Impact assessment of short-term electricity market. design on the performance of plug-in electric vehicle. aggregators: An integrated approach

Transcription

1 Impact assessment of short-term electrcty market desgn on the performance of plug-n electrc vehcle aggregators: An ntegrated approach Stylanos I. Vagropoulos Power System Laboratory, School of Electrcal & Computer Engneerng, Arstotle Unversty of Thessalonk, Greece E-mal: Abstract: In ths paper a herarchcal, four-level optmzaton framework for ntegraton assessment of plug-n Electrc Vehcles (EVs) n electrcty markets s presented. The developed framework ncorporates coupled optmzaton routnes to model the optmal energy and regulaton market partcpaton strategy and the optmal realtme chargng management of an EV fleet n a combned approach, whch expands from day-ahead to second-ahead tme horzon. The developed tool allows for an n-depth assessment of electrcty market desgns n ntegratng EV fleets through ntermedary players, the EV Aggregators (EVAs). The performance of state-of-the-art market products, such as the performance-based regulaton market compensaton ruled by FERC, can also be quantfed. A detaled case study of 1000 EVs s examned, where the PJM market s modeled as the reference desgn. Emphass s gven on the regulaton market modelng and the reference regulaton market desgn s compared wth two other cases, one that allows asymmetrc regulaton capacty offerng and one where EVs respond to tradtonal, rather than dynamc regulaton control sgnals. Fnally, the case of perfect estmaton of EV fleet behavor s compared wth the case that the EV fleet behaves dfferently from what was ntally forecasted. The results presented unvel the value of the proposed framework. Keywords: Electrc vehcles, electrcty markets, regulaton market, electrc vehcle aggregator, optmzaton, stochastc programmng

2 Nomenclature and abbrevatons Nomenclature Indces (I ) t (T ) k (K ) (Ω ) ndex (set) of electrc vehcles ndex (set) of hourly tme ntervals ndex (set) of regulaton control sgnal ntervals,.e. 4 seconds ndex (set) of scenaros ndex of current operatng hour Parameters s scenaro s probablty of occurrence, DA E t day-ahead forecasted energy prce, n $/MWh Rup(/ dn) t forecasted regulaton up(/down) prce, n $/MWh, RT E, t real-tme energy prce durng hour t (average of sub-hourly real-tme prces wthn hour t), n $/MWh dc, up(/ dn) r, R up (/down) dspatch-to-contract rato Varables DA e t day-ahead demand bd, n MWh RTup(/ dn) t, r up (/down) regulaton offer, n MW-h de t, devaton between real-tme energy consumpton and day-ahead demand bd, n MWh I t, de nstructed devaton between real-tme energy consumpton and day-ahead demand bd, n MWh de U t, unnstructed devaton between real-tme energy consumpton and day-ahead demand bd, n MWh pop t, preferred operatng pont of the EV fleet durng real-tme operaton, n MWh 5mn pop preferred operatng pont of the th EV durng a 5mn nterval, n kw 4s sp chargng set-pont of the th EV durng a 4sec nterval, n kw.

3 Abbrevatons BOR Balancng Operatng Reserve RTM: Real-Tme Market DAM: Day-Ahead Market RCS: Regulaton Control Sgnal D. RCS: Dynamc Regulaton Control Sgnal RMCP: Regulaton Market Clearng Prce EV: Electrc Vehcle ( plug-n) RMCCP: Regulaton Market Capablty Clearng Prce EVA: Electrc Vehcle Aggregator RMPCP: Regulaton Market Performance Clearng Prce FERC Federal Energy Regulatory Commsson SO: System Operator OD: Operatng Day SOE: State-of-Energy OH: Operatng Hour T. RCS: Tradtonal Regulaton Control Sgnal 1. Introducton The expected penetraton of plug-n Electrc Vehcles (EVs) n the near future (IEA, 2015) creates prospects for a cleaner, more sustanable, and more decarbonzed future. However, a large EV penetraton rate should be carefully addressed, snce rregular EV chargng could have detrmental effects on power systems and electrcty market operaton as well as on power qualty at the dstrbuton level. In ths context, there s a vvd nterest n developng tools that would meet these challenges effectvely and an ongong debate on optmal desgn of electrcty markets that could effectvely ntegrate these emergng technologes (Green, 2008; NREL, 2013). Most research works that deal wth the ntegraton of EVs n electrcty market operatons adopt the dea of an ntermedary party, the plug-n Electrc Vehcle Aggregator (EVA) (MERGE, 2010) as a market player that partcpates n the market arrangements on behalf of the EV fleet that the EVA represents. However, besdes the market operatons, EVAs can control the EV chargng process durng real-tme operaton, can coordnate the chargng management of the EV fleet and smultaneously take advantage of the flexblty n the chargng process by provdng ancllary servces to the System Operator (SO), for example provson of regulaton servce by respondng to Regulaton Control Sgnal (RCS) requests (Tomc and Kempton, 2007; Brooks, 2002). Although prevous studes hghlghted the potental of EVs to provde varous knds of ancllary servces (Soshans and Denholm, 2010), regulaton servce s consdered the most valuable (Kempton et al., 2001).

4 EVA optmal partcpaton n the Day-Ahead Market (DAM) has been nvestgated n the past. Indcatve works can be found n Sortomme and El-Sharkaw (2011), Vagropoulos and Bakrtzs (2013), Momber et al. (2015), Vaya and Andersson (2015). Works that focus on the real-tme chargng management problem and RCS allocaton algorthms based on chargng prorty crtera can be found n Sortomme and Cheung (2012), He et al. (2013), Mohammed et al. (2014), Su and Chow (2012), Sun et al.(2014) and Vagropoulos et al.(2015). Works related to the optmal EVA partcpaton n DAM and Real Tme Market (RTM) can be found n Soares et al. (2014) and Yang et al. (2014) but they do not consder RCS allocaton to EVs. Lnkng between day-ahead market partcpaton and real-tme chargng management can be found n Sortomme and El-Sharkaw (2011) and Bessa and Matos (2014) where algorthms for real-tme chargng control are presented, however no RS allocaton prorty s ncorporated, battery dynamcs are gnored and n Sortomme and El-Sharkaw (2011) RCS uncertanty management s not ncluded. Fnally, there are works n the bblography that study the mpact of EV ntegraton n electrcty markets and regulaton servce, such as Donadee and Ilc (2014) and Goebel and Callaway (2013), However, n these works nether RCS allocaton n real-tme nor the mpact of dfferent RCS type selecton (tradtonal or dynamc) on the chargng process has been addressed. Ths work goes beyond the state-of-the-art and proposes for the frst tme a new herarchcal optmzaton framework sutable for mpact assessment of short-term electrcty market desgns on EV ntegraton n electrcty market and power system operatons. The developed platform ncorporates both algorthms for optmal bddng strategy of EVAs n the DAM and subsequent RTM sessons durng the Operatng Day (OD) as well as algorthms for the real-tme chargng management of EVs durng real-tme and the allocaton of the RCS to the EVs n a coordnated manner. Numerous qualtatve and quanttatve results can be derved from ths platform, for example assessment of both the effcency of a canddate market desgn n ntegratng EVs and the effcency of EV ntegraton n an exstng market settlement. To the best of our knowledge, no such detaled approach has been proposed before. The man contrbutons of ths paper are: Development of a herarchcal, four-level, optmzaton framework that ncludes both market partcpaton tools and real-tme chargng management n a combned approach. Optmzaton problems for three of the four levels have been developed n prevous works of the author (Vagropoulos and Bakrtzs, 2013;Vagropoulos et al., 2015). A level 2 problem, whch models the rollng, hour-ahead optmzaton strategy for RTM

5 partcpaton, s developed n ths work and t s ntegrated nto the framework. Ths level s crucal for accurate modelng of state-of-the-art market desgns snce t s the ntermedary step that lnks DAM partcpaton wth real-tme EV fleet chargng management. A qualtatve assessment of the regulaton market remuneraton mechansm under performance-based regulaton market desgn. To the best of our knowledge, t s the frst tme that such an n-depth evaluaton has been carred out. Comparson of three dfferent regulaton market desgns. The reference regulaton market desgn s compared wth two other cases, one that allows asymmetrc regulaton capacty offerng and one where EVs respond to a tradtonal, rather than dynamc regulaton control sgnal. Fnally, the case of perfect foresght of EV fleet behavor s compared wth the case that the EV fleet behaves dversely from what was ntally forecasted. Prelmnary presentaton of two nnovatve tools that have been developed and ncorporated nto the framework, one for RCS scenaro generaton and one for dynamc update of the EV fleet status durng realtme operaton. In secton 2 the developed framework s descrbed, and n secton 3 a detaled case study s set up. Conclusons are summarzed n secton Descrpton of the developed optmzaton framework In ths paper an EVA manages a fleet of I EVs and partcpates n the short-term DAM and RTM by submttng optmal demand bds and regulaton capacty offers. Undrectonal nteracton wth the grd s adopted,.e. the EVs are not capable of dschargng energy back to the grd: they can only devate from ther scheduled operatng pont, by reducng or ncreasng ther chargng rate. Although bdrectonal nteracton seems to be more proftable addtonal hardware and protecton are needed, and t leads to ncreased cyclng wear of the battery. Although expanson of the framework for bdrectonal nteracton s easy, the paper focuses only on undrectonal nteracton whch s consdered by the author as the most approprate choce for the ntal EV ntegraton phase. The EVA also controls the chargng process of each ndvdual EV n the fleet: once an EV s plugged n the EVA algorthm s responsble for modulatng the EV chargng power. In exchange, the EVA offers attractve tarffs to EV owners by sharng part of the profts. The EV tarff structure s outsde the scope of ths paper.

6 2.1 Consderatons on market partcpaton strategy The developed framework can practcally be parameterzed for any knd of electrcty market desgn that ncludes day-ahead, ntra-day and real-tme energy and regulaton markets. In ths paper the PJM market 1, consdered by the author as one of the most advanced pool-based markets worldwde, s modeled as the reference case for two reasons. Frstly, t s the only market that provdes free access to 2-sec RCS data (PJM, 2015c) whch are hghly valuable for the problem under consderaton. Secondly, t s the frst regonal market under FERC survellance that adopted the performance-based regulaton compensaton mechansm, whch s an advanced market desgn that ncentvzes the resources that are more effcent n provdng regulaton. The presentaton of the basc aspects of the reference market desgn n ths subsecton wll help the reader to follow the developed framework more easly. PJM operates a DAM, an RTM (balancng market), and markets for ancllary servce provson. In ths paper, there s a focus on DAM, RTM and regulaton markets (.e. automatc response servce to SO Automatc Generaton Control commands for Area Control Error correcton), (PJM, 2015a;PJM, 2015b). Focusng on DAM partcpaton, submsson perod for DAM offers/bds closes at 12:00 day-ahead (PJM, 2015a). Before that tme, the market partcpants (unts, load-servng enttes) submt supply-offers / demand-bds for energy to the SO n the form of quantty-prce pars (mult-step functons). The SO clears the day-ahead energy and schedules reserve market by co-optmzng energy and reserves usng least-cost securty constraned resource commtment and dspatch. The SO computes the cleared quanttes system-wde and per partcpant as well as the day-ahead energy Locatonal Margnal Prces. EVAs are assumed to execute ther optmal DAM partcpaton program (level 1) at 11:30 day-ahead [Fgure 2(2A)]. It s noted that n both DAM and RTM, the EVA s consdered as a self-scheduled, prce-takng, market partcpant (ratonal assumpton for small EV fleets) that submts quantty-only demand bds at the market prce cap and regulaton capacty offers at zero offer prce (PJM, 2015a; PJM, 2015b). It s assumed that the submtted regulaton offers are fully cleared, therefore the assgned regulaton capacty equals the submtted offer. The same s true for the submtted demand bds. Platform expanson for bddng curves s possble but t s not modeled here. 1 PJM Regonal Transmsson Organzaton, USA.

7 The resource owners that want to provde regulaton n the PJM balancng area are requred to submt no later than 18:00 day-ahead a) The maxmum MW amount - Offer MW - of regulaton capacty that the resource s wllng to provde for the next OD. b) a prce - Offer Prce - that should reflect the capablty of the resource n $/MW and the performance of the resource n $/ΔMW 2. Snce the EVA s a self-scheduled partcpant, the Offer Prce s zero. However, the above submssons are not bndng. Untl 60mn pror to the begnnng of the Operatng Hour (OH), when the regulaton market actually closes, partcpants may submt revsed regulaton capacty offers (whch are bndng) wth the followng restrctons: a) Offer Prce may not be changed; t s fxed to the one submtted before 18:00 day-ahead (n case of EVA t remans zero) b) Offer MW may be revsed to reflect the most recent operatng condtons; however, revsed offer quantty may not be hgher than the one submtted before 18:00 day-ahead. No penaltes are mposed for revsng the regulaton capacty offers (PJM, 2015b). Accordng to PJM rules, the resources must offer a regulaton capacty band,.e. the upward capacty equals the downward capacty (PJM, 2015b). The mnmum accepted quantty s 0.1 MW. After collectng regulaton offers, the SO adjusts them based on hstorcal performance ndces, ranks them n ascendng order and calculates the regulaton prce components, the Regulaton Market Capablty Clearng Prce (RMCCP), the Regulaton Market Performance Clearng Prce (RMPCP) and fnally the Regulaton Market Clearng Prce (RMCP) and posts the results no later than 30 mnutes pror to the start of the OH (PJM, 2015b). The opportunty for revsed regulaton offers 1-hour before the OH, s actually the strongest motvaton for the development of a level 2 optmzaton program whch s assumed to be executed hourly, 75mn before the OH, n a rollng manner (n lne wth PJM rules), by takng nto consderaton the latest EV fleet status and market condtons. When a resource partcpates n a PJM regulaton market, t can follow one of two canddate RCS; the tradtonal RCS (T. RCS) and the dynamc RCS (D. RCS). Actually, T. RCS s the low flter Area Control Error sgnal whch s sent to the tradtonal regulatng resources and D. RCS s the hgh flter Area Control Error sgnal 2 $/ΔΜW offer s part of the recent performance-based regulaton mechansm that PJM has adopted, where the compensaton for regulaton provson s based on the performance of the provdng resources. For more nformaton the reader s referred to (PJM, 2015b).

8 sent to the dynamc regulatng resources. D. RCS s desgned for resources wth hgh MW ramp rates and rapd turnaround, such as batteres and flywheels. The resultng D. RCS sgnal pushes movement to the outer edges of the resource maxmum capacty, however, t has a slght energy bas due to the duraton lmtatons of these resource types. T. RCS was desgned for resources wth lmted ramp rate, but wth no lmtaton on duraton. T. RCS and D. RCS are complementary, that s, dynamc resources respond quckly but lack the ablty to reman at that level for an extended perod of tme whle tradtonal resources requre tme to follow the sgnal but have unlmted duraton (PJM, 2015b). Fgure 1(a) depcts T. RCS and D. RCS for a day. The dfference n the energy bas of the sgnals and the requested resources movement (mleage) s obvous. PJM broadcasts RCS every 2 sec. RCS s postve f the SO commands the provson of upward reserve (consumpton reducton n case of EVA) or negatve f the SO commands the provson of downward reserve (consumpton ncrease n case of EVA). RCS value (p.u.) (a) PJM Regulaton Control Sgnal Rdc value (p.u.) Tme horzon (4sec ntervals) T. RCS D. RCS (b) 15mn Dspatch-to-Contract rato coeffcents Tme horzon (15mn ntervals) Rdc Up (T. RCS) Rdc Down (T. RCS) Rdc Up (D. RCS) Rdc Down (D. RCS) Fgure 1: a) T. RCS and D. RCS (p.u.) for Aprl 22, 2014 (PJM, 2015x) and b) the correspondng ntervals. dc R coeffcent n 15mn An easy way to calculate the energy bas of an RCS provded to a resource s to calculate the dspatch-tocontract rato, dc R, defned as the rato of the real-tme actvated energy to the contracted regulaton capacty of ths resource, durng a defned tme nterval. Gven that an RCS s broadcast by the SO every 4sec, dc R for upward

9 actvaton s calculated n (1). The formula s the same for downward regulaton but for RCS values < 0. In PJM the percentage of the RCS allocated to one resource s proportonal to the percentage of assgned regulaton capacty of the specfc resource, relatve to the total SO assgned regulaton capacty (PJM, 2015d). Therefore, the RCS nstructed to the EVA equals the SO per unt (p.u.) RCS [Fgure 1(a)] multpled by the EVA assgned regulaton capacty. The correspondng Fgure 1(b). It s obvous that one drecton for longer tme. dc, up R and dc, dn R coeffcents for the RCS presented n Fgure 1(a) are presented n dc R coeffcents for T. RCS are much more energy based than D. RCS and follow RCS dc, up 15mn ( pu..) RS0 R ( pu..) (1) 225 After regulaton market clearng and after regulaton provson durng an OH the resources are compensated for ther partcpaton for that OH as follows. Regulaton Clearng Prce Credt = Regulaton RMCCP Credt + Regulaton RMPCP Credt = Assgned Regulaton (MW) x Actual Performance Score x (RMCCP + Mleage Rato x RMPCP) (2) In (2) Mleage Rato s the rato between the requested mleage for the RCS assgned to the regulaton resource and the RCS assgned to the tradtonal resource. That s : Mleage T. RCS For a tradtonal regulaton resource, mleage rato = 1 Mleage T. RCS (by defnton) Mleage D. RCS For a dynamc regulaton resource, mleage rato = 1 Mleage T. RCS Mleage Rato s untless and t s used only n Settlement for Regulaton Performance credt to resource. In ths paper, the mleage rato for dynamc resources equals 2.93, whch s the PJM mean value for June 2014 (PJM, 2015x). As stated before, the dfference n mleage between D. RCS and T. RCS s obvous n Fgure 1(a). In addton, the actual regulaton credts are dependent on the performance of the resource n provdng regulaton. In detal, the credts are proportonal to the actual hourly performance score (2) that the resource wll acheve, whch vares between 1 for perfect performance and zero (0) for no performance. The performance score conssts of three factors, correlaton, delay and precson score 0, weghted equally. Based on the very fast response capablty of the lthum-on batteres of EVs, correlaton and delay scores can be assumed to be equal to 1 and the

10 only factor that needs to be calculated s the hourly precson score, whch s calculated at 10 sec samples from the absolute response error as a functon of the resource s assgned regulaton capacty n (3) and (4) where n s the number of samples (.e. 360) n hour t. 1 Actual Performance Score t = Precson score t 1 errork n kt (3) Error k Responsek RCSk Assgnment ( MW ) t (4) Fgure 2: (1) Interactons between the EVA, the Market Operator (MO), the SO, and the EVs. Level 1 (blue, dotted lne), level 2 (purple, dashed lne), level 3 (red lne) and level 4 (green, dashed lne) nteractons. In yellow,the EV nformaton that s exchanged once wth the EVA (e.g. desred State-of-Energy, EV battery sze). Market operator and SO could be the same entty n some electrcty markets. (2) Descrpton of the EVA optmzaton problems. Tme arrangements are parameterzed for the PJM market. The colors are n lne wth the frst dagram. Each dot declares the tme that each problem s solved, and the sold part of lne n levels 1 and 2 express the tme nterval for whch bndng decsons are produced.

11 2.2 EVA optmzaton problems The herarchcal, four-level optmzaton structure of the developed smulaton platform s descrbed below. Interactons between the nvolved partes and the optmzaton problems of the EVA are presented n Fgure 2. An overvew of the bndng and advsory schedules that are produced by the four optmzaton problems are presented n Table 1 and analyzed n greater detal below. Table 1: Overvew of bndng and advsory decsons produced by the optmzaton problem of each level Executon tme Bndng schedules Scenaro-dependent, advsory schedules Level 1 OD-1, at 11:30 DA t e, t[1, T ] r RTup t,, r RTdn t,, de t,, t[1, T ], Ω Level 2 Once an hour, OH-75mm RTup RTdn r, r, de U RTup RTdn r t, r t, U t de, t[ 1, T ], Ω Level 3 Level 4 Every 5mn Every 4sec 5mn pop - 4s sp - A. Level 1: Optmal DAM partcpaton strategy The frst optmzaton level ncludes the problem of optmal partcpaton n the DAM sesson of the Operatng Day (OD) [Fgure 2(2A)]. The DAM optmzaton strategy of ths paper s based on the framework developed n Vagropoulos and Bakrtzs (2013), namely a two-stage stochastc lnear program wth recourse whch produces optmal frst-stage decsons and second-stage, scenaro dependent schedules. Frst-stage decsons are selfscheduled, quantty-only demand bd submssons n the DAM, DA e t. Second-stage schedules are produced for the EV fleet preferred operatng pont durng the OH, pop t, and the revsed regulaton capacty offers (Offer MW) RTup t, r and r RTdn, for the OH. The second stage varables are not bndng, they are just advsory schedules, gven the t real-tme operaton uncertanty whch s expressed va approprate scenaros for future realzatons of the random varables of the problem. The fnal bndng values pop, RTup r and RTdn r for each OH are produced by the rollng soluton of the level 2 problem [Fgure 2(2B)]. It s worth pontng out the mportance of the two-stage stochastc problem of ths level, snce t handles the nterdependency between nstructed devaton de I t, and unnstructed devaton de U t, n a systematc way. Devaton s referred to a dfference between the DAM cleared quantty, DA e t and the actual real-tme consumpton, former s devaton owng to System Operator commands for regulaton reserve actvaton durng real-tme operaton RT e t. The

12 and the latter s devaton owng to the EVA. Due to the lmted energy nature of EV batteres as power system resources, regulaton actvaton whch nstructs a PEV fleet to charge more or charge less than the scheduled preferred operatng pont, pop t,, could possbly lead to an unnstructed devaton n a future operatng hour. Ths s a result of the fact that the total chargng demand request for a PEV fleet s a-pror defned (by the actual chargng needs), therefore any nstructed devaton whch affects the remanng chargng demand mght be self-cancelled by an unnstructed energy devaton n a subsequent tme nterval. Otherwse, early battery depleton or early battery saturaton may be nevtable, makng the PEV fleet unable to honor the assgned regulaton. Fnally, an mportant feature whch s hghlghted through the developed model s the fact that the EVA can take advantage of the unnstructed devatons and arbtrage between DAM and RTM under a two-settlement system (Stoft, 2002), DA,, DA E ( DA RT, ) RT E t t t t t, e e e $, (5) where the term n parenthess equals the total energy devaton between the day-ahead poston and realtme actual energy delvery, de t,, (6) whch s traded at the RT energy prce,, RT E t,. Instructed devaton, gven dc R coeffcents presented earler, s calculated n (7). Advsory pop t, s calculated n (8). The EVA s objectve functon (9) s the mnmzaton of the cost of energy purchased both n DAM and RTM (assumng a two-settlement system) mnus the revenue from regulaton market partcpaton. Also, penaltes for excessve unnstructed mbalances between DAM and RTM are mposed. Unnstructed devatons greater than 20% between DAM and RTM are penalzed wth the Balancng Operatng Charge (BOR) (PJM, 2015a). Results of the level 1 problem are presented later n the case study. For the detaled problem formulaton and a more n-depth analyss of the problem the reader s referred to Vagropoulos (2013). DA RT I U t, t t, t, t, de e e de de (6) I dc, up RTup dc, dn RTdn t, t, t, t, t, de R r R r (7) DA U t, t t, pop e de (8) ( ) e r r de pnlty pnlty (9),,,, DA E DA Rup RTup, Rdn RTdn, RT E,, U Up, U Dn t t t t t t t t t t, t t t

13 B. Level 2: Optmal RTM partcpaton strategy Level 2 optmzaton ncludes the rollng process that generates optmal bndng schedules for r RTup RTdn, r and de U durng the OH ( ). Ths problem takes nto account the DAM clearng results DA e t whch are already known, and optmzes the RTM quanttes usng two-stage stochastc lnear programmngg wth recourse ncludng the latest avalable nformaton about the EV fleet status and market condtons. It s executed once an hour, 75mn before the OH. In Fgure 3, an llustratve example of two consecutve executons s presented. The scheduled quanttes are bndng only for the second upcomng nterval (purple lne) and advsory for the recedng tme horzon (look-ahead capablty). Ths step s also presented n Fgure 2(2B). The objectve functon (10) results from modfcaton of (9). The problem now expands from the current OH to the end of the recedng horzon. Frst stage decsons RTup are r, r RTdn and de U and second stage decsonss are the values of the same varables for the recedng horzon. Non-antcpatvty constrants have been added for hour. Resultss of ths level are presented later n the case study. For more nformaton on the omtted constrants, the reader s referred to Vagropoulos and Bakrtzs (2013). RT, E I, ( de, U de ) ( pnlty UUp, pnlty U, Dn ) T t 1 RT, E t, de U, Up U, Dn t, ( pnltyt, pnlty t, ) (10) Fgure 3: Rollng soluton of the level 2 problem. An example of one hour of the market partcpaton phlosophy of levels 1 and 2 and the nterdependence between I t, U, de and de t, s presented n Fgure 4. It s assumed that the EVA executes levell 1 problem and submts a demand bd of 9 MWh n the DAM whch s cleared. Before 18:00 the EVA submts a regulaton offer of 6 MW (both upward and downward) whch s the maxmum value of the RTup(/ dn) r t, between all second-stage scenaros

14 (producedd also n levell 1). 75 mnutes before the OH the EVA solves the level 2 problem that produces pop (8) RTdn whch s (let s say) 5 MWh and the bndng regulaton offer for the OH, (let s say) r r U t, example de = 9-5=4 MWh (8). BOR charges are mposed on devatons greater than 20% of MWh,10..8 MWh] zone, therefore a BOR charge s debted for (7.2-5=) 2.2 MWh. Gven that the regulaton offer s cleared, let us assume that durng real-tme the EVA s commanded to provde regulaton whch leads to an energy I t bas of 1. 3 MWh. Therefore, de, =1.3 MWh. From (6) the fna al t, de =1.3+ +(-4)=-2.7 MWh. RTdn 5 MW. In ths DA e t,.e. outsde [7.2 Fgure 4: Example for energy devaton calculaton. C. Level 3: Optmal preferred operatng pont allocaton strategy The optmzaton problem of level 3 allocates pop (whch has been determned 75mn before the OH from level 2 (8)) to the EVs durng the OH. pop allocaton s not arbtrarly selected but t s based on prorty crtera. The prorty crtera are expressed by prorty weghts w and the smaller the weght, the hgher the chargng prorty of an EV. Two man parameters determne the prorty weght for each EV: the energy requred to complete the chargng, r E, and the tme remanng untl dsconnecton tme, T. For example, two EVs wth the same chargng energy request wll not be gven the same prorty f the frst dsconnects after one hour and the second dsconnects r after fve hours. The frst EV s assgned hgher chargng prorty. The optmzaton framework for 5mn pop specfcaton based on prorty weghts has been developed n Vagropoulos et al. (2015). The basc dea of the optmzaton problem s presented n (11)-(13). An evaluaton of the mpact of the combned prorty weght parameterzaton s carred out n Vagropoulos et al. (2015). Due to the dynamcally evolvng nature of prorty

15 weghts, the problem for pop re-allocaton should be executed very often. A reasonable value for ths control level s a 5mn nterval [Fgure 2(2C)]. In ths case, the level 3 problem s solved 12 tmes durng an OH. Mnmze 5mn w pop (11) subject to r 5mn pop pop (12) r w f( E, T ) (13) D. Level 4: Optmal RCS allocaton strategy The fourth level ncludes the optmal allocaton of the RCS to the EVs. Durng real-tme operaton the EVA s requested to respond to RCS whch s generally broadcast from the SO every few seconds (e.g., n PJM RTO every 2 s, n New York ISO every 6 s). Therefore, each tme a new RCS s broadcast, the EVA solves the level 4 problem whch adopts the same phlosophy of the level 3 problem,.e. when regulaton down s requested, the EV wth the hgher chargng prorty charges frst. Ths level s nested n level 3, snce the fnal EV chargng setpont determnaton, 4s sp, depends on the earler 5mn pop specfcaton. A regulaton up request mples 5mn pop reducton. On the contrary, a regulaton down request mples 5mn pop ncrease. The full problem descrpton s presented n Vagropoulos et al. (2015). 2.3 Scenaro generaton methodology for regulaton control sgnal The RCS s hghly uncertan and almost mpossble to be forecasted. Therefore, an nnovatve methodology for RCS scenaro generaton has been developed and has been ncorporated nto the optmzaton framework that generates artfcal 4-sec RCS tme seres whch keep the statstcal propertes of the authentc RCS (.e. autocorrelaton). The tool s called every hour, before the soluton of the level 2 problem. The tool s based on an teratve process that uses an Artfcal Neural Network and has been mplemented n Matlab. After RCS scenaro generaton the dc, up(/ dn) t, R coeffcents are calculated (1) and are ncorporated nto the level 2 model. Due to space lmtatons, the mathematcal background s omtted from ths paper. However, for the whole dea the reader s referred to Vagropoulos et al. (2016), where the same methodology has been proposed to create scenaros for other random varables (lke electrc load, photovoltac and wnd energy producton). The ANN has been traned ndependently for

16 scenaro generaton of D. RCS and T. RCS. In Fgure 5 an example of D. RCS scenaro generaton s presented. The full presentaton of the methodology wll be presented n future work. Regulaton control sgnal (p.u.) Tme horzon (4sec ntervals) PJM D. RCS Scenaro 1 Scenaro 2 Fgure 5: Scenaro generaton for the D. RCS. At the 500 th- tme nterval the scenaro generaton begns. Two created RCS scenaros that expand two hours ahead are depcted n the fgure. lo T exp1 T h T dep T exp SOE act SOE lo T act exp1 T T h T dep T act SOE lo T T act exp1 T h T dep T lo T exp2 T h T dep T exp SOE lo T exp3 h T T dep T exp SOE lo T h T dep T act SOE lo T h T act T dep T Fgure 6: The basc features of the proposed tool for dynamc EV fleet status update 2.4 Tool for dynamc EV fleet status update When the EVA solves the level 1 problem, the optmal decsons are based on estmatons/expectatons about the EV fleet behavor, most possbly based on hstorcal records. However, t s lkely that durng real-tme

17 operaton the EVs wll not behave as expected and changes n arrval tme and State-of-Energy (SOE) at arrval tme mght be recorded. These changes should be taken nto account when the rollng soluton of the level 2 problem s carred out, snce n dfferent cases the decsons wll be based on naccurate nformaton. A new tool has been developed and has been ncorporated nto the optmzaton framework that dynamcally updates the EV fleet status wth updated estmatons as the optmzaton wndow moves forward n tme or wth the actual nformaton when an EV plugs for chargng. The basc dea of the tool s presented n Fgure 6. Let us assume that the arrval tme of each EV s recorded. After many recordngs, the EVA can ft a dstrbuton to the arrval tme, between mn. and max. arrval tme, and the EVA calculates the mean value of the dstrbuton, lo h T and T. A unform dstrbuton s selected exp1 T [Fgure 6 (a)] whch, when combned wth the expected arrval SOE, exp exp1 SOE together form the par of the ntally estmated EV behavor ( T, SOE exp ) 3. As the level 2 problem s executed sequentally and as long as the OH, s stll earler thant ( T exp1 ), the par ( exp1 T, SOE exp ) s stll used as the estmated EV behavor [Fgure 6 (a)]. In case the EV arrves earler than expected, act data are updated wth the actual ones ( T, SOE act exp1 ) [Fgure 6 (b)]. If the EV arrves at the estmated tme but wth act SOE exp SOE the actual act exp1 SOE s taken nto account n the level 2 problem, ( T, SOE act ) [Fgure 6 (c)]. When exceeds and exp1 T and the EV has not arrved yet, a new exp2 T s calculated as the mean value between h T [Fgure 6 (d)]. Ths recalculaton s executed dynamcally each tme equals exp( n) T exp1 T and the EV has not arrved yet [Fgure 6 (e)]. In case that exp ( n ) T reaches T h and the EV has not arrved yet, then the algorthm assumes that the EV wll not arrve at all and gnores t from the followng executons of the level 2 problem [Fgure 6 (f)]. Fnally, there s always the chance that the EV wll arrve much later. In that case, whenever t arrves the EV act status s updated wth ( T, SOE act ) [Fgure 6 (g)]. Ths proposed tool s very powerful as t manages the uncertanty n EV fleet behavor dynamcally nto the optmzaton routnes and to the best of our knowledge t s the frst tme that such a tool has been proposed. A better nsght n the tool functonaltes wll be gven n the case study below. 3 dep dep Departure tme T and desred SOE at T are consdered known and unchangeable n ths paper, thus the tool focuses only on uncertanty n arrval tme and SOE at arrval tme.

18 3. Case Study The developed optmzaton framework s examned n a resdental, nght chargng case study where the EVA partcpates both n DAM and RTM sessons, whle modulatng the chargng of 1000 PHEVs durng the realtme operaton. All smulatons were carred out n an Intel Xeon workstaton, wth CPU E5-2687W v2 at 3.4 GHz. The system has 128 MB of nstalled RAM memory. The optmzaton problems were modeled n GAMS envronment and CPLEX solver was used. A reference EV fleet has been created and ts characterstcs are produced by random number generators that follow the probablty dstrbutons of Table 2. Two EV fleet scenaros, Fleet A and B, are then created and evaluated. Fleet A equals the reference fleet, assumng perfect EV fleet behavor estmaton durng real-tme. Fleet B however behaves dfferently from what was ntally forecasted (reference fleet). It s assumed that durng real-tme operaton 25% of the fleet (250 EVs) plugs n for chargng 1 to 3 hours later than the expected arrval tme wth an ntal SOE devaton rangng between [-15%,+15%] from the expected, followng a unform dstrbuton. Another 25% of the fleet wll never plug n and the rest 50% wll behave exactly as t was expected. The management of the EV fleet behavor durng the real-tme operaton s carred out by the tool developed n subsecton 2.3. In Fgure 7, the EV number that plug n per hour s presented for the two EV fleet scenaros, together wth the aggregated chargng energy requested by the EVs that plug n per hour. The rated chargng power s 3kW and the desred fnal SOE s set at 97% for all the EVs. Table 2: Probablty Dstrbutons for the EV Fleet Parameters Dstrbuton Mean value St. devaton Mn. value Max. value Battery capacty (kwh) UD* Arrval Tme TGD* 19:00 2 h 16:00 1:00 Departure Tme TGD* 7:00 2 h 5:00 12:00 Intal Battery SOE (%) TGD* * UD: unform dstrbuton, TGD: truncated Gaussan dstrbuton

19 Energy (kwh) Tme horzon (h) Energy, Fleet A Energy, Fleet B EV number, Fleet A EV number, Fleet B Ev number Fgure 7: Aggregated chargng energy requested by the EVs that plug n per hour and number of EVs that plug n per hour. Three canddate regulaton market desgns are compared, Cases A, B and C. Case A s the current desgn of the PJM market, where the EVA submts symmetrc regulaton capacty offers and responds to D. RCS. Ths should be consdered as the reference case. In case B, the EVA stll responds to D. RCS, however t has the opportunty to submt asymmetrc regulaton capacty offers,.e. RTup r s not necessarly equal to r RTdn. Fnally, n Case C the EVA submts symmetrc regulaton capacty offers but now t responds to T. RCS. The characterstcs of the examned regulaton market desgns are summarzed n Table 3. For each case both EV fleet scenaros are evaluated. Table 3: Characterstcs of the regulaton market desgns Market Desgn case RCS provson Regulaton offerng Fleet scenaros RTup RTdn Case A D. RCS Symmetrc, rt, r t, 2 scenaros: Fleet A and Fleet B RTup RTdn Case B D. RCS Asymmetrc, rt, r t, 2 scenaros, Fleet A and Fleet B RTup RTdn Case C T. RCS Symmetrc, rt, r t, 2 scenaros, Fleet A and Fleet B The nput data related to market parameters for level 1 and level 2 problems are presented n Table 4. Some nput parameters are modeled as smple pont forecasts and some others are modeled va scenaros. In the level 1 problem, 100 equprobable scenaros are gven as nputs (10 for Rt, and 10 for dc RT, E t, ), whle n the level 2 dc problem the equprobable scenaros are 10 (10 Rt, scenaros produced dynamcally by the tool descrbed n subsecton 2.2). Tuesday, 22 Aprl 2014 s selected (arbtrarly) as the OD under examnaton. BOR charge s consdered /MWh (PJM, 2015c). Fgure 8 depcts some prce tme seres that are used as nput n level 1 and level 2 problems. Pont forecasts are not too close to the actual prces, especally for regulaton market prces. Ths devaton however s challengng, snce the level 2 problem should produce an optmal decson based on the updated prces, takng also nto account level 1 bndng schedules whch were produced based on non-perfect prce forecasts. Prce forecastng s out of the scope of the current paper.

20 Table 4: Input data for level 1 and level 2 optmzaton problems of the case study. Data source: PJM (2015c). Input Type Data OD: Tuesday, 22 Aprl 2014 Level 1 problem, t DAE Pont Forecast up t and dn t Pont Forecast 4 Weghted DAM prce of the PJM regon of 21 Apr s used as naïve prce forecast for the next day, the OD. RMCP for dynamc and tradtonal resources (dverse values due to dfferent mleage rato are calculated from (2)). RMCPC and RMPCP of 20 Apr were used as naïve forecasts for the OD. Perfect performance score, equal to 1, n used n (2) for RMCP calculaton., t RTE, 10 Scenaros Dfferences between DAM-RTM prce for the prevous ten days (between Apr. 2014) are calculated and then appled to DAM prce pont forecast to generate 10 prce scenaros. dc, up(/ dn) R t, 10 Scenaros 15mn dspatch-to-contract rato (up/down) calculaton based on (1) from the real-world PJM D. RCS and T. RCS between Apr Level 2 problem, t RTE Pont Forecast RTM prce of 22 Aprl 2014 up t and dn t Pont Forecast RMCP prce of 22 Aprl 2014 dc, up(/ dn) R t, 10 Scenaros Executon of the RCS scenaro generaton tool presented n subsecton 2.3 every hour, 75mn before each OH. Dspatch-to-contract rato coeffcents are then calculated based on (1) Prce ( /MWh) Tme horzon (h) Forecasted DAM prce Actual DAM prce Forecasted T. RMCP Actual T. RMCP Actual RTM prce Forecasted D. RMCP Actual D. RMCP Fgure 8: Input prce tme seres for level 1 and level 2 optmzaton problems. In Fgure 9, results from the level 1 problem for DAM partcpaton are presented for Cases A, B and C. For both EV fleet scenaros the DAM strategy s the same, snce the problem at ths level s based on the ntal EV fleet estmaton (reference case). RTup t RTdn t DA e t for submsson n the DAM s presented. The 100 scenaro-dependent second stage, advsory r,, r, are also depcted and the dversty of ther possble future realzatons per scenaro s 4 RMCP remunerates the regulaton capacty band. As an example, a regulaton band of 3 MW, mples 3 MW of regulaton up and 3 MW of regulaton down. For consstency wth ths rule and ablty for dscrete remuneraton of regulaton up and down n case B, up up t t ( RMCP)/2 n (9) and (10) n all cases.

21 obvous. In Case A, based on the rule for symmetrc offers, rt, rt,. However, n case B there s a clear preference for greater provson of regulaton down rather than regulaton up. Ths s an ntutve result because, n contrast to regulaton up, regulaton down provson concdes wth the man target of the EVA, EV chargng. Thus, the EVA creates a proft by sellng regulaton down capacty and chargng the EVs durng real-tme by respondng to regulaton down actvaton commands. Fnally, n Case C the strategy s smlar to Case A, but greater standard devaton among the second-stage advsory schedules s recorded. In the same fgure, the aggregated maxmum rated chargng power of the fleets presented (purple lne) together wth the aggregated, scenaro-dependent max. RT chargng power whch gets reduced as the EV fleet batteres reach hgh SOE. Ths reducton s a result of the ncorporaton nto the optmzaton models of the Constant Current-Constant Voltage (CC-CV) chargng strategy whch s very popular for lthum-on battery systems. The SOE threshold for method change s consdered 85% for all the EVs. The reader s referred to Vagropoulos and Bakrtzs (2013) and Vagropoulos et al. (2015) for detaled nformaton of CC-CV modelng. It s fnally notced that the energy purchased n DAM by the EVA s lower than the total chargng needs of the reference fleet ( kwh) because of (a) the expectaton for regulaton down provson whch commands the EVs to charge and (b) the arbtrage between DAM and RTM market. Arbtrage opportunty s obvous at hours 1:00-2:00. For these hours scenaro-dependent popt, schedules are produced whch RTup equal the rt, values of the correspondng scenaro. However, the EVA does not submt demand bds n the DAM for those schedules, because the model estmates that energy purchase n RTM would be more proftable. In Fgure 10, regulaton down capacty offer results from the rollng optmzaton process of level 2 are presented for one scenaro (out of ten). As stated before, the level 2 problem s executed 75 mnutes before the OH and only the regulaton capacty offers for the next OH are bndng. As an example, the soluton of the problem at 15:45 (rght axs) creates bndng schedules for the OH that begns at 17:00 (front axs). The schedules for the subsequent tme horzon are just advsory and are replaced by the next rollng executons (.e. the executon at 16:45 creates bndng schedules for the OH that begns at 18:00). Only results for fleet B are depcted due to space lmtatons. Snce the rollng process s contnuously updated wth the latest EV fleet status, the advsory schedules are modfed n each soluton. It s obvous that the lower number of EVs that fnally plug n for chargng (Fgure 7) lead to contnuously reduced regulaton down capacty offers as the problem evolves n tme. In cases A and C regulaton down offer s much lower than n case B whch s an expected result, as dscussed earler for level 1 RTup RTdn

22 results (Fgure 9). Fnally, an nterestng result s that the advsory schedules produced by the level 2 problem (Fgure 10) are not closely related to level 1 advsory schedules (Fgure 9). The updated nformaton close to the OH leads to updated advsory schedules and more robust decsons. (a) Case A: D. RCS, symmetrc regulaton offerng DA and RT Quanttes (kw-h) Tme horzon (h) DA and RT Quanttes (kw-h) DA and RT Quanttes (kw-h) (b) Case B: D. RCS, asymmetrc regulaton offerng Tme horzon (h) (c) Case C: T. RCS, symmetrc regulaton offerng Tme horzon (h) DA DA demand bd ( e t ) Rated chargng power ( RTup PL Pchrg ) RT regulaton up offer ( rt, ) RTdn RT max RT regulaton down offer ( rt, ) Max. RT chargng power ( PL p,, t ) Fgure 9 : Results of the level 1 problem (optmal DAM partcpaton strategy) 5. In Fgure 11, the fnal bndng regulaton capacty offers are presented for the whole tme horzon, together wth the actual RCS broadcast to the EVA at a 4sec frequency for Fleet A scenaro. In Fgure 12, the same quanttes are presented for fleet B scenaro. By comparng Fgure 11 and Fgure 12 t can be nferred that the regulaton offerng strategy s smlar n two scenaros but n fleet B scenaro the regulaton offers are lower, snce the level 2 model s contnuously updated wth the latest nformaton about the EV fleet. In addton, the lower offers n fleet B scenaro 5 chrg P RT max s the rated chargng power of each chargng staton and pt,, s the maxmum chargng power whch becomes lower than hgh SOE (Vagropoulos and Bakrtzs, 2013;Vagropoulos et al., 2015). PL s a parameter whch equals 1 as long as an EV s plugged n. chrg P at

23 lead to lower RCS magntude. Up and down regulaton offers are equal n cases A and C, as expected, whle n case B the tremendous ncrease of regulaton down offer s obvous. Fnally, the RCS requestss that could not be served are presented n black color. In fleet A scenaro, the porton of RCS that s not served s almost neglgblee n Cases A and B and very low n case C. The unserved RCS requests however ncreasee n fleet B scenaro, manly durng the frst hours of the OD. Ths result s explaned by the varable behavor of fleet B. The level 2 problem s ntally based on the referencee fleet estmaton whch s not accurate. As tme goes by, the algorthm s updated wth the latest EV data and the offers are adjusted to meet actual condtons. So, after some unanswered RCS requests n the begnnng, the EVA can respond to the RCS requests for the remanng perod of tme. Fnally, the dfference n T. RCS trajectory s obvous n Case C compared to the D.RCS trajectory of cases, A and B. Fgure 10: Regulaton capacty offers produced from level 2, look-ahead optmzaton problem for one scenaro out of ten. In black the bndng offers, n other colors advsory, look-ahead schedules.

24 Power (kw) Power (kw) Power (kw) (a) Case A: Dynamc RCS, symmetrc regulaton offerng (b) Case B: Dynamc RCS, asymmetrc regulaton offerng (c) Case C: Tradtonal RCS Tme horzon (4s) Assgned up regulaton EVA RCS Assgned down regulaton EVA RCS not served Fgure 11: Fleet A. Regulaton market results for cases A, B and C for the whole problem horzon Power (kw) Power (kw) Power (kw) (a) Case A: Dynamc RCS, symmetrc regulaton offerng (b) Case B: Dynamc RCS, asymmetrc regulaton offerng (c) Case C: Tradtonal RCS Tme horzon (4s) Assgned up regulaton EVA RCS Assgned down regulaton EVA RCS not served Fgure 12 : Fleet B. Regulaton market results for cases A, B and C for the whole problem horzon

25 In Fgure 13, the actual real-tme chargng process of one EV (out of 1000 EVs) s presented. The reduced chargng power above 85% SOE due to CC-CV chargng method modelng s obvous. The chargng schedule s a result of level 3 and level 4 programs. The level 3 program allocates pop 5mn n to the EV. When 5mn pop s assgned, regulaton up provson can be requested by the EV, whch mples a reducton of the chargng rate that can vary between zero and popp 5mn. Regulaton down can be requested when the EV charges wth a rate lower than the maxmumm possble. Allocated popp 5mn (produced n level 3), s presented together wth regulaton up and down requests (produced n level 4). The summaton of 5mn pop and regulaton up and down requests results to 4s sp. Power (kw) POP pop 5mn n T m e horzon (4s) Regulaton up request Regulaton down request SOE 100% 90% 80% 70% 60% State-of-Energy Fgure 13: 5mn pop, regulaton up and down requests and SOE trajectory for one EV. Fgure 14: Advsory chargng schedules of the level 2 problem for one EV out of and one scenaro out of 10. One feature of the level 2 problem s that ts look-ahead strategy creates look-ahead advsory chargng scheduless for the EVs. In Fgure 14, these advsory look-ahead schedules are presented for one EV and for one scenaro. Level 2 problems produce these schedules n quarters. The value of the tool for dynamc EV fleet status

26 update (subsecton 2.3) s obvous. The EV was ntally expected at 18:00 wth ntal SOE 65%, thus the problem produces advsory schedules untl 18:00 when t s realzed that the EV has not plugged n. Then, a new expected arrval tme s calculated and assgned to the EV [Fgure 6(d)] for the next executon. The EV fnally plugs n at 20:00 wth ntal SOE 50%. The actual data are then taken nto account and the advsory schedules are based on them. The precson score of the cases under evaluaton s calculated from (3) and s depcted n Fgure 15. Its value wll determne the fnal compensaton based on the performance-based regulaton mechansm (2). For Cases A and C one score s calculated (referred to the regulaton band) but for case B a dverse score s calculated for upward and downward regulaton. For the majorty of hours, the precson score s greater than 99%. Lower scores ( 97.5%) are recorded for case B, fleet B at hours 16:00 and 17:00 and for Case C at hours 18:00 and 2:00. Focusng on Case C, fleet B scores the lowest value, 24.5% at hour 18:00. Ths s an expected result based on the unserved RCS request of the thrd hour of Fgure 12(c). However, apart from the low score of ths partcular hour a general comment s that even under uncertan EV fleet behavor, the optmzaton framework can handle the uncertanty, manly due to the rollng executon of the level 2 problem and the developed tool for dynamc EV fleet status update. The EVA s able to acheve a) hgh precson score that does not reduce the regulaton profts notceably and b) partcpaton as a relable regulaton provder n the regulaton market. 1 Precson score Tme horzon (h) Case A: Fleet A Case A: Fleet B Case B: Fleet A (dn) Case B: Fleet B (dn) Case C: Fleet A Case C: Fleet B Fgure 15: Precson score calculaton. For case B, only the score for regulaton down score s presented. The score for regulaton up s always 1. Fnally, n Table 5, numercal results after the executon of the developed framework for the OD are presented. In rows 3-6, the dfferent cost/proft components and the total chargng cost (row 7) for the OD s gven. DAM strategy s ndependent of the fleet scenaro. It s obvous that the EVA pays more n the RTM than n the DAM. Ths s an expected result, snce as explaned earler (Fgure 9), the DAM demand bds are lower than the requested energy. What s also worth pontng out s that n Case B, there s a bg reducton n DAM cost and a