer requests eergy demad wth the amout chose [,6] MWh. The commsso rate s set toγ =.9, N. Each PHEV has radom cost fucto parameters η [,5] ad υ [,] for quadratc cost fucto ad β = for the lear cost fucto. The algorthm always starts by settg a =, I, N. A. Small Numbers of Buyers ad Aggregators We smulate the cases wth small umbers of buyers ad aggregators. We cosder 5 buyers (K = 5) each case ad we compare our two-layer approach wth a greedy approach, whch each PHEV always proposes to sell. Fg. 3 shows the average results of depedet smulato rus for each case. Fgs. 3(a) ad 3(b) preset the average utlty per aggregator correspodg to the lear ad quadratc cost fuctos, respectvely. We ca see that our approach always gves hgher average utlty tha the greedy oe, as show Fgs. 3(a) ad 3(b). I the cases of lear cost, we ca see that the average utlty start by creasg wth N but the, t starts to decrease whe the umber of aggregators reaches that of buyers (N = 6). Ths result s due to the fact that, for small N, a crease the umber of partcpatg aggregators leads to a larger amout of eergy sold whch, subsequetly, mproves the average utlty. However, when 6, a crease the umber of aggregators N wll yeld a decrease the settled prce whch leads to a decrease the utlty. I the cases wth quadratc cost, the average utlty creases wth N o the grouds that more aggregators partcpate the market resultg a larger amout of total eergy sold. Hece, geeral, the equlbrum tradg prce decreases wth N as more aggregators lead to a creased competto, whch subsequetly mposes a lower market prce. Average u.lty per aggregator Average u.lty per aggregator Number of tera-os Fg. 3. Proposed layer approach Greedy approach Prce Number of aggregators (N) (a) Total utlty ad prce for lear cost Proposed layer approach Greedy approach/ Prce Number of aggregators (N) (b) Total utlty ad prce for quadratc cost Lear cost Quadra6c cost Number of aggregators (N) (c) Iteratos requred for covergece Prce (P) Prce (P) Basc smulatos for small umbers of buyers ad aggregators. Fg. 3(c) shows the average umber of teratos requred to reach a equlbrum. Clearly, as more aggregators partcpate the market, the umber of teratos tll covergece creases. Moreover, Fg. 3(c) shows that the covergece tme s faster the case wth quadratc cost. Wth a lear cost fucto, each each terato, ad thus, the algorthm s more lke to oscllate more aroud the equlbrum pot before covergece. Wth a quadratc cost fucto, due to the cocavty of the utlty, the algorthm moves toward the equlbrum a smoother maer whch s further corroborated the subsequet smulatos. PHEV takes ether or B. Large Numbers of Buyers ad Aggregators Here, we smulate cases whch a large umber of buyers (K = ) ad aggregators (N = ) are deployed so as to verfy the aalytcal results duced from the lear approxmato studed Secto III-A. As prevously metoed, whe N (K) creases, the supply (demad) curve approaches a lear fucto as all radom umbers are geerated uformly. We frst study the results wth a fxed demad curve (.e. wth β ad Q fxed) ad they correspod to the stuatos whe the value

7 (a) Total utlty each terato Fg.. Fg Demad (b) Supply ad demad curves Lear cost fucto wth buyers (K) ad aggregators (N) (a) Total utlty each terato 3 Demad (b) Supply ad demad curves Quadratc cost fucto wth buyers (K) ad aggregators (N) (a) Total Utlty each case Fg Supply (b) Supply ad demad curves Fxed Q wth buyers (K) ad aggregators (N) evolves a partcular smulato. Fg. shows the results for lear PHEV cost fuctos whe the algorthm terates. Fg. (a) gves the total utlty computed from double aucto for each terato whle we have the correspodg supply ad demad curves Fg. (b) ( the part shows tersecto pots oly). We ca see that the total utlty decreases wth the supply slope (α). For example, we cosder teratos ad. α s larger tha α ad we have the utlty gaed terato s smaller tha that terato. We also study the quadratc PHEV cost fuctos ad the smlar results are show Fg. 5. However, wth the quadratc cost fucto, the algorthm coverges faster ad smoother. Next we study the results for sx dfferet demad curves wth a fxed supply curve (.e. α fxed). Fg. 6 shows the sx cases wth a fxed Q. The smulato also algs the results deduced Secto III-A: the larger β, the smaller the utlty. V. CONCLUSION We have studed the VG eergy tradg market, whch PHEVs sell ther excessve eergy to some loads the dstr- The umbers Subfgure (b) correspod to terato/case umbers Subfgure (a). For clearer demostrato, I Subfgure (b), oly the curves correspodg to the frst few teratos/cases are gve. buto etwork. We have proposed a mult-layer system to coordate the tradg where those PHEVs a close geographcal area are represeted by a aggregator. I the macro layer, the eergy buyers ad the aggregators egage a double aucto to determe the tradg prce ad the actual eergy quatty sold for each aggregator. I the mcro layer, each aggregator helps ts maaged PHEVs maxmze ther utltes. A mechasm s proposed to coordate the teracto betwee the macro ad mcro layers. We have aalyzed the system performace whe the umbers of buyers ad aggregators are large. Smulato results show that our mechasm s always better tha the greedy approach ad verfy some of our aalytcal results. REFERENCES [] T. A. Becker ad I. Sdhu, Electrc vehcles the uted states: A ew model wth forecasts to 3, Ceter for Etrepreeurshp & Techology, Uversty of Calfora, Berkeley, Tech. Rep. 9..v.., Aug. 9. [] A. N. Brooks ad S. H. These, PG&E ad Tesla motors: Vehcle to grd demostrato ad evaluato program, Proc. 3rd Iteratoal Electrc Vehcles Symposum ad Exposto, Aahem, CA, USA, Dec. 7. [3] Electrc Power Research Isttute (EPRI), PAP- electrc vehcle roamg scearos, EPRI Research Program, Use Case, Ju.. [Ole]. Avalable: [] Natoal Isttute for Stadards ad Techology (NIST), SGIP CoS: SAE J836 use cases for commucato betwee plug- vehcles ad the utlty grd, NIST Stadards, Apr.. [Ole]. Avalable: [5] C. Gulle ad G. Gross, A coceptual framework for the vehcle-to-grd (VG) mplemetato, Eergy Polcy, vol. 37, o., pp , Nov. 9. [6] B. K. Sovacool ad R. F. Hrsh, Beyod batteres: A examato of the beefts ad barrers to plug- hybrd electrc vehcles (PHEVs) ad a vehcle-to-grd (VG) trasto, Eergy Polcy, vol. 37, o. 3, pp. 95 3, Mar. 9. [7] J. Plla ad B. Bak-Jese, Vehcle-to-grd for sladed power system operato borholm, Power ad Eergy Socety Geeral Meetg, IEEE, july, pp. 8. [8] C. Wu, H. Mohsea-rad, ad J. Huag, Vehcle-to-aggregator teracto game, IEEE Tras. Smart Grd, to appear. [9] M. Erol-Katarc ad H. Mouftah, Maagemet of phev batteres the smart grd: Towards a cyber-physcal power frastructure, Wreless Commucatos ad Moble Computg Coferece (IWCMC), 7th Iteratoal, july, pp [] N. Matta, R. Rahm-Amoud, L. Merghem-Boulaha, ad A. Jrad, A cooperatve aggregato-based archtecture for vehcle-to-grd commucatos, Global Iformato Ifrastructure Symposum (GIIS),, aug., pp. 6. [] E. Sortomme ad M. A. El-Sharkaw, Optmal schedulg of vehcle-togrd eergy ad acllary servces, Smart Grd, IEEE Trasactos o, vol. PP, o. 99, p.,. [] W. Saad, Z. Ha, H. V. Poor, ad T. Basar, A ocooperatve game for double aucto-based eergy tradg betwee phevs ad dstrbuto grds, Proc. IEEE Iteratoal Coferece o Smart Grd Commucatos (SmartGrdComm), Brussels, Belgum, Oct.. [3] V. Krsha, Aucto Theory, A. Press, Ed.,. [] P. Huag, A. Scheller-Wolf, ad K. Sycara, A strategy-proof multut double aucto mechasm, Proceedgs of the frst teratoal jot coferece o Autoomous agets ad multaget systems: part, ser. AAMAS. New York, NY, USA: ACM,, pp [Ole]. Avalable: [5], Desg of a mult-ut double aucto e-market, Computatoal Itellgece, vol. 8, o., pp , Feb.. [6] D. Fredma ad J. Rust, The Double Aucto Market: Isttutos, Theores, ad Evdece. Boulder, CO, USA: Westvew Press, 993. [7] C. Slva, M. Ross, ad T. Faras, Evaluato of eergy cosumpto, emssos ad cost of plug- hybrd vehcles, Elsever Eergy Coverso ad Maagemet, vol. 5, o. 7, pp , Jul. 9. [8] T. Motors, Roadster ovatos: Motor, Feb..