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Nash-Stackelberg-Nash three-layer mixed game optimal control strategy for multi-integrated energy systems considering multiple uncertainties

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  • Li, Xinyan
  • Wu, Nan
  • Lei, Lin

Abstract

With the development of distributed energy technology, traditional energy users are transitioning to energy prosumer (EP) with independent power generation capacity. To further improve the absorption rate of renewable energy and the interactive benefits of each subject, and solve the problem of cooperative optimization operation of integrated energy system (IES) with multiple EPs in the same distribution network. In this paper, a multi-IES three-layer mixed game optimal control strategy considering multiple uncertainties is proposed. Chance constrained programming and robust optimization method are used to deal with the uncertainty of renewable energy and electricity price respectively. The upper level determines the electricity price and heat price to minimize the IES operating cost, and the lower level responds to the IES electric heating decision to maximize the EP benefit. Then, Karush-Kuhn-Tucker (KKT) condition is used to solve the Stackelberg game between IES and EP by combining Big-M and McCormick method, and the cooperative game between EP and IES is solved by combining alternating direction multiplier method (ADMM). Case shows that the strategy proposed can effectively solve the complex model with three-layer mixed game, significantly improves total system revenue by 4.97 % and reduces total carbon emissions by 20.69 %.

Suggested Citation

  • Li, Xinyan & Wu, Nan & Lei, Lin, 2025. "Nash-Stackelberg-Nash three-layer mixed game optimal control strategy for multi-integrated energy systems considering multiple uncertainties," Energy, Elsevier, vol. 320(C).
    • Handle: RePEc:eee:energy:v:320:y:2025:i:c:s0360544225010606
    DOI: 10.1016/j.energy.2025.135418
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    References listed on IDEAS

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    1. Zhao, Bingxu & Duan, Pengfei & Fen, Mengdan & Xue, Qingwen & Hua, Jing & Yang, Zhuoqiang, 2023. "Optimal operation of distribution networks and multiple community energy prosumers based on mixed game theory," Energy, Elsevier, vol. 278(PB).
    2. Xu, Jiazhu & Yi, Yuqin, 2023. "Multi-microgrid low-carbon economy operation strategy considering both source and load uncertainty: A Nash bargaining approach," Energy, Elsevier, vol. 263(PB).
    3. Haibing Wang & Chengmin Wang & Weiqing Sun & Muhammad Qasim Khan, 2022. "Energy Pricing and Management for the Integrated Energy Service Provider: A Stochastic Stackelberg Game Approach," Energies, MDPI, vol. 15(19), pages 1-15, October.
    4. Li, Xu & Deng, Jianhua & Liu, Jichun, 2024. "A two-layer and three-stage dynamic demand response game model considering the out of sync response for gases generators," Renewable Energy, Elsevier, vol. 228(C).
    5. Li, Songrui & Zhang, Lihui & Nie, Lei & Wang, Jianing, 2022. "Trading strategy and benefit optimization of load aggregators in integrated energy systems considering integrated demand response: A hierarchical Stackelberg game," Energy, Elsevier, vol. 249(C).
    6. Wang, Yubin & Zheng, Yanchong & Yang, Qiang, 2023. "Day-ahead bidding strategy of regional integrated energy systems considering multiple uncertainties in electricity markets," Applied Energy, Elsevier, vol. 348(C).
    7. Zhang, Rongquan & Bu, Siqi & Li, Gangqiang, 2024. "Multi-market P2P trading of cooling–heating-power-hydrogen integrated energy systems: An equilibrium-heuristic online prediction optimization approach," Applied Energy, Elsevier, vol. 367(C).
    8. Yan, Yi & Liu, Mingqi & Tian, Chongyi & Li, Ji & Li, Ke, 2024. "Multi-layer game theory based operation optimisation of ICES considering improved independent market participant models and dedicated distributed algorithms," Applied Energy, Elsevier, vol. 373(C).
    9. Sun, Guoqiang & Shen, Sichen & Chen, Sheng & Zhou, Yizhou & Wei, Zhinong, 2022. "Bidding strategy for a prosumer aggregator with stochastic renewable energy production in energy and reserve markets," Renewable Energy, Elsevier, vol. 191(C), pages 278-290.
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