Maximizing Aggregator Profit through Energy Trading by Coordinated Electric Vehicle Charging

Transcription

1 Maxmzng Aggregator Proft through Energy Tradng by Coordnated Electrc Vehcle Chargng James J.Q. Yu, Junhao Ln, Albert Y.S. Lam, and Vctor O.K. L Department of Electrcal and Electronc Engneerng The Unversty of Hong Kong Pokfulam Road, Hong Kong Emal: {jqyu, jhln, ayslam, vl}@eee.hku.hk arxv: v2 [cs.sy] 25 Apr 2017 Abstract Due to the ncreasng concern for greenhouse gas emssons and fossl fuel securty, electrc vehcles (EVs) have attracted much attenton n recent years. EVs can aggregate together consttutng the vehcle-to-grd system. Coordnaton of EVs s benefcal to the power system n many ways. In ths paper, we formulate a novel large-scale EV chargng problem wth energy tradng n order to maxmze the aggregator proft. Ths problem s non-convex and can be solved wth a centralzed teratve approach. To overcome the computaton complexty ssue brought by the non-convexty, we develop a dstrbuted optmzaton-based heurstc. To evaluate our proposed approach, a modfed IEEE 118 bus testng system s employed wth 10 aggregators servng EVs. The smulaton results ndcate that our proposed dstrbuted heurstc wth energy tradng can effectvely ncrease the total proft of aggregators. In addton, the proposed dstrbuted optmzaton-based heurstc strategy can acheve near-optmal performance. I. INTRODUCTION Wth the ncreasng concern for greenhouse gas emssons, electrc vehcles (EVs) are expected to reach a sgnfcant market share n the near future. Wth the emergng vehcleto-grd (V2G) technologes, EVs can potentally help allevate the securty concern for the supply of fossl fuels and mtgate the power network nstablty caused by the hghly penetrated ntermttent renewable energy generatons [1]. However, the network securty and economc operaton can be sgnfcantly adversely nfluenced by the uncoordnated chargng behavors of a large number of EVs [2]. By effcently utlzng the system capacty, coordnated chargng strateges can reduce the possble adverse mpacts on the power system [3]. In addton, other merts can also be obtaned, such as reducng the total operatonal cost and mtgatng the varablty of the renewable energy sources [4]. Hence, coordnaton of EVs s benefcal to the power system n many dfferent perspectves. A large populaton of EVs can be clustered nto aggregators to facltate the coordnaton of chargng behavors. Coordnated EV chargng wthn one aggregator has been studed extensvely n recent years. Prevous research generally focused on the grd structure wth aggregators managng a large number of EVs. Based on where the chargng decsons are made, the methodologes can be classfed nto two types: centralzed and dstrbuted methods. In the centralzed methods, EVs need to send ther parkng and battery nformaton to the assocated aggregator, whch then decdes how each ndvdual EV should be charged n a centralzed manner. The decson s mostly drven by maxmzng the aggregator proft [3], [5], mnmzng EV owners power cost [6], [7], and achevng power balance [8]. On the other hand, aggregators n the dstrbuted methods send power prcng scheme and related nformaton to EVs. The EVs then utlze ther own knowledge to establsh ther chargng plans, whch are later delvered to the aggregator. Usually ths process repeats untl an agreement or equlbrum s reached. As the chargng strateges are developed by the EV, most exstng efforts employ the energy costs ncurred for the EV owners as the performance metrc [9]. User utlzaton rato [10] and power balance [11] are also studed as metrcs. In general, all these manly focus on the coordnated chargng behavor wthn a sngle aggregator. There s few efforts studyng the nteractons among multple EV aggregators, e.g., [12], [13]. One common feature s the utlzaton of a herarchcal archtecture where aggregators coordnate wth others under the control of the system operator. Whle ths archtecture effcently reduces the computatonal burden of developng coordnated chargng plans, drect nteractons among aggregators are generally not consdered. In ths paper, we focuses on maxmzng the aggregators total proft through coordnated EV chargng when consderng multple aggregators connected to the grd. Dfferent from the prevous work, we nvestgate the possblty of achevng Inter-aggregator Energy Tradng (IET) to further explot profts from tradng energy drectly among aggregators. There exsts prevous research nvestgatng the possble energy trades among EVs, e.g., [14] and [15], and they demonstrated mproved total costs of EVs when compared wth those models wthout energy tradng. Therefore t s lkely that energy tradng among aggregators s more proftable wth drect aggregator nteractons. In addton, we consder the Locatonal Margnal Prcng (LMP) n ths work to manage the system congeston cost to further ncrease the proft. The remander of ths paper s organzed as follows. Secton II presents the system framework of our proposed approach. We formulate the aggregator proft maxmzaton problem and propose a centralzed coordnated chargng strategy n Secton III. Secton IV demonstrates an optmzaton-based heurstc approach for the problem. In Secton V we provde a case study to llustrate the performance of our developed approach. Fnally we conclude ths paper n Secton VI.

2 II. SYSTEM ARCHITECTURE In ths work, we adopt a typcal herarchcal EV chargng archtecture [12], whch s composed of three components: system operator (SO), aggregators, and plug-n EVs. The man purpose of ntroducng aggregators s to smplfy the system model and unbundle the electrc loads, e.g., EVs, from the power network nfrastructure [16]. By collectng the chargng nformaton from the clustered EVs and prcng nformaton from SO, each aggregator can develop ts own optmal chargng schedule such that the aggregators profts are maxmzed whle the varous EV chargng requrements are all satsfed. SO manpulates the real-tme power prce to balance power consumpton of each bus n the power grd to allevate power congeston. We consder EVs as dspatchable power applances whose chargng rates can be adjusted by the correspondng aggregators by takng the system requrements and economc consderaton nto account [10]. Smlar to [17], upon the arrval of an EV, we assume that ts battery capacty and current state of charge (SoC) can be obtaned by ts aggregator va approprate vehcular communcaton technques. In addton, the departure tme of the EV s also assumed to be avalable to ts aggregator. We allow EVs to perform early departure f needed. In such case, a penalty can be mposed to the EV owner [18]. In our proposed framework, EVs are categorzed nto two classes based on ther respectve capabltes: un-drectonal,.e., chargng from the grd to vehcles, or b-drectonal,.e., both chargng from and dschargng to the grd. Enablng power flow from EVs to the grd can effectvely ncrease the proft by explotng the power prce fluctuatons [3], [5], [19]. To encourage V2G b-drecton operaton, aggregators may compensate the EV owners battery agng loss by offerng lower chargng cost or free battery replacement plan [20]. The objectve of IET s to effectvely utlze the dschargng power from aggregators for the beneft of aggregator proft. The aggregators typcally purchase power from SO for chargng at a prce, and sell power to SO at a lower prce. Meanwhle, nstead of tradng wth SO, the dschargng aggregators can trade wth other chargng aggregators at a better prce, between the SO power buyng and sellng prces. For nstance, suppose that Aggregator A1 s chargng power P 1 > 0 from the grd wth power purchasng prce C1 ch and Aggregator A2 s dschargng power P 2 < 0 to the grd wth power sellng prce C2 dch. Then the total cost for the aggregators s P 1C1 ch+p 2C2 dch. Suppose that A2 desres to sell P trade > 0 to A1 at C trade. The power cost for A1 becomes (P 1 P trade )C1 ch +P trade C trade and A2 s s (P 2 + P trade )C2 dch P trade C trade, renderng a total cost at P 1 C1 ch + P 2C2 dch + (C2 dch C1 ch)p trade. Therefore the trades between A1 and A2 can decrease the cost, thus ncrease the aggregators total proft when C2 dch > C1 ch. III. AGGREGATOR PROFIT MAXIMIZATION PROBLEM In ths secton, we formulate the aggregator proft maxmzaton problem wth IET. We employ model predctve control to develop chargng control strateges of the mmedate tme slot, takng future EV departures and power prce profle nto account. Specfcally, the problem s defned over a fnte tme-horzon T = {t q t q = t 0 + q t, q = 0, 1,, q max }. Informaton n the current tme slot t 0 s consdered accurate whle the future nformaton may be mprecse. Snce the soluton of the problem,.e., the overall chargng strategy, should be jontly optmal over the entre T, the mplemented chargng strategy of the current tme slot wll also contrbute to the total proft maxmzaton over T, nstead of one sngle tme slot. The problem shall be solved whenever EVs requre chargng operatons, renderng the process onlne. All symbols used n ths paper and ther meanngs are lsted n Table I. In the problem, a set of m aggregators A = {A 1, A 2,, A,, A m } are consdered. Aggregator A serves n EVs at a tme denoted by V = {V,1, V,2,, V,j,, V,n }. The objectve functon for tme slot t s mathematcally formulated as follows: 1 R t = where α,jp,jc,j A A V,j V } {{ } Chargng Income ( α,jp,j P trade )C A A V,j V }{{} Margnal Energy Cost C = { C ch C dch + (1 α,j)p,jc ch,j A A V,j V }{{} Penalty Income f V,j V α,j P,j P trade 0, otherwse, whch means that the chargng prce s employed f the aggregator draws power from the grd. Otherwse the dschargng prce s used. The ncome of aggregators s composed of two parts: chargng and penalty ncomes. The frst term n Eq. (1) s the chargng fee mposed on the EVs, whch s arbtrarly formulated as follows: 2 { C V C V mn{ T,j /T V, 1} C,j = C U C U mn{ T,j /T U, 1} bdrectonal chargng, undrectonal chargng, (3) where the bdrectonal chargng allows both chargng and dschargng behavors, and the undrectonal chargng supports chargng only. The second term n Eq. (1) s the penalty ncome (parkng fee) mposed on the EVs for any late departure. Ths ncome can be neglected n resdental area scenaros. The thrd term n Eq. (1) s the cost of the consumed power purchased from SO. The cost s frstly generated usng dayahead energy prces, then takng LMP nto consderaton n optmzaton of the later tme slots. If the chargng power s negatve, the correspondng aggregator wll perform V2G energy sellng operaton and ths term wll become negatve. Besdes real tme proft generaton, aggregators can also utlze the dspatchable characterstcs of EVs to delay the chargng process to further ncrease the proft. Ths results n a mult-tme-slot jont optmzaton as follows: 1 For the sake of smplcty, the symbol t for tme s omtted n equatons (1) (3), (6), and (8) (11), when no confuson may be caused. 2 More complcated contract formulatons are avalable n practce and can be easly ncorporated nto the proposed optmzaton problem. (1) (2)

3 TABLE I SETS, PARAMETERS, AND VARIABLES USED Parameter Descrpton Parameter Descrpton. A Set of aggregators n the system. Pl lne Maxmum power flow on lne l. A -th aggregator n the system. G mn s,gmax s Mnmum and maxmum generaton output for the V Set of Electrc Vehcles (EVs) served by A. generator on bus s. V,j j-th EV served by A. t Current tme slot. V,u u-th undrectonal chargng EV served by A. R t The total aggregator proft at t. T Tme horzon of optmzaton. P Total chargng power of A. T,j Parkng tme of V,j. P,j Chargng power of V,j. t 0,t q The current and the q-th future tme slot. α,j Bnary ndcator for whether V,j s stll parked after q max The total number of future tme slots. the regstered departure tme. t Duraton of each tme slot. S,j SoC of V,j. t dpt,j The regstered departure tme of V,j. S,j rmn Mnmum reserved State-of-Charge (SoC) of V,j. C ch Power chargng prce from the power grd at A. G s Generaton output for the generator on bus s. C dch Power dschargng prce from the power grd at A. P s Aggregator njecton on bus s. C V,C U The base contract prce for b-drectonal and un- C,j Chargng fee of V,j when the regstered parkng tme drectonal vehcle-to-grd (V2G) chargng enabled EVs. s T,j. C V, C U The margnal prce decrease for b-drectonal and C trade Power tradng prce among aggregators. un-drectonal V2G chargng enabled EVs. C Power tradng prce from the power grd at A. T V,T U Parkng tme for mnmal chargng fee of b-drectonal P trade Trade power of A. and un-drectonal V2G chargng enabled EVs. P spl Total avalable aggregator power supply n the trade P,j ch,p dch,j Maxmum chargng and dschargng rate of V,j. at C. η,j ch,j Chargng and dschargng effcency of V,j. P dmd Total avalable aggregator power demand n the trade E,j Battery capacty of V,j. at C. S,j mn,smax,j Mnmum and maxmum State-of-Charge (SoC) of V,j. P cap Trade capacty at C. S req,j Requred SoC on departure of V,j. C s(g s) Power generaton cost functon for the generator on bus N Number of buses n the power system. s when generatng G s power. L Number of lnes n the power system. λ,µ l Lagrangan multplers. D s Inelastc load on bus s. γs mn,γs max Lagrangan multplers. F l s Generaton shft factor from bus s to lne l. maxmze R t subject to (4a) P,j,t,P trade,t t T P,j dch P,j,t P,j, ch t T, 0 P,u,t P,u, ch t T, P,j,t t + (t dpt ch,j t 1)P,j (S req,j S,j,t)E,j/ηch,j, t T, P,j,t tη,j ch (S req S,j,t)E,j, t T, (4e) A A P trade,t,j (4b) (4c) (4d) P trade,t = 0, t T, (4f) P,j,t 0, t T, (4g) V,j V P,j,t P,t trade 0, t T. (4h) V,j V Eq. (4b) mposes rgd upper bounds for chargng power of all EVs onlne. Eq. (4c) further lmts the un-drectonal chargng EVs to perform chargng operatons only durng the whole parkng process. Eq. (4d) ensures that the current chargng power of an EV s feasble only f the battery can be charged to the requred SoC when the chargng powers of all succeedng tme slots are set to the maxmum rate. Ths constrant s consdered when the optmzaton horzon T does not contan the departure tme t dpt m,,.e., max{t } < tdpt m,, m,. Otherwse, an alternatve constrant s consdered nstead of Eq. (4d), as: t T P,j,t tη ch,j (S req,j S,j,t)E,j. (5) Ths constrant guarantees that EVs wll be charged to ther requred SoC on departure. Other practcal strateges to prevent nsuffcent chargng, e.g., penaltes on aggregators, can be easly mplemented n our model. Eq. (4e) prevents the battery from beng over charged by lmtng the current chargng rate. Eqs. (4d) and (4e) cooperate to manpulate the chargng rates of EVs to satsfy the SoC constrants. Eq. (4f) ensures that the amount of energy bought and sold n the aggregator tradng market are equal. Non-convex constrant Eq. (4g) prevents the aggregators, that are consumng power from the power grd, from tradng energy to other aggregators, and vce versa. As P,t trade and V,j V P,j,t are ndependent and can be both postve and negatve. Eq. (4h) mposes that the aggregators cannot sell more energy than they generate through dschargng behavors, and cannot buy more energy than they request to fulfll the EV chargng demand. When gven constant power prces C s, the optmzaton problem formulated n Eq. (4) can develop optmal EV chargng profles for maxmzng aggregator proft. However, the optmzed chargng powers of each aggregator P = V,j V α,j P,j may change the power flow of the grd, resultng n changng C s. Therefore, we also employ an Optmal Power Flow (OPF) based LMP optmzaton together wth Eq. (4) to develop C s subject to aggregators changng P values. Upon the recept of chargng power requests from the aggregators, SO performs OPF to route the power flow. In our proposed framework, an LMP strategy s employed for

4 START EVs send local nformaton to the central controller for optmzaton. Central controller maxmze the total aggregator proft usng the current power prce nformaton Are new chargng profles the same wth prevous teraton? Yes STOP No Aggregators send ther chargng/dschargng power to the system operator. System operator solves optmal power flow problem and determnes the locatonal margnal prce. Fg. 1. Flow chart for the proposed centralzed coordnated chargng strategy for aggregator proft maxmzaton. Yes START EVs send local nformaton to the aggregator they are parkng wth. Aggregators maxmze ther profts accordng to the EV nformaton, current and predcted power prce. Are new chargng profles the same wth prevous teraton? No Aggregators send ther aggregated chargng/dschargng nformaton to others as bds. STOP Aggregators determne a global tradng prce and correspondngly ther amount of power for trade. Aggregators maxmze ther proft usng the addtonal aggregator tradng prce nformaton. Aggregators send ther chargng/dschargng power to the system operator. System operator solves optmal power flow problem and determnes the locatonal margnal prce. Fg. 2. Flow chart for the proposed optmzaton-based heurstc coordnated chargng strategy for aggregator proft maxmzaton. congeston control [21]. As we focus on the real tme power dspatch of the aggregators for EV chargng, t s assumed that the Unt Commtment problem has been solved and all generators consdered are onlne [4]. The SO level OPF problem s formulated as a classcal OPF problem [22], where the LMP of buses are optmzed wth the partal dervatve of the Lagrangan of OPF (see [21], [22] for elaboratons). Optmzaton problem (4) and OPF-based LMP optmzaton together compose the aggregator proft maxmzaton problem. Ths problem ams to develop optmal EV chargng plans to maxmze the aggregator proft. It can be solved n an teratve manner as depcted n Fg. 1. Problem (4) and OPF are optmally solved alternately untl an equlbrum s reached, where a stable IET-enabled EV chargng profle s developed. At the begnnng of each tme slot, Eq. (4) s solved to generate optmal chargng strateges for all EVs n the system, usng the day-ahead energy prce. After the scheduled aggregated chargng powers are optmzed, they are reported to the SO for calculatng the new LMP. Utlzng these new prces, the central controller solves Eq. (4) agan, and ths process repeats untl an optmal chargng strategy s developed. IV. DISTRIBUTED AGGREGATOR HEURISTIC The aggregator proft maxmzaton problem develops optmal EV chargng profles for maxmzng aggregator proft. However, the problem can become ntractable when there s a large number of EVs to schedule. As Eq. (4) s a non-convex problem, exstng solvers may encounter effcency ssues when solvng large problem nstances. In order to address ths problem, we propose a dstrbuted heurstc algorthm to solve Eq. (4). The heurstc-enabled aggregator proft maxmzaton strategy s shown n Fg. 2. We bascally dvde the shaded step n Fg. 1 (whch consttutes the non-convexty) nto the three shaded sub-steps n Fg. 2. They respectvely correspond to the three steps of the proposed heurstc: aggregator proft optmzaton (shaded sub-step on the left n Fg. 2), power tradng (top-rght), and supply-demand balancng (mddlerght). A. Aggregator Proft Optmzaton At the begnnng of each optmzaton teraton, all onlne EVs send ther vehcle and battery nformaton, ncludng the maxmum chargng rate, scheduled departure tme, and battery sze and current SoC, to ther correspondng aggregator. Wth ths nformaton, each aggregator maxmzes ts proft ndependently usng a modfed formulaton of Eq. (1): R,t = α,jp,jc,j + (1 α,j)p,jc ch,j V,j V V,j V ( α,jp,j P trade )C P trade C trade. (6) V,j V The major dfference between Eqs. (1) and (6) les n the ntroducton of the tradng cost term P trade C trade. P trade s set to zero at the begnnng of the teraton, and set to ether a constant value or to V,j V α,j P,j based on the supply and demand equlbrum, whch wll be elaborated n Secton IV-B. Therefore, Eq. (4) s transformed nto max P,j,t t T R,t subject to (4b), (4c), (4d) or (5), (4e), (7) to maxmze each aggregator s proft. Eq. (7) consders all EV constrants, and energy tradng constrants Eqs. (4f) (4h) are handled n the power tradng heurstc algorthm. B. Power Tradng Heurstc When all aggregators have fnshed ther proft maxmzaton processes, they broadcast ther P values to the others n the aggregator tradng market n the form of bds. In ths step, the aggregators utlze all the power bds to perform a modfed second-prce aucton [23]. When submttng bds, each aggregator calculates ts P from the result of Eq. (7), and places a bd n the form of (P, C ) par. A postve P makes C = C ch, and a negatve P makes C = C dch. The bds are then broadcast to the others and the aucton starts n the aggregator tradng market when all bds have been placed and announced. After all bds are generated, the aucton evaluates the avalable chargng (demand) and dschargng (supply) power for trade at all possble tradng prces C trade, whose values are selected from all C values n the bds: P spl = A k A spl P k, P dmd = A k A dmd P k, (8)

5 where A spl = {A k A P k < 0, C k C trade }, (9) A dmd = {A k A P k > 0, C k C trade }. (10) The tradng capacty for C trade s accordngly calculated by P cap = mn{ P spl, P dmd } C trade. (11) Consequently, the value of C trade s set to the optmal C value whch yelds the largest P cap. After determnng the tradng prce, another round of optmzaton Eq. (7) s conducted to utlze the addtonal proft contrbuted by the tradng behavor. The generated chargng profle s consdered fnal and reported to SO for LMP calculaton. V. CASE STUDIES We employ the IEEE 118 Bus system [24] to assess the proft maxmzaton performance of our proposed approach. 10 aggregators are nstalled n the system on Buses 7, 14, 17, 28, 44, 58, 72, 84, 97, and 115. The settngs of the system parameters are presented n Table II. The power prce nformaton s acqured from the PJM [25] data, and the aggregators are assgned wth the prces of dfferent buses. In the test system, EVs are accommodated. We consder two models of vehcles, namely the Tesla Model S AWD-85D (Telsa Model S) and Nssan Leaf 2014 model (Nssan Leaf). We assume 60% of all EVs n the system are Tesla Model S EVs wth 85 kwh batteres and 34 kwh/100 mles energy expendture performance, and the remanng 40% are Nssan Leaf EVs wth 24 kwh batteres and kwh/100 mles energy expendture performance. The maxmum chargng rates for these two models are 22 kw and 6.6 kw, respectvely, and the maxmum dschargng rates are also set to the same values [26]. Among all EVs n the system, 80% EVs enabled b-drectonal V2G operatons. 5% of the EVs wll perform a late departure up to a maxmum of one hour. For practcal stuatons, these parameters can be manpulated by the EV owners. The European Commsson Strategc Energy Technologes Informaton System reported a moblty survey on the drvng and parkng patterns of European car drvers [27]. The results of the survey are utlzed to formulate the EV drvng dynamcs. Smlar methods have also been adopted n the lterature, e.g, [4]. We perform smulatons on a horzon of 72 hours, and the length of each tme slot s 15 mnutes. Thus the total proft of all 288 tme slots are combned as the performance metrc. As Problem (4) cannot be solved drectly n a tmely manner, we frst nvestgate the performance of the dstrbuted heursrcenabled aggregator proft maxmzaton strategy proposed n Secton IV, whose optmalty wll be studed later. The dstrbuted soluton s labeled All for ease of demonstraton. In addton, four other varants are consdered to demonstrate the relatonshp of Eq. (7) and LMP calculaton, and ther contrbutons to the proft maxmzaton performance. These four varants are developed by removng one or multple components from All : TABLE II PARAMETER SETTINGS Param Value Param Value Param Value q max 23 R V $0.015/6hrs η,j ch,j 0.9 t 15 mnutes R D $0.015/6hrs S,j mn 0.0 R V $0.08/kWh T V 6 hours S,j max 1.0 R U $0.10/kWh T U 6 hours S req,j 0.9 TABLE III PROFIT MAXIMIZATION PERFORMANCE Mode All NoTrade NoLMP Plannng Greedy Proft($) ) The NoTrade mode removes all possble trades between aggregators. Ths mode works lke a V2G enabled verson of [22]. 2) The NoLMP mode removes the LMP adaptaton step. Energy trades among aggregators are allowed. 3) The Plannng mode removes both tradng steps and the LMP adaptaton step. Ths mode works smlar to a V2G-enabled verson of [19]. 4) The Greedy mode performs the greedy chargng strategy. Upon the arrval of an EV, t s charged at the maxmum rate untl the SoC requrement s met. Table III presents the total profts generated by the compared chargng approaches. It can be easly seen that our proposed approach can sgnfcantly ncrease the aggregator profts, and both the aggregator tradng and LMP adaptaton have a postve nfluence on the proft maxmzaton process when compared wth the Greedy mode. In addton, the computatonal tme of the proposed approach s also crucal as the algorthm s supposed to be mplemented onlne. Wth EVs n the system and 24 optmzed tme slots, each teraton of our proposed algorthm can be fnshed n 9.13 seconds. All tme slots can be optmzed wthn a maxmum of sx teratons,.e., one tme slot can be fnshed n one mnute. In addton to the proft maxmzaton performance comparson, we also nvestgated the optmalty of our proposed approach n Secton IV ( All mode) comparng wth the orgnal one n Secton III, and the behavor of aggregators n response to the power prce. The detaled results are presented n [28], and we observe that All s only 3.7% worse than the optmal soluton of the convex-relaxed problem, and the gap between the true optmal and our approxmaton must be smaller. Fg. 3 demonstrates the total chargng power dynamcs of our proposed approach wth the changes on the average power purchasng prce. We can observe that the chargng power s mostly hgh when the prce s relatvely low. Ths shows the effcacy of the multple tme slot optmzaton n savng aggregators power cost. The mpact of ntroducng the proposed strategy on the power system stablty s also llustrated n [28], and the concluson can be drawn that adjacent buses to aggregators wll be nfluenced more by the power lne congeston, whch s represented n the form of LMP changes. VI. CONCLUSION In ths paper we propose a coordnated chargng problem consderng IET for maxmzng the proft of multple aggre-

6 Chargng Power (MWh) Total Chargng Power of "All" mode Average Power Prce Day 1 6:00AM Day 1 6:00PM Day 2 6:00AM Day 2 6:00PM Day 3 6:00AM Day 3 6:00PM Day 4 5:45AM Fg. 3. Total chargng loads for all tme slots. Power Prce ($/MWh) gators. A model predctve control based centralzed teratve approach s devsed to fnd the optmal EV chargng strateges for proft maxmzaton. Consderng the non-convexty nature of the optmzaton problem, we develop an aggregator-level coordnated chargng heurstc to construct the EV chargng schedules. To explot the potental of employng energy trade among aggregators for proft maxmzaton, we propose an aucton-based heurstc to handle the tradng detals. In addton, the teratve approach utlzed by our developed strategy can further adapt the EV chargng schedules to the grd congeston cost. To valdate the performance of the proposed approach, we employ a ten-aggregator system wth EVs for smulaton. 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