IDEAS home Printed from https://ideas.repec.org/a/eee/appene/v408y2026ics0306261925019956.html

Bi-level distributionally robust coordinated optimization of integrateed energy system and hydrogen refueling station based on stackelberg game

Author

Listed:
  • Zhang, Zongnan
  • Shen, Xiaojun
  • Liu, Xubin
  • Chang, Mingjiang
  • Dai, Zhuocheng

Abstract

The coordinated operation of integrated energy system (IES) and hydrogen refueling station (HRS) is crucial for advancing the hydrogen vehicle industry and achieving dual carbon goals. However, competition between their interests, along with uncertainties in renewable energy generation and hydrogen demand, significantly compromises system economics, stability, and hydrogen storage safety. Traditional scheduling models inadequately address the thermal and electrical demands of carbon capture system (CCS) and struggle to balance robustness in handling uncertainty with computational efficiency, thereby limiting their engineering applicability. This study proposes a bi-level distributionally robust coordination mechanism based on stackelberg game theory, developing a refined model for the coordinated operation of combined heat and power (CHP), CCS, and power-to-gas (P2G) technologies. An equivalent reformulation strategy is designed to transition from two-stage distributionally robust optimization (TSDRO) to two-stage robust optimization (TSRO), incorporating distributionally robust chance constraint (DRCC) for the safe capacity of hydrogen storage tank. The proposed sequential bound tightening nested improved constraint & column generation (SBT-nested-IC&CG) algorithm, offers efficient computational solutions. Simulation results indicate that the method effectively balances the interests of both parties, enhances robustness against multiple uncertainties, maintains reasonable hydrogen storage safety levels, and reduces computation time by approximately 50 % compared to traditional nested column & constraint generation (NC&CG) algorithm, thus providing a feasible engineering solution for the coordinated scheduling of IES and HRS

Suggested Citation

  • Zhang, Zongnan & Shen, Xiaojun & Liu, Xubin & Chang, Mingjiang & Dai, Zhuocheng, 2026. "Bi-level distributionally robust coordinated optimization of integrateed energy system and hydrogen refueling station based on stackelberg game," Applied Energy, Elsevier, vol. 408(C).
  • Handle: RePEc:eee:appene:v:408:y:2026:i:c:s0306261925019956
    DOI: 10.1016/j.apenergy.2025.127265
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0306261925019956
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.apenergy.2025.127265?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhou, Chenghan & Jia, Hongjie & Jin, Xiaolong & Mu, Yunfei & Yu, Xiaodan & Xu, Xiandong & Li, Binghui & Sun, Weichen, 2023. "Two-stage robust optimization for space heating loads of buildings in integrated community energy systems," Applied Energy, Elsevier, vol. 331(C).
    2. Guo, Panhao & Xue, Qingwen & Wang, Jingyi & Bai, Pengyun & Gu, Mei & Hua, Jing & Duan, Pengfei, 2025. "The exploration of the essential need for decarbonization and the achievement of zero energy consumption in the CHP + carbon capture system," Energy, Elsevier, vol. 316(C).
    3. 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).
    4. Che, Ping & Zhang, Chaoyu & Liu, Yuqing & Zhang, Yanyan, 2025. "An integrated learning and optimization approach to optimal dynamic retail electricity pricing of residential and industrial consumers," Applied Energy, Elsevier, vol. 382(C).
    5. Khan, Muhammad Ahsan & Rehman, Talha & Kim, Hak-Man, 2025. "Hierarchical energy management for heterogeneous multi-energy microgrid community: Integrating hydrogen into the water-energy nexus," Applied Energy, Elsevier, vol. 397(C).
    6. Gu, Bo & Li, Fangxing & Mao, Chengxiong & Wang, Dan & Fan, Hua & Liu, Bin & Li, Wenhao, 2025. "A Bilevel robust coordination model for community integrated energy system with access to HFCEVs and EVs," Applied Energy, Elsevier, vol. 390(C).
    7. Li, Xinyan & Wu, Nan, 2024. "A two-stage distributed robust optimal control strategy for energy collaboration in multi-regional integrated energy systems based on cooperative game," Energy, Elsevier, vol. 305(C).
    8. Zhou, Yizhou & Li, Xiang & Han, Haiteng & Wei, Zhinong & Zang, Haixiang & Sun, Guoqiang & Chen, Sheng, 2024. "Resilience-oriented planning of integrated electricity and heat systems: A stochastic distributionally robust optimization approach," Applied Energy, Elsevier, vol. 353(PA).
    9. Hou, Min & Liu, Xinrui & Li, Ming & Li, Yushuai & Wang, Rui & Li, Zhengmao & Sun, Qiuye, 2025. "Towards intelligent cooperation of urban electric-traffic coupling network: A distributionally robust hierarchical optimization method with dependency of uncertainties," Energy, Elsevier, vol. 338(C).
    10. Liu, Mao & Kong, Xiangyu & Lian, Jijian & Wang, Jimin & Yang, Bohan, 2025. "Distributionally robust coordinated day-ahead scheduling of Cascade pumped hydro energy storage system and DC transmission," Applied Energy, Elsevier, vol. 384(C).
    11. Dong, Lei & Li, Yang & Zhang, Tao & Wang, Zibo & Pu, Tianjiao, 2025. "A Distributionally robust game approach for integrated energy systems with prosumer interactive transactions," Applied Energy, Elsevier, vol. 396(C).
    12. Wu, Zhenyu & Zhao, Xia & Mao, Yang & Liu, Ruimeng, 2024. "Flexibility quantification of desalination plants for demand response: An adaptive robust optimization methodology," Applied Energy, Elsevier, vol. 373(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhu, Haohao & Wang, Xiluo & Wen, Yutong & Zhu, Jizhong & Li, Jiayi & Luo, Qingju & Liao, Chenlei, 2025. "A review of integrated energy system modeling and operation," Applied Energy, Elsevier, vol. 400(C).
    2. Tian, Ye & Xu, Yinliang & Sun, Hongbin & Tai, Nengling, 2025. "Frequency-constrained microgrid-distribution network coordinated load restoration: A distributed carbon-aware optimization approach," Applied Energy, Elsevier, vol. 395(C).
    3. Liu, Jiejie & Li, Yao & Ma, Yanan & Qin, Ruomu & Meng, Xianyang & Wu, Jiangtao, 2023. "Two-layer multiple scenario optimization framework for integrated energy system based on optimal energy contribution ratio strategy," Energy, Elsevier, vol. 285(C).
    4. Lv, Chaoxian & Chai, Yuanyuan & Qu, Kaiping & Liang, Rui, 2025. "Multi-entity pricing-enabled supply recovery for electricity-gas energy system with coordinated flexibilities: a hierarchical game approach," Energy, Elsevier, vol. 334(C).
    5. Cui, Yuting & Jurasz, Jakub & Ming, Bo & Su, Chengguo & Canales, Fausto A., 2026. "Review of sizing methodologies for hydropower-based hybrid energy systems: a techno-economic perspective," Renewable and Sustainable Energy Reviews, Elsevier, vol. 232(C).
    6. He Jiang & Baoqi Tong & Zongjun Yao & Yan Zhao, 2025. "Hierarchical Distributed Low-Carbon Economic Dispatch Strategy for Regional Integrated Energy System Based on ADMM," Energies, MDPI, vol. 18(17), pages 1-28, August.
    7. Zhu, Ying & Li, Xinying & Ma, Yinjie & Long, Zhi & Liu, Hanwen & E, Jiaqiang, 2026. "A comprehensive review of microgrids with hydrogen energy systems: energy management strategies and system optimization," Renewable and Sustainable Energy Reviews, Elsevier, vol. 229(C).
    8. Yang, Dongfeng & Zhan, Tong & Liu, Xiaojun & Jiang, Chao & Huang, Gang & Wang, Hui, 2025. "Scenario information gap planning for electricity-gas-hydrogen integrated energy systems considering the impact of grid interaction locations," Energy, Elsevier, vol. 335(C).
    9. Xu, Rong-Hong & Ma, Huan & Sun, Qing-Han & He, Ke-Lun & Zhao, Tian & Chen, Qun, 2025. "Two-stage robust optimization of distributed energy systems considering nonlinear multi-energy transmission and conversion," Energy, Elsevier, vol. 335(C).
    10. Wang, Qihui & Li, Zhengshuo, 2026. "Learning-to-optimize infused decentralized disaggregation for multi-entity technical VPP considering equity and privacy," Applied Energy, Elsevier, vol. 405(C).
    11. Wang, Qi & Liu, Yankui, 2025. "Planning a robust echelon utilization network for used electric vehicle batteries based on two decision-making criteria," Applied Energy, Elsevier, vol. 384(C).
    12. Zhou, Chengang & Zhou, Yizhou & Zang, Haixiang & Chen, Sheng & Sun, Guoqiang & Wei, Zhinong, 2026. "Safe and efficient dispatch of integrated electricity-hydrogen systems via robust constrained reinforcement learning with adversarial training," Energy, Elsevier, vol. 344(C).
    13. Lu, M.L. & Sun, Y.J. & Kokogiannakis, G. & Ma, Z.J., 2024. "Design of flexible energy systems for nearly/net zero energy buildings under uncertainty characteristics: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 205(C).
    14. Deng, Lirong & Fu, Yang & Guo, Qinglai & Li, Zhenkun & Xue, Yixun & Zhang, Zhiquan, 2024. "Energy and reserve procurement in integrated electricity and heating system: A high-dimensional covariance matrix approach based on stochastic differential equations," Energy, Elsevier, vol. 304(C).
    15. Dong, Lei & Li, Yang & Zhang, Tao & Wang, Zibo & Pu, Tianjiao, 2025. "A Distributionally robust game approach for integrated energy systems with prosumer interactive transactions," Applied Energy, Elsevier, vol. 396(C).
    16. Zhang, Sen & Hu, Weihao & Du, Jialin & Cao, Xilin & Bai, Chunguang & Liu, Wen & Wang, Daojuan & Chen, Zhe, 2025. "Hierarchical distributionally robust scheduling strategy for distributed energy systems in the energy-sharing environment," Applied Energy, Elsevier, vol. 388(C).
    17. Li, Yang & Wu, Jiang & Xu, Zhanbo & Shen, Yuanjun & Zou, Jianhua & Guan, Xiaohong, 2026. "Decentralized cooperative operation of multi-energy prosumers with heterogeneous thermal properties," Renewable Energy, Elsevier, vol. 256(PI).
    18. Wang, Xiaoyu & Jia, Hongjie & Jin, Xiaolong & Mu, Yunfei & Wei, Wei & Yu, Xiaodan & Liang, Shuo, 2024. "Bi-level optimal operations for grid operator and low-carbon building prosumers with peer-to-peer energy sharing," Applied Energy, Elsevier, vol. 359(C).
    19. Yang, Meng & Chen, Yue & Huang, Shihan & Chen, Laijun, 2025. "Recent advances in coordination and optimization of power-transportation systems: An overview," Renewable and Sustainable Energy Reviews, Elsevier, vol. 220(C).
    20. Wu, Wencong & Du, Yuji & Qian, Huijin & Fan, Haibin & Jiang, Zhu & Huang, Shifang & Zhang, Xiaosong, 2024. "Industrial Park low-carbon energy system planning framework: Heat pump based energy conjugation between industry and buildings," Applied Energy, Elsevier, vol. 369(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:appene:v:408:y:2026:i:c:s0306261925019956. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/405891/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.