考虑排队时间和充电费用的电动汽车充电站选址模型

摘要: 电动汽车充电站的合理布局对于降低里程焦虑、提高出行舒适度和电动汽车的普及率具有关键作用。为克服现有研究对充电排队时间和充电费用考虑的不足，构建以里程焦虑、充电费用最小化为目标的改进充电站选址优化模型，并明确考虑充电排队和充电绕行行为。分析电动汽车充电行为特征，引入路径容许偏离距离建立充电绕行路径距离约束，由此降低路网中偏离路径集的规模；分析充电站排队系统特征，推导出系统平均排队时间的解析表达式，建立可接受排队时间阈值、预算成本等约束条件；基于里程焦虑产生规律和阶梯电价收费方式，构建里程焦虑和充电费用最小化的决策目标，采用Lingo软件求解；选取西安市某局部路网进行算例分析。研究结果表明：在同等条件下，所提出模型计算得到的系统总充电排队时间为5.84 h，系统总充电费用为1 440元，与未考虑排队时间和充电费用的模型相比，系统排队时间减少了1.19 h，系统总充电费用减少了240元；分析充电站预算成本B的取值发现，当B≤5亿元时，系统总里程焦虑和充电费用随B增加而减小；当B＞5亿元时，B的增加无法进一步降低系统总里程焦虑和充电费用。在预算成本B = 3，4，5亿元的条件下，分别分析路径偏离距离η的取值对优化目标的影响，随着路径偏离距离η由0 km增加到4 km时，系统总里程焦虑和充电费用均呈下降趋势。
- 交通工程 /
- 电动汽车 /
- 充电站选址 /
- 排队论 /
- 充电费用 /
- 里程焦虑
Abstract: A reasonable layout of electric vehicle charging stations plays a crucial role in reducing range anxiety, improving travel comfort, and promoting the adoption of electric vehicles. To overcome the limitations of existing studies that overlooks the consideration of queuing time and charging cost, an improved site selection model for charging stations is established with the objectives of minimizing range anxiety and charging costs. This model explicitly considers queueing and detouring behaviors in charging. The characteristics of charging behavior of electric vehicles are analyzed, and a distance constraint for allowable path deviations is introduced to establish a limit on detour distances in charging paths, thereby reducing the scale of the set of deviation paths in the road network. The characteristics of the charging station queueing system are analyzed, and an analytical expression for the average queueing time of the system is derived with constraints such as acceptable queueing time threshold and budget cost. Considering the patterns of range anxiety and the stepped electricity pricing, a site selection model for charging stations is proposed to minimize range anxiety and charging costs, and the Lingo software is used to solve the model. A case study is conducted on a partial road network in the city of Xi'an. The results show that based on the proposed model, a total queue time and a total charging cost are 5.84 h and 1 440 Yuan, respectively. Compared to the model without considering queue time and charging costs, the system queue time and the total charging cost are decreased by 1.19 h and 240 Yuan, respectively. An Analysis of the charging station budget cost B shows that when B ≤ 500 million Yuan, the total range anxiety and charging costs decrease as B increases. However, when B > 500 million Yuan, further increase in B does not result in further reduction of total range anxiety and charging costs. Under the conditions of budget costs B = 300 million, 400 million, and 500 million Yuan, respectively, the impact of path deviation distance η on the optimization objective is analyzed. As the path deviation distance η increases from 0 km to 4 km, the total range anxiety and charging costs show a decreasing trend.
- traffic engineering /
- electric vehicle /
- charging station location /
- queuing theory /
- charging fees /
- range anxiety

HTML全文

图 1 1次充电循环中剩余电量和里程焦虑的变化情况

Figure 1. Variation of SOC and range anxiety during a single charge cycle

下载: 全尺寸图片幻灯片

图 2 整个行程中剩余电量和里程焦虑的变化情况

Figure 2. Variation of SOC and range anxiety on the entire trip

下载: 全尺寸图片幻灯片

图 3 西安市某区域路网详情图

Figure 3. Detail map of road network in an area of Xi'an

下载: 全尺寸图片幻灯片

图 4 预算成本B值对目标函数、里程焦虑和充电费用的影响

Figure 4. Effects of budget cost B value on objective function, range anxiety and charging cost

下载: 全尺寸图片幻灯片

图 5 路径容许偏差η对计算时间和目标函数的影响

Figure 5. Effects of allowable path deviation η on calculation time and objective function

下载: 全尺寸图片幻灯片

表 1 相关参数取值

Table 1. Values of related parameters

符号	取值
θ₁	0.9
θ₂	0.1
B /亿元	4
E/（kW·h）	10
E_O/（kW·h）	7
E_D/（kW·h）	7
E_comf/（kW·h）	5
μ_i/（pcu/h）	20
L₁ /km	10.9
L₂ /km	13
m /个	5
g₀ /元	1
g_i /元	2
ξ/（kW·h）	5
q_max /h	1.5

下载: 导出CSV

表 2 模型计算结果

Table 2. Model calculation results

序号	起点	终点	路径	长度/km	最短长度/km	充电站	充电费用/元	里程焦虑
1	1	14	1-2-3-6-10-14	10.9	10.9	2、10	1 440	3 441.07
2	3	11	3-2-5-4-8-7-11	14.1	13.0	2、5、7	1 440	3 441.07

下载: 导出CSV

表 3 DCSP模型计算结果

Table 3. DCSP model calculation results

序号	起点	终点	路径	距离/km	最短距离/km	充电站	充电费用/元	里程焦虑
1	1	14	1-2-5-6-10-14	11.1	10.9	2、6、10	1 680	1 733.87
2	3	11	3-2-1-7-11	13.0	13.0	2、7	1 680	1 733.87

下载: 导出CSV

表 4 2种模型的对比分析

Table 4. Comparative analysis of the two models

模型	里程焦虑	充电费用/元	排队时间/h	迭代次数	计算时间/s
DCSP模型	1 733.87	1 680	7.03	16 568	4.34
改进模型	3 441.07	1 440	5.84	160 259	117.68

下载: 导出CSV

表 5 不同预算成本下的模型最优解

Table 5. The optimal solution of the model under different budget costs

预算成本B/亿元	里程焦虑	充电费用/元	目标函数	路径1	距离1/km	路径2	距离2/km	充电站	充电站数
3	5 370.85	1 640	0.529 7	1-2-3-6-10-14	10.9	3-2-1-7-11	13.0	2、7、10	3
4	5 091.60	1 520	0.467 8	1-2-5-6-10-14	11.1	3-2-1-7-11	13.0	2、5、7、10	4
5	3 086.72	1 360	0.310 8	1-2-5-9-10-14	11.3	3-2-5-8-12-11	14.5	2、5、8、10、11	5
6	3 086.72	1 360	0.310 8	1-2-5-9-10-14	11.3	3-2-5-8-12-11	14.5	2、5、8、10、11	5
7	3 086.72	1 360	0.310 8	1-2-5-9-10-14	11.3	3-2-5-8-12-11	14.5	2、5、8、10、11	5
8	3 086.72	1 360	0.310 8	1-2-5-9-10-14	11.3	3-2-5-8-12-11	14.5	2、5、8、10、11	5

下载: 导出CSV

表 6 不同充电站数量下，不同η取值的模型结果

Table 6. The model results of different η values under different number of charging stations

η/km	B = 3				B = 4				B = 5
η/km	计算时间/s	里程焦虑	充电费用/元	目标函数	计算时间/s	里程焦虑	充电费用/元	目标函数	计算时间/s	里程焦虑	充电费用/元	目标函数
0	2	5 223.98	2 453	0.542 8	4	5 100.87	2 450	0.536 1	5	1 823.45	1 970	0.442 0
1	85	5 141.92	2 410	0.533 7	119	5 009.27	1 900	0.470 2	149	3 587.47	1 380	0.429 1
2	341	6 814.13	1 600	0.530 2	478	5 321.67	1 750	0.469 7	651	3 527.47	1 370	0.424 2
3	402	5 370.85	1 640	0.529 7	564	5 091.60	1 520	0.467 8	589	3 086.72	1 360	0.310 8
4	478	4 874.67	2 300	0.507 7	608	3 527.47	1 370	0.334 7	776	3 086.72	1 360	0.310 8

下载: 导出CSV

参考文献(25)

[1]	GONG L L, CAO W, LIU K L, et al. Optimal charging strategy for electric vehicles in residential charging station under dynamic spike pricing policy[J]. Sustainable Cities and Society, 2020, 63: 104-124.
[2]	OUYANG X, XU M, ZHOU B J. An Elastic demand model for locating electric vehicle charging stations[J]. Networks and Spatial Economics, 2022, 22(1): 1-31. doi: 10.1007/s11067-021-09546-5
[3]	ZHANG Y, ZHANG Q, FARNOOSH A, et al. GIS-based multi-objective particle swarm optimization of charging stations for electric vehicles[J]. Energy, 2019, 169: 844-853. doi: 10.1016/j.energy.2018.12.062
[4]	TAO Y, HUANG M H, CHEN Y P, et al. Review of optimized layout of electric vehicle charging infrastructures[J]. Journal of Central South University, 2021, 28 (10): 3268-3278. doi: 10.1007/s11771-021-4842-3
[5]	LIN W T, HUA G W. The flow capturing location model and algorithm of electric vehicle charging stations[C]. International Conference on Logistics, Informatics and Service Sciences, Beijing: Beijing Jiaotong University, 2015.
[6]	XIAO S Q, LEI X, HUANG T, et al. Coordinated planning for fast charging stations and distribution networks based on an improved flow capture location model[J]. CSEE Journal of Power and Energy Systems, 2023, 9(4): 1505-1516.
[7]	KIM J G, KUBY M. The deviation-flow refueling location model for optimizing a network of refueling stations[J]. International Journal of Hydrogen Energy, 2012, 37(6): 5406-5420. doi: 10.1016/j.ijhydene.2011.08.108
[8]	OUYANG X, XU M, ZHOU B J. An elastic demand model for locating electric vehicle charging stations[J]. Networks & Spatial Economics, 2022, 22(1): 1-31.
[9]	WU Z, ZHUANG Y, ZHOU S, et al. Bi-level planning of multi-functional vehicle charging stations considering land use types[J]. Energies, 2020, 13(5): 1283-1301. doi: 10.3390/en13051283
[10]	GUO F, YANG J, LU J Y. The battery charging station location problem: Impact of users' range anxiety and distance convenience[J]. Transportation Research Part E: Logistics & Transportation, 2018, 114: 1-18.
[11]	XU M, MENG Q. Optimal deployment of charging stations considering path deviation and nonlinear elastic demand[J]. Transportation Research Part B: Methodological, 2020, 135: 120-142. doi: 10.1016/j.trb.2020.03.001
[12]	张智禹, 王致杰, 杨皖昊, 等. 基于充电需求预测的电动汽车充电站选址规划研究[J]. 电测与仪表, 2023, 4(20): 1-19. https://www.cnki.net/KCMS/detail/detail.aspx?dbcode=IPFD&filename=ZGGS202306002010&dbname=IPFDLAST2023 ZHANG Z Y, WANG Z J, YANG W H, et al. Research on location planning of electric vehicle charging station based on charging demand prediction[J]. Electrical Measurement & Instrumentation, 2023, 4(20): 1-19. (in Chinese) https://www.cnki.net/KCMS/detail/detail.aspx?dbcode=IPFD&filename=ZGGS202306002010&dbname=IPFDLAST2023
[13]	XIAO D, AN S, CAI H, et al. An optimization model for electric vehicle charging infrastructure planning considering queuing behavior with finite queue length[J]. The Journal of Energy Storage, 2020, 29: 101317. doi: 10.1016/j.est.2020.101317
[14]	SHAHRAKI N, CAI H, TURKAY M, et al. Optimal locations of electric public charging stations using real world vehicle travel patterns[J]. Transportation Research Part D: Transport and Environment, 2015, 41: 165-176. doi: 10.1016/j.trd.2015.09.011
[15]	HUANG Y, KOCKELMAN K M. Electric vehicle charging station locations: Elastic demand, station congestion, and network equilibrium[J]. Transportation Research Part D: Transport and Environment, 2020, 78: 102-118.
[16]	CHEN T D, KOCKELMAN K M, KHAN M. Locating electric vehicle charging stations: Parking-based assignment method for Seattle, Washington[J]. Transportation Research Record, 2018, 2385(1): 28-36.
[17]	罗思杰, 邹复民, 郭峰, 等. 基于轨迹数据的出租车充电站选址方法[J]. 计算机工程与应用, 2022, 58(8): 273-282. https://www.cnki.com.cn/Article/CJFDTOTAL-JSGG202208029.htm LUO S J, ZOU F M, GUO F, et al. Taxi charging station location method based on trajectory data[J]. Computer Engineering and Applications, 2022, 58(8): 273-282. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSGG202208029.htm
[18]	GENG L, LU Z, GUO X, et al. Coordinated operation of coupled transportation and power distribution systems considering stochastic routing behaviour of electric vehicles and prediction error of travel demand[J]. IET Generation, Transmission & Distribution, 2021, 15(14): 2112-2116.
[19]	ZHAO Y Q, GUO Y, GUO Q L, et al. Deployment of the electric vehicle charging station considering existing competitors[J]. IEEE Transactions on Smart Grid, 2020, 11(5): 4236−4248. doi: 10.1109/TSG.2020.2991232
[20]	XU M, YANG H, WANG S A. Mitigate the range anxiety: Siting battery charging stations for electric vehicle drivers[J]. Transportation Research Part C: Emerging Technologies, 2020, 114(2): 164-188.
[21]	黄柳, 胡丹丹. 考虑路径偏差和里程焦虑下充/换电站联合布局定容优化[J]. 物流技术, 2021, 40(6): 68-75. https://www.cnki.com.cn/Article/CJFDTOTAL-WLJS202106012.htm HUANG L, HU D D. Constant capacity optimization of joint layout of charging/changing station considering path deviation and mileage anxiety[J]. Logistics Technology, 2021, 40(6): 68-75. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-WLJS202106012.htm
[22]	邵赛, 关伟, 毕军. 考虑排队时间和里程约束的竞争充电站选址问题[J]. 交通运输系统工程与信息, 2016, 16(6): 169-175. https://www.cnki.com.cn/Article/CJFDTOTAL-YSXT201606026.htm SHAO S, GUAN W, BI J. Competitive charging station location problem considering queuing time and mileage constraints[J]. Transportation System Engineering and Information, 2016, 16(6): 169-175. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSXT201606026.htm
[23]	胡诚, 黄合来, 李欣彤, 等. 考虑心理潜变量的城市电动自行车用户出行决策行为[J]. 交通信息与安全, 2021, 39(3): 111-120. doi: 10.3963/j.jssn.1674-4861.2021.03.014 HU C, HUANG H L, LI X T, et al. Travel decision-making behavior of urban electric bicycle users considering psychological latent variables[J]. Journal of Transport Information and Safety, 2019, 39(3): 111-120. (in Chinese) doi: 10.3963/j.jssn.1674-4861.2021.03.014
[24]	武渊, 叶宁. 城市路网中电动汽车充电站双层多目标选址定容模型[J]. 山西大学学报(自然科学版), 2021, 44(4): 695-704. https://www.cnki.com.cn/Article/CJFDTOTAL-SXDR202104009.htm WU Y, YE N. Two-layer multiobjective siting capacity model of electric vehicle charging stations in urban road network[J]. Journal of Shanxi University(Natural Science Edition), 2021, 44(4): 695-704. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SXDR202104009.htm
[25]	AGRAWAL A, BARRATT S, BOYD S. Learning convex optimization models[J]. IEEE/CAA Journal of Automatica Sinica, 2021, 8(8): 1355-1364.