Collaborative optimization of charging pile quantity and price for electric vehicle charging platform
Xi-qun CHEN1(),Yi-wei QIAN2,Dong MO1
1. Institute of Intelligent Transportation Systems, College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China 2. Polytechnic Institute & Institute of Intelligent Transportation Systems, Zhejiang University, Hangzhou 310058, China
A driver behavior decision model on the user side of electric vehicle (EV) charging platform was proposed based on the random utility maximization theory. Under the requirements of vehicle service and the constraints of charging stations, the Karush-Kuhn-Tucker (KKT) conditions, optimal quantity and charging price of different functions were derived for the objective functions of platform profit maximization and social welfare maximization, respectively. The parameter sensitivity was analyzed through the numerical experiments. The optimization results show that the appropriate charging price and the number of charging piles determine EV drivers’ willingness to different regions, the number of charging piles and the charging price have optimal solutions in multiple regions and periods. The model results show that, in spatial terms, the price and the quantity decrease with the distance increasing; in temporal terms, the pricing during the peak period is higher than that during the low period, and inter-regional pricing differences during the low period are more significant than those during the peak periods. Compared with different goals, the optimal charging price in social welfare maximization state is lower than that in profit maximization state, and the optimal number of charging piles to achieve maximum social welfare is more than that to achieve maximum profit. Results of sensitivity parameter analysis showed that, the battery capacity, the charging duration for unit battery capacity, and the sensitivity factor of multinomial Logit (MNL) model were negatively correlated with the target results, while positively correlated with users’ perceived utility.
Xi-qun CHEN,Yi-wei QIAN,Dong MO. Collaborative optimization of charging pile quantity and price for electric vehicle charging platform. Journal of ZheJiang University (Engineering Science), 2023, 57(9): 1785-1793.
Tab.1National public tax situation in 2017—2021 亿元
行政区
$ {D}_{j}^{0} $
$ {D}_{j}^{1} $
上城区
8 000
4 500
西湖区
6 000
3 100
余杭区
4 000
1 800
Tab.2Daily charging demand in three districts in Hangzhou 车次
Fig.1Distribution of charging piles and average daily demand for charging in three districts in Hangzhou
行政区
Lij
上城区
西湖区
余杭区
上城区
0
15
30
西湖区
15
0
42
余杭区
30
42
0
Tab.3Interarea traffic cost 元
Fig.2Multi-regional coordinated price adjustment decision and profit trend change
Fig.3Multi-regional coordinated price adjustment decision and social welfare trend change
行政区
$ \mathop p\nolimits_i^t $/元
Ni
$ \mathop N\nolimits_{it}^{\rm{v}} $
高峰期
低谷期
高峰期
低谷期
上城区
1.67
1.35
288
51
85
西湖区
1.62
1.32
278
58
106
余杭区
1.57
1.28
183
50
92
Tab.4Optimal price and number of charging piles under profit maximization
行政区域
$\mathop D\nolimits_{ij}^t $
行政区域
$\mathop D\nolimits_{ij}^t $
高峰期
低谷期
高峰期
低谷期
上城区?上城区
1374
1194
余杭区?西湖区
40
28
西湖区?上城区
232
184
上城区?余杭区
27
22
余杭区?上城区
12
8
西湖区?余杭区
64
48
上城区?西湖区
348
292
余杭区?余杭区
820
551
西湖区?西湖区
1112
856
——
——
——
Tab.5Daily charging demand under profit maximization 车次
行政区
$\mathop p\nolimits_i^t $/元
Ni
$ \mathop N\nolimits_{it}^{\rm{v}} $
高峰期
低谷期
高峰期
低谷期
上城区
1.62
1.28
309
52
86
西湖区
1.56
1.23
300
59
108
余杭区
1.51
1.20
195
51
94
Tab.6Optimal price and number of charging piles under social welfare maximization
行政区域
$\mathop D\nolimits_{ij}^t $
行政区域
$\mathop D\nolimits_{ij}^t $
高峰期
低谷期
高峰期
低谷期
上城区?上城区
1490
1308
余杭区?西湖区
44
31
西湖区?上城区
250
201
上城区?余杭区
29
25
余杭区?上城区
13
9
西湖区?余杭区
69
54
上城区?西湖区
381
328
余杭区?余杭区
889
613
西湖区?西湖区
1216
952
——
——
——
Tab.7Daily charging demand under social welfare maximization 车次
Fig.4Sensitivity analysis curves for battery capacity and charging sensitivity factor
Fig.5Sensitivity analysis curves for users perceived utility and sensitivity factor of MNL model
[1]
冯昊, 孙秋洁, 杨云露, 等 基于风险价值的电动汽车充电桩效益风险评估[J]. 现代电力, 2020, 37 (5): 501- 509 FENG Hao, SUN Qiu-jie, YANG Yun-lu, et al Benefit and risk assessment for electric vehicle charging pile based on value at risk[J]. Modern Electric Power, 2020, 37 (5): 501- 509
[2]
BIAN C, LI H, WALLIN F, et al Finding the optimal location for public charging stations–a GIS-based MILP approach[J]. Energy Procedia, 2019, 158: 6582- 6588
doi: 10.1016/j.egypro.2019.01.071
[3]
FANG Y, WEI W, MEI S, et al Promoting electric vehicle charging infrastructure considering policy incentives and user preferences: an evolutionary game model in a small-world network[J]. Journal of Cleaner Production, 2020, 258: 120753
doi: 10.1016/j.jclepro.2020.120753
[4]
孙丙香, 阮海军, 许文中, 等 基于静态非合作博弈的电动汽车充电电价影响因素量化分析[J]. 电工技术学报, 2016, 31 (21): 75- 85 SUN Bing-xiang, RUAN Hai-jun, XU Wen-zhong, et al Quantitative analysis of influence factors about EV’s charging electricity price based on the static non-cooperative game theory[J]. Transactions of China Electrotechnical Society, 2016, 31 (21): 75- 85
[5]
洪奕, 刘瑜俊, 徐青山, 等 基于积分制和分时电价的电动汽车混合型精准需求响应策略[J]. 电力自动化设备, 2020, 40 (11): 106- 116 HONG Yi, LIU Yu-jun, XU Qing-shan, et al Hybrid targeted demand response strategy of electric vehicles based on integral system and time-of-use electricity price[J]. Electric Power Automation Equipment, 2020, 40 (11): 106- 116
[6]
赵星宇, 胡俊杰 集群电动汽车充电行为的深度强化学习优化方法[J]. 电网技术, 2021, 45 (6): 2319- 2327 ZHAO Xing-yu, HU Jun-jie Deep reinforcement learning based optimization for charging of aggregated electric vehicles[J]. Power System Technology, 2021, 45 (6): 2319- 2327
[7]
GONG L, CAO W, LIU K, et al Optimal charging strategy for electric vehicles in residential charging station under dynamic spike pricing policy[J]. Sustainable Cities and Society, 2020, 63: 102474
doi: 10.1016/j.scs.2020.102474
[8]
AUJLA G S, KUMAR N, SINGH M, et al Energy trading with dynamic pricing for electric vehicles in a smart city environment[J]. Journal of Parallel and Distributed Computing, 2019, 127: 169- 183
doi: 10.1016/j.jpdc.2018.06.010
[9]
高建树, 王明强, 宋兆康, 等 基于遗传算法的机场充电桩布局选址研究[J]. 计算机工程与应用, 2018, 54 (23): 210- 216 GAO Jian-shu, WANG Ming-qiang, SONG Zhao-kang, et al Study on site selection of airport charging pile based on genetic algorithm[J]. Computer Engineering and Applications, 2018, 54 (23): 210- 216
CAPAR I, KUBY M, LEON V J, et al An arc cover–path-cover formulation and strategic analysis of alternative-fuel station locations[J]. European Journal of Operational Research, 2013, 227 (1): 142- 151
doi: 10.1016/j.ejor.2012.11.033
[12]
CHEN L, HUANG X, CHEN Z, et al Study of a new quick-charging strategy for electric vehicles in highway charging stations[J]. Energies, 2016, 9 (9): 744
doi: 10.3390/en9090744
[13]
宋建. 基于博弈模型的电动汽车有序充电研究[D]. 北京: 北京交通大学, 2019. SONG Jian. Study on orderly charging of electric vehicle based on game model [D]. Beijing: Beijing Jiaotong University, 2019.
