Optimal Recharging Strategy for Battery-Switch Stations for Electric Vehicles in France

Transcription

1 Optmal Rechargng Strategy for Battery-Swtch Statons for Electrc Vehcles n France Margaret Armstrong, Charles El Hajj Moussa, Alan Gall, Phlppe Rvère, Jérôme Adnot To cte ths verson: Margaret Armstrong, Charles El Hajj Moussa, Alan Gall, Phlppe Rvère, Jérôme Adnot. Optmal Rechargng Strategy for Battery-Swtch Statons for Electrc Vehcles n France <hal > HAL Id: hal Submtted on 9 Nov 2012 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.

2 Interdscplnary Insttute for Innovaton Optmal Rechargng Strategy for Battery-Swtch Statons for Electrc Vehcles n France Margaret Armstrong Charles El Hajj Moussa Jérôme Adnot Alan Gall Phlppe Rvère Workng Paper 12-ME-07 November 2012 CERNA, MINES ParsTech 60 boulevard Sant Mchel Pars, France Emal: ferrera@mnes-parstech.fr

3 Optmal Rechargng Strategy for Battery-Swtch Statons for Electrc Vehcles n France M Armstrong 1, C El Hajj Moussa 2, J Adnot 2, A Gall 1 & P Rvere 2 1. Cerna, Mnes-ParsTech, 60 Boulevard Sant-Mchel, Pars France 2. Centre Energétque et Procédés, Mnes-ParsTech, 60 Boulevard Sant-Mchel, Pars France Correspondng author: Margaret Armstrong Abstract Date: 27 June 2012 Most papers that study the rechargng of electrc vehcles focus on chargng the batteres at home and at the work-place. The alternatve s for owners to exchange the battery at a specally equpped battery swtch staton (BSS). Ths paper studes strateges for the BSS to buy and sell the electrcty through the day-ahead market. We determne what the optmal strateges would have been for a large fleet of EVs n 2010 and 2011, for the V2G and the G2V cases. These gve the amount that the BSS should offer to buy or sell each hour of the day. Gven the sze of the fleet, the quanttes of electrcty bought and sold wll dsplace the market equlbrum. Usng the aggregate offers to buy and the bds to sell on the day-ahead market, we compute what the new prces and volumes transacted would be. Whle buyng electrcty for the G2V case ncurs a cost, t s possble to generate revenue n the V2G case, f the arrvals of the EVs are evenly spaced durng the day. We compare the total cost of mplementng the strateges proposed wth the cost of buyng the same quantty of electrcty from EDF. Keywords: day-ahead aucton market, vehcle-to-grd, grd-to-vehcle 1

4 Introducton Over the next years most European countres are plannng to ntroduce electrc vehcles (EV) n order to reduce greenhouse gas emssons and to cut polluton levels n urban areas. Accordng to Hacker et al (2009), the German government plans to have 1 mllon EVs by 2020 and 5 mllon by 2025; the Irsh government ams for 10% of the natonal fleet to be electrc by 2020 whle the Spansh government has commtted to havng 1 mllon electrc or hybrd cars on Spansh roads by The French grd operator has developed two scenaros for the ntroducton of EVs (RTE, 2009). In the reference scenaro there wll be 1 mllon EVS n 2020 and 2.7 mllon n 2025; the second scenaro s more ambtous: t envsages 3.5 mllon EVs n 2020 and 6.7 mllon n In both cases the demand for electrcty wll ncrease consderably. The mpact on the system wll depend on when the batteres are recharged. Schneder et al (2011) studed three scenaros for rechargng the batteres of one mllon EVs n the Washngton-Baltmore Metropoltan Area: unmanaged chargng, consumer-prce ncentvzed rechargng where prce dfferentals n electrcty tarffs are desgned to dssuade car owners from rechargng ther batteres durng peak perods, gettng a central network operator (CNO) to coordnate the chargng of a large number of batteres n response to real-tme prces. They concluded that the thrd opton would lead to lower wholesale electrcty prces as well as reducng load peaks. So n ths paper we only consder the case where the chargng of the batteres s coordnated. Broadly speakng there are two ways of chargng batteres: by pluggng the EVs nto a smart plug at the owner s home or workplace, or by exchangng the depleted battery for a fully charged one at a battery swtch staton (BSS). The mpact of the frst opton has been studed by many authors ncludng Rousselle (2009) for France, and Hadley and Tsvetkova (2009) and Lyon et al (2012) for the USA. In a study sponsored by the French grd operator RTE, Rousselle (2009) smulated the recharge tmes 2

5 and the state of charge n the battery, n order to estmate the total load curve. Her analyss hghlghted the mpact of unmanaged chargng on the load curves. She dd not study the mpact on electrcty prces. Hadley & Tsvetkova (2009) determned the margnal generaton type n 12 regons n the USA, and hence the mpact on wholesale prces for dfferent rechargng scenaros. A recent study of the economc mpact of smart meters by Lyon et al (2012) was motvated by a decson by the Colorado Publc Utlty Commsson to dsallow part of the costs of the Smart Grd Cty project n Boulder, Co, on the grounds that the benefts of the smart meters had not been adequately establshed. Usng data from two dfferent ndependent system operators, MISO n the Mdwest and PJM on the east coast, they demonstrated that shftng chargng from daytme to off-peak perods could lead to bllons of dollars of savngs. They concluded that whle tme-of-use prcng s worthwhle n both systems, the economc benefts of optmal chargng of EVs dd not appear to justfy the costs of nvestng n the smart grd nfrastructure requred to mplement real tme prcng. To take advantage of the tme-of-use prcng homeowners only need an applance tmer costng between $12 and $60 whereas they need a smart meter worth $150 to respond to the real-tme prcng. As the opton to recharge batteres at home or at the workplace has already been studed thoroughly, ths paper focuses on the battery exchange opton, and uses France to llustrate how the strateges could work. Intally we assumed that the BSS operator captured 10% of a fleet of 3 mllon EVs as ts clents and that these 300,000 vehcles were recharged twce per week, gvng 85,700 batteres to recharge per day on average. Ths corresponds to the usage pattern for the second famly car n urban areas. But t rapdly became clear that the economcs of the BSS depends on the number of batteres to be recharged per day and the number of spare batteres held by the BSS but not on the total number of EVs. For example, f 10,000 taxs sgn up for a battery exchange contract, they would requre an exchange battery at the end of each drver s shft (and possbly another whle watng for a fare at the arport). Ths alone would account for 20,000 to 30,000 batteres per day. 3

6 The number of spare batteres held by the BSS has a marked nfluence on when the batteres are recharged. If the BSS has only a small number of batteres, t would be oblged to recharge them as soon as they arrve n order to have fully charge batteres avalable as clents arrve. As ths would put a stran on the power supply at peak perods, we assume that the BSS has enough spare batteres to recharge them n off-peak perods. Another mportant choce for the BSS operator s whether to provde power to the grd durng peak hours (that s, operate n vehcle-to-grd mode, V2G) or just to buy power (that s, grd-to-vehcle G2V mode). The postve effects of vehcle-to-grd power transfers (V2G) are well-known: t lowers wholesale electrcty prces and reduces the load at peak hours (Kempton and Tomc, 2005; Denholm and Short, 2006; Tomc and Kempton, 2007; Scott et al 2007). So we develop strateges for both the V2G and G2V operatons. In contrast to the PJM area whch uses real-tme locatonal margnal prces, few countres n Europe currently use nodal prcng, Poland beng an excepton (Svorsk, 2011), even though a recent study (Neuhoff et al, 2011) advocated t to reduce congeston. At present the day-ahead aucton market s the man wholesale electrcty market n western European countres. In some countres such as Ireland (Fnn et al, 2012) and the Iberan Pennsula (Tomé Sarava, 2007; Camus et al, 2011) there s a pool, but n Scandnava and n the Central West Europe market (Benelux, France and Germany) only part of the electrcty s sold through the organzed market. To buy/sell through the day-ahead aucton market nterested partes must send frm offers specfyng prces and quanttes for each 1-hour perod (30 mnutes n Ireland), before 11am or 12 noon on the day pror to delvery. The electrcty bourse comples the aggregate curves of bds to buy electrcty and of offers to sell for each hour and computes the ntersecton of the two curves to determne the market fxng prce. Ths prce apples to all buyers and sellers provded that the nterconnecton capacty s suffcent to allow the requred transfers. Wthn France, the transmsson and dstrbuton grds are dense enough so that the same prce apples throughout the country. If a BSS were to set up busness n France, the management could negotate a contract to buy power drectly from the hstorc utlty, EDF, or one 4

7 of ts compettors. Alternatvely the BSS could trade through the day-ahead market run by the bourse, Epexspot, but n order to trade, t would need a strategy for decdng how much to offer for each hour of the day 1. Ths paper proposes strateges for buyng and sellng power through bourse, whch have been optmzed assumng that the management of the BSS ams to maxmze corporate profts n the long-term by mnmzng the operatng costs of rechargng the EVs n the short-term. Fnally we compare the cost of usng these strateges to recharge the batteres of the EVs wth the cost of purchasng the same quantty of electrcty at the prce specfed by the new NOME law 2 : 40 n 2011 and 42 per MWh n Ths s not the frst paper to propose algorthms for chargng EVs. Taher et al (2011) developed a demand response servce for a fleet of around 10,000 PHEVs. They assume that vehcles plug n perodcally over a gven perod of tme (say 12 hours) and report ther drvng schedule for the next n hours. To ensure that the total amount of electrcty suppled to EVs stays wthn lmts that are acceptable to utltes they put an hourly cap on chargng. Earler on, Han et al (2011) and Wu et al (2011) had constructed decson-makng algorthms for mnmum-cost rechargng schedules whch consdered the vehcles ndvdually rather than collectvely as a fleet. Ma et al (2010) optmsed the rechargng to fll up the overnght valley. But none of these papers consdered buyng and sellng va the day-ahead aucton market. The paper s structured s follows. The next secton descrbes the methodology used and explans the assumptons that have been made. The results are presented n Secton 3: frstly, the schedules for rechargng the batteres; secondly, the cost of carryng out these schedules and thrdly ther mpact on the day-ahead market (.e. on prces and on the volumes transacted). The conclusons follow n Secton 4. 1 We assume that the BSS operator s a prce-taker who offers to buy/sell a certan quantty whatever the prce. In the future we plan to work on optmsng the prce at whch the BSS offers to buy/sell power. 2 The French government recently passed the NOME law (short for Nouvelle Organsaton des Marchés de l Electrcté) whch requres the hstorc utlty, EDF, to provde base-load electrcty from nuclear power plants to new entrants at a regulated tarff (40 n 2011 and 42 per MWh n 2012). Ths prce was desgned to cover the full cost of nuclear energy ncludng nvestments, producton, decommssonng and the long-term storage of nuclear waste, as a benchmark for evaluatng the cost of chargng the batteres. 5

8 Research methodology The frst step when optmsng the schedules for rechargng batteres s to decde what data to use. One possblty would be to use the data over a long perod of tme (e.g. several years). Three factors made us thnk that ths s not approprate. Frstly data from before the creaton of the CWE market n November 2010 comes from a tme when the market structure was dfferent. Secondly, the markets are evolvng gradually because of the ntroducton of renewable energy. The producton mx s changng and so wll the strateges of buyers and sellers on the bourse. Thrdly, electrcty consumpton s nherently seasonal, wth marked dfferences between summer and wnter, as well as between the dfferent days of the week. For all these reasons we thnk that more robust strateges can be developed by usng a relatvely short tranng set that reflects the current market structure and tradng practces. We chose a movng tranng set consstng of the aggregated offers to buy/sell electrcty on the day-ahead aucton market durng the prevous 4 weeks. As the usage patterns vary from one day of the week to another, dfferent strateges are developed for each day of the week and the tranng set conssts of same day of the week over the prevous four weeks. Publc holdays are taken nto account because electrcty consumpton s dfferent on holdays compared to workng days. Care s also requred wth the day n sprng when Europe changes over from wnter tme to summer tme and agan n autumn wth the change back to wnter tme 3. Market data for the past two years, 2010 and 2011, were used n the study. Over the past 5 years several mportant changes have been made to the structure of electrcty markets n Western Europe. Frstly n 2007 the markets n France, Belgum and the Netherlands were coupled. Ths means that provded the transmsson capacty was suffcent, the three countres had a common prce. In November 2010 the Central Western European market was formed by couplng Germany wth those three countres. So our study covers the perod before and after a major structural change n the French electrcty market. One of our objectves was to see how much the 3 On the Saturday nght n March of the change-over to day-lght savng, there are only 23 hours, whereas n autumn there s a day wth 25 hours. 6

9 optmal strateges changed because of the market couplng wth Germany, and whether there were problems just after the change-over when the tranng set uses data before the market couplng to determne the strateges appled afterwards. The next pont to decde was when the clents were lkely to arrve and when the batteres would be charged. To smplfy the computatons we assumed that no clents arrve between 10pm and 6am. In G2V mode, the batteres are recharged from 10pm untl 6am 4 and all vehcles must be fully charged by 6am when clents start arrvng. The G2V strategy gves the optmal amount to buy for each of these 8 hours. In V2G mode, all the batteres must also be fully charged by 6am but as the BSS can buy or sell at any tme durng the 24 hour perod, the optmal strategy gves the amounts to buy or sell for each of the 24 hours. In contrast to the G2V case, the arrval tmes durng the day have a marked effect on the V2G strategy. Two extreme scenaros are consdered: (A) all EVs arrve at 6am and (B) the arrval of the EVs s spread evenly from 6am untl 10pm. It s assumed that on arrval batteres contan 10% of the nomnal charge (24KWh). Secondly due to techncal losses between the grd and the battery, 5% s lost each tme a battery s charged or dscharged (Badey, 2012 p13; Dang et al, 2010). By way of comparson, Lyon et al (2012) consdered a battery capacty of 16 KWh and a chargng effcency of 88% based on the specfcatons of the 2011 Chevy Volt. Lke them we do not take account of the wear and tear on batteres due to chargng and dschargng. The key step n the study s to determne the mpact of buyng or sellng more power on the day-ahead market. Fgure 1 shows a schematc representaton of the offers to buy and the bds to sell electrcty for a gven hour 5. As we have assumed that the BSS operator s a prce-taker, an offer to buy power would shft the aggregate offers to buy to the rght, leadng to a hgher prce (Fgure 2 left). Fgure 2 (rght) llustrates the effect of sellng electrcty, whch drops the prce. 4 The tmes 10pm and 6am correspond to a cheap tarff proposed by EDF for heatng hot water systems. 5 In ths fgure the mnmum prce s 0. Ths was the case before the market couplng wth Germany. Snce then the market has adopted the German conventon of havng a mnmum 7

10 Prce Volume Fgure 1: Aggregate offers to buy and sell electrcty durng a gven hour. The ntersecton of the two curves gves the market fxng prce and volume. Prce Prce Volume Volume Fgure 2: Aggregate offers. If the BSS wshes to buy power, the aggregate curve of offers to purchase would be shfted to rght leadng to a hgher prce (left); conversely f the BSS wshes to sell power, the aggregate curve of offers to sell would be shfted to rght, leadng to a lower prce (rght). Optmsaton procedure Our objectve s to determne the quanttes q of electrcty to charge nto or dscharge from the batteres n the th hour for =1, 24, to ensure that all the batteres are fully charged by 6am the next day. By conventon q s postve when the battery s beng charged and negatve when t s beng dscharged. The quanttes to be bought or sold on the bourse depend on the extent of losses when chargng and dschargng the batteres. If the quantty q s charged nto the batteres after losng 5% of energy durng the chargng process, then the quantty bought on the bourse was 1.05q ; and conversely f q s dscharged from the batteres, then 0.95q wll be avalable for sale on the bourse. prce of It may seem unnatural to sell electrcty for a negatve prce but some producers prefer to pay to contnue to produce rather than havng to stop. 8

11 Havng chosen 6am s the reference tme when all batteres must be fully charged, t s natural to number the hours as shown n Table 1. Hours numbered =1 through to 18 correspond to hours H7 to H24 on the bourse, whle hours numbered =19 to 24 correspond to H1 to H6 the next day. Table 1: Conventon for numberng the 24 hours n the day, wth =19, 24 beng on the next day = Hour H7 H8 H24 H1 H6 When the BSS sells electrcty, the revenue generated s postve; conversely when t buys power, t ncurs a cost. Let p(q ) be the contrbuton to the BSS s revenue from chargng or dschargng the quantty q n the th hour on a gven day. Now we develop the equatons for optmsng the V2G case. Those for the G2V case are very smlar except that q 1 = 0, q 2 = 0 q 18 = 0 and q 19 0, q 20 0 q In both cases, the objectve functon 6 has to be maxmsed subject to a certan number of constrants: q p( q ) 24 φ =. Let M be the number of spare batteres held by the BSS. Let N mn be the mnmum number of batteres to be kept fully charged n case more clents than expected arrve on a gven day. Let A be the number of EVs expected to arrve n the th hour that day. Clearly example, M = 100,000; N mn = 10,000 and 24 = 1 = 1 24 = 1 M > A + N mn. In our A = For smplcty we have assumed that the same number of batteres has to be charged each day of the week, but the methodology would be exactly the same f t vared. Let k be the capacty of each battery. On arrval batteres stll have 10% resdual charge. Snce all M batteres must be fully charged at 6am each 6 To smplfy the analyss the ntal captal expendture has been consdered a sunk cost and has not been ncluded n the objectve functon because t does not nfluence the optmsaton of the day-to-day tradng strateges. Smlarly we gnore the revenue for tarffs pad by users. 9

12 day, the frst constrant concerns the net ncrease n the charge n the batteres: q = 0.9k A = 1 = 1 As the charge n the batteres cannot be less than zero or more than 100% of the capacty, there are also lmts on the quantty that can be physcally charged nto the batteres or dscharged from them n any gven hour, and hence on the quanttes that can be bought or sold. For the V2G case, these depend on the expected hourly arrvals A. Durng the frst hour, A 1 EVs are expected to arrve. After those batteres have been exchanged and the quantty q 1 s charged nto the batteres, the total charge left n the M batteres n the BSS wll be Mk 0.9A1k + q1 Ths amount must be greater than N mn k and less than Mk: N k Mk 0.9A k + q mn 1 1 ( ) 0 M N 0.9A k + q mn 1 1 Mk 0.9A k + q Mk q 0.9A k By the th hour n the day, a total of (A 1 + +A ) EVs should have arrved. The cumulatve amount put nto the batteres and dscharged from the batteres wll be (q 1 + +q ), so the total charge left n the batteres n the BSS wll be j j= 1 j= 1 Mk 0.9k A + q Ths gves the nequaltes j 0 M N 0.9 A k + q j j= 1 j= 1 q 0.9k A mn j j= 1 j= 1 j for =1, 23 for =1, 23 Because all the batteres must be fully charged by 6am, the constrant on the 24 th hour of the day s: q = 0.9k A = 1 = 1 10

13 Summng up, the system to be maxmsed s: 24 φ = = 1 ( ) q p q Subject to the constrants 0 M N 0.9 A k + q j j= 1 j= 1 q 0.9k A = = 1 = 1 q 0.9k A mn j j= 1 j= 1 j for =1, 23 for =1, 23 for =24 Ths system was solved usng Matlab 7 for every day of the year n 2010 and 2011 for the three cases: the G2V case, the V2G case for scenaro A when all the EVs arrve at 6am and the V2G case for scenaro B when the arrvals of the EVs are evenly spread over the 16 hours from 6am untl 10pm. The revenue generated by mplementng ths strategy (.e. the optmal revenue that could be generated) was also computed. In addton we computed the new market fxng prce and the new volume of transactons. Ths procedure gves the strategy that would have been optmal ex post; that s, when all the other bds are known but t clearly cannot be mplemented ex ante. The schedule that we propose to use s the average of the optmal strateges for the four days n the tranng set. We call ths the realsed schedule. The revenue that would actually be generated by applyng ths strategy n practce (.e. usng the actual aggregate curves for that day) s also computed. By defnton ths must be less than or equal to the optmal revenue. Fnally we computed the average of the four optmal revenues correspondng to the four days n the tranng, to see whether t gave a good estmate of how much revenue the realsed strategy would generate. We refer to t as the estmated revenue. 7 The only dffculty was to fnd a quck way of evaluatng the functon p(q) wthout havng to compute the ntersecton of the updated aggregate curves to buy and to sell power. Ths s 11

14 Results The results wll be presented n the followng order: frstly the optmal and realsed schedules for rechargng the batteres; secondly, the values generated by carryng out these schedules and thrdly the mpact that rechargng the batteres would have on the day-ahead market (.e. on prces and on the volumes transacted). Optmal and Realsed Schedules The schedules gve the quantty of electrcty n MW to buy or sell each hour of the day on the day-ahead market. The optmal schedules were averaged over perods of 13 weeks n wnter and summer 2010 (Fgure 3) and n 2011 (Fgure 4). Fgures 5 and 6 present the correspondng averages of the realsed schedules. In each case the sold black lne s for the V2G case for scenaro A (when all EVs arrve at 6am), whle the thck black dotted lne s for the V2G case for scenaro B (when the arrvals of EVs are evenly spread from 6am untl 10pm) and the sold red lne s for the G2V case. Both the optmal and the realsed schedules vary from one day of the week to another but the man dfferences are between the weekend and the other fve workng days. To save space only two typcal cases are presented: the schedules for 6am Sunday to 6am Monday, and for 6am Tuesday to 6am Wednesday. Lookng at these fgures we see that: done by pre-calculatng the ntersectons for a set of 100 evenly spaced ponts above and below the orgnal market fxng and nterpolatng lnearly n between these ponts. 12

15 Fgure 3: Average of the optmal schedules for the V2G case wth scenaro A where all EVs arrve at 6am (sold black lne), for the V2G case wth scenaro B where the arrvals of EVs are evenly spread from 6am untl 10pm (thck black dotted lne) and for the G2V case (sold red lne). In each case the averages (n MW) were computed over 13 weeks n 2010, n Jan-March (above) or July-Sept (below). The upper panel n each set of fgures corresponds to Sun-Mon; the lower one, to Tues Wed. 13

16 Fgure 4: Average of the optmal schedules for the V2G case wth scenaro A where all EVs arrve at 6am (sold black lne), for the V2G case wth scenaro B where the arrvals of EVs are evenly spread from 6am untl 10pm (thck black dotted lne) and for the G2V case (sold red lne). In each case the averages (n MW) were computed over 13 weeks n 2011, n Jan-March (above) or July-Sept (below). The upper panel n each set of fgures corresponds to Sun-Mon; the lower one, to Tues Wed 14

17 Fgure 5: Average of the realsed schedules for the V2G case wth scenaro A where all EVs arrve at 6am (sold black lne), for the V2G case wth scenaro B where the arrvals of EVs are evenly spread from 6am untl 10pm (thck black dotted lne) and for the G2V case (sold red lne). In each case the averages (n MW) were computed over 13 weeks n 2010, n Jan to March (above) or July- Sept (below). The upper panel n each set of fgures corresponds to Sun-Mon; the lower one, to Tues-Wed 15

18 Fgure 6: Average of the realsed schedules for the V2G case wth scenaro A where all EVs arrve at 6am (sold black lne), for the V2G case wth scenaro B where the arrvals of EVs are evenly spread from 6am untl 10pm (thck black dotted lne)and for the G2V case (sold red lne). In each case the averages (n MW) were computed over 13 weeks n 2011, n Jan to March (above) or July- Sept (below). The upper panel n each set of fgures corresponds to Sun-Mon; the lower one, to Tues-Wed For both V2G cases n wnter, the BSS sells power durng the noon peak perod, recharges the batteres durng the afternoon when prces are 16

19 lower, then sells power agan durng the evenng peak perod and recharges the batteres durng the nght; n summer, the evenng peak prce s not as hgh so less power s sold on the market. The rechargng schedule for the V2G case scenaro A when all the EVs arrve at 6am s qute dfferent from scenaro B when the arrvals are spread evenly from 6am untl 10pm. Much more power s bought and sold n scenaro B. The rechargng schedule for the G2V s almost the same as for scenaro A of the V2G case durng the nght-tme (10pm to 6am). Ths s why the sold red lne has almost covered up the sold black lne. The optmal schedules are qute smlar to the realsed schedules, but both vary from wnter to summer because of dfferent usage patterns because electrcal heatng s wdely used n wnter n France. Values generated by carryng out these schedules The value generated by mplementng these strateges can be ether negatve (.e. a cost that the BSS must pay) or postve (.e. revenue for the BSS). Three sets of values were computed for each case: the estmated value obtaned by averagng the optmal values for the days n the tranng set; the optmal value (obtaned by optmsng the schedule ex post) the realsed value obtaned usng the proposed schedule and the actual nformaton for the day. We had expected the estmated value to be a good predctor of the future value but ths turned out to be ncorrect. To llustrate ths pont, Fgure 7 shows the cross-plot of the estmated value (left) and the realsed value (rght) as a functon of the optmal value for the 24 hour perod Sunday to Monday n The correlaton coeffcent n the left panel s compared 0.97 n the rght one. That s, there s a strong correlaton between the realsed value and the optmal value, but vrtually none between the estmated value and the optmal one. Consequently the estmated value wll not be consdered n the rest of the study. 17

20 Fgure 7: The cross-plots of the estmated value (left) and the realsed value (rght) as a functon of the optmal value for the 24 hour perod from Sunday to 6am Monday mornng. As the correlaton on the left s -0.37, the estmated value s not a good predctor of optmal value or of the realsed value. However the optmal and the realsed values are strongly correlated (0.97) Next we compare the averages of the optmal and the realsed values. But before dong ths, t s mportant to note that by defnton the optmal value s equal to or greater than the realsed value. The only way that the realsed value could be equal to the optmal value would be f the rechargng schedule obtaned from the tranng set happened to be equal to that by optmsng the schedule ex post. Table 2 gves the averages of the optmal and the realsed values for the three cases: V2G scenaro A, V2G scenaro B and G2V, for 2010 and 2011 f there are no losses when chargng and dschargng the batteres, whle Table 3 gves the correspondng values f there are 5% losses. As expected, the values for the G2V case are systematcally negatve (costs). The values for the V2G depend on when the EVs arrve. For scenaro A, the optmal values are postve on Sunday (revenue) but not for the other days of the week. For scenaro B, the values are systematcally postve (revenue). Ths hghlghts the mportance of knowng the arrval tmes of the EVs. Fgures 8 and 9 present the optmal value of the three strateges for each day of the year n 2010 and The sold black lne corresponds to 18

21 Scenaro A for the V2G case, the dotted black corresponds to Scenaro B of the V2G case whle the sold red lne s for the G2V case. In each fgure the case where there are no losses s n the upper panel, whle the lower panels corresponds to the case where there are 5% losses. The optmal value for G2V case s almost always less than the other two; the optmal value for scenaro B of the V2G case s almost always hgher than the other two. Table 2: Optmal values (OptVal) and realsed values (RVal) for the V2G case scenaro A (where all EVS arrve at 6am), for the V2G case scenaro B (where the arrvals of the EVs are evenly spread from 6am untl 10pm) and for the G2V case, for 2010 and 2011 when there are no losses transferrng power to and from the batteres Sun Mon Tues Wed Thu Fr Sat OptValA RValA OptValB RValB OptValG2V RValG2V Sun Mon Tues Wed Thu Fr Sat OptValA RValA OptValB RValB OptValG2V RValG2V

22 We had wondered to what extent the creaton of the CWE market would perturb the strateges snce the data from before the change was beng used afterwards. In partcular we had been expectng to see changes n the realsed values, or a dscontnuty n the optmal value. Lookng at Fgure 8, there are no obvous dfferences toward the end of that year. So the strateges are qute stable even when confronted wth a major structural change n the market. Table 3: Optmal values (OptVal) and realsed values (RVal) for the V2G case scenaro A (where all EVS arrve at 6am), for the V2G case scenaro B (where the arrvals of the EVs are evenly spread from 6am untl 10pm) and for the G2V case, for 2010 and 2011 when there s a 5% losses transferrng power to and from the batteres Sun Mon Tues Wed Thu Fr Sat OptValA RValA OptValB RValB OptValG2V RValG2V Sun Mon Tues Wed Thu Fr Sat OptValA RValA OptValB RValB OptValG2V RValG2V

23 Fgure 8: The optmal values are presented for scenaro A of the V2G case (sold black lne), for scenaro B of the V2G case (thck black dotted lne) and the G2V case (sold red lne), for the cases where there are no losses (upper panel) and when there are 5% losses, for The optmal value for G2V case s almost always less than the other two; the optmal value for scenaro B of the V2G case s almost always hgher than the other two. 21

24 Fgure 9 The optmal values are presented for scenaro A of the V2G case (sold black lne), for scenaro B of the V2G case (thck black dotted lne) and the G2V case (sold red lne), for the cases where there are no losses (upper panel) and when there are 5% losses, for The optmal value for G2V case s almost always less than the other two; the optmal value for scenaro B of the V2G case s almost always hgher than the other two. 22

25 Impact of the strateges for rechargng the batteres on the day-ahead market As the strateges were desgned to optmse the revenue for the BSS, we want to fnd out what effect ths wll have on the wholesale electrcty market. To be more precse, we are nterested n ther mpact on the hourly dayahead prces for electrcty and on the volumes of transactons. The average prces were computed over a 13 week perod n wnter and agan n summer, n 2010 and Fgures 10 and 11 show these for wnter and summer 2010, and wnter and summer 2011, respectvely. As before the averages are shown for the 24 hour perod from 6am Sunday untl 6 am Monday, and from 6 am Tuesday untl 6 am Wednesday. Four curves are shown n each fgure: a sold black lne for scenaro A for the V2G case, a thck black dotted lne for scenaro B for the V2G case, a sold red lne for the G2V case and fnally a fne black lne showng the orgnal prces (that s, the observed prces). The red lne correspondng to the G2V case s only shown from 10pm untl 6am because t does not affect prces or volumes durng the daytme. As expected the orgnal prces are hgher than those for the two V2G cases durng the evenng peak hour especally n wnter. Scenaro B n the V2G case leads to a greater drop at peak hours and to a correspondngly hgher prce n the early mornng off-peak perod. In contrast to electrcty prces whch drop durng peak hours n the V2G cases, the volumes of electrcty bought and sold through the aucton market rse n both peak hours and off peak perods. Ths s partcularly marked for scenaro B n the V2G case. In the case studed where 300,000 EVs have sgned up wth the BSS, the mpact on the market prces and volumes are not very marked. But the French government has plans to have 10 tmes as many EVs on the roads. In that case the mpact of coordnated changng would lead to a much more pronounced drop n peak prces. 23

26 Fgure 10: Average prce on the day-ahead market n France: for scenaro A of the V2G case (sold black lne), for scenaro B of the V2G case (thck black dotted lne), for the G2V case (sold red lne) and the orgnal prces (thn black lne), for a typcal weekday and for the weekend, for wnter 2010 (upper panel) and summer 2010 (lower panel) 24

27 Fgure 11: Average volumes on the day-ahead market n France: for scenaro A of the V2G case (sold black lne), for scenaro B of the V2G case (thck black dotted lne), for the G2V case (sold red lne) and the orgnal prces (thn black lne), for a typcal weekday and for the weekend, for wnter 2010 (upper panel) and summer 2010 (lower panel) 25

28 Dscusson and Conclusons Most papers that study the rechargng of electrc vehcles focus on chargng the batteres at home and n the work-place. The alternatve s for owners to exchange the battery at a specally equpped battery swtch staton (BSS). Ths paper proposes strateges for the BSS to buy and sell the electrcty through the day-ahead aucton market. To do ths the BSS would have to submt frm offers specfyng the amounts of electrcty that t s offerng to buy or sell durng each hour of the day, before noon on the day pror to delvery. So the management needs a procedure for determnng those quanttes. We determned what the optmal strateges would have been for a large fleet of EVs each day n 2010 and 2011, for the V2G and the G2V cases. As one of the key factors nfluencng the optmal strateges for the V2G case s the expected arrval tme of the EVs, two farly extreme possbltes were consdered: frstly an unfavourable case where all the EVs arrve frst thng n the mornng and secondly when ther arrvals are spread evenly throughout the day. Another factor that was taken nto account was losses when chargng and dschargng batteres. Table 4 gves the annual revenue n mllons of euros from buyng and sellng on the day-ahead market, for the three scenaros consdered wth and wthout losses. Postve values correspond to revenue whle negatve ones are costs. These can be compared wth the amount (27 M euro) that t would cost to buy the same quantty of electrcty at the benchmark base-load prce of 40 per MWh at whch the government oblges EDF to sell nuclear power to compettors. 26

29 Table 4: Annual revenue n mllons of euro for the three scenaros consdered, wth and wthout losses, for 2010 and Postve values correspond to revenue; negatve ones, to costs ncurred. These should be compared to the benchmark cost (-27 M ) at the benchmark base-load prce of 40 euro per MWh. Optmum Value 2010 No losses %5 Losses 2011 No losses %5 Losses V2G A M M V2G A M M V2G B M M V2G B M M G2V M M G2V M M Realsed Value 2010 No losses %5 Losses 2011 No losses %5 Losses V2G A M M V2G A M M V2G B M M V2G B 6.48 M 6.48 M G2V M M G2V M M Lookng at the fgures we see frstly that all of the strateges are more cost-effectve than buyng drectly from a utlty. Secondly, there s lttle dfference between the cost of chargng the batteres n 2010 and 2011 for the G2V case, but the dfferences are qute marked for both the V2G cases. There s a sgnfcant dfference between the revenue that can be generated n the V2G case for scenaro B and the cost for scenaro A. Ths hghlghts the mportance of havng a good understandng of arrval tmes of the EVs. It also suggests that t mght be worthwhle proposng advantageous tarffs for EV owners who exchange ther batteres at certan tmes n the day. As the optmal strateges were found for a reasonably large fleet of 300,000 EVs, the quanttes of electrcty bought and sold wll dsplace the market equlbrum. Table 5 gves the new average prces for the 8 hour perod from 10pm to 6am (when batteres are charged n the G2V case) and for the rest of the day, and also the average prce for the same tmes n the orgnal data. As expected, the nght prce rose n all three scenaros and the V2G prces decreased n the day-tme. Much more marked effects could be expected wth a larger fleet. 27

30 Table 5: Average prces for electrcty, for the three scenaros consdered, wth and wthout losses, durng the tmes from 6am to 10pm and from 10pm to 6am for 2010 and H7 to H22 H23 to H No losses %5 Losses 2010 No losses %5 Losses V2G A V2G A V2G B V2G B G2V NA NA G2V Orgnal NA Orgnal NA 2011 No losses %5 Losses 2011 No losses %5 Losses V2G A V2G A V2G B V2G B G2V NA NA G2V Orgnal NA Orgnal NA One mportant feature of the results s the stablty of the strateges durng the last two months of 2010 just after the creaton of the CWE market. As data from the French market were used to set up the strategy after the French and German markets were combned, we had wondered how robust the strateges would be. No nstabltes were found. We thnk that ths s because the basc patterns for electrcty consumpton remaned the same despte the structural changes n the market. Fnally, the mplcatons of ths study for polcy-makng should be drawn. As we analysed the results of ths study, t occurred to us that BSS mght be an economcally vable alternatve to chargng the batteres at home or at the workplace, and not just a back-up for longer journeys. The advantages of BSS are: 1. Rather than havng to upgrade the whole electrcty dstrbuton network and nstall mllons of smart meters, the grd would only have to be upgraded for several thousand BSS, granted at a hgher voltage; 2. The owners of EVs do not need to have the same level of trust n the aggregator snce they just drop off the depleted battery and get a 28

31 fully charged battery n exchange. No one s chargng/dschargng the battery n THEIR car. The batteres reman anonymous; 3. From a mathematcal pont of vew t s much smpler to optmze the chargng/dschargng of a large set of anonymous batteres. There s no need to know the owners travel detals ndvdually, or to store and process vast quanttes of prvate nformaton; 4. Most nterestng of all, no new specal ncentves are needed to convnce the BSS operator to charge the batteres n a socally optmal way durng offpeak perods. It s n hs/her nterest to reduce the cost of chargng the EVs to ncrease the proftablty of the busness, and as we have shown, n V2G mode ths acheves the socally desrable outcome of havng the BSS sell power to the grd durng peak hours (thereby reducng prces and the need for new peakng power plants) and buyng durng off-peak perods when some of the generaton capacty s under-used. Ths s why we thnk that f the cost of the batteres drops suffcently and f they resst the addtonal wear-and-tear due to the addtonal chargng/ dschargng cycles, a pure BSS busness mght actually be a vable economc proposton - as well as beng socally useful. References Badey, Q. (2012) Etude des mécansmes et modélsaton du vellssement des batteres lthum-on dans le cadre d un usage automoble, PhD Thess, Unversté Pars-Sud, 260pp avalable from Camus C., T. Faras,and J. Esteves 2011 Potental mpacts assessment of plug-n electrc vehcles on the Portuguese energy market, Energy Polcy, 39 (10) Oct 2011 pp Dang V.T.T., C. Fourner, S. Morel, J. Adnot & J. Oostebaan (2010) Batteres Management for Mnmzaton of Electrc Vehcles Envronmental Impacts n A Lfe Cycle Assessment Framework, EcoBalance2010, 9 th Internatonal Conference on EcoBalance, 9-12 Nov, 2010, Tokyo 29

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