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Coordinated operation framework for multi-integrated energy systems with electricity-carbon interaction based on Nash-Stackelberg-Nash game and distributionally robust chance-constraints

Author

Listed:
  • Duan, Fuyan
  • Luo, Yi
  • Huang, Zebo

Abstract

With gradual deepening of coupling between electricity market and carbon market, and advancement of energy technology, interest coupling between multi-integrated energy systems (MIES) and multi-prosumers (MP) has become increasingly close. At same time, output of renewable energy (RE) within system is uncertain. Therefore, it is urgently necessary to establish scheduling framework that can coordinate MIES and MP to effectively address uncertainty of RE output and achieve collaborative operation. For this purpose, this paper proposes three-layer game distributionally robust chance-constrained (DRCC) scheduling strategy of MIES electricity-carbon interaction Nash-Stackelberg-Nash (N-S-N). Firstly, Nash game of electricity between MP, Stackelberg game between MP and IES, and Nash game of electricity-carbon interaction between MIES are constructed by using game theory. Then, three-layer MIES N-S-N game model is constructed to precisely describe interaction characteristics between MIES and MP. Based on this, uncertainty of RE output is characterized by using rectangular information fuzzy set, and generalized DRCC model is established. Coupling this model with N-S-N three-layer game model, N-S-N three-layer game DRCC framework is proposed. Furthermore, Stackelberg game between IES and MP is handled by applying Karush-Kuhn-Tucker conditions and McCormick envelope method. DRCC is reformulated as second-order cone programming problem that is easy to solve through Conditional Value at Risk (CVaR). Nesterov-accelerated prediction-correction alternating direction method of multipliers (NAPC-ADMM) is adopted to determine optimal interaction volumes between distributed decision-making MIES. Finally, case analysis verified effectiveness of proposed method.

Suggested Citation

  • Duan, Fuyan & Luo, Yi & Huang, Zebo, 2026. "Coordinated operation framework for multi-integrated energy systems with electricity-carbon interaction based on Nash-Stackelberg-Nash game and distributionally robust chance-constraints," Renewable Energy, Elsevier, vol. 256(PF).
    • Handle: RePEc:eee:renene:v:256:y:2026:i:pf:s0960148125019998
    DOI: 10.1016/j.renene.2025.124335
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    References listed on IDEAS

    as
    1. Ma, Kai & Zhang, Rencai & Yang, Jie & Song, Debao, 2023. "Collaborative optimization scheduling of integrated energy system considering user dissatisfaction," Energy, Elsevier, vol. 274(C).
    2. Xue, Qingwen & Wang, Ao & Jiang, Sihang & Wang, Zhichao & Yang, Yingxia & Cheng, Yuanda & Zheng, Zhonghai, 2025. "Stochastic optimization of energy systems configuration for nearly-zero energy buildings considering load uncertainties," Renewable Energy, Elsevier, vol. 243(C).
    3. Shen, Yi & Zhai, Junyi & Kang, Zhongjian & Zhao, Bei & Gao, Xianhui & Li, Zhengmao, 2025. "Distributionally robust chance-constrained energy management for island DC microgrid with offshore wind power hydrogen production," Energy, Elsevier, vol. 316(C).
    4. Matamala, Yolanda & Das, Tapas K. & Feijoo, Felipe, 2025. "A stochastic Stackelberg problem with long-term investment decisions in Power-To-X technologies for multi-energy microgrids," Energy, Elsevier, vol. 314(C).
    5. Zhu, Xingxu & Zhao, Guiqing & Li, Junhui & Liu, Haojun & Zhao, Zhiqiang & Li, Cuiping & Li, Zhi & Zhou, Hongwei, 2025. "Stackelberg game for shared energy storage and wind farm bilateral trading with multi-market participation," Energy, Elsevier, vol. 326(C).
    6. Jia, Wenhao & Ding, Tao & Yuan, Yi & Mu, Chenggang & Zhang, Hongji & Wang, Shunqi & He, Yuankang & Sun, Xiaoqiang, 2025. "Decentralized distributionally robust chance-constrained operation of integrated electricity and hydrogen transportation networks," Applied Energy, Elsevier, vol. 377(PA).
    7. Wang, Peng & Guo, Zixuan & Zhang, Shengyu & Zhu, Lin & Yi, Liqi & Song, Xiaohua, 2024. "Strategic behaviors of renewable energy generation companies participating in the electricity and carbon coupled markets based on non-cooperative game theory," Energy, Elsevier, vol. 312(C).
    8. Laimon, M. & Yusaf, T., 2024. "Towards energy freedom: Exploring sustainable solutions for energy independence and self-sufficiency using integrated renewable energy-driven hydrogen system," Renewable Energy, Elsevier, vol. 222(C).
    9. Dong, Yingchao & Wuken, Edehong & Zhang, Hongli & Ren, Peng & Zhou, Xiaojun, 2025. "Bi-level coordinated operation optimization of multi-park integrated energy systems considering categorized demand response and uncertainty: A unified adaptive robust optimization approach," Renewable Energy, Elsevier, vol. 241(C).
    10. Ma, Miaomiao & Long, Zijuan & Liu, Xiangjie & Lee, Kwang Y., 2025. "Distributionally robust optimization of electric–thermal–hydrogen integrated energy system considering source–load uncertainty," Energy, Elsevier, vol. 316(C).
    11. Li, Fei & Wang, Dong & Guo, Hengdao & Zhang, Jianhua, 2024. "Distributionally Robust Optimization for integrated energy system accounting for refinement utilization of hydrogen and ladder-type carbon trading mechanism," Applied Energy, Elsevier, vol. 367(C).
    12. Wang, Haiyang & Li, Ke & Zhang, Chenghui & Chen, Jianfei, 2024. "Capacity and operation joint optimization for integrated energy system based on Nash bargaining game," Energy, Elsevier, vol. 305(C).
    13. Liu, Xiao & Li, Sinan & Zhang, Cuo & Liu, Meng & Zhu, Jianguo, 2025. "Holistic mutual benefits aware P2P2G market among microgrids in a distribution network: A decentralized data-driven approach," Applied Energy, Elsevier, vol. 387(C).
    14. 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).
    15. Zhang, Liwen & Liu, TingHao & Xu, Chenzhou & Zhang, Jun & Gao, Yujie & Li, Xin Cheng & Wang, HaoTian & Li, Xin & Mir, Mahdi, 2025. "A risk-averse cooperative framework for neighboring energy hubs under joint carbon, heat and electricity trading market with P2G and renewables," Renewable Energy, Elsevier, vol. 250(C).
    16. Xie, Yujie & Li, Zhengrong & Jiang, Yating & Wang, Heyu & Johnson, Brian C. & Zhu, Han, 2025. "Optimal coordinated design of building mix ratios and energy systems under uncertainty," Renewable Energy, Elsevier, vol. 246(C).
    17. Chen, Haipeng & Song, Jianzhao & Li, Zhiwei & Shui, Siyuan, 2025. "Distributionally robust electricity-carbon collaborative scheduling of integrated energy systems based on refined joint model of heating networks and buildings," Renewable Energy, Elsevier, vol. 251(C).
    18. Qi, Xin & Ju, Liwei & Yang, Shenbo & Gan, Wei & Li, Gen & Bai, Xiping, 2025. "A bi-level peer-to-peer interactive trading optimization model and distributed solution algorithm for rural distributed energy system group based on Stackelberg-Nash game strategy," Energy, Elsevier, vol. 318(C).
    19. Zhang, Yue & Wu, Qiong & Ren, Hongbo & Li, Qifen & Zhou, Weisheng, 2025. "A multi-agent distributed electricity-carbon shared trading strategy considering regional carbon inclusion," Renewable Energy, Elsevier, vol. 239(C).
    20. Li, Fei & Wang, Dong & Guo, Hengdao & Liu, Zhan & Zhang, Jianhua & Lin, Zhifang, 2025. "Two-stage Distributionally robust optimization for hydrogen-IES participation in energy-carbon trading-frequency regulation ancillary services market," Energy, Elsevier, vol. 328(C).
    21. Lou, Chengwei & Jin, Zekai & Zhou, Yue & Tang, Wei & Zhang, Lu & Yang, Jin, 2025. "Privacy-protected P2P electricity and carbon emission trading markets based on distributionally robust proximal atomic coordination algorithm," Applied Energy, Elsevier, vol. 384(C).
    22. Hoque, Md Murshadul & Khorasany, Mohsen & Azim, M. Imran & Razzaghi, Reza & Jalili, Mahdi, 2024. "A framework for prosumer-centric peer-to-peer energy trading using network-secure export–import limits," Applied Energy, Elsevier, vol. 361(C).
    23. Fan, Wei & Tan, Qingbo & Zhang, Amin & Ju, Liwei & Wang, Yuwei & Yin, Zhe & Li, Xudong, 2023. "A Bi-level optimization model of integrated energy system considering wind power uncertainty," Renewable Energy, Elsevier, vol. 202(C), pages 973-991.
    24. Qiao, Yiyang & Hu, Fan & Xiong, Wen & Guo, Zihao & Zhou, Xiaoguang & Li, Yajun, 2023. "Multi-objective optimization of integrated energy system considering installation configuration," Energy, Elsevier, vol. 263(PC).
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