EV Charging Station Placement Considering Traffic Flow Tianqi Lu1, a, Qiang Ma2, b, Zheng Gu3,c

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1 6th Internatonal Conference on Informaton Engneerng for Mechancs and Materals (ICIMM 2016) EV Chargng Staton Placement Consderng Traffc Flow Tanq Lu1, a, Qang Ma2, b, Zheng Gu3,c 1 State Grd Laonng Electrc Power Company Lmted Economc Research Insttute, Shenyang, Chna 2 State Grd Laonng Electrc Power Company Lmted Economc Research Insttute, Shenyang, Chna 3 State Grd Laonng Electrc Power Company Lmted Economc Research Insttute, Shenyang, Chna a emal: lutanq @sna.com, bemal: @qq.com,cemal: @qq.com Keywords: The flow refuelng model; Mult-objectve optmzaton; NSGA-Ⅱ Abstract. The flow refuelng locaton model s adopted to descrbe the traffc network consderng the shortest and the second shortest paths. Three objectve functons of the electrc vehcle chargng staton placement optmal model are defned to maxmze the captured traffc flow, to mnmze the nvestment cost, and to mnmze the average voltage devaton. Then, the non-domnated sortng genetc algorthm-Ⅱ s used to solve the mult-objectve model. Wth the example of the IEEE 33node power dstrbuton network and the 25-node traffc network, the basc characterstcs of the presented model and solvng method are llustrated. INSTRUCTIONS Wth the growng promnence of energy and envronmental ssues n recent years and the development of related technologes, more attenton has been pad on electrc vehcles (EVs) for ther advantages n savng the energy and protectng the envronment. EV chargng statons, whch are both publc servce facltes and power load facltes, need to be carefully planned before constructng. The nfluence of not only the traffc network, but also the power grd should be consdered. Many works have been done about EV chargng staton placement. [1] ntroduces plannng of EV chargng and chargng staton constructon from macro pont of vew, ncludng the factors affectng the layout of EV chargng statons and overall prncples of chargng staton plannng.in [2],the objectve s set to mnmzetotal constructon cost, subject to constrants of chargng staton coverage and convenence for drvers to charge ther EVs. Lterature [3] proposes a well-organzed system archtecture operatonal schedulng method for chargng and dschargng of EVs.Multobjectve framework ams at mnmzng total operaton cost and emssons.benders decomposton technque s used to solve the proposed model.influence of the traffc flow s ncluded n the plannng model[4], and the super-effcency data envelopment analyss s employed to transfer multobjectve optmzaton nto a sngle-objectve one. In ths paper, we adopt the flow refuelng locaton mode consderng shortest and second shortest paths, to descrbe effect of traffc network.three objectves of the optmal EV chargng staton placement model s to maxmze the captured traffc flow, as well as to mnmze the nvestment cost and average voltage devaton. EV chargng staton placement model Model optmal objectves The optmal objectves we proposed n ths paper are to maxmze the traffc flow that chargng statons capture, to mnmze the nvestment cost and to mnmze the power bus voltage devaton. To maxmze the captured traffc flow The authors - Publshed by Atlants Press 186

2 Assumng every tme a drver passes a chargng staton, he wll choose to fully charge hs EV. Max f = f g y (1) 1 q q Q r Rq In (1), q represents a par of start node and termnal node; Q represents all there pars; r represents the shortest path or the second shortest path; R s the set of the shortest path and the q second shortest path between the node par q ; f s the traffc flow on the shortest path between q the node par q ; g s the proporton of drvers who are wllng to take the path between the node par q ; y shows whether the traffc flow on path r between the node par q can be captured by the chargng statons on ths path, y = 1 f the traffc flow can be captured, otherwse y = 0. To mnmze the nvestment cost Assumng nvestment cost ncludes 3 parts: constructon cost of the chargng statons, cost of power capacty expanson, and cost of network power loss after chargng statons are constructed. Mn f = c x + c x + c P (2) 2 1, k CS, k 2, SR, 3 loss k K N Where, k s the a canddate poston where chargng statons can be bult; K s the set of all the canddate postons; x CS, k shows whether a chargng staton s bult at the poston k, x CS, k = 1 f the chargng staton s bult; represents a power bus; N s the set of all the power buses; x SR, shows whether a power bus capacty need to be expanded, x SR, = 1 f t needs to be expanded; P loss s the power network loss; c 1,k s the constructon cost of buldng a chargng staton at node k ; c 2, s the cost of expandng the power capacty at bus ; c 3 s the cost of network power loss; n ths paper c 1,k, c 2, and c 3 are set as constants. To mnmze the voltage devaton V V0 Mn f3 = γ N V (3) 0 Where, V s the voltage at bus ; V 0 s the voltage at swng bus; γ s the factor representng the mportance of bus. Model constrants Node combnaton constrant Only when the chargng statons are bult at a combnaton of nodes on a path, whch meets the EVs refuelng requrements and allows them to go from the start to the end and return to the start, the traffc flow on ths path can be counted as captured. In ths stuaton, we call the combnaton of nodes feasble. Then we defne a parameter v h to represent whether a combnaton of nodes h s open. To a path q, f chargng statons are bult at every node of a feasble node combnaton h, we say the combnaton s open and v h = 1, otherwse v h = 0. The constrant for varable y s 1 vh 1 h H y = (4) 0 vh = 0 h H Where, H s the set of all the feasble node combnaton on a path. Equaton (4) shows that when chargng statons are bult at every node of at least one feasble node combnaton on a path, then the traffc flow on ths path can be captured, and y = 1. Chargng staton number constrant The number of all the chargng statons we plan to construct s p. xcs, k = p k K (5) 187

3 Power bus capacty constrant x SR, 1 P + x P > P = 0 P + x P P, k CS, k c, k,max k K, k CS, k c, k,max k K Where, k, K s the set of traffc nodes whch are correspondng to power bus ; ck, of the chargng staton bult at node k ; P s the lmt of actve power of bus. P s the orgnal power load of bus, whch s correspondng to the traffc node k ; P s the chargng power,max In (6), we need to calculate the chargng power of the staton bult at node k. In ths paper, accordng to hstorc data, we assume the total chargng power P c, total n the plannng area s a known parameter, and the chargng power of each chargng staton s drectly proportonal to the rato between the traffc flow captured by the staton and the total traffc flow. fk, k =, total (7) fk k Ks Power flow equaton constrant Power flow equaton s the basc constrant n power system. Where, k, N P, k xcs, k, k = V, kvj ( Gj cosθj + Bj sn θj ) j= N Q, k xcs, kqc, k = V, kvj ( Gj snθj Bj cos θj ) j= P and Q k, respectvely represent the orgnal actve power and reactve power at bus whch s correspondng to the traffc node k ; P ck, and Q ck, respectvely represent the actve and reactve power the chargng staton consumes at node k ; G j and B j are respectvely the real part and magnary part of the bus admttance matrx; θ j s the phase angle dfference between the voltages of the two termnals of the lne j. Solvng method Take (1)-(3) as objectves, and (4)-(8) as constrants, we get the EV chargng staton placement model, whch s a mult-objectve nonlnear nteger optmzaton problem. To solve ths model, we choose the non-domnated sortng genetc algorthm-Ⅱ(nsga-Ⅱ) [10] as the solvng method. By usng ths algorthm, we can get a set of pareto solutons, among whch no soluton can domnate the others,.e. can be better than the others n all 3 objectve drectons. The flow refuelng locaton model The flow capturng locaton allocaton model M. John Hodgson proposed the flow capturng model n 1990 [5]. In ths model, traffc flow s movng on the road and passes the traffc nodes. Assumng there s a traffc path whch starts at node A and ends at node D. If at least one servce faclty s constructed among all the nodes from A to D, then all the traffc flow on ths path can be captured. The objectve of the model s to capture the traffc as much as possble. (8) (6) Fgure 1. A path from node A to D (unt: km) The flow refuelng model for EV chargng statons The flow capturng locaton model n 2.1 assumes only one faclty can capture all the traffc flow on the path, whch avods the repettve countng of the captured traffc flow when more than one faclty s constructed on the path. However, when t comes to EV chargng staton plannng, we need to consder the constrant of EVs battery capacty,.e. the EVs range. For example, n fgure 1, when an EV s range s between 90 km and 180 km, t wll requre more than one chargng staton to refuel n order to fnsh a trp from A to D, and back to A. In fact, the EV can fnsh the mentoned trp only when 3 chargng statons are bult at nodes (A, C, D) or (B, C, D). 188

4 When we take the constrant of EVs range nto consderaton, we need to fgure out n order to capture the traffc flow on a path, at whch nodes we should construct the chargng statons. After knowng all the nodes a path passes and an EV s range, we can use the method n [6] to get the combnaton of nodes whch can meet the EV s chargng need to acheve a round trp. The choce of drvng paths In the flow refuelng model, an mportant parameter s the combnaton of all the nodes on the path from a start to a termnal. Consderng most drvers now have navgaton equpment, we assume they wll choose the shortest path. Also, under some crcumstances, drvers may need to take a detour to get the destnaton, so we assume some drvers wll choose the second shortest paths. We use the Floyd algorthm [7] to get the shortest paths, then, we can use the cut edge method [8] to obtan the second shortest paths. By usng the above-mentoned algorthms, we have both the shortest and second shortest paths that we need. To smulate the traffc flow on the shortest paths, we choose the smple gravty spatal nteracton model [4] to calculate. Whle for the second shortest paths, consderng the fact that not all drvers are wllng to choose them, accordng to the model Km and Kuby proposed [9], we multply the traffc flow on the shortest paths by a path devaton factor whch s smaller than 1, to smulate the traffc flow on the second shortest paths. Smulaton Test case The test case used n ths paper s combned by IEEE 33-bus power dstrbuton system and 25- node traffc system. And we assume the traffc nodes 1 to 25 are correspondng to the power buses The topologes of the power dstrbuton system and the traffc system are shown n fgure 2 and fgure 3. Fgure 2. The topology of IEEE 33-bus power dstrbuton system Results Fgure 3. The topology of 25-node traffc system The populaton sze of NSGA-Ⅱ algorthm we used n ths paper s set as 50. The captured traffc flow (whch we multply wth -1 to change maxmzng to mnmzng), ntal populaton and bus voltage devaton of the ntal populaton that randomly chose are shown n the 3-dmenton fgure 4(a). After 60 teratons, values of the above-mentoned 3 objectves of the fnal populaton 189

5 are show n fgure 4(b). It s obvous that after optmzaton, all the 3 objectve values of the populaton become better, whch shows the effectveness of the proposed method. (a) (b) Fgure 4. The objectve values of the ntal and optmzed populaton By usng NSGA-Ⅱ algorthm, we can have multply pareto solutons smultaneously, whch are wdely spread n the feasble regon. We choose the solutons solved once to llustrate the result. In 4 ths soluton, the total traffc flow of the traffc network s unts. When 5 statons are 4 bult, the captured traffc flow s unts, whch s 76.4% of the total flow. Under the crcumstance that the chargng statons capture most traffc flow, the postons of 5 statons are shown n fgure 5. Fgure 5. The postons of chargng statons when they capture most traffc flow We can fnd n fgure 5, all the chargng statons are bult n the mddle and west areas, the reason s there are more roads n these areas and accordngly, the traffc flow s more than east area. So when the total number of statons are not too many (n our test we only buld 5 statons), they are manly bult n mddle and west areas. Especally, although the roads from node 14 to node 25 are n the corner of the map, but n our test case, the weghts of node 24 and 25 are very hgh n the smple gravty spatal nteracton model we use, whch means the traffc flow on these paths takng node 24 and 25 as destnatons are qute much. In order to capture these traffc flow, t s easy to understand that we buld chargng statons at node 14 and 24. Whlst node 14 s the only way vehcles can get to node 24 and 25, much traffc flow wll pass here, based on the fact that the chargng power of a staton s proportonal to the traffc flow t captured n our model, we can predcted the chargng power of the staton at node 14 wll be very hgh. By assumng that the total chargng power n the whole area s 800 kwh and calculatng the chargng power of every statons, the results are as followed.,4 = 134kW,8 = 190kW,14 = 219kW,19 = 98kW,24 = 159kW When we lay more mportance on the nvestment cost, t s a lttle dffcult to analyze the results because the nvestment cost contans constructon cost, power expanson cost and power loss cost. Generally speakng, we need to consder the 3 aspects comprehensvely. By solvng the model, the cost s lowest when we buld chargng statons at node 1, node 2, node 6, node 15 and node

6 When more attenton s pad on bus voltage devaton, because the power dstrbuton network s usually operated n radal topology, we can have the general dea that the voltage devaton s lower when the chargng statons are bult at the begnnng nodes. We can observe from the results that the 5 chargng statons are bult at node 1, node 2, node 19, node 20 and node 21 to lower the voltage devaton, and the devaton under ths stuaton s The bus voltage of every power bus s shown n fgure 6 when the voltage at swng bus 1 s set as kv 电压水平 6 /k V 节点编号 Fgure 6. The bus voltages when the devaton s lowest By analyzng the results as above, we can see the populaton s optmzed n all three objectve dmensons after we solve the model usng NSGA-Ⅱ algorthm. At the same tme, we should also notce that because NSGA-Ⅱ algorthm s an ntellgent optmzaton method based on randomly searchng, t s not certan that we can fnd the global optmal solutons every tme. But t can help us fnd the most accurate soluton by solvng the problem several tmes and analyze the results from all the solutons we get. Concluson By optmally plannng the EV chargng statons, we can better serve the EV owners and at the same tme help the power dstrbuton system keep stable. In ths paper, the EV chargng staton placement model amng at maxmze the captured traffc flow, mnmzng the nvestment cost and mnmzng the bus voltage devaton s formulated. By solvng the model usng NSGA-Ⅱ algorthm, we can get a set of pareto solutons, from whch the decson maker can choose the most sutable one. Based on ths paper, there are several ways that we can mprove. For example, we can further mprove our model by consderng more than shortest paths and second shortest paths. Also, we can modfy the crossover and mutaton operators n NSGA-Ⅱ algorthm to shorten the solvng tme. References [1] XU Fan, Yu Guoqn, Gu Lnfeng, et al. Tentatve Analyss of Layout of Electrcal Vehcle Chargng Statons [J]. East Chna Electrc Power, 2009 (10): [2] Lam A, Leung Y W, Chu X. Electrc vehcle chargng staton placement[c]//smart Grd Communcatons (SmartGrdComm), 2013 IEEE Internatonal Conference on. IEEE, 2013: [3] Zakarazadeh A, Jadd S, Sano P. Mult-objectve schedulng of electrc vehcles n smart dstrbuton system[j]. Energy Converson and Management, 2014, 79: [4] WANG Hu, WANG Gubn, ZHAO Junhua, et al. Optmal Plannng for Electrc Vehcle Chargng Statons Consderng Traffc Network Flows [J]. Automaton of Electrc Power System, 2013, 37(13): [5] Hodgson M J. A Flow Capturng Locaton Allocaton Model[J]. Geographcal Analyss, 1990, 22(3): [6] Kuby M, Lm S. The flow-refuelng locaton problem for alternatve-fuel vehcles [J]. Soco- Economc Plannng Scences, 2005, 39(2): [7] HU Jezhou. An Algorthm for Dstrbuton Center Based on the Floyd-Shortest-Path [J]. Journal of Hunan Agrcultural Unversty (Natural Scences), 2004, 30(4):

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