Equilibrium charging strategy for electric vehicles in residential areas based on distributed gradient projection

CAO Wangzhang; LU Yonghao; JIN Fengyuan; YANG Hao; JIN Xin; WANG Zongyi; ZHAO Boyang

doi:10.11930/j.issn.1004-9649.202512027

English Version Journal Login

您当前的位置：

首页 >

文章列表页 >

Equilibrium charging strategy for electric vehicles in residential areas based on distributed gradient projection

更新时间：2026-04-30

- Equilibrium charging strategy for electric vehicles in residential areas based on distributed gradient projection
- Vol. 59, Issue 4, Pages: 140-149(2026)
- 作者机构：
  
  1. 南方电网科学研究院有限责任公司,广东,广州,510640
  2. 西安交通大学电气工程学院,陕西,西安,710049
  3. 南方电网有限责任公司,广东,广州,510623
- 作者简介：
- 基金信息：
- DOI：10.11930/j.issn.1004-9649.202512027
  CLC：
- Online First：20 April 2026，
  
  Published：2026
- 稿件说明：
移动端阅览
曹望璋, 陆泳昊, 靳丰源, 阳浩, 金鑫, 王宗义, 赵勃扬. 基于分布式梯度投影的居民区电动汽车均衡充电策略[J]. 中国电力, 2026, 59(4): 140-149.

CAO Wangzhang, LU Yonghao, JIN Fengyuan, et al. Equilibrium charging strategy for electric vehicles in residential areas based on distributed gradient projection[J]. 2026, 59(4): 140-149.
曹望璋, 陆泳昊, 靳丰源, 阳浩, 金鑫, 王宗义, 赵勃扬. 基于分布式梯度投影的居民区电动汽车均衡充电策略[J]. 中国电力, 2026, 59(4): 140-149. DOI： 10.11930/j.issn.1004-9649.202512027.

CAO Wangzhang, LU Yonghao, JIN Fengyuan, et al. Equilibrium charging strategy for electric vehicles in residential areas based on distributed gradient projection[J]. 2026, 59(4): 140-149. DOI： 10.11930/j.issn.1004-9649.202512027.

摘要

居民充电负荷管理是抑制大规模电动汽车对电网不利影响的重要举措，但集中式管理对用户隐私不利，分时电价下用户的自主响应易引发新的负荷高峰。首先，在居民小区引入动态电价机制，构建聚合博弈模型，引导用户自发调整充电行为，规避峰谷倒置。然后，提出分布式梯度投影算法实现聚合博弈纳什均衡的快速求解，充分保护车主隐私。最后，基于中国南方某居民小区用电数据开展仿真分析。结果表明：所提方法可有效平抑电动汽车充电引发的尖峰负荷，效果随电动汽车数量增加而提升；相比于分时电价机制，可有效避免新的负荷高峰产生，满足电动汽车不断增长下的充电负荷管理要求。

Abstract

Residential charging load management is a key means to mitigate the adverse impacts of large-scale electric vehicle (EV) integration on the power grid. However

centralized management compromises users' privacy

and the autonomous response of users under time-of-use electricity prices tends to induce new load peaks. Firstly

a dynamic electricity pricing mechanism is introduced in residential communities

and an aggregative game model is constructed to guide users to spontaneously adjust their charging behaviors and avoid peak-valley reversal. Then

a distributed gradient projection algorithm is proposed to rapidly achieve the Nash equilibrium of the aggregate game

which fully protects the privacy of vehicle owners. Finally

simulation analysis is carried out based on the electricity consumption data of a residential community in southern China. The results show that the proposed method can effectively smooth the peak load caused by EV charging

and the effect is enhanced with the increase in the number of EVs. Compared with the time-of-use pricing mechanism

it can effectively avoid the emergence of new load peaks and meet the requirements of charging load management under the growing penetration of electric vehicles.

关键词

Keywords

references

1朱继忠, 何子浩, 郑洁云, 等. 基于场景生成方法的配电网运营商主从博弈定价与电动汽车充电管理策略[J]. 南方电网技术, 2025, 19 (6): 72- 84.

ZHU Jizhong, HE Zihao, ZHENG Jieyun, et al. Stackelberg game pricing strategy and EV charging management for distribution network operator based on scenario generation method[J]. Southern Power System Technology, 2025, 19 (6): 72- 84.

3胡鹏, 艾欣, 张朔, 等. 基于需求响应的分时电价主从博弈建模与仿真研究[J]. 电网技术, 2020, 44 (2): 585- 592.

HU Peng, AI Xin, ZHANG Shuo, et al. Modeling and simulation study of TOU Stackelberg game based on demand response[J]. Power System Technology, 2020, 44 (2): 585- 592.

5ZHANG L, LI Y. Optimal management for parking-lot electric vehicle charging by two-stage approximate dynamic programming[J]. IEEE Transactions on Smart Grid, 2015, 8 (4): 1- 9.

6王锡凡, 邵成成, 王秀丽, 等. 电动汽车充电负荷与调度控制策略综述[J]. 中国电机工程学报, 2013, 33 (1): 1- 10.

WANG Xifan, SHAO Chengcheng, WANG Xiuli, et al. Survey of electric vehicle charging load and dispatch control strategies[J]. Proceedings of the CSEE, 2013, 33 (1): 1- 10.

7张美霞, 张安, 杨秀, 等. 基于交通均衡理论的电动汽车充电负荷预测[J]. 南方电网技术, 2025, 19 (8): 147- 159.

ZHANG Meixia, ZHANG An, YANG Xiu, et al. Prediction of electric vehicle charging load based on traffic equilibrium theory[J]. Southern Power System Technology, 2025, 19 (8): 147- 159.

8胡俊杰, 陆家悦, 马文帅, 等. 面向电网调峰的电动汽车运营商多层级实时控制策略[J]. 电力系统自动化, 2024, 48 (22): 84- 95.

HU Junjie, LU Jiayue, MA Wenshuai, et al. Multi-level real-time control strategy for electric vehicle aggregators oriented to grid peak shaving[J]. Automation of Electric Power Systems, 2024, 48 (22): 84- 95.

9NIMALSIRI N I, MEDIWATHTHE C P, RATNAM E L, et al. A survey of algorithms for distributed charging control of electric vehicles in smart grid[J]. IEEE Transactions on Intelligent Transportation Systems, 2020, 21 (11): 4497- 4515.

12陈奎, 马子龙, 周思宇, 等. 电动汽车两阶段多目标有序充电策略研究[J]. 电力系统保护与控制, 2020, 48 (1): 65- 72.

CHEN Kui, MA Zilong, ZHOU Siyu, et al. Charging control strategy for electric vehicles based on two-stage multi-target optimization[J]. Power System Protection and Control, 2020, 48 (1): 65- 72.

13邓慧琼, 张晓飞, 曾凡淦, 等. 动态分时电价机制下的电动汽车充放电调度策略研究[J]. 智慧电力, 2023, 51 (3): 59- 66, 78.

DENG Huiqiong, ZHANG Xiaofei, ZENG Fangan, et al. Electric vehicle charging and discharging scheduling strategy under dynamic time-of-use electricity price mechanism[J]. Smart Power, 2023, 51 (3): 59- 66, 78.

14王世谦, 贾一博, 白宏坤, 等. 分时电价下电动汽车参与虚拟电厂的经济优化调度方法[J]. 电力需求侧管理, 2023, 25 (5): 19- 26.

WANG Shiqian, JIA Yibo, BAI Hongkun, et al. Economic optimization scheduling method of electric vehicle participating in virtual power plant under time-of-use price[J]. Power Demand Side Management, 2023, 25 (5): 19- 26.

15张良, 孙成龙, 蔡国伟, 等. 基于PSO算法的电动汽车有序充放电两阶段优化策略[J]. 中国电机工程学报, 2022, 42 (5): 1837- 1852.

ZHANG Liang, SUN Chenglong, CAI Guowei, et al. Two-stage optimization strategy for coordinated charging and discharging of EVs based on PSO algorithm[J]. Proceedings of the CSEE, 2022, 42 (5): 1837- 1852.

16邓衍辉, 李剑, 卢国强, 等. 考虑分区域动态电价机制引导的电动汽车充电优化策略[J]. 电力系统保护与控制, 2024, 52 (7): 33- 44.

DENG Yanhui, LI Jian, LU Guoqiang, et al. Charging optimization strategy of electric vehicles guided by the dynamic tariff mechanism of a subregion[J]. Power System Protection and Control, 2024, 52 (7): 33- 44.

17MRITYUNJAY K M, SANJOY K P. A game theoretic horizon decomposition approach for real-time demand-side management[J]. IEEE Transactions on Smart Grid, 2022, 13 (5): 3532- 3545.

18MARTIN H, JEAN-FRANÇOIS T, ITALO A, et al. Pricing electricity in residential communities using game-theoretical billings[J]. IEEE Transactions on Smart Grid, 2023, 14 (2): 1621- 1631.

19MA Z, CALLAWAY D S, HISKENS I A. Decentralized charging control of large populations of plug-in electric vehicles[J]. IEEE Transactions on Control Systems Technology, 2013, 21 (1): 67- 78.

20JACQUOT P, WAN C. Nonatomic aggregative games with infinitely many types[J]. North-Holland, 2021. DOI:10.1016/J.EJOR.2021.11.025.

21王一飞, 王秀丽, 黄晶, 等. 动态电价机制下电动汽车竞争性充电的阻塞管理模型[J]. 电力系统自动化, 2023, 47 (12): 103- 110.

WANG Yifei, WANG Xiuli, HUANG Jing, et al. Congestion management model for competitive charging of electric vehicles under dynamic electricity pricing mechanism[J]. Automation of Electric Power Systems, 2023, 47 (12): 103- 110.

22JACQUOT P, BEAUDE O, GAUBERT S, et al. Analysis and Implementation of an hourly billing mechanism for demand response management[J]. IEEE Transactions on Smart Grid, 2019, 10 (4): 4265- 4278.

23PACCAGNAN D, GENTILE B, PARISE F, et al. Nash and Wardrop equilibria in aggregative games with coupling constraints[J]. IEEE Transactions on Automatic Control, 2019, 64 (4): 1373- 1388.

24李明祁. 成都市居民小区电动汽车充电桩建设的问题研究[D]. 电子科技大学, 2024.

LI Mingqi. Research on the problems of the construction of electric vehicle charging piles in residential areas in Chengdu[D]. Chengdu: University of Electronic Science and Technology of China, 2024.

25张仕鹏, 彭超逸, 黄楚鸿, 等. 包含电动汽车充电站的区域电网优化调度[J]. 南方电网技术, 2025, 19 (3): 52- 60.

ZHANG Shipeng, PENG Chaoyi, HUANG Chuhong, et al. Optimal scheduling for regional power grid including electric vehicle charging stations[J]. Southern Power System Technology, 2025, 19 (3): 52- 60.

26喻磊, 谈竹奎, 王扬, 等. 基于深度强化学习的电动汽车有序充电优化方法[J]. 南方电网技术, 2024, 18 (12): 148- 156.

YU Lei, TAN Zhukui, WANG Yang, et al. Deep reinforcement learning based optimization method for ordered charging of electric vehicle[J]. Southern Power System Technology, 2024, 18 (12): 148- 156.

27郑佳俊, 段小宇, 胡泽春, 等. 组件式移动充电设施布局优化方法与投放策略[J]. 中国电力, 2025, 58 (4): 107- 118.

ZHENG Jiajun, DUAN Xiaoyu, HU Zechun, et al. Modular mobile charging facility layout optimization method and deployment strategy[J]. Electric Power, 2025, 58 (4): 107- 118.

28颜俊, 罗宇杰, 颜安, 等. 计及用户响应特性的电动汽车充电站设备优化配置方法[J]. 中国电力, 2025, 58 (4): 140- 147.

YAN Jun, LUO Yujie, YAN An, et al. Optimal equipment configuration method for electric vehicle charging stations considering user response characteristics[J]. Electric Power, 2025, 58 (4): 140- 147.

29苏大威, 范旖晖, 赵天辉, 等. 基于价格激励的城市公共充电站填谷潜力评估[J]. 中国电力, 2025, 58 (4): 131- 139.

SU Dawei, FAN Yihui, ZHAO Tianhui, et al. Valley-filling potential evaluation of urban public charging stations based on price incentive[J]. Electric Power, 2025, 58 (4): 131- 139.

30屈克庆, 赵登辉, 毛玲, 等. 考虑城市空间结构和用户有限理性的电动汽车快充负荷预测[J]. 南方电网技术, 2024, 18 (10): 151- 160.

QU Keqing, ZHAO Denghui, MAO Ling, et al. Fast charging load forecasting of electric vehicles considering urban spatial structure and user's bounded rationality[J]. Southern Power System Technology, 2024, 18 (10): 151- 160.

31袁建华, 张天宇, 陈广生, 等. 基于补偿机制的电动汽车区域多维补电优化调度策略[J]. 中国电力, 2025, 58 (4): 119- 130.

YUAN Jianhua, ZHANG Tianyu, CHEN Guangsheng, et al. Optimization and scheduling strategy for regional multi-dimensional charging of electric vehicles based on compensation mechanism[J]. Electric Power, 2025, 58 (4): 119- 130.

32李晓涵, 曹伟. 弹性充电需求下电动汽车调频激励机制及控制策略[J]. 中国电力, 2025, 58 (4): 148- 158.

LI Xiaohan, CAO Wei. Frequency regulation incentive mechanism and control strategy for electric vehicles under elastic charging demand[J]. Electric Power, 2025, 58 (4): 148- 158.

33GLICKSBERG I L. A further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points[J]. Proceedings of the American Mathematical Society, 1952, 3 (1): 170- 174.

34FACCHINEI FRANCISCO , PANG JONG-SHI. Finite-dimensional variational inequalities and complementarity problems [M]. Berlin, Germany: Springer, 2007.

35孙志颖, 李青, 张凯. 考虑活动-出行需求特性的大规模电动汽车入网影响力分析[J]. 南方电网技术, 2024, 18 (12): 138- 147.

SUN Zhiying, LI Qing, ZHANG Kai. Influences analysis of large-scale electric vehicles interconnected with power system regarding activity-travel demand characteristics[J]. Southern Power System Technology, 2024, 18 (12): 138- 147.

36CALAMAIP H, MORÉ J J. Projected gradient methods for linearly constrained problems [M]. Math Program, 1987, 23.

37潘廷哲, 靳丰源, 陆泳昊, 等. 智能小区电动汽车充电动态电价策略设计[J]. 中国电力, 2025, 58 (11): 14- 24, 37.

PAN Tingzhe, JIN Fengyuan, LU Yonghao, et al. Design of dynamic pricing strategy for electric vehicles charging in smart communities[J]. Electric Power, 2025, 58 (11): 14- 24, 37.

38丁屹峰, 曾爽, 张宝群, 等. 光伏-直流智能充电桩有序充电策略与应用效果[J]. 中国电力, 2024, 57 (5): 70- 77.

DING Yifeng, ZENG Shuang, ZHANG Baoqun, et al. Orderly charging strategy and application effect of PV-DC intelligent EV chargers[J]. Electric Power, 2024, 57 (5): 70- 77.

39戚佳金, 尹淑淙, 张良, 等. 虚拟电厂与电动汽车运营商的主从-演化混合博弈调度方法[J]. 电力系统保护与控制, 2025, 53 (18): 131- 141.

QI Jiajin, YIN Shucong, ZHANG Liang, et al. A master-slave evolutionary hybrid game-based scheduling method for virtual power plants and electric vehicle operators[J]. Power System Protection and Control, 2025, 53 (18): 131- 141.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Bidding operation strategies for charging stations considering various vehicle-grid interactive scenarios

Design of Dynamic Pricing Strategy for Electric Vehicles Charging in Smart Communities

Economic Scheduling of Electric-Heat-Water Multi-Energy Coupling Systems Considering Electric Vehicles and Demand Response

Optimization of Distribution-side Distributed Photovoltaic Market Trading Strategies Considering Source-Grid-Load-Storage Coordination

Low-carbon scheduling decision method for industrial park users considering production characteristics

Related Author

WANG Shiqian

HUA Yuanpeng

LI Qiuyan

LIU Bo

YANG Jianping

XIANG Yue

PAN Tingzhe

JIN Fengyuan

Related Institution

State Grid Henan Electric Power Company Economic and Technology Research Institute

State Grid Henan Electric Power Company

College of Electrical Engineering, Sichuan University

Electric Power Research Institute,, Guangzhou

Department of Electrical Engineering, Xi'an Jiaotong University

AI问答

⁰