GROWING awareness of energy and environmental crises

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1 SUBMITTED TO IEEE TRANSACTIONS ON SMART GRID, DECEMBER Profit-wre Online Vehicle-to-Grid Decentrlized Scheduling under Multiple Chrging Sttions Abbs Mehrbi, Student Member, IEEE, Aresh Ddlni, Seungpil Moon, nd Kiseon Kim, Senior Member, IEEE rxiv: v2 [cs.sy] 19 Dec 2016 Abstrct Fluctutions in electricity triffs induced by the spordic nture of demnd lods on power grids hs initited immense efforts to find optiml scheduling solutions for chrging nd dischrging plug-in electric vehicles (PEVs) subject to different objective sets. In this pper, we consider vehicle-togrid (V2G) scheduling t geogrphiclly lrge scle in which PEVs hve the flexibility of chrging/dischrging t multiple smrt sttions coordinted by individul ggregtors. We first formulte the objective of mximizing the overll profit of both, demnd nd supply entities, by defining weighting prmeter. We then propose n online decentrlized greedy lgorithm for the formulted mixed integer non-liner progrmming (MINLP) problem, which incorportes efficient heuristics to prcticlly guide ech incoming vehicle to the most pproprite chrging sttion (CS). The better performnce of the presented lgorithm compred to n lterntive lloction strtegy is demonstrted through simultions in terms of the overll chievble profit nd fltness of the finl electricity lod. Moreover, the results of simultions revel the existence of optiml number of deployed sttions t which the overll profit cn be mximized. Index Terms Electric vehicle-to-grid (V2G), profit mximiztion, mixed integer non-liner progrmming (MINLP), online greedy scheduling, V2G penetrtion. I. INTRODUCTION GROWING wreness of energy nd environmentl crises hs ctlyzed the evolutionry shift towrds electrifying personl trnsporttion. In recent yers, investments on electric vehicles (EVs) s eco-friendly nd cost-efficient substitutes for conventionl fuel-propelled utomobiles tht exhust nturl resources hve been over-whelming. Clssified brodly bsed on their mode of propulsion, plug-in electric vehicles (PEVs) which re purely bttery electric vehicles hve benefits fr more brod thn conventionl vehicles [1]. These benefits however, re ccompnied by vrious new chllenges s more EVs re integrted into the power grid. Prime concerns include power distribution instbility nd trnsmission congestion due to the unmnged chrging nd/or dischrging of EVs t grid-connected electric vehicle supply equipments, commonly known s chrging sttions (CSs). From the reserch prospective, optiml chrging nd dischrging of EVs hve been widely scrutinized due to their significnt impct on the lod regultion of vehicle-to-grid (V2G) systems [2], [3], [5], [6]. The bidirectionl flow of power between EVs nd power grid fcilittes lod flttening A. Mehrbi, A. Ddlni, nd K. Kim re with the School of Electricl Engineering nd Computer Science, Gwngju Institute of Science nd Technology (GIST), Gwngju 61005, South Kore (e-mil: {mehrbi,ddlni,kskim}@gist.c.kr). S. Moon is with Kore Electric Power Reserch Institute (KEPRI), Dejeon , South Kore (e-mil: spmoon@kepri.re.kr). by shifting the demnds of chrging EVs from pek lod hours to off-pek periods [7]. With regrd to power costs t different time intervls nd uncertinty in EV rrivl times, smrt scheduling techniques re required to not only stisfy profit expecttions, but lso prevent the grid from crshing through power lod flttening [3], [9]. The geogrphicl scle over which existing works on V2G scheduling re studied cn be clssified in terms of the number of ggregtors involved. Non-preemptive lloction of EVs for chrging/dischrging opertions occur either t single CS mnged by single ggregtor (SCS-SA) [3], [9], [10], where the scheduler hs globl informtion on the energy requirement nd deprture time of ech EV, or t multiple CSs coordinted by n ggregtor (MCS-SA) [3], where the scheduling optimiztion problem is loclly solved in ech group. The V2G scheduling of EVs, comprising of multiple number of sptilly-distributed CSs ech mnged by individul ggregtors hs however, not yet been investigted under which EVs seeking service experience higher degree of flexibility in selecting the sttion tht yields the most chievble profit. Under this scenrio, the overll profit cn be ffected by vritions rising in the system prmeters such s CS crdinlity nd mximum vehicle cpcity t ech CS. Hence, selection of optiml system prmeters cn essentilly llevite the net uxiliry nd estblishment costs incurred by the CSs. Moreover, the uthors of [3] nd [9] merely focus on the gross profit of EV owners without ccounting for the profit of CSs in their objective functions. On the other side, the EVs scheduling problem in [22] considers the objective of mximizing the overll obtinble profit of only ggregtors. From the V2G mngement system point of view, in order to encourge the energy utility provider to estblish CSs for delivering the energy to EVs, it necessittes to shre reltively the obtinble profit between EVs nd the CSs. Inspired by the before-mentioned limittions nd this lter motivtion, the min contributions of this pper re highlighted s follows: The problem of profit mximiztion considering reltime pricing for EV chrging/dischrging scheduling in lrge-scle V2G system composed of multiple sttionsmultiple ggregtors (MCS-MA) is formulted. A mixed integer non-liner progrmming (MINLP) optimiztion model is then proposed for the problem formultion which, in contrst to the previous models, ccounts for djustble profit between EV owners nd CSs. To cope with the scheduling problem involving stochstic rel-time EV rrivls, n online greedy lgorithm employing internl heuristics is proposed to guide ech

2 SUBMITTED TO IEEE TRANSACTIONS ON SMART GRID, DECEMBER incoming EV to the most profitble sttion. The proposed lgorithm hs low time nd messge complexities per vehicle, which mkes it pplicble for lrge-scle V2G deployments. Outperformnce of the proposed lgorithm in comprison to n lterntive lloction strtegy in terms of overll chievble profit s well s the fltness of finl electricity lod re shown through simultion results. Furthermore, optiml point for the number of deployed sttions is lso ttined by system prmetric djustments. This optiml point cn help V2G system designers to optimize their investment budget. The reminder of this pper is structured s follows. Relted works on EV scheduling in smrt grids re briefly reviewed in Section II. Section III introduces the system model nd nottions, followed by scheduling problem formultion in Section IV. The proposed online greedy lgorithm nd its theoreticl nlysis re detiled in Section V. Simultion setup nd results re provided in Section VI. Finlly, Section VII concludes the pper. II. RELATED WORKS Alloction strtegies for EV chrging/dischrging with different objectives hve been studied in mny recent works [2]- [5], [9]- [11]. The min chllenge in devising rel-time lloction lgorithms in V2G is the uncertinty of future deprture times nd chrging demnds of EVs priori. The non-preemptive scheduling problem studied by He et l. [3] ccounts for the rel-time pricing nd degrdtion/fluctution costs of btteries in obtining the minimum chrging costs. They consider the scenrio of online EVs rrivl to severl smll nd closely-locted CSs mnged by single ggregtor nd design decentrlized loclly-optiml lgorithm. In [11], the uthors provide closed-form solution to determine the optiml chrging power of single EV under time-of-use (ToU) pricing model nd uncertin deprture time. The uthors of [5] proposed n online lgorithm with proven competitive rtio for obtining sub-optiml solution with slightly higher cost s compred to the offline optiml solution, while stisfying the desired energy requirements imposed by the vehicles. While mny other set-ups nd pproches hve been pplied to envisge vehicle-to-grid interctions in the literture [12], [13], scheduling in lrge-scle V2G environment in which EVs hve the flexibility of getting service t multiple chrging sttions coordinted by their individul ggregtors, referred to s MCS-MA in this pper, hs not been explored so fr. Therefore, to fill this gp, we investigte the problem of profit mximiztion under multiple CSs by proposing n optimiztion model tht incorportes the prcticlly existing constrints on the cpcity nd ssocited uxiliry costs of ech sttion. By considering the indeterministic rrivl of EVs during the scheduling process, we propose n online greedy lgorithm tht guides incoming EVs to the most suitble CS. We note tht the most closing work to ours hs been ddressed in [22] in which the uthors investigte the problem of profit mximiztion considering multiple geogrphiclly distributed CSs. However, our work is different from [22] in TABLE I: Nottions nd descriptions of system modeling prmeters Nottion K M = M CG M DG M V 2G C mx k d,k, F MC k /LC k t A,k /D,k T,k = {t f,k, tf+1,k,..., tl,k } S,k (t) N t k Pc mx /Pd mx Number of CSs Description Set of rriving EVs ( M = m) including the set of EVs with only chrging/only dischrging/both services Mximum EV ccommodtion cpcity of CS k Distnce of EV from its home to chrging sttion CS k nd the force of its electric motor Vehicle mintennce/lbor costs per time slot unit t CS k Time durtion of ech time slot Arrivl/deprture times of EV t sttion CS k Chrging/dischrging intervl of EV t CS k form the strting to ending time slots Set of time slots before slot t in service intervl of EV t CS k Number of EVs in time slot t t CS k Mximum chrging/dischrging powers of EV in ech time slot Prmeters for bttery degrdtion, fluctution, α, β, δ nd djustble profit control E initil /E finl Initil/finl energy levels of EV B Bttery cpcity of EV Finl frctionl energy control prmeter r (0 < r 1) L t k, zt k x t,k, et,k Bse lod of other devices excluding EVs nd totl lod in time slot t t CS k Binry lloction of EV to CS k nd its corresponding power in time slot t the following wys: We consider multiple ctegories of PEVs nd investigte the mximiztion of reltive obtinble profit of both supply nd demnd entities. Furthermore, in contrst to [22], more relistic system prmeters re incorported into the proposed optimiztion model such s PEV s bttery s well s the ncillry ssocited costs with CSs. Furthermore, we chieve more insightful results through extensive simultions under the problem objective such s the optiml number of CSs under the proposed V2G system. III. SYSTEM MODEL We consider system comprising of K CSs, ech indexed s CS k where k {1, 2,..., K}, nd set of incoming EVs, denoted by M such tht M = m, which ccording to [3] is ctegorized into three groups such tht M CG M DG M V 2G = m. Here, M CG represents the set of EVs tht only require chrging from the grid, M DG is the set of EVs tht only dischrge energy to the grid, nd M V 2G denotes the set of EVs prticipting in bi-directionl V2G opertions. EVs leve their homes during time in the morning nd select chrging sttion on the wy to their offices. Note tht the set of PEVs in M DG re those which hve enough energy to rech their offices nd re willing to sell some portions of bttery s

3 SUBMITTED TO IEEE TRANSACTIONS ON SMART GRID, DECEMBER energy by returning bck to the grid. Assuming time to be discrete s in [9], [14], the scheduling period over single dy is T eqully divided time slots, ech of durtion t hour. The mintennce cost of n EV t CS k is tken to be MC k. Correspondingly, we lso ssume n identicl lbor/service cost denoted s LC k. Note tht the mintennce cost is pid by EV to the sttion while on the other side, for performing the mintennce, the CS hs to py the service cost to the lbor. We consider non-preemptive lloction of EVs for chrging nd dischrging ctivities t ech sttion with A,k nd D,k s the rrivl nd deprture times of vehicle t CS k. For given EV, T,k = {t f,k, tf+1,k,..., tl,k } represents set of the consecutive time slots in chrging/dischrging intervl t CS k, stisfying the following constrint: A,k (t f,k 1) t < tl,k t D,k. (1) Model prmeters regrding bttery degrdtion due to high chrging/dischrging frequencies (α) nd fluctutions (β) re lso tken into ccount to include the uxiliry costs ssocited with EV btteries [1], [3]. The decision vribles, chrging/dischrging power, s well s the prmeters on energy requirement of EVSs hve been ll summrized in Tble I. Furthermore, the prmeters d,k represent the distnce of EV from its home to CS k nd F, the force of its electric motor. Hence, the energy consumed during the trvelled distnce from home to CS k by EV is computed s d,k F. A. Communiction Schem Fig. 1 outlines the communiction flow for EV scheduling in n MCS-MA environment, where EVs re llowed to select their CS for service. Ech CS is coordinted by n individul ggregtor which fcilittes the bidirectionl informtion nd energy flow between EVs nd the power grid. Given the totl number of EVs in the system, their respective rrivl epochs t the CS vry rndomly over discrete time. Prior to CS selection, ech EV sends scheduling-relted dt to the ggregtors of ll CSs. Such dt includes informtion regrding rrivl to/deprture from ech sttion, initil energy, bttery cpcity, nd energy level desired by the vehicle. Dt trnsmission between EVs nd the ggregtors is fesible vi cellulr or stellite wireless communiction depending on the underlying infrstructure of the network [1], [15]. Ech ggregtor then forwrds the received dt to its locl scheduler t the CS in order to compute the chievble profit t tht sttion. The computed profit t ech locl CS is then piggy-bcked on the reply messge sent bck to the EV by the ggregtors. B. Pricing Model In the context of smrt scheduling, the chrging nd dischrging power of EVs is modulted by the electricity price t tht time instnt. The rel-time pricing (RTP) model hs been pprecited in which the time-dependent price is driven by the totl electricity lod t tht instnt [3]. As n lterntive model, the combintion of inclining block rtes (IBR) nd RTP hs lso been proposed, in which the price remins unchnged up to threshold point determined by the energy utility compny, beyond which it increses s either liner or non-liner Power Grid Aggregtor 1 Chrging Sttion 1 Smrt Meter V2G Control System Aggregtor 2 Chrging Sttion 2 Aggregtor Chrging Sttion Fig. 1: Bi-directionl informtion/energy flow between MCS- MA nd V2G control system. function [17] of the current lod. For ske of simplicity, we however dopt the RTP model where the instntneous price, P (k, t), is liner function of the lod in tht time slot, i.e. P (k, t) = c 0 + c 1 zk t, where c 0 nd c 1 re non-negtive rel numbers symbolizing the intercept nd slope, respectively, nd zk t is the lod t CS k t time t. Denoting the bse lod generted t CS k by demnds excluding EVs s L t k, the instnt lod zk t is given s: z t k = L t k + M x t,k e t,k, 1 k K; 1 t T. (2) C. Overll Profit Clcultion Under the RTP model, the overll profit gin of n EV owner (P EV (k, t)) is equl to the overll revenue due to chrging/dischrging opertions (R EV (k, t)) minus the mintennce nd bttery degrdtion/fluctution costs (C EV (k, t)) in ech slot of its llocted time intervl. The revenue which is obtined for ech EV t given time slot is equl to the integrtion of pricing reltion with the electricity lod chnging from the bse to the current chrging/dischrging lod t tht time slot. Therefore, quntity R EV (k, t) cn be clculted s follows: R EV (k, t) = z t k L t k (c 0 + c 1 z τ k)dz τ k. (3) Note tht since for chrging nd dischrging opertions respectively negtive nd positive revenue is obtined by the owner of EV, hence, the negtive sign hs been considered in the right hnd side of eqution (3). The uxiliry cost of EV t sttion CS k is computed s the summtion of its mintennce nd bttery fluctution/degrdtion costs during its service intervl t CS k given by the following summtion: C EV (k, t)= ( x t,k MC k + α(e t,k) 2 + β(e t,k e t 1,k )2). M (4) Therefore, the profit tht the EV owner cn obtin in time slot t t CS k is: P EV (k, t) = R EV (k, t) C EV (k, t). (5)

4 SUBMITTED TO IEEE TRANSACTIONS ON SMART GRID, DECEMBER It is esy to see tht EV owners gin positive revenue when the energy flow from vehicles to the grid is more thn the flow in the opposite direction. On the other side, the profit mde by CSs due to the energy demnd of EVs (P CS (k, t)) is the sme s in (5), where R CS (k, t) is the negtion of (3), with the uxiliry cost (C CS (k, t)) given s below: C CS (k, t)= M x t,k (LC k MC k ). (6) Since the ultimte im of the energy utility provider is to mximize the overll joint profit of both, EV owners nd CSs, we consider weighting control prmeter 0 δ 1, such tht EV owners receive mximum profit when δ = 0 nd the CSs obtin highest profit when δ = 1. Hence, the totl obtinble profit for both deling sides in T time slots is: T T K K P tot =(1 δ) P EV (k, t) + δ P CS (k, t). (7) k=1 t=1 k=1 t=1 IV. PROBLEM STATEMENT In this section, we define the problem of offline EV scheduling for chrging nd dischrging in n MCS-MA set-up, where ll informtion regrding the EVs in the system re vilble priori. The im is to ssign EVs to CSs such tht overll profit proportion of both, EV owners nd CSs, is mximized. The problem formultion tkes into ccount the cpcity nd instnt electricity price t ech sttion. By considering the binry time slot lloctions t CSs nd the continuous energy flow during the chrging/dischrging process, the problem cn be written in the following MINLP form: mximize P tot (8) subject to A,k t f,k tl,k D,k, M, 1 k K (9) x t,k = 0, M, 1 k K, K t [1, t f,k 1] [tl,k + 1, T ] (10) x t,k 1, M (11) k=1 t T,k x t,k x t,k = 0, M, 1 k k K, t,t t T,k x t,k = ( M t T,k, t T,k (12) t T,k x t,k) T,k, M, 1 k K (13) x t,k C mx k, 1 k K, 1 t T (14) z t k = L t k + M x t,k e t,k, 1 k K, 1 t T 0 E initil d,k F + t S,k (t) x,k e t,k B, (15) M, 1 k K, t T,k (16) Algorithm 1 GreedyMCS Input: Dt(, k) = (A,k, D,k, T,k, E initil, B, E finl, r ) for vehicle M nd 1 k K, nd δ. Output: Alloction of to the most profitble CS. 1: while vehicle M rrives do 2: Brodcst messge contining Dt(, k) to ll CS k ; 3: for ll CS k do 4: if M CG then 5: Execute ComputeProfit Chrge(k); 6: else if M DG then 7: Execute ComputeProfit Dischrge(k); 8: else 9: Execute ComputeProfit V2G(k); 10: Send bck reply messge including P EV (, k) nd P CS(, k) from ggregtor t ll CS k to vehicle ; 11: Send reservtion messge to CS k where k is given s: k = rg mx k { (1 δ)pev (, k) + δp CS(, k) } ; 12: for ll t T,k do 13: N t k N t k + 1; 14: Solve LP problem in (21) to find optiml schedule for vehicle t CS k ; E finl =E initil d,k F + K k=1 t T,k x t,k e t,k = r B, M, 1 k K (17) 0 e t,k Pc mx, 1 k K, M CG, t T,k (18) Pd mx e t,k 0, 1 k K, M DG, t T,k (19) P mx d e t,k P mx c, 1 k K, M V 2G, t T,k (20) The objective function (8) ims to mximize the totl djustble profit of EV owners nd CSs which is derived in (7). Constrint (10) gurntees tht ech EV is llocted only to the time slots within its service intervl for chrging/dischrging t ech chrging sttion. Constrints (11)-(13) stte tht ech EV cn be llocted to the set of non-preemptive time slots t only one chrging sttion nd the eqution (14) imposes the limittion on the mximum number of vehicles tht cn be ccommodted in CS t ech time slot. Moreover, (15) defines the lod of ech CS in terms of the bse lod nd EV chrging/dischrging powers in ech time slot. Constrint (16) ensures tht the finl energy stored in the bttery of the EV during its service period is non-negtive nd bounded by its mximum bttery cpcity. Eqution (17) mkes sure tht the finl energy stored in the EV bttery t the end of its service intervl stisfies the demnd requirement initilly set by the EV owner. Finlly, constrints (18)-(20) specify the fesible rnges for chrging/dischrging powers in ech slot bsed on the vehicle type. V. PROPOSED ONLINE GREEDY ALGORITHM The MCS-MA problem defined in (8)-(20) belongs to the clss of NP-Hrd problems due to the integrlity decision of llocting EVs to CSs. For the offline scenrio, when complete informtion on EV scheduling throughout dy is known before hnd, the combintion of brnch-nd-bound (BB) nd liner progrmming relxtion (LPR) cn be pplied to find

5 SUBMITTED TO IEEE TRANSACTIONS ON SMART GRID, DECEMBER the optiml solutions to the problem [18]. Nonetheless, the computtionl complexity of BB increses significntly with the number of EVs, time slots or number of CSs. Moreover, in rel-time scheduling, dt regrding future incoming EVs re not vilble in dvnce, therefore mking BB n imprcticl pproch. In line of such shortcomings, we rely on n efficient online greedy lgorithm yielding lower overll profit compred to the optiml solution obtined in offline nlysis. Referred to s GreedyMCS, the proposed lgorithm is given in Algorithm 1. A. GreedyMCS Algorithm Design As vehicle rrives t the system, its corresponding dt is brodcst to the ggregtor of ll CSs vi remote wireless communiction. Depending on the vehicle type, either one of the three procedures nmely, ComputeProfit Chrge, ComputeProfit Dischrge, or ComputeProfit V2G is executed by the locl scheduler in every sttion so s to determine the service pln of the EV nd the locl profit ttinble t ech sttion. For vehicle t CS k, the prtil revenue tht the EV cn contribute to the totl obtinble revenue during time slot t T,k is given by negting the integrtion of pricing function with the vrible lod chnging form the current lod zk t to the updted lod zt k + et k. Accounting for the uxiliry costs including the bttery fluctution/degrdtion nd the mintennce costs incurred in ll time slot during the service intervl of EV, its contributed profit is computed ccording to reltion (5). A similr clcultion is performed to compute the prtil profit for CS k from llocting EV. The profit tht cn be obtined t ll CSs is sent long with the response messge to the EV. On receiving response messges from ll CSs nd compring their profits, ccording to line 11 of Algorithm 1, the EV decides on the most suitble CS where the loclly mximum reltive profit counting the profit of both EV nd CS cn be obtined. A reservtion messge is then trnsmitted bck to the selected CS by the EV. After the EV is plugged-in to the designted sttion, sy CS k, the ggregtor requests the energy exchnge between vehicle nd the grid during its service period by solving the following root men-squre devition (rmsd) bsed optimiztion: t T minimize (zt,k k + e t,k z k ) 2 (21) T,k Subject to constrints (16)-(20) when the sttion index k is substituted in the equtions. Here, z k is the verge lod over ll time slots t CS k. The energy exchnge between the ggregtor of the trget sttion nd the power grid is regulted by the V2G control system nd monitored by the smrt meter. The profit computtion procedure executed t ech CS works bsed on n updting heuristic. With respect to the EV prticiption type, every locl scheduler runs the corresponding profit computtion procedure to find the locl profit for both, EV owners nd CSs, bsed on the rrivl/deprture times, initil nd finl energy, bttery cpcity, nd rel-time electricity price in ech time slot. At first, the verge electricity price over ll slots in the service intervl of the EV is clculted nd its energy requirement is eqully distributed over the Algorithm 2 ComputeProfit Chrge(k) 1: if t [ A,k, D,k ], Nk t + 1 Ck mx 2: for t := t f,k to tl,k do 3: e t,k (E finl E initil )/ T,k ; then 4: for t := t f,k to tl,k 1 do 5: vgp rice t T,k P rice(k, t)/ T,k ; 6: e t,k ( (2 vgp rice P rice(k, t ))/vgp rice ) e t 7: if e t,k > Pc mx then 8: e t,k Pc mx ; 9: if e t,k < 0 then 10: e t,k 0; 11: totlchrge t 12: vgchrge (E finl t=t f e t,k;,k totlchrge)/ ( T,k t ); 13: if vgchrge > Pc mx then 14: e (tl,k t )(vgchrge Pc mx ) ; E initil t t f,k c ; 15: vgchrge P mx 16: else if vgchrge < 0 then 17: e (tl,k t )vgchrge ; t t f,k 18: vgchrge 0; 19: e t,k e t,k + e, t [t f,k, t ]; 20: e t,k vgchrge, t [t + 1, t l,k]; 21: Updte zk t with e t,k, t [t f,k, tl,k]; 22: P rice(t) c 0 + c 1z t k, t [t f,k, tl,k]; 23: Compute P EV (, k); 24: Compute P CS(, k); 25: return P EV (, k) nd P CS(, k),k; intervl. Within consecutive itertions over the intervl size, the power of the EV is updted in ech time slot bsed on the difference between the current nd verge price. Once determined, the chrging/dischrging power in the following time slots is djusted such tht constrints (16) nd (17) re both stisfied. Consequently, the electricity lod is then updted in ccordnce with (2). In the finl step, the procedures return the locl prtil profits P EV (, k) nd P CS (, k). We note tht the pseudocode for dischrging opertion hs been omitted here due to its similrity with procedure ComputeProfit Chrge. The procedure ComputeProfit V2G hs been lso neglected here due to the spce limittion nd is vilble upon the request. B. Customer Stisfction Blncing energy efficiency nd user stisfction is nother unresolved chllenge in smrt grids. The corollries tht follow ddress this issue in the context of our problem. Corollry 1. The locl procedures for profit computtion t ech CS gurntees tht constrint (16) is stisfied t the end of ech time slot during the service period of the EV. Proof. The proof hs been omitted due to the spce limittion nd is vilble upon the request. Corollry 2. The GreedyMCS lgorithm gurntees tht the finl energy demnd of ech EV is stisfied.

6 SUBMITTED TO IEEE TRANSACTIONS ON SMART GRID, DECEMBER Proof. The proof hs been omitted due to the spce limittion nd is vilble upon the request. C. Complexity Anlysis For nlyzing the messge complexity of GreedyMCS lgorithm, ech EV is ssumed to hve the cpbility of trnsmitting multiple messges simultneously. As evident in Algorithm 1, ech EV sends messge contining its dt to every CS in O(1). After completion of locl profit computtion t ech sttion, the ggregtors send bck the computed profit to the EV in O(1). Therefore, for system with m EVs nd K CSs, the messge complexity of the lgorithm is of order O(mK) in the worst cse. The overll computtionl time of the lgorithm includes the time complexity of the locl profit computtion t ech CS s well s the computtion time for finding the mximum locl profit t the EV side. Since ech CS executes the profit computing procedure independently, investigting the time complexity of only single CS suffices. Considering the worst cse scenrio where the service intervl of n EV my spn the entire dy, ccounting the selection of most suitble sttion ccording to line (11) of GreedyMCS s well s the time tken by optimiztion problem (21) denoted by t opt, it is seen tht the overll time complexity of the proposed ( lgorithm with m) vilble EV in the system is of order m( T 2 + K + t opt ) in the worst cse, where T is the totl number of time slots in scheduling dy. VI. SIMULATION RESULTS AND DISCUSSIONS In the former results presented in this section, we evlute the performnce of GreedyMCS in terms of overll chievble profit while the ltter sub-section is dedicted to performnce nlysis of the lgorithm from the perspective of ncillry services nmely, pek shving nd vlley fitting. We compre the proposed lgorithm with RndomMCS, which serves s bseline where n EV is llocted to rndomly chosen CS tht cn stisfy the service period demnd requested by the EV [4]. The lgorithms were implemented using Mtlb, while the rmsd-bsed optimiztion problem t ech CS ws solved using the CVX pckge [20]. A. Simultion Set-up We consider single dy V2G scheduling opertion eqully discretized into T = 24 time slots, ech of durtion t = 1 hour. The totl number of 1000 EVs leve their homes for office during morning time rndomly chosen form the uniform intervl U[5.m., 12p.m.] nd the number of CSs is ssumed to be 10. Unless explicitly mentioned, we ssume 50% of EVs prticipting in V2G progrm nd the equl remining 25% prticipte in only chrging nd dischrging. The distnce between the home of Ev nd CS k (d,k ), its verge speed nd the force of its electric motor re chosen from the uniform intervls [2km, 5km], U[3kw.h/km, 5kw.h/km] nd [50km/hrs, 60km/hrs], respectively. Depending on the EVs speed nd the distnce of their home to ech CS, their rrivl time to ech CS vries. Furthermore, ech EV chooses Electricity Bse Lod (kw) Bse Lod : [10 kw, 70 kw] 1AM PM AM Time of the Dy (1 AM 12 AM) Fig. 2: A typicl bse lod profile for summer dy [3]. preferred time period for its sty durtion t ech CS ccording to its time scheduling tht however for the ske of simplicity, we ssume to be chosen form the uniform intervl U[3hrs, 6hrs]. On the other side, the CS opertor specifies the strting nd ending time slots for the service intervl of EV t CS k with rndomly selected integer vlues from U [ A,k, A,k + ( D,k A,k )/2 ] nd U [ D,k ( D,k A,k )/2, D,k ], respectively. E initil t the time of deprture from the home follows the uniform intervl U[70%B, 90%B ] while the energy vilble in the bttery of EV t the time of rrivl to ech chrging sttion is clculted bsed on its distnce to tht sttion nd the force of its motor. For every PEV t chrging stte, the finl energy trget set by the owner follows the uniform distribution U[70%B, 90%B ] while for dischrging, the finl energy trget fter dischrging is set from the uniform intervl U[min(40%B, E initil d k F ), min(60%b, E initil d k F )] where here E initil represents the initil energy stored in the bttery of EV t the time of its deprture from the home. An idel bttery cpcity of 100kW h is considered for ll EVs. With bttery chrging rte of 1C s defined in [21], we consider the mximum chrging nd dischrging powers in ech time slot to be 15kW h nd 10kW h, respectively. The bttery degrdtion/fluctution prmeters nd the coefficients in the pricing model re set to respectively α = 10 3 $/kw h 2, β = $/kw h 2 nd c 0 = 10 3 $/kw h, c 1 = $/kw h/kw. The mximum EV cpcity t ech time slot of CSs re tken from the uniform intervl U [ m K +5, m K +10]. In ddition, we dopt typicl dily bse lod forecst from [3], with electricity lod fluctutions t 10kW (low) nd 70kW (high) for n entire dy. An instnce of the bse lod t rndomly selected CS during summer dy hs been depicted in Fig. 2. We lso ssume the mintennce nd service costs ssocited with EVs per time slot to follow distributions U[$0.3, $0.5] nd U[$0.2, $0.4], respectively. B. Discussions on Achievble Profit 1) Impct of Weighting Prmeter δ: In n MCS-MA setup with m = 1000 nd K = 10, we compre the performnce of the proposed lgorithm with its rndom counterprt in terms of the totl ttinble profit for both, EV owners nd CSs, by controlling the δ prmeter. As depicted in Fig. 3, GreedyMCS outperforms RndomMCS in term of the overll profit for vrying δ vlues. This is becuse the former strtegy

7 SUBMITTED TO IEEE TRANSACTIONS ON SMART GRID, DECEMBER Overll Obtinble Profit (US $) Reltive Profit (US $) GreedyMCS RndomMCS () The overll obtinble profit versus δ GreedyMCS PEVs GreedyMCS CSs RndomMCS PEVs RndomMCS CSs Weighting Prmeter (δ) (b) Reltive profit versus δ Fig. 3: Overll profit s function of δ for the proposed nd bseline strtegies. () Totl system profit for vrying δ vlues. (b) Profits mde by EV owners nd CSs through δ djustments. employs internl updting heuristics in order to wisely guide ech EV to the most profitble CS. Fig. 3b shows the gross profit tht cn be obtined by EV owners nd CSs for different vlues of δ. In contrst to the bseline pproch, GreedyMCS lloctes EVs to CSs in wy tht ech side mkes the mximum reltive profit depending on the weighting prmeter δ. Specificlly, lloction of EVs to CSs using GreedyMCS results in higher profit for EV owners when δ < 0.5 nd lrger profits for CSs when δ > 0.5. Hence, settling on n greeble δ vlue tht would minimize loss on either deling sides is vitl to ll locl schedulers. For instnce, it is pprent in Fig. 3b tht δ = 0.4 would yield minimum profit of $200 for CSs with tolernce of mximum $350 lost s profit to EV owners. Or, CSs cn chieve minimum profit of $1000 with minimum loss in profit of EVs for δ = ) Impct of Number of CSs: For fixed number of EVs in the system, we now study the effect of vrying number of CSs on the chievble profit. We set the number of EVs to 1000 ssuming ll of them prticipte in only chrging, δ = {0, 1}, nd K rnging from 5 to 60. Fig. 4 shows the result of this simultion. As we cn see, for δ = 0, the increse in the number of CSs leds to the increse in the overll obtinble profit. This is becuse s the number of sttions increses, EVs hve more choices in selecting more profitble CS for their service. On the contrr, for δ = 1, the profit mde by the CSs decreses with increse in K since though the revenue of CSs increse with K, their uxiliry costs re comprtively higher, thus contributing to their profit drop. As it is seen from the result in Fig. 4, fter K = 40 number of sttions, very smll increse in profit is chieved which therefore revels this point s the optiml number of sttions Obtinble Profit (US $) Optiml Number of CSs Number of Chrging Sttions (K) δ = 0 δ = 1 Fig. 4: Overll profit s function of number of CSs. for this prticulr prmetric setting. C. Discussions on Ancillry Services 1) Impct of V2G Penetrtion on Pek Reduction: In Fig. 5, the effect of incresing V2G penetrtion on pek lod reduction using GreedyMCS is shown. In this cse study, we hve considered two levels of penetrtion: 10% nd 20% with m = 1000, K = 10 nd δ = 0 ssuming the uniform time intervl U[8.m., 10.m.] for the leving time of EVs in the morning nd sty durtion chosen from the intervl U[6hrs, 9hrs] t ech CS. The figure depicts the percentge of pek reduction during the time intervl 11.m. to 4p.m. t CS 5. Note tht the percentge of pek reduction during specified time intervl t given chrging sttion is computed bsed on the difference between the mximum bse lod nd the lod generted by the lgorithm during tht intervl t the given sttion [7]. As seen in Fig. 5, pek lod reduces with increse in the V2G penetrtion level since the EVs return the energy stored in their btteries bck to the grid during high power demnds. In our simultion, reduction of 10.7% nd 28.5% is chieved for 10% nd 20% penetrtion levels respectively, throughout the time period [11.m., 4p.m.]. 2) Lod Shifting: Performnce comprison results for GreedyMCS nd RndomMCS in terms of finl electricity lod on the power grid generted during [11.m., 8p.m.] t CS 5 is presented in Fig. 6, where m = 1000, K = 10, nd δ = 0. EVs re divided into eqully 50% only chrging nd only dischrging with the leving time from the intervl U[10.m., 12p.m.] nd sme sty durtion s the previous scenrio. We observe tht our greedy pproch performs better in flttening the finl electricity lod thn the uncontrolled rndom strtegy. We use the root men-squre devition (rmsd) from the mximum bse lod during specified time intervl for vlley filling t given chrging sttion [7]. At CS 5, using the lgorithms GreedyMCS nd RndomMCS, the rmsd vlues respectively nd re obtined during the time intervl [3p.m., 8p.m.]. VII. CONCLUSIVE REMARKS This pper proposes n online scheduling lgorithm for EVs in geogrphiclly distributed re comprising of multiple chrging sttions, ech controlled by n individul ggregtor. Such set-up offers flexibility in chrging sttion

8 SUBMITTED TO IEEE TRANSACTIONS ON SMART GRID, DECEMBER Electricity Lod (kw) Electricity Lod (kw) V2G Penetrtion Percentge : 10% Pek Reduction Percentge : 10.7% Chrging Sttion 5 Time Intervl : [11 m, 4 pm] Bse Lod GreedyMCS () When V2G penetrtion level is 10%. V2G Penetrtion Percentge : 20% Pek Reduction Percentge : 28.5% 35 1h m 11 m 12 pm 1 pm 2 pm 3 pm 4 pm 5 pm 6 pm Time of the Dy (10 m 6 pm) (b) When V2G penetrtion level is 20%. Fig. 5: Pek lod reduction under different V2G penetrtion levels. () 10% penetrtion nd (b) 20% penetrtion. Electricity Lod (kw) GreedyMCS : rmsd = RndomMCS : rmsd = Bse Lod 40 GreedyMCS Chrging Sttion 5 RndomMCS m 12 pm 1 pm 2 pm 3 pm 4 pm 5 pm 6 pm 7 pm 8 pm Time of the Dy (11 m 8 pm) Fig. 6: Comprison in term of vlley filling t CS 5. selection for the incoming EV owners with service demnds. Accounting for the vritions in rel-time electricity pricing t different sttions, mixed integer non-liner progrmming optimiztion model is formulted to mximize the overll profit of both prticipnts, i.e. EV owners nd chrging sttions. Under uncertin EV rrivl times, our proposed greedy online scheduling lgorithm, nmely GreedyMCS, dopts weighting prmeter to djust the overll chievble profit nd uses efficient updting heuristics to guide ech EV to the most profitble chrging sttion. Results of simultion justify tht the proposed lgorithm not only improves the overll profit for the system, but lso results in better vlley flttening. Furthermore, the result lso revel the existence of n optiml number of chrging sttions for ny given number of EVs nd locl bse lod which, depending on locl system prmeters, cn ssist V2G system designers in optimizing their investment budget t ech loclity. 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