Robust Optimization Model for Coordinated Frequency Regulation of Electric Vehicle Cluster and Units Considering Uncertainties of Frequency Regulation and Excitation

WANG Qingyuan; WANG Mingshen; MU Yunfei; CUI Li; ZHAO Nan; GE Le

doi:10.7500/AEPS20241203002

您当前的位置：

首页 >

文章列表页 >

Robust Optimization Model for Coordinated Frequency Regulation of Electric Vehicle Cluster and Units Considering Uncertainties of Frequency Regulation and Excitation

Basic Research | 更新时间：2025-09-25

- Robust Optimization Model for Coordinated Frequency Regulation of Electric Vehicle Cluster and Units Considering Uncertainties of Frequency Regulation and Excitation
- Automation of Electric Power Systems Vol. 49, Issue 18, Pages: 146-158(2025)
- 作者机构：
  
  1.国网江苏省电力有限公司高邮市供电分公司，江苏省扬州市 225699
  2.南京工程学院电力工程学院，江苏省南京市 211167
  3.国网江苏省电力有限公司电力科学研究院，江苏省南京市 211103
  4.智能电网教育部重点实验室（天津大学），天津市 300072
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(52477101)
- DOI：10.7500/AEPS20241203002
  CLC：
- Received：03 December 2024，
  
  Revised：2025-04-24，
  
  Published Online：31 July 2025，
  
  Published：25 September 2025
- 稿件说明：
移动端阅览
王庆园,王明深,穆云飞等.考虑调频-激励不确定性的EV集群与机组协同调频鲁棒优化模型[J].电力系统自动化,2025,49(18):146-158.

WANG Qingyuan,WANG Mingshen,MU Yunfei,et al.Robust Optimization Model for Coordinated Frequency Regulation of Electric Vehicle Cluster and Units Considering Uncertainties of Frequency Regulation and Excitation[J].Automation of Electric Power Systems,2025,49(18):146-158.
王庆园,王明深,穆云飞等.考虑调频-激励不确定性的EV集群与机组协同调频鲁棒优化模型[J].电力系统自动化,2025,49(18):146-158. DOI： 10.7500/AEPS20241203002.

WANG Qingyuan,WANG Mingshen,MU Yunfei,et al.Robust Optimization Model for Coordinated Frequency Regulation of Electric Vehicle Cluster and Units Considering Uncertainties of Frequency Regulation and Excitation[J].Automation of Electric Power Systems,2025,49(18):146-158. DOI： 10.7500/AEPS20241203002.

摘要

新能源高比例接入电网导致调频难题日益凸显，电动汽车（EV）集群作为调频资源，存在缺乏有效的激励机制、充放电不确定性高、独立调频风险高等问题。针对这些问题，文中考虑市场调频环境和EV集群调频激励的双重不确定性，提出EV集群与传统调频机组协同调频的鲁棒优化模型，以实现协同调频经济的最优。首先，利用随机优化法对历史调频数据进行聚类分析，构建EV集群与机组协同调频的调频信号场景集。然后，提出考虑用户行为偏好的充放电激励机制，采用核密度估计区间预测EV用户主动参与充放电调控的概率，利用基于条件风险价值的分布鲁棒优化法分析激励下的EV充电行为不确定性问题。接着，以调频成本最小为目标构建EV集群与机组协同调频的分布鲁棒优化模型，并将该模型重构为二阶锥规划问题。最后，算例验证了协同调频在收益期望、收益标准差和条件损失期望方面的优势，协同调频相较于传统机组调频有效提升了经济效益。

Abstract

The high proportion of renewable energy connected to the power grid has led to increasingly prominent problems in frequency regulation. As a frequency regulation resource

the electric vehicle (EV) cluster faces the problems such as the lack of effective incentive mechanisms

high uncertainty in charging and discharging

and significant risks associated with independent frequency regulation. To solve these problems

considering the dual uncertainties of the market frequency regulation environment and the EV cluster frequency regulation incentive

this paper proposes a robust optimization model for coordinated frequency regulation of the EV cluster and conventional frequency regulation units

so as to achieve the optimization of coordinated frequency regulation economy. Firstly

by using the random optimization method to cluster and analyze historical frequency regulation data

a frequency regulation signal scenario set for coordinated frequency regulation of the EV cluster and units is constructed. Secondly

the charging and discharging incentive mechanisms considering user behavior preferences are proposed. The kernel density estimation interval is used to predict the probability of EV users actively participating in charging and discharging regulation. The distributionally robust optimization method based on conditional value at risk is used to analyze the uncertainty of EV charging behavior under incentives. Thirdly

to minimize the frequency regulation cost

a distributionally robust optimization model for coordinated frequency regulation of the EV cluster and units is constructed

and the model is reconstructed as a second-order cone programming problem. Finally

the case verifies the advantages of coordinated frequency regulation in terms of expected revenue

standard deviation of revenue

and conditional loss expection. Compared with traditional unit frequency regulation

coordinated frequency regulation effectively improves economic benefits.

关键词

Keywords

references

裴铭，叶林，罗雅迪，等 . 计及频率响应时空相关性的新能源电力系统惯量估计方法［J］. 电力系统自动化， 2024 ， 48 （ 8 ）： 53 - 66 .

PEI Ming ， YE Lin ， LUO Yadi ， et al . Inertia estimation method for power system with renewable energy considering spatio-temporal correlation of frequency response ［J］. Automation of Electric Power Systems ， 2024 ， 48 （ 8 ）： 53 - 66 .

滕贤亮，谈超，昌力，等 . 高比例新能源电力系统有功功率与频率控制研究综述及展望［J］. 电力系统自动化， 2023 ， 47 （ 15 ）： 12 - 35 .

TENG Xianliang ， TAN Chao ， CHANG Li ， et al . Review and prospect of research on active power and frequency control in power system with high proportion of renewable energy ［J］. Automation of Electric Power Systems ， 2023 ， 47 （ 15 ）： 12 - 35 .

国家能源局南方监管局 . 广东电力市场现货电能量交易实施细则（2022年试行版）［EB/OL］.［ 2024-11-20 ］. https：//nfj.nea.gov.cn/file_upload/20220107/54731641528690168_e76e8223-638a-4112-a797-16171699396d.pdf https://nfj.nea.gov.cn/file_upload/20220107/54731641528690168_e76e8223-638a-4112-a797-16171699396d.pdf .

South China Energy Regulatory Bureau of National Energy Administration of the People’s Republic of China . Detailed rules for the implementation of spot electricity energy trading in Guangdong electricity market（trial version 2022）［EB/OL］. ［ 2024-11-20 ］. https：//nfj.nea.gov.cn/file_upload/20220107/54731641528690168_e76e8223-638a-4112-a797-16171699396d.pdf https://nfj.nea.gov.cn/file_upload/20220107/54731641528690168_e76e8223-638a-4112-a797-16171699396d.pdf .

闫斯哲，王维庆，李笑竹，等 . 储能-机组联合调频的动态经济环境跨区灵活性鲁棒优化调度［J］. 电力系统自动化， 2022 ， 46 （ 9 ）： 61 - 70 .

YAN Sizhe ， WANG Weiqing ， LI Xiaozhu ， et al . Cross-regional flexible robust optimal scheduling in dynamic economic environment with joint frequency regulation of energy storage and units ［J］. Automation of Electric Power Systems ， 2022 ， 46 （ 9 ）： 61 - 70 .

程杉，李沣洋，刘炜炜，等 . 电动汽车协助火电机组参与调频辅助服务优化控制策略［J］. 电力系统保护与控制， 2024 ， 52 （ 6 ）： 142 - 151 .

CHENG Shan ， LI Fengyang ， LIU Weiwei ， et al . Optimal control strategy of thermal power units with electric vehicles participating in frequency regulation auxiliary services ［J］. Power System Protection and Control ， 2024 ， 52 （ 6 ）： 142 - 151 .

王明深，潘益，缪惠宇，等 . 考虑用户多样化需求的电动汽车集群调频控制策略［J］. 现代电力， 2024 ， 41 （ 3 ）： 565 - 573 .

WANG Mingshen ， PAN Yi ， MIAO Huiyu ， et al . Frequency regulation strategy of EV aggregator considering various user requirements ［J］. Modern Electric Power ， 2024 ， 41 （ 3 ）： 565 - 573 .

GAO S ， DAI R X ， CAO W J ， et al . Combined provision of economic dispatch and frequency regulation by aggregated EVs considering electricity market interaction ［J］. IEEE Transactions on Transportation Electrification ， 2023 ， 9 （ 1 ）： 1723 - 1735 .

孙毅，葛明洋，王献春，等 . 考虑补偿激励的电动汽车多区域优化调度策略［J］. 上海交通大学学报， 2024 ， 58 （ 5 ）： 636 - 646 .

SUN Yi ， GE Mingyang ， WANG Xianchun ， et al . Multi-region optimal scheduling strategy for electric vehicles considering compensation incentives ［J］. Journal of Shanghai Jiao Tong University ， 2024 ， 58 （ 5 ）： 636 - 646 .

WANG H ， JIA Y W ， SHI M G ， et al . A hybrid incentive program for managing electric vehicle charging flexibility ［J］. IEEE Transactions on Smart Grid ， 2023 ， 14 （ 1 ）： 476 - 488 .

潘益，王明深，缪惠宇，等 . 车网互动技术激励机制演化分析［J/OL］. 上海交通大学学报［ 2024-11-20 ］. https：//link.cnki.net/doi/10.16183/j.cnki.jsjtu.2023.603 https://link.cnki.net/doi/10.16183/j.cnki.jsjtu.2023.603 .

PAN Yi ， WANG Mingshen ， MIAO Huiyu ， et al . Incentive mechanism of V 2 G： an evolutionary game approach［J/OL］. Journal of Shanghai Jiao Tong University ［ 2024-11-20 ］. https：//link.cnki.net/doi/10.16183/j.cnki.jsjtu.2023.603 https://link.cnki.net/doi/10.16183/j.cnki.jsjtu.2023.603 .

许梦瑶，艾小猛，方家琨，等 . 考虑用户积极性的电动汽车与机组联合调频的两阶段随机优化调度模型［J］. 电网技术， 2022 ， 46 （ 6 ）： 2033 - 2041 .

XU Mengyao ， AI Xiaomeng ， FANG Jiakun ， et al . Two-stage stochastic optimal scheduling model for joint regulation of EV and thermal units considering users enthusiasm ［J］. Power System Technology ， 2022 ， 46 （ 6 ）： 2033 - 2041 .

ESFAHANI M ， ALIZADEH A ， AMJADY N ， et al . A distributed VPP-integrated co-optimization framework for energy scheduling， frequency regulation， and voltage support using data-driven distributionally robust optimization with Wasserstein metric ［J］. Applied Energy ， 2024 ， 361 ： 122883 .

YANG L F ， YANG Y ， CHEN G ， et al . Distributionally robust framework and its approximations based on vector and region split for self-scheduling of generation companies ［J］. IEEE Transactions on Industrial Informatics ， 2022 ， 18 （ 8 ）： 5231 - 5241 .

王沿胜，何川，刘绚，等 . 考虑极端灾害下系统韧性约束的气电联合配网分布鲁棒扩展规划［J］. 工程科学与技术， 2023 ， 55 （ 1 ）： 80 - 92 .

WANG Yansheng ， HE Chuan ， LIU Xuan ， et al . Distributionally robust expansion planning of integrated gas-electricity distribution system considering system resilience constraints under extreme disasters ［J］. Advanced Engineering Sciences ， 2023 ， 55 （ 1 ）： 80 - 92 .

ZHANG Y M ， DONG C Y ， XIAO Q ， et al . Discrete spectrum iteration based comprehensive stability assessment method for the delayed cyber-physical system with electric-vehicle frequency regulation ［J］. IEEE Access ， 2020 ， 8 ： 137209 - 137225 .

SONG M ， AMELIN M . Purchase bidding strategy for a retailer with flexible demands in day-ahead electricity market ［J］. IEEE Transactions on Power Systems ， 2017 ， 32 （ 3 ）： 1839 - 1850 .

DENG X S ， ZHANG Q ， LI Y ， et al . Hierarchical distributed frequency regulation strategy of electric vehicle cluster considering demand charging load optimization ［J］. IEEE Transactions on Industry Applications ， 2022 ， 58 （ 1 ）： 720 - 731 .

王明深，李毅强，王伟亮，等 . 考虑充放电响应度的电动汽车聚合商与机组协同参与调频市场运营策略［J/OL］. 电网技术［ 2024-12-02 ］. https：//link.cnki.net/doi/10.13335/j.1000-3673.pst.2024.1637 https://link.cnki.net/doi/10.13335/j.1000-3673.pst.2024.1637 .

WANG Mingshen ， LI Yiqiang ， WANG Weiliang ， et al . Collaborative frequency market operation strategy of electric vehicle aggregator and units considering charging and discharging responsiveness ［J/OL］. Power System Technology ［ 2024-12-02 ］. https：//link.cnki.net/doi/10.13335/j.1000-3673.pst.2024.1637 https://link.cnki.net/doi/10.13335/j.1000-3673.pst.2024.1637 .

侯慧，唐俊一，王逸凡，等 . 价格与激励联合需求响应下电动汽车长时间尺度充放电调度［J］. 电力系统自动化， 2022 ， 46 （ 15 ）： 46 - 55 .

HOU Hui ， TANG Junyi ， WANG Yifan ， et al . Long-time-scale charging and discharging scheduling of electric vehicles under joint price and incentive demand response ［J］. Automation of Electric Power Systems ， 2022 ， 46 （ 15 ）： 46 - 55 .

WANG M S ， LI X ， DONG C Y ， et al . Day-ahead optimal bidding for a retailer with flexible participation of electric vehicles ［J］. IEEE Transactions on Smart Grid ， 2023 ， 14 （ 2 ）： 1482 - 1494 .

葛乐，王庆园，王明深，等 . 考虑充放电激励机制的电动汽车聚合商参与能量-调频市场多阶段运营策略［J］. 电力自动化设备， 2024 ， 44 （ 6 ）： 176 - 184 .

GE Le ， WANG Qingyuan ， WANG Mingshen ， et al . Multi-stage operation strategy of electric vehicle aggregator participating in energy and frequency regulation markets considering charging and discharging incentive mechanisms ［J］. Electric Power Automation Equipment ， 2024 ， 44 （ 6 ）： 176 - 184 .

FU Y Y ， HAN X ， BAKER K ， et al . Assessments of data centers for provision of frequency regulation ［J］. Applied Energy ， 2020 ， 277 ： 115621 .

YU H ， WEN G Q ， GAN J Z ， et al . Self-paced learning for K-means clustering algorithm ［J］. Pattern Recognition Letters ， 2020 ， 132 ： 69 - 75 .

ZOU R M ， SONG M M ， WANG Y ， et al . Deep non-crossing probabilistic wind speed forecasting with multi-scale features ［J］. Energy Conversion and Management ， 2022 ， 257 ： 115433 .

SERRANO-GUERRERO X ， BRICEÑO-LEÓN M ， CLAIRAND J M ， et al . A new interval prediction methodology for short-term electric load forecasting based on pattern recognition ［J］. Applied Energy ， 2021 ， 297 ： 117173 .

王晓玲，韩国玺，余佳，等 . TBM掘进速率区间预测Bootstrap-IHHO-BiLSTM模型［J］. 水力发电学报， 2023 ， 42 （ 12 ）： 159 - 171 .

WANG Xiaoling ， HAN Guoxi ， YU Jia ， et al . Interval prediction Bootstrap-IHHO-BiLSTM model for TBM advance rate ［J］. Journal of Hydroelectric Engineering ， 2023 ， 42 （ 12 ）： 159 - 171 .

ALI M U ， ZAFAR A ， NENGROO S H ， et al . Towards a smarter battery management system for electric vehicle applications： a critical review of lithium-ion battery state of charge estimation ［J］. Energies ， 2019 ， 12 （ 3 ）： 446 .

YIN W J ， JI J B ， WEN T ， et al . Study on orderly charging strategy of EV with load forecasting ［J］. Energy ， 2023 ， 278 ： 127818 .

ACHARKI N ， BERTONCELLO A ， GARNIER J . Robust prediction interval estimation for Gaussian processes by cross-validation method ［J］. Computational Statistics & Data Analysis ， 2023 ， 178 ： 107597 .

LU J ， DING J . Mixed-distribution-based robust stochastic configuration networks for prediction interval construction ［J］. IEEE Transactions on Industrial Informatics ， 2020 ， 16 （ 8 ）： 5099 - 5109 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Optimal Control of Electric Vehicle Cluster Participating in Frequency Regulation Market Considering User Preferences

Two-stage Robust Optimization Method for Spatio-Temporal Coordination of Data Center Considering Thermal Dynamic Characteristics of Buildings

Distributed Algorithm for Robust Economic Dispatch of Integrated Transmission and Distribution System Considering Wind Power Uncertainty

Collaborative Robust Planning of Electric and Thermal Flexibility Resources Considering Reserve Optimization

Related Author

WANG Qingyuan

MAO Meiqin

GE Xing

YANG Cheng

WANG Yuanyue

DU Yan

SHI Yong

QIN Xuexue

Related Institution

Gaoyou Power Supply Company, State Grid Jiangsu Electric Power Co., Ltd.

Research Center for Photovoltaic Systems Engineering of Ministry of Education, Hefei University of Technology

State Grid Anhui Electric Power Co., Ltd.

State Grid Anhui Electric Vehicle Service Co., Ltd.

Anhui Province Key Laboratory of Semiconductor Packaging and Reliability, Hefei University of Technology

⁰