Distributionally Robust Optimization-Based Dynamic Pricing Model and Solution Method for Multiple Virtual Power Plants Stackelberg Game

CHEN Qu; YANG Ping; CHEN Nianhao; LIU Genrao; YAN Lu

PDF(1751 KB)

Electric Power Construction ›› 0

Distributionally Robust Optimization-Based Dynamic Pricing Model and Solution Method for Multiple Virtual Power Plants Stackelberg Game

CHEN Qu, YANG Ping, CHEN Nianhao, LIU Genrao, YAN Lu

Author information +

History +

Abstract

[Objective] In response to the Stackelberg game framework involving multiple virtual power plants (VPPs) and a distribution system operator (DSO), where existing dynamic pricing models inadequately capture the impact of renewable energy generation uncertainty on game strategies, and conventional solution methods suffer from poor solution quality in high-dimensional decision spaces, this paper proposes a dynamic pricing model and solution approach based on distributionally robust optimization (DRO) within a Stackelberg game framework. [Methods] A Stackelberg game dynamic pricing model is established, with the DSO as the leader and multiple VPPs as followers. In the VPP optimization model, a distributionally robust chance constraint is introduced to characterize wind power output uncertainty. By constructing an ambiguity set using only the first and second moments of wind power, the chance constraint is transformed into a deterministic equivalent form via the Cantelli inequality. Furthermore, a neural network-enhanced regional particle swarm optimization (NN-RPSO) algorithm is proposed, which builds a predictive model for VPP behavior to replace frequent calls to the lower-level optimization and integrates a regional partitioning strategy to achieve efficient search. [Results] Decision-makers can balance operational risk and cost by adjusting the risk budget parameters. Compared with the regional particle swarm optimization (RPSO) algorithm, the proposed algorithm increases the DSO's revenue by 47.2% while reducing the number of lower-level model calls by approximately 67.4%. [Conclusions] The proposed DRO model provides decision-makers with a flexible approach to handle uncertainty, and the proposed solution algorithm significantly improves solution quality, offering an effective solution for the multi-agent Stackelberg game problem.

Key words

multiple virtual power plants / distribution system operator / Stackelberg game / distributionally robust optimization / dynamic pricing / neural network-enhanced regional particle swarm optimization（NN-RPSO）

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

CHEN Qu, YANG Ping, CHEN Nianhao, LIU Genrao, YAN Lu. Distributionally Robust Optimization-Based Dynamic Pricing Model and Solution Method for Multiple Virtual Power Plants Stackelberg Game[J]. Electric Power Construction. 0

References

[1] 孙荣富,王歌,闵睿,等.面向新型电力系统的虚拟电厂交易机制设计[J/OL].电力系统自动化,1-18[2026-03-02].
Sun Rongfu, Wang Ge, Min Rui, et al.Design of virtual power plant trading mechanism for new-type power systems[J/OL]. Automation of Electric Power Systems, 1-18[2026-03-02].
[2] 高明,曾平良,冯永朝.新型电力系统中的虚拟电厂研究综述[J].电力工程技术,2025,44(06):143-154.
Gao Ming, Zeng Pingliang, Feng Yongchao.A review of virtual power plant research in new-type power systems[J]. Electric Power Engineering Technology, 2025, 44(06): 143-154.
[3] 罗祾,陈甜甜,华珉,等. 考虑点对点交易的虚拟电厂联盟协同优化策略[J]. 浙江电力, 2025, 44
Luo Ling, Chen Tiantian, Hua Min, et al.Collaborative optimization strategy of virtual power plant alliance considering peer-to-peer trading[J]. Zhejiang Electric Power, 2025, 44(12): 55-66.
[4] 宋铎洋,薛田良,李艺瀑,等. 考虑风光不确定性的虚拟电厂合作博弈调度及收益分配策略[J]. 电力工程技术, 2025, 44(1): 193-206.
Song Duoyang, Xue Tianliang, Li Yipu, et al.Cooperative game scheduling and revenue distribution strategy of virtual power plants considering wind and solar uncertainty[J]. Electric Power Engineering Technology, 2025, 44(1): 193-206.
[5] 余英,王海云,王维庆,等.虚拟电厂参与下含高渗透可再生能源系统的运行策略[J].电测与仪表,2023,60(01):94-103.
Yu Ying, Wang Haiyun, Wang Weiqing, et al.Operation strategy of system with high-penetration renewable energy considering participation of virtual power plant[J]. Electrical Measurement & Instrumentation, 2023, 60(01): 94-103.
[6] Wang H, Jia Y, Shi M, et al.A mutually beneficial operation framework for virtual power plants and electric vehicle charging stations[J]. IEEE Transactions on Smart Grid, 2023, 14(6): 4634-4648.
[7] 陈永权,方瑜. 多组合虚拟电厂中氢储能低碳经济配置与优化[J]. 电网与清洁能源, 2024, 40(3): 107-118.
Chen Yongquan, Fang Yu.Low-carbon economic configuration and optimization of hydrogen storage in multi-portfolio virtual power plants[J]. Power System and Clean Energy, 2024, 40(3): 107-118.
[8] 吴亚雄,申展,吴科成.考虑配电系统运营商和多主体博弈的配电网规划方法[J].高压电器,2025,61(12):209-218.
Wu Yaxiong, Shen Zhan, Wu Kecheng.Distribution network planning method considering distribution system operator and multi-agent game[J]. High Voltage Apparatus, 2025, 61(12): 209-218.
[9] 陈耀威,米阳,马思源,等. 绿证-碳交易市场下基于广义纳什博弈的多虚拟电厂点对点交易策略[J]. 浙江电力, 2025, 44(12): 43-54.
Chen Yaowei, Mi Yang, Ma Siyuan, et al.Peer-to-peer trading strategy for multiple virtual power plants based on generalized Nash game under green certificate-carbon trading market[J]. Zhejiang Electric Power, 2025, 44(12): 43-54.
[10] 史林军,燕志伟,李杨,等.基于动态电价机制的配网运营商与用户储能商双层协调多目标优化策略[J].太阳能学报,2024,45(06):75-85.
Shi Linjun, Yan Zhiwei, Li Yang, et al.Bi-level coordinated multi-objective optimization strategy for distribution network operators and user energy storage providers based on dynamic pricing mechanism[J]. Acta Energiae Solaris Sinica, 2024, 45(06): 75-85.
[11] 檀勤良,曾贾斌,吕函谕,等.考虑源网荷储协同的配网侧分布式光伏市场交易策略优化[J].中国电力,2025,58(10):39-49.
Tan Qinliang, Zeng Jiabin, Lyu Hanyu, et al.Optimization of distribution-side distributed photovoltaic market trading strategy considering source-network-load-storage coordination[J]. Electric Power, 2025, 58(10): 39-49.
[12] 舒征宇,朱凯翔,王灿,等. 考虑碳交易的虚拟电厂日前电力市场竞价策略 [J]. 电力工程技术, 2024, 43 (5): 58-68+149.
Shu Zhengyu, Zhu Kaixiang, Wang Can, et al. Bidding strategy of virtual power plant in day-ahead electricity market considering carbon trading[J]. Electric Power Engineering Technology, 2024, 43(5): 58-68+149.
[13] 王贵召,程静,胡利.基于纳什谈判和主从博弈的多园区综合能源系统电-碳共享运行优化策略[J].太阳能学报,2026,47(01):274-287.
Wang G Z, Cheng J, Hu L.Optimization strategy for electricity-carbon sharing operation of multi-park integrated energy system based on Nash negotiation and Stackelberg game[J]. Acta Energiae Solaris Sinica, 2026, 47(1): 274-287.
[14] 张儒峰,吴昊泽,吴昊,等.基于能量流-物质流耦合的高耗能工业负荷需求响应主从博弈优化方法[J/OL].中国电机工程学报,1-14[2026-03-02].
Zhang Rufeng, Wu Haoze, Wu Hao, et al.Stackelberg game optimization method for demand response of high-energy-consumption industrial loads based on energy flow-mass flow coupling[J/OL]. Proceedings of the CSEE, 1-14[2026-03-02].
[15] 谢敏,卢颖,魏东,等.基于双重交互主动博弈的新能源与用户双边协商交易策略[J/OL].电力系统自动化,1-25[2026-03-02].
Xie Min, Lu Ying, Wei Dong, et al.Bilateral negotiation trading strategy between new energy and users based on dual-interaction active game[J/OL]. Automation of Electric Power Systems, 1-25[2026-03-02].
[16] 高鑫,魏立保,梁岩. 基于主从博弈的配电网-多微网双层优化调度[J]. 电网与清洁能源, 2025, 41(4): 12-17.
Gao Xin, Wei Libao, Liang Yan.Bi-level optimal dispatch of distribution network and multi-microgrid based on Stackelberg game[J]. Power System and Clean Energy, 2025, 41(4): 12-17.
[17] 徐慧慧,田云飞,赵宇洋,等.考虑绿证-碳交易的多虚拟电厂混合博弈优化调度[J].智慧电力,2024,52(03):1-7+16.
Xu Huihui, Tian Yunfei, Zhao Yuyang, et al. Hybrid game optimal dispatching of multiple virtual power plants considering green certificate-carbon trading[J]. Smart Power, 2024, 52(03): 1-7+16.
[18] 栗然,王炳乾,彭湘泽,等.基于主从博弈的多虚拟电厂动态定价与优化调度[J].可再生能源,2024,42(07):986-994.
Li Ran, Wang Bingqian, Peng Xiangze, et al.Dynamic pricing and optimal dispatch of multiple virtual power plants based on Stackelberg game[J]. Renewable Energy Resources, 2024, 42(07): 986-994.
[19] 赵琛,彭思远,和萍,等.电-碳-绿证交易耦合下多虚拟电厂动态定价模型与博弈分析[J].电力系统自动化,2026,50(01):188-198.
Zhao Chen, Peng Siyuan, He Ping, et al.Dynamic pricing model and game analysis of multiple virtual power plants under electricity-carbon-green certificate trading coupling[J]. Automation of Electric Power Systems, 2026, 50(01): 188-198.
[20] 董雷,涂淑琴,李烨,等.基于元模型优化算法的主从博弈多虚拟电厂动态定价和能量管理[J].电网技术,2020,44(03):973-983.
Dong Lei, Tu Shuqin, Li Ye, et al.Dynamic pricing and energy management of multiple virtual power plants based on master-slave game using meta-model optimization algorithm[J]. Power System Technology, 2020, 44(03): 973-983.
[21] Wang X, Lu H, Zhang Y, et al.Decentralized coordinated operation model of VPP and P2H systems based on stochastic-bargaining game considering multiple uncertainties and carbon cost[J]. Applied Energy, 2022, 312: 118750.
[22] 邱斌. 基于主从博弈的含氢虚拟电厂鲁棒优化调度研究[D].南昌大学,2024.
Qiu Bin.Research on robust optimal dispatch of hydrogen-containing virtual power plant based on Stackelberg game[D]. Nanchang University, 2024.
[23] 宋嘉启,杨永标,徐青山,等.多虚拟电厂参与日前电力市场的鲁棒竞标博弈方法[J].电力自动化设备,2023,43(05):77-85.
Song Jiaqi, Yang Yongbiao, Xu Qingshan, et al.Robust bidding game method for multiple virtual power plants participating in day-ahead electricity market[J]. Electric Power Automation Equipment, 2023, 43(05): 77-85.
[24] 王愿,李彦斌,宋明浩,等.计及多重不确定性和时间相关性的虚拟电厂参与碳-绿证协同交易优化调度[J].电网技术,2024,48(12):4938-4947.
Wang Y, Li Y B, Song M H, et al.Optimal scheduling of virtual power plant participating in carbon-green certificate collaborative trading considering multiple uncertainties and temporal correlation[J]. Power System Technology, 2024, 48(12): 4938-4947.
[25] 赵晨阳,艾芊,李晓露,等.基于分布鲁棒模型的冷热电联供虚拟电厂日前-日内协同优化调度策略[J].供用电,2025,42(10):3-15.
Zhao Chenyang, Ai Qian, Li Xiaolu, et al.Day-ahead and intra-day coordinated optimal dispatching strategy for combined cooling, heating and power virtual power plant based on distributionally robust model[J]. Distribution & Utilization, 2025, 42(10): 3-15.
[26] 许桐,唐彦嫣,马超,等.计及数据驱动与Wasserstein度量的虚拟电厂分布鲁棒优化方法研究[J].可再生能源,2025,43(08):1120-1129.
Xu Tong, Tang Yanyan, Ma Chao, et al.Research on distributionally robust optimization method for virtual power plant considering data-driven and Wasserstein metric[J]. Renewable Energy Resources, 2025, 43(08): 1120-1129.
[27] 齐彩娟,陈宝生,韦冬妮,等.考虑主从博弈定价模式的共享储能分布鲁棒优化配置方法研究[J].中国电力,2024,57(07):40-53.
Qi C J, Chen B S, Wei D N, et al.Distributionally robust optimal configuration for shared energy storage based on Stackelberg game pricing model[J]. Electric Power, 2024, 57(7): 40-53.
[28] 汪进锋,李金鹏,许银亮,等.考虑不确定性和绿证交易的虚拟电厂与配电网分布式优化[J].中国电力,2025,58(04):21-30+192.
Wang J F, Li J P, Xu Y L, et al.Distributed optimization for VPP and distribution network operation considering uncertainty and green certificate market[J]. Electric Power, 2025, 58(4): 21-30, 192.
[29] Cheng L, Wang K, Peng P, et al.Multi-agent stackelberg game for joint optimization of electricity spot and deep peak regulation markets: strategies and implications for system flexibility[J]. International Journal of Electrical Power & Energy Systems, 2025, 171: 111041.
[30] Li X, Wu N, Lei L.Nash-Stackelberg-Nash three-layer mixed game optimal control strategy for multi-integrated energy systems considering multiple uncertainties[J]. Energy, 2025, 320: 135418.
[31] 王作玮,张真源,杜月芳.考虑调峰辅助服务的综合能源系统主从博弈优化调度[J].电力需求侧管理,2025,27(06):37-44.
Wang Zuowei, Zhang Zhenyuan, Du Yuefang.Master-slave game optimal scheduling of integrated energy system considering peak regulation auxiliary service[J]. Power Demand Side Management, 2025, 27(06): 37-44.
[32] Amasyali K, Olama M M, Chen Y.Genetic algorithm for demand response: a stackelberg game approach[C]//2020 Spring Simulation Conference (SpringSim). IEEE, 2020: 1-12.
[33] 蒋东荣,向洪伟,王一雯,等.基于主从博弈的负荷聚合商奖励价格制定策略及可控负荷调度研究[J].重庆理工大学学报(自然科学),2018,32(05):169-176.
Jiang Dongrong, Xiang Hongwei, Wang Yiwen, et al.Research on reward price setting strategy and controllable load dispatching of load aggregator based on Stackelberg game[J]. Journal of Chongqing University of Technology (Natural Science), 2018, 32(05): 169-176.
[34] 祁兵,曹望璋,李彬,等.计及负载特征及响应特性的多数据中心双层优化模型[J].电力系统自动化,2022,46(21):30-41.
Qi Bing, Cao Wangzhang, Li Bin, et al.Bi-level optimization model for multiple data centers considering load characteristics and response characteristics[J]. Automation of Electric Power Systems, 2022, 46(21): 30-41.
[35] 李国庆,王冲,雷顺波,等.考虑碳捕集技术的电力系统双层优化配置[J].电力自动化设备,2023,43(01):25-31.
Li Guoqing, Wang Chong, Lei Shunbo, et al.Bi-level optimal configuration of power system considering carbon capture technology[J]. Electric Power Automation Equipment, 2023, 43(01): 25-31.
[36] Li J, Yu J, Wang Q, et al. Differentiable bilevel programming for stackelberg congestion games[J]. arXiv preprint arXiv:2209.07618, 2022.
[37] 王博闻,张博涵,鲁宇,等.考虑碳交易的多虚拟电厂主从博弈协调策略[J].电力需求侧管理,2025,27(01):80-87.
Wang Bowen, Zhang Bohan, Lu Yu, et al.Master-slave game coordination strategy for multiple virtual power plants considering carbon trading[J]. Power Demand Side Management, 2025, 27(01): 80-87.
[38] 王辉,金子蓉,方航,等.基于动态定价的虚拟电厂博弈能源管理模型[J].南方电网技术,2023,17(04):101-108.
Wang Hui, Jin Zirong, Fang Hang, et al.Game-based energy management model for virtual power plant considering dynamic pricing[J]. Southern Power System Technology, 2023, 17(04): 101-108.
[39] Lin Y, Liu K, Han D, et al.Statistical privacy-preserving online distributed Nash equilibrium tracking in aggregative games[J]. IEEE Transactions on Automatic Control, 2023, 69(1): 323-330.
[40] Yang K, Yang D, Zhang Z, et al.A Chebyshev's Inequality-based Distributionally Robust Chance-Constrained Model for Distribution Network Reactive Power Optimization[J]. Journal of Physics: Conference Series, 2025, 3012(1): 012085.
[41] 漆磊,高扬,艾芊.基于能量共享的虚拟电厂多产消者混合博弈策略[J].电力建设,2025,46(01):1-13.
Qi L, Gao Y, Ai Q.Virtual power plant and multi-prosumer hybrid game strategy based on energy sharing[J]. Electric Power Construction, 2025, 46(1): 1-13.