Convexification of Charging and Discharging Model and Constraint Set Contraction Method for Accurate Electric Vehicle Aggregation

WU Ziran; YU Tao; WU Yufeng; PAN Zhenning; WANG Keying

doi:10.7500/AEPS20250814007

您当前的位置：

首页 >

文章列表页 >

Convexification of Charging and Discharging Model and Constraint Set Contraction Method for Accurate Electric Vehicle Aggregation

Key Technologies and Practical Applications of Vehicle\-to\-Grid in New Power System | 更新时间：2026-08-21

- Convexification of Charging and Discharging Model and Constraint Set Contraction Method for Accurate Electric Vehicle Aggregation
- Automation of Electric Power Systems Vol. 50, Issue 15, Pages: 148-157(2026)
- 作者机构：
  
  华南理工大学电力学院，广东省广州市 510640
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(U24B6010)
- DOI：10.7500/AEPS20250814007
  CLC：
- Received：14 August 2025，
  
  Revised：2026-01-03，
  
  Online First：17 June 2026，
  
  Published：10 August 2026
- 稿件说明：
移动端阅览
巫子然,余涛,吴毓峰等.面向电动汽车精确聚合的充放电模型凸化及约束集内缩方法[J].电力系统自动化,2026,50(15):148-157.

WU Ziran,YU Tao,WU Yufeng,et al.Convexification of Charging and Discharging Model and Constraint Set Contraction Method for Accurate Electric Vehicle Aggregation[J].Automation of Electric Power Systems,2026,50(15):148-157.
巫子然,余涛,吴毓峰等.面向电动汽车精确聚合的充放电模型凸化及约束集内缩方法[J].电力系统自动化,2026,50(15):148-157. DOI： 10.7500/AEPS20250814007.

WU Ziran,YU Tao,WU Yufeng,et al.Convexification of Charging and Discharging Model and Constraint Set Contraction Method for Accurate Electric Vehicle Aggregation[J].Automation of Electric Power Systems,2026,50(15):148-157. DOI： 10.7500/AEPS20250814007.

摘要

海量电动汽车聚合控制技术是实现大规模电动汽车高效参与车网互动的关键。然而，现有聚合方法面临两大挑战：一是电动汽车充放电互斥特性导致功率可行域呈现非凸性；二是不同用户偏好下电动汽车的功率约束边界差异显著。前者将导致对电动汽车可调边界的高估，后者使电动汽车可调边界评估趋于保守。针对上述问题，首先通过重构电动汽车功率可行域的数学表达，实现了非凸可行域的凸化表征，有效解决了充放电互斥约束的建模难题；其次，设计了一种基于约束集内缩的聚合算法，通过提高传统聚合算法的内逼近自由度，显著提高了边界差异下可调边界的评估精确度。算例分析表明，所提方法有效提高了海量电动汽车调度的计算效率和聚合精度。

Abstract

Massive electric vehicle (EV) aggregation control technology is the key to achieving efficient participation of large-scale EVs in vehicle-to-grid (V2G). However

existing aggregation methods face two major challenges: first

the mutually exclusive characteristics of EV charging and discharging lead to non-convexity in the power feasible region; second

the power constraint boundaries of EVs with different user preferences exhibit significant differences. The former will result in overestimation of the adjustable boundaries of EVs

while the latter makes the evaluation of adjustable boundaries of EVs tend to be conservative. To address the above problems

this paper first achieves convex characterization of the non-convex feasible region by reconstructing the mathematical expression of the EV power feasible region

effectively solving the modeling problem of mutually exclusive charging-discharging constraints. Second

a constraint set contraction based aggregation algorithm is designed

which significantly improves the evaluation accuracy of adjustable boundaries under boundary differences by enhancing the inner approximation degrees of freedom of traditional aggregation algorithms. Case study analysis demonstrates that the proposed method effectively improves the computational efficiency and aggregation accuracy of massive EV scheduling.

关键词

Keywords

references

吴珊，边晓燕，张菁娴，等 . 面向新型电力系统灵活性提升的国内外辅助服务市场研究综述［J］. 电工技术学报， 2023 ， 38 （ 6 ）： 1662 - 1677 .

WU Shan ， BIAN Xiaoyan ， ZHANG Jingxian ， et al . A review of domestic and foreign ancillary services market for improving flexibility of new power system ［J］. Transactions of China Electrotechnical Society ， 2023 ， 38 （ 6 ）： 1662 - 1677 .

中国汽车技术研究中心有限公司 . 中国汽车品牌发展报告（2022）［M］. 北京：社会科学文献出版社， 2022 .

China Automotive Technology & Research Center Co.， Ltd . China automobile brand development report （2022）［M］. Beijing ： Social Sciences Literature Publishing House ， 2022 .

王明深，袁晓冬，曾飞，等 . 电动汽车充电设施规划运行关键技术研究综述［J］. 电力自动化设备， 2025 ， 45 （ 5 ）： 65 - 76 .

WANG Mingshen ， YUAN Xiaodong ， ZENG Fei ， et al . Review of key technologies research for electric vehicle charging facilities planning and scheduling ［J］. Electric Power Automation Equipment ， 2025 ， 45 （ 5 ）： 65 - 76 .

WEN Y L ， HU Z C ， YOU S ， et al . Aggregate feasible region of DERs： exact formulation and approximate models ［J］. IEEE Transactions on Smart Grid ， 2022 ， 13 （ 6 ）： 4405 - 4423 .

TIWARY H R . On the hardness of computing intersection， union and Minkowski sum of polytopes ［J］. Discrete & Computational Geometry ， 2008 ， 40 （ 3 ）： 469 - 479 .

SHI X Y ， XU Y L ， GUO Q L ， et al . Optimal dispatch based on aggregated operation region of EV considering spatio-temporal distribution ［J］. IEEE Transactions on Sustainable Energy ， 2022 ， 13 （ 2 ）： 715 - 731 .

廖思阳，贺聪，李玲芳，等 . 考虑电力网络约束的工业园区虚拟电厂调控边界求解方法［J］. 电力系统自动化， 2024 ， 48 （ 18 ）： 66 - 75 .

LIAO Siyang ， HE Cong ， LI Lingfang ， et al . Solution method of regulation boundary for industrial park virtual power plant considering power network constraints ［J］. Automation of Electric Power Systems ， 2024 ， 48 （ 18 ）： 66 - 75 .

童宇轩，胡俊杰，杜昊明，等 . 基于虚拟电池模型的外逼近闵可夫斯基热泵负荷调节可行域聚合方法［J］. 电网技术， 2024 ， 48 （ 8 ）： 3340 - 3349 .

TONG Yuxuan ， HU Junjie ， DU Haoming ， et al . Feasible region aggregation method for load regulation of minkowski heat pump based on external approximation of VB model ［J］. Power System Technology ， 2024 ， 48 （ 8 ）： 3340 - 3349 .

赵文猛，黄豪江，朱建全，等 . 内近似约束空间整合的灵活性资源集群响应方法［J］. 电网技术， 2023 ， 47 （ 7 ）： 2621 - 2629 .

ZHAO Wenmeng ， HUANG Haojiang ， ZHU Jianquan ， et al . Flexible resource cluster response based on inner approximate and constraint space integration ［J］. Power System Technology ， 2023 ， 47 （ 7 ）： 2621 - 2629 .

栗子豪，李铁，吴文传，等 . 基于Minkowski Sum的热泵负荷调度灵活性聚合方法［J］. 电力系统自动化， 2019 ， 43 （ 5 ）： 14 - 21 .

LI Zihao ， LI Tie ， WU Wenchuan ， et al . Minkowski sum based flexibility aggregating method of load dispatching for heat pumps ［J］. Automation of Electric Power Systems ， 2019 ， 43 （ 5 ）： 14 - 21 .

王思远，吴文传 . 灵活性资源聚合参考模型与量化指标体系［J］. 电力系统自动化， 2024 ， 48 （ 3 ）： 1 - 9 .

WANG Siyuan ， WU Wenchuan . Aggregation reference model and quantitative metric system of flexible energy resources ［J］. Automation of Electric Power Systems ， 2024 ， 48 （ 3 ）： 1 - 9 .

YI Z K ， XU Y L ， GU W ， et al . Aggregate operation model for numerous small-capacity distributed energy resources considering uncertainty ［J］. IEEE Transactions on Smart Grid ， 2021 ， 12 （ 5 ）： 4208 - 4224 .

ZHANG M Y ， XU Y L ， SHI X Y ， et al . A fast polytope-based approach for aggregating large-scale electric vehicles in the joint market under uncertainty ［J］. IEEE Transactions on Smart Grid ， 2024 ， 15 （ 1 ）： 701 - 713 .

JIAN J ， ZHANG M Y ， XU Y L ， et al . An analytical polytope approximation aggregation of electric vehicles considering uncertainty for the day-ahead distribution network dispatching ［J］. IEEE Transactions on Sustainable Energy ， 2024 ， 15 （ 1 ）： 160 - 172 .

JIAN J ， XU Y L ， YI Z K . An electric vehicle aggregation region approach for active distribution network optimal dispatch ［C］// 2022 IEEE/IAS Industrial and Commercial Power System Asia （I&CPS Asia）， July 8-11 ， 2022 ， Shanghai， China ： 1765 - 1770 .

TAHERI S ， KEKATOS V ， VEERAMACHANENI S ， et al . Data-driven modeling of aggregate flexibility under uncertain and non-convex device models ［J］. IEEE Transactions on Smart Grid ， 2022 ， 13 （ 6 ）： 4572 - 4582 .

LI G ， YANG J ， WU F Z ， et al . Electric vehicle aggregation in a PV-battery charging station： a contract-based approach ［J］. IEEE Transactions on Power Systems ， 2024 ， 39 （ 2 ）： 2475 - 2490 .

潘振宁，余涛，王克英 . 考虑多方主体利益的大规模电动汽车分布式实时协同优化［J］. 中国电机工程学报， 2019 ， 39 （ 12 ）： 3528 - 3540 .

PAN Zhenning ， YU Tao ， WANG Keying . Decentralized coordinated dispatch for real-time optimization of massive electric vehicles considering various interests ［J］. Proceedings of the CSEE ， 2019 ， 39 （ 12 ）： 3528 - 3540 .

曹家乐，任永峰，薛宇，等 . 考虑用户偏好及动态定价的“车-站-能”优化调度策略［J］. 电力自动化设备， 2026 ， 46 （ 2 ）： 148 - 155 .

CAO Jiale ， REN Yongfeng ， XUE Yu ， et al . Optimal scheduling strategy of EV-charging station-energy considering user preference and dynamic pricing ［J］. Electric Power Automation Equipment ， 2026 ， 46 （ 2 ）： 148 - 155 .

YI Z K ， XU Y L ， GU W ， et al . A multi-time-scale economic scheduling strategy for virtual power plant based on deferrable loads aggregation and disaggregation ［J］. IEEE Transactions on Sustainable Energy ， 2020 ， 11 （ 3 ）： 1332 - 1346 .

LAI S Y ， DONG Z Y ， YANG H M ， et al . Renewable energy following strategy via quantified aggregated heterogeneous electric vehicle flexibility ［J］. IEEE Transactions on Smart Grid ， 2025 ， 16 （ 5 ）： 3873 - 3886 .

WU X ， JIANG X Y ， YAO L J ， et al . Heterogeneous aggregation control model for hybrid EV clusters with random charging behavior ［J］. IEEE Transactions on Power Systems ， 2025 ， 40 （ 6 ）： 4702 - 4717 .

PEVEC D ， BABIC J ， CARVALHO A ， et al . A survey-based assessment of how existing and potential electric vehicle owners perceive range anxiety ［J］. Journal of Cleaner Production ， 2020 ， 276 ： 122779 .

GESKE J ， SCHUMANN D . Willing to participate in vehicle-to-grid （V2G）？ Why not！［J］. Energy Policy ， 2018 ， 120 ： 392 - 401 .

MÜLLER F L ， SZABÓ J ， SUNDSTRÖM O ， et al . Aggregation and disaggregation of energetic flexibility from distributed energy resources ［J］. IEEE Transactions on Smart Grid ， 2019 ， 10 （ 2 ）： 1205 - 1214 .

潘振宁，张孝顺，余涛，等 . 大规模电动汽车集群分层实时优化调度［J］. 电力系统自动化， 2017 ， 41 （ 16 ）： 96 - 104 .

PAN Zhenning ， ZHANG Xiaoshun ， YU Tao ， et al . Hierarchical real-time optimized dispatching for large-scale clusters of electric vehicles ［J］. Automation of Electric Power Systems ， 2017 ， 41 （ 16 ）： 96 - 104 .

ARTHUR D ， VASSILVITSKII S . k -means++： the advantages of careful seeding ［R］. Stanford， USA ： Stanford University ， 2006 .

CHEN X ， DALL’ANESE E ， ZHAO C H ， et al . Aggregate power flexibility in unbalanced distribution systems ［J］. IEEE Transactions on Smart Grid ， 2020 ， 11 （ 1 ）： 258 - 269 .

ZHAO L ， ZHANG W ， HAO H ， et al . A geometric approach to aggregate flexibility modeling of thermostatically controlled loads ［J］. IEEE Transactions on Power Systems ， 2017 ， 32 （ 6 ）： 4721 - 4731 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Transmission and Distribution Coordinated Day-ahead and Real-time Optimal Scheduling Considering Active Support of Vehicle-to-Grid

Vehicle-to-Grid for Large-scale Applications: Practical Progress, Key Bottlenecks, and Technical Pathways

Optimal Low-carbon Scheduling with Vehicle-Grid Spatio-temporal Coordination Considering Carbon Quotas for Life Cycle of Electric Vehicles

Review of Key Vehicle-side Technologies for Vehicle-to-Grid

Multi-dimensional Analysis and Prospect of Mechanism for Large-scale Electric Vehicles Participating in Electricity Ancillary Service Market

Related Author

JIANG Tao

WU Chenghao

LI Xue

ZHANG Rufeng

FU Linbo

HUANG Xueliang

LIU Yongdong

ZHANG Ziqi

Related Institution

Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology, Ministry of Education (Northeast Electric Power University)

School of Electrical Engineering, Southeast University

Standardization Center, China Electricity Council

NARI School of Electrical and Automation Engineering, Nanjing Normal University

DERI-TELD Energy Research Institute Co., Ltd.

⁰