基于分布式梯度投影的居民区电动汽车均衡充电策略

doi:10.11930/j.issn.1004-9649.202512027

中国电力 ›› 2026, Vol. 59 ›› Issue (4): 140-149.DOI: 10.11930/j.issn.1004-9649.202512027

基于分布式梯度投影的居民区电动汽车均衡充电策略

曹望璋¹(), 陆泳昊²(), 靳丰源²(), 阳浩³, 金鑫¹, 王宗义¹, 赵勃扬²

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

收稿日期:2025-12-15 发布日期:2026-04-20 出版日期:2026-04-28
作者简介:
曹望璋（1993），男，博士，助理工程师，从事电力需求侧管理、负荷管理研究，E-mail：caowz@csg.cn
陆泳昊（2000），男，通信作者，博士研究生，从事电力需求侧管理研究，E-mail：louislu@stu.xjtu.edu.cn
靳丰源（1998），女，博士研究生，从事电力需求侧管理、博弈论方面研究，E-mail：fychin@stu.xjtu.edu.cn
基金资助:
国家自然科学基金资助项目（面向再电气化的大规模可控负荷均衡分析与调控理论研究，52177113）；中国南方电网有限责任公司科技项目（ZBKJXM20232273）。

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

CAO Wangzhang¹(), LU Yonghao²(), JIN Fengyuan²(), YANG Hao³, JIN Xin¹, WANG Zongyi¹, ZHAO Boyang²

1. China Southern Power Grid Electric Power Research Institute Co., Ltd., Guangzhou 510640, China
2. School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China
3. China Southern Power Grid Co., Ltd., Guangzhou 510623, China

Received:2025-12-15 Online:2026-04-20 Published:2026-04-28
Supported by:
This work is supported by National Natural Science Foundation of China (Theory on User Equilibrium Analysis and Regulation in Large-Scale Demand Response for Further Electrification Revolution, No.52177113), Science and Technology Project of China Southern Power Grid Co., Ltd. (No.ZBKJXM20232273).

摘要/Abstract

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。

关键词: 电动汽车, 需求响应, 聚合博弈, 纳什均衡, 动态电价

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.

Key words: electric vehicles, demand response, aggregative game, Nash equilibrium, dynamic price

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, YANG Hao, JIN Xin, WANG Zongyi, ZHAO Boyang. Equilibrium charging strategy for electric vehicles in residential areas based on distributed gradient projection[J]. Electric Power, 2026, 59(4): 140-149.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202512027

https://www.electricpower.com.cn/CN/Y2026/V59/I4/140

图/表 10

图 1 并行梯度投影算法流程

Fig.1 Flowchart of parallel gradient projection algorithm

图 2 具体实施流程

Fig.2 Flowchart of implementation process

图 3 基础负荷与总负荷曲线

Fig.3 Fixed load and total load curves

图 4 迭代时间与次数随电动汽车数量变化关系

Fig.4 Variation of iteration time and iteration count with the number of EVs

表 1 迭代次数对比

Table 1 Comparison of iteration times 单位：次

算法和准则组合	电动汽车规模
算法和准则组合	100辆	200辆	500辆	1000辆	1500辆
最优响应+普通收敛准则	2	—	—	—	—
最优响应+优化收敛准则	2	5	16	—	—
本文算法+普通收敛准则	5	9	—	—	—
本文算法+优化收敛准则	4	6	5	8	11

表 2 计算时间对比

Table 2 Comparison of computation time 单位：s

算法和准则组合	电动汽车规模
算法和准则组合	100辆	200辆	500辆	1000辆	1500辆
最优响应+普通收敛准则	1.4	—	—	—	—
最优响应+优化收敛准则	1.4	6.5	50.9	—	—
本文算法+普通收敛准则	1.2	6.9	—	—	—
本文算法+优化收敛准则	1.2	2.3	2.3	9.6	10.7

图 5 分时电价与动态电价下填谷效果对比

Fig.5 Comparison of valley-filling effects under time-of-use and dynamic electricity prices

表 3 不同场景下系统负荷指标比较

Table 3 System load indicators under different scenarios

指标	动态电价机制	分时电价机制
22:00—次日06:00时段最低负荷水平/kW	27192	21708
22:00—次日06:00时段最高负荷水平/kW	27393	35596
22:00—次日06:00时段负荷标准差/kW	67	4487
全日峰谷差/kW	22808	28292

表 4 2种机制下可控负荷数量对夜间最低负荷水平的影响

Table 4 Impact of controllable loads on minimum nighttime load

负荷水平	电动汽车规模
负荷水平	100辆	500辆	1000辆	1500辆	2000辆
动态电价下最低负荷/MW	19.43	21.19	22.49	23.57	24.41
分时电价下最低负荷/MW	19.43	20.06	20.31	20.51	20.88

图 6 分时与动态电价下充电成本与电量验证

Fig.6 Charging cost and energy verification under time-of-use and dynamic electricity prices

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基于分布式梯度投影的居民区电动汽车均衡充电策略

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

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基于分布式梯度投影的居民区电动汽车均衡充电策略

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

RichHTML

PDF (PC)

可视化

摘要/Abstract

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图/表 10

参考文献 39

相关文章 15

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