Energy and Power Engneerng, 2013, 5, 1393-1397 do:10.4236/epe.2013.54b264 Publshed Onlne July 2013 (http://www.scrp.org/ournal/epe) Optmal Plannng of Chargng Staton for Phased Electrc Vehcle * Yang Gao, Yandong Guo School of Electrcal and Electronc Engneerng, North Chna Electrc Power Unversty, Baodng, Chna Emal: commoncat@163.com Receved March, 2013 ABSTRACT Constructon of electrc vehcle chargng staton s the premse of the popularty of electrc vehcles. In ths paper, electrc vehcle chargng facltes plannng s dvded nto two stages: publc demonstraton stage and commercal operaton stage. In publc demonstraton stage, Ths Paper apples maxmal coverng model nto chargng staton locaton, and then be solved by the branch and bound method. In commercal operaton stage, the chargng staton s servce areas dvson s studed based on Vorono dagram. Wth the concernng techncal restrans, an optmal plannng method s presented for newly-ncreased staton postonng and servce regon dvson. The method usng the most greatly ar crcut method and local dynamc characterstcs of Vorono dagram guarantees the reasonable dstrbuton of statons. Then chargng staton model of optmal load allocaton s establshed by usng M/M/c model. In the end, the correctness and valdty of the model s verfed through smulaton of chargng staton plannng. Keywords: Chargng Demand; Electrc Vehcle; Plannng Layout; Vorono 1. Introducton Wth the deteroratng global envronment and the lack of ol resources, the socety has begun to focus on the use of electrc vehcles. However, constructon of electrc vehcle chargng staton s the premse of the popularty of electrc vehcles [1-3]. At present, constructon of chargng statons n Chna s manly for market demonstraton wth no clear and reasonable layout, so establshng an effectve chargng staton layout and a scale settng tool have become an urgent need at the moment. In [4], the advantages and dsadvantages of the electrc vehcle chargng system have been revewed and the external access methods of chargng statons, nstalled capacty and ts nfluencng factors are consdered as a prelmnary nqury for the plannng of chargng statons. In [5], the overall demand of the chargng load and plannng nfluencng factors, ncludng the operatng model of electrc vehcles chargng statons have been analyzed; prncple recommendatons such as plannng of chargng statons should meet the radus requrements of the chargng statons, traffc densty, dstrbuton of electrc vehcle chargng demand and the overall urban road plannng have been made. In [6], takng the geographcal factors and the servce radus * Ths work was supported n part by the Natonal Natural Scence Foundaton of Chna under Grant 51177047, Fundamental Research Funds for the Central Unverstes under Grant 12MS107. nto account, a two-step screenng method to dentfy canddate stes for chargng statons has been presented. Combned wth varous sectons of the electrc vehcle drvng condtons and chargng needs, n publc demonstraton stage maxmum coverage model has been presented to strke the optmal locaton under fundng constrants; n commercal operaton stage, Vorono dagram s used to dstrbute demand, an optmzed model s presented. 2. Analyss of Demand for Electrc Vehcle Chargng Assumng vehcle chargng demand s equal the power consumpton on the secton L. V(, k) Calculate the class-k electrc vehcle electrc consumpton n V(, k) on the secton L(): Vk (, ) gk ( ) L () qk (, ) (1) The power consumpton of varous types of electrc vehcles on the secton of L (): m V () Vk (, ) (2) k 1 In the equaton (1) (2): g s electrcty consumpton of vehcles per klometer constraned by vehcle type, vehcle load and travel speed. Ths model uses the concept of the average electrcty consumpton for a partcular class
1394 Y. J. GAO, Y. D. GUO of electrc vehcles and average power consumpton s a fxed value; q () s the number of vehcles through a road secton n a unt tme (vehcles / day). Q (, k) s the traffc volume at pont I for class-k cars n a two-way traffc flow; L () s the length of the road secton. 3. Chargng Staton Plannng n Publc Demonstraton Stage The current stage of electrc vehcle technology s not yet fully mature and effectve and sustanable market mechansm to promote the development of electrc vehcles has not yet formed. The total amount of electrc vehcles accounts for a very low proporton and electrc vehcle ndustry reles on government subsdes and advocacy, n the publc demonstraton stage, chargng facltes plannng can be seen as a short-term plannng. Because of the characterstcs of ths stage, the ntal nvestment of chargng statons coverng all chargng needs may lead to excessve fscal spendng. As a result, due to the lmtatons of the actual budget may, chargng statons may cover less demand. The model s shown as follows: max Z Vm ( ) (3) I plannng problem s a 0-1 nteger programmng problem and wll be solved by the branch and bound method n the follow. 4. Chargng Staton Plannng n Commercal Operaton Stage In ths stage, the electrc vehcle technology s assumed bascally mature and the total amount of vehcles reaches a certan sze. So n ths stage, electrc vehcle chargng facltes plannng can be seen as a long-term plannng. 4.1. Method of Alternately Postonng n Commercal Operaton Stage In ths stage, adequate chargng facltes begn to be establshed to meet the chargng demand of electrc vehcle. Assume that electrc car owners are always lookng for the nearest chargng staton for ther servces, the assumpton coordnates a great smlarty wth the Vorono dagram [7]. Program flow of alternately postonng n commercal operaton stage s shown n Fgure 1: Method of alternately postonng n commercal operaton stage s as follows: s.t. m n, I (4) N n p (5) J n, m {0,1} I, J (6) In the model, J s a set of canddate ponts of exstng gas staton scalable wth chargng facltes and I s a set of chargng requrements. m stands for whether chargng demand pont could receve chargng servces and the value of 1 shows chargng demand n pont can receve chargng servce, on contrary the value s zero. N s a set of canddate faclty whch could cover chargng demand n pont and t can be expressed as N = { d s }, where d stands for dstance between pont and and s stands for the maxmum acceptable canddate faclty charge dstance. The obectve functon of formula (3) targets to coverng most of the chargng requrements by chargng facltes wth the p; constrant condton Equaton (4) ndcates that the number that chargng statons can be searched by chargng demand pont wthn a maxmum acceptable servce dstance s greater or equal wth the value of 1; constrant formula (5) represents the total number of facltes s lmted to the number of p. The constrant formula (6) constrans the value of m and n to the value of 0 or 1. Descrbed by the formula (3)~(6), the chargng staton Fgure 1. Flow charts.
Y. J. GAO, Y. D. GUO 1395 1) Usng chargng staton stes n the frst stage, the Vorono dagram s generated. In the Vorono dagram, the radus of the hollow crcle where the vertex n are sorted n descendng order. The center of the hollow crcle of whch radus s greater than the radus of the chargng statons hollow crcle s set as the ntal ste. 2) Based on the exstng stes and the new canddate ste, Vorono dagram s regenerated to determne the optmal servce range for the new chargng staton. In the servce range of the new staton, Use the gravty method to determne the optmum poston for the new chargng staton. 3) Repeat 2) untl the value of locaton coordnate of the new stes s less than bookng precson. 4.2. The Number of the Optmal Chargers n Chargng Staton From the current developng stuaton of electrc vehcle and hstorcal data at gas statons, the followng assumptons are made: Per charge quantty s a fxed value Q. The arrvals of electrc vehcles are a Posson stream of rate λ. The chargng tme s a negatve exponental dstrbuton wth μ. Wth the above assumptons, the chargng staton, as a chargng servce system, s a mult servce desk and fnte watng room ( M / M / c ) system. There are sectons n area, V s the electrc consumpton n area : V V() (7) 1 N s the number of tmes of electrc vehcles charge n area N V / Q (8) Assumng vehcle chargng staton s open from 8 am to 10 pm. N /14 (9) The model of optmzng the quantty of chargers n chargng statons s as follow: n r (1 r ) mn F c T Y N k W q (1 ) 1 0 0 n r0 L q ma (10) L (11) x In (10), F s the cost of the chargng staton I, c s the number of chargers, T s the charger cost, Y s the annual operatng cost of the chargng staton.k s the user s tme value, t can be estmated by the user s ncome n the area. n s the deprecable lfe, W q s the average wat tme. In (11), L q s the mathematcal expectaton of the number of watng EVs, L max s the maxmum acceptable number of watng EVs n staton. The problem wll be solved by the LINGO n the follow. 5. Example Analyss In ths paper, plannng of chargng statons s taken for example: the regon s a total area of 36.48 km 2 whch spans 6.4 km from east to west and 5.7 km from north to south and can be dvded nto 58 sectons. In realty, the type of electrc vehcles dffer from drvng load and traffc status, charge cost wll also be dfferent. However, to smplfy the problem, the example assumes that power consumpton of vehcles per klometer s a fxed value, g = 0.13 kwh/km. The map as well as the exstng gas staton locaton wth lnk numbers s shown n Fgure 2. 5.1. Chargng Staton Plannng n Publc Demonstraton Stage The regon s planned to construct 5 chargng statons n the frst batch and the predetermned range of the chargng staton s 2 km. Accordng to the data n the Equaton (1)(2), the chargng demands of dfferent sectons are obtaned. Accordng to the chargng staton plannng model n publc demonstraton stage constraned by Equaton (3)~(6), the demand s set to weght, then solve by branch and bound method n lndo software. The max Z s 14862 kwh and the most optmal poston s shown n Fgure 3. By the optmal locaton, Vorono dagram s generated, the scope of each chargng staton s determned and each demand pont s allocated, shown n Fgure 3. 5.2. Chargng Staton Plannng n Commercal Operaton Stage In Fgure 3, the hollow crcle radus greater than the radus of the chargng statons hollow crcle center are set as the ntal locaton. Usng the exstng statons wth Fgure 2. Cty network dagram.
1396 Y. J. GAO, Y. D. GUO new stes to generate Vorono dagram, the scope of servces of the new staton s determne, n other words, demand s dstrbuted agan. Wthn the range of ts servces, Use the gravty method to determne the optmum poston for the new chargng staton. Usng the exstng statons wth new optmal ste to generate new Vorono dagram and solve the problem agan wth the new servce scope dvson of chargng statons untl the teratve adustment s less than the default precson of 0.1 km 2. The locaton of the new staton and ts servce range s shown n Fgure 4. The new ste s located n pont 6. 5.3. The Number of the Optmal Chargers n Chargng Staton Takng nto account the nterests of chargng statons and users, the sum of chargng statons servce cost and customers watng fees s chosen as the obectve functon for the optmal allocaton of chargers. Relevant parameters are shown n Table 1. Usng the methods descrbed n ths artcle, the problem has been calculated by LINGO, and then followng results have been obtaned n Table 2. Fgure 3. Chargng staton plannng n publc demonstraton stage. Fgure 4. Chargng staton plannng n commercal operaton stage. Table 1. Related parameter selecton. sgn Value sgn Value Q 20.8kWh g 0.13kWh/km L max 20 r 0 0.1 T 0.1mllon yuan k 25yuan/hour Y 0.2mllon yuan n 20 Table 2. The number of optmal chargers. Staton number The number of the optmal chargers 1 7 2 6 3 12 4 11 5 11 6 7 6. Conclusons In ths paper, usng sectons consumpton to smulate randomly chargng requrements of electrc vehcles s able to provde new deas for future research on forecastng electrc vehcle chargng load; n publc demonstraton stage, ths Paper apples maxmal coverng model nto chargng staton locaton, and then be solved by the branch and bound method. In commercal operaton stage, usng Vorono dagram features s able to provde automatc postonng of the chargng statons and new chargng Staton by servce area dvson and would also be an attempt to solve the problem of optmzed chargng staton optmzed plannng; then chargng staton model of optmal load allocaton s establshed by usng M/M/c model. The presented models are verfed to be effectveness through a practcal example. REFERENCES [1] Hattonce, Beellask, Brezetc, et al., Chargng Staton for Urban Settngs: The Desgn of a Product Platform for Electrc Vehcle Infrastructure n Dutch Cte, World Electrc Vehcle Journal, Vol. 3, 2009, pp.1-13. [2] M. lu, Home and Abroad Electrc Vehcle Chargng Facltes Development, Journal of Central Chna Power, Vol. 5, 2010, pp.16-30. [3] J. Y. Yao, Electrc Vehcle Chargng System Constructon Applcaton Analyss, East Chna electrc power, Vol. 4, 2008, pp.107-110. [4] J. G. Kang, Z. L.We, D. M. Cheng, etc., Electrc Vehcle Chargng Mode and Chargng staton Constructon Research, Power demand sde management, Vol. 5, 2009, pp. 64-66. [5] F. Xu, G. Q. Yu, L. Gu, etc., Electrc Vehcle Chargng
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