王琛,林顺富,李志强,吴卓翔,钱亮
WANG Chen,LIN Shunfu,LI Zhiqiang,WU Zhuoxiang,QIAN Liang

• 1:上海电力大学电气工程学部
• 2:浙江华云电力工程设计咨询有限公司

摘要(Abstract)：

多乡村综合能源系统协同运行可提升能源利用效率与用能灵活性，因此提出一种计及电能交互的多乡村综合能源系统分布鲁棒优化运行策略。首先，考虑可再生能源出力和负荷需求的不确定性，引入基于Wasserstein距离的分布鲁棒优化模型，并利用Lipschitz函数理论将其转化为可求解的确定性等价模型。其次，搭建基于纳什谈判理论的多乡村综合能源系统电能共享合作调度模型，最小化系统协同运行总成本。针对各参与主体电能交互量的差异，提出一种基于非对称纳什议价机制的收益分配方法，采用交替方向乘子法进行求解，实现各主体合作收益公平分配。通过仿真算例验证，该策略能够有效降低系统运行成本，并在乡村综合能源系统间实现公平高效的合作运行。
To improve energy utilization efficiency and operational flexibility in multiple rural integrated energy systems(IESs), a distributionally robust optimization strategy is proposed for coordinated operation considering electricity interaction among systems. First, to address uncertainties in renewable energy generation and load demand, a distributionally robust optimization(DRO) model based on the Wasserstein distance is introduced, which is further reformulated into a tractable deterministic equivalent model using Lipschitz function theory. Second, a cooperative operation model for electricity sharing among multiple rural IESs is developed based on Nash bargaining theory, aiming to minimize the total cost of coordinated system operation. To handle disparities in electricity interaction among participating entities, a profit allocation method based on an asymmetric Nash bargaining mechanism is proposed, and the alternating direction method of multipliers(ADMM) is adopted for solution, enabling fair distribution of cooperative benefits. Simulation results demonstrate that the proposed strategy effectively reduces system operating costs while achieving fair and efficient cooperative operation among rural integrated energy systems.

关键词(KeyWords)： 综合能源系统;能量交互;分布鲁棒;Wasserstein距离;非对称纳什议价
integrated energy system;energy interaction;distributionally robust;Wasserstein distance;asymmetric Nash bargaining

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金（52577119）

作者(Author): 王琛,林顺富,李志强,吴卓翔,钱亮
WANG Chen,LIN Shunfu,LI Zhiqiang,WU Zhuoxiang,QIAN Liang

DOI: 10.19585/j.zjdl.202608009

参考文献(References)：

• [1]中共中央国务院关于全面推进乡村振兴加快农业农村现代化的意见[N].人民日报，2021-02-22.
• [2]Abir M,Dilip P,Nga N,et al.Distributed energy resources based microgrid:review of architecture,control,and reliability[J]. Ieee Transactions on Industry Applications,2021,57(3):2223-2235.
• [3]周孝信，赵强，张玉琼，等.“双碳”目标下我国能源电力系统发展趋势分析：绿电替代与绿氢替代[J].中国电机工程学报，2024,44(17):6707-6721.Zhou Xiaoxin,Zhao Qiang,Zhang Yuqiong,et al.Analysis of the development trend of China’s energy and power system under the dual carbon target:green electricity substitution and green hydrogen substitution[J].Proceedings of the CSEE,2024,44(17):6707-6721.
• [4]邓莉荣，杨大炜，符杨.基于多参数规划的园区综合能源系统解耦报价策略[J].中国电机工程学报，2025,45(10):3752-3763.Deng Lirong,Yang Dawei,Fu Yang. Decoupled bidding strategy for community integrated energy system based on multi-parameter programming[J]. Proceedings of the CSEE,2025,45(10):3752-3763.
• [5]袁志鑫，韩丽，王晓静，等.计及网荷热惯性的综合能源系统低碳优化调度[J].电力系统自动化，2025,49(22):145-155.Yuan Zhixin,Han Li,Wang Xiaojing,et al.Low-carbon optimal scheduling of integrated energy system consideringthermal inertia of grid and load[J].Automation of Electric Power Systems,2025,49(22):145-155.
• [6]袁晓冬，曾飞，缪惠宇，等.电热氢综合能源系统建模及容量规划研究[J].高压电器，2024,60(7):34-47.Yuan Xiaodong,Zeng Fei,Miu Huiyu,et al.Study on modelling and capacity planning of electric-thermal-hydrogen integrated energy systems[J]. High Voltage Apparatus,2024,60(7):34-47.
• [7]杨冬锋，贺子谦，赵冠雄，等.基于混合博弈的综合能源多园区运行策略研究[J].智慧电力，2024,52(7):56-63.Yang Dongfeng,He Ziqian,Zhao Guanxiong,et al. Integrated energy multi-community operation strategy based on hybrid game[J].Smart Power,2024,52(7):56-63.
• [8]聂永辉，李宗锴.基于纳什谈判和主从博弈的多园区综合能源系统优化调度[J].智慧电力，2024,52(5):37-43.Nie Yonghui,Li Zongkai. Optimal scheduling of multipark integrated energy system based on nash negotiation and master-slave game[J]. Smart Power,2024,52(5):37-43.
• [9]朱俊铭，柏晶晶.基于改进遗传算法的园区综合能源系统规划研究[J].电力需求侧管理，2024,26(3):76-81.Zhu Junming,Bai Jingjing.Research on multi-objective optimal allocation of park integrated energy system based on improved genetic algorithm[J].Power Demand Side Management,2024,26(3):76-81.
• [10]袁红斌，易晓东.计及碳捕集和需求响应的综合能源系统低碳经济调度策略[J].电力需求侧管理，2024,26(1):86-92.Yuan Hongbin,Yi Xiaodong.A low carbon economic dispatch strategy for integrated energy systems with carbon capture and demand response[J]. Power Demand Side Management,2024,26(1):86-92.
• [11]高建伟，张艺，高芳杰，等.农业综合能源系统多场景置信间隙决策低碳调度[J].电力建设，2024,45(5):105-117.Gao Jianwei,Zhang Yi,Gao Fangjie,et al. Low-carbon scheduling for multi-scenario confidence gap decision making for integrated energy systems in agriculture[J].Electric Power Construction,2024,45(5):105-117.
• [12]黄宏旭，梁睿，李嘉翔，等.光-沼协同下的乡村综合能源系统运行优化[J].中国电机工程学报，2026,46(2):634-646.Huang Hongxu,Liang Rui,Li Jiaxiang,et al. Optimal scheduling of PV-biogas coordinated rural integrated energy systems[J].Proceedings of the CSEE,2026,46(2):634-646.
• [13]李咸善，李晨杰，张磊.氢耦合区域综合能源系统集群双层博弈随机优化调度策略[J].电力自动化设备，2023,43(12):238-247.Li Xianshan,Li Chenjie,Zhang Lei. Dispatching strategy of hydrogen-coupled regional integrated energy system cluster based on two-level game stochastic optimization[J]. Electric Power Automation Equipment,2023,43(12):238-247.
• [14]王杰，贾宏杰，靳小龙，等.基于电-氢-热P2P交易的分布式智能电网低碳优化运行方法[J].电力系统自动化，2025,49(9):40-51.Wang Jie,Jia Hongjie,Jin Xiaolong,et al.Low-carbon operation optimization method for distributed smart grid based on electricity-hydrogen-heat peer-to-peer trading[J].Automation of Electric Power Systems,2025,49(9):40-51.
• [15]Ye T,Huang Y,Yang W,et al.Safe multi-agent deep reinforcement learning for decentralized low-carbon operation in active distribution networks and multi-microgrids[J].Applied Energy,2025,387:125609.
• [16]黎海涛，刘伊然，杨艳红，等.基于改进联邦竞争深度Q网络的多微网能量管理策略[J].电力系统自动化，2024,48(8):174-184.Li Haitao,Liu Yiran,Yang Yanhong,et al.Energy management strategy for multi-microgrid based on improved federated dueling deep Q network[J].Automation of Electric Power Systems,2024,48(8):174-184.
• [17]张宇桐.考虑楼宇不同供热模式的区域电-热综合能源系统分布式协调优化调度[D].吉林：东北电力大学，2022.Zhang Yutong.Considering the distributed coordinated optimization and scheduling of regional electric-thermal integrated energy systems for different heating modes in buildings[D].Jilin:Northeast Dianli University,2022.
• [18]李梦婷.区域综合能源系统集群多主体博弈协同优化[D].北京：华北电力大学，2022.Li Mengting. Collaborative optimization of multi-agent game in regional integrated energy system cluster[D].Beijing:North China Electric Power University,2022.
• [19]Zhao Y,Han F,Zeng J,et al.Coordinated optimization of integrated rural multiple regional energy systems considering electricity to ammonia and improved Shapley value revenue allocation[J].Energy,2024,313:133855.
• [20]Liu X. Low-carbon scheduling research of integrated energy system based on Stackelberg game under sharing mode[J].Energy,2024,303:131928.
• [21]马瑞，夏绪卫，闫振华，等.基于双层合作博弈的微电网群与共享储能联合调度优化策略[J].电网与清洁能源，2025,41(5):133-139.Ma Rui,Xia Xuwei,Yan Zhenhua,et al.The optimization strategy for joint scheduling of microgrids cluster and shared energy storage based on bi-level cooperation game[J].Power System and Clean Energy,2025,41(5):133-139.
• [22]汤君博，潘凯岩，王富友，等.基于纳什议价法的多主体虚拟电厂优化调度及效用分配策略[J].太阳能学报，2025,46(5):79-88.Tang Junbo,Pan Kaiyan,Wang Fuyou,et al. Optimal scheduling and utility allocation strategy for multi-agent virtual power plants based on Nash bargaining method[J].Acta Energiae Solaris Sinica,2025,46(5):79-88.
• [23]张栋梁，魏奇，赵阳，等.基于动态运行包络的多微网合作运行方法[J].电力系统保护与控制，2025,53(6):51-62.Zhang Dongliang,Wei Qi,Zhao Yang,et al. Multimicrogrids cooperative operation method based on dynamic operating envelopes[J]. Power System Protection and Control,2025,53(6):51-62.
• [24]Hang Wang,Qunli Wu,Huiling Guo,et al.Low-carbon optimal operation strategy of multi-energy multi-microgrid electricity-hydrogen sharing based on asymmetric Nash bargaining[J].Sustainability,2025,17(10):4703-4703.
• [25]袁桂丽，张睿，赵洵，等.含碳捕集机组的虚拟电厂热电联合随机优化调度[J].太阳能学报，2024,45(12):627-636.Yuan Guili,Zhang Rui,Zhao Xun,et al.Stochastic optimal dispatch of combined heat and power in virtual power plant with carbon capture units[J].Acta Energiae Solaris Sinica,2024,45(12):627-636.
• [26]张磊，杨子龙，叶婧，等.考虑热阻和风电不确定性变化影响的多重随机电热耦合系统优化调度[J].高压电器，2025,61(5):41-52.Zhang Lei,Yang Zilong,Ye Jing,et al.Optimal scheduling of multiple random considering electric-thermal coupled system thermal resistance and wind power uncertainty[J].High Voltage Apparatus,2025,61(5):41-52.
• [27]Zhang R,Chen Y,Li Z,et al.Two-stage robust operation of electricity-gas-heat integrated multi-energy microgrids considering heterogeneous uncertainties[J]. Applied Energy,2024,371:123690.
• [28]Ju L,Bai X,Li G,et al.Two-stage robust transaction optimization model and benefit allocation strategy for new energy power stations with shared energy storage considering green certificate and virtual energy storage mode[J].Applied Energy,2024,362:122996.
• [29]Xu D,Liu Z,Hou K,et al. Distributionally robust frequency constrained low-carbon scheduling considering flexibility of carbon capture power plants[J]. Energy,2025,332:137171.
• [30]梁睿，袁乐童，黄宏旭，等.变温影响下乡村生物质能发电系统跨周期滚动优化运行方法[J].中国电机工程学报，2025,45(8):3067-3078.Liang Rui,Yuan Letong,Huang Hongxu,et al. Multihydraulic retention time rolling optimal operation method for rural biomass power generation system under uncertain temperature[J]. Proceedings of the Chinese Society for Electrical Engineering,2025,45(8):3067-3078.
• [31]Rodrigues O H,Betina K S,Annika B,et al.Biogas potential of biowaste:a case study in the state of Rio de Janeiro,Brazil[J].Renewable Energy,2024,221:119751.
• [32]王豪.含风光互补的冷热电联供系统运行策略优化[D].武汉：湖北工业大学，2018.Wang Hao. Optimization of the operation strategy of CCHP system with complementary wind and solar energy[D].Wuhan:Hubei University of Technology,2018.
• [33]马腾飞，裴玮，肖浩，等.基于纳什谈判理论的风-光-氢多主体能源系统合作运行方法[J].中国电机工程学报，2021,41(1):25-39.Ma Tengfei,Pei Wei,Xiao Hao,et al.Cooperative operation method for wind-solar-hydrogen multi-agent energy system based on Nash bargaining theory[J]. Proceedings of the CSEE,2021,41(1):25-39.
• [34]吴锦领，楼平，管敏渊，等.基于非对称纳什谈判的多微网电能共享运行优化策略[J].电网技术，2022,46(7):2711-2723.Wu Jinling,Lou Ping,Guan Minyuan,et al.Operation optimization strategy of multi-microgrids energy sharing based on asymmetric Nash bargaining[J].Power System Technology,2022,46(7):2711-2723.
• [35]Cui Shichang,Wang Yanwu,Liu Xiaokang,et al. Economic storage sharing framework:asymmetric bargainingbased energy cooperation[J].IEEE Transactions on Industrial Informatics,2021,17(11):7489-7500.
• [36]Britz V,Herings P J,Predtetchinski A. Non-cooperative support for the asymmetric Nash bargaining solution[J].Journal of Economic Theory,2010,145(5):1951-1967.
• [37]Kawamori T. A noncooperative foundation of the asymmetric Nash bargaining solution[J].Journal of Mathematical Economics,2014,52:12-15.
• [38]周丽红，于浩，李鹏.考虑居民热负荷主动需求响应的园区综合能源系统分布式优化运行方法[J].电网技术，2023,47(5):1989-2000.Zhou Lihong,Yu Hao,Li Peng.Distributed optimal operation method of park-level integrated energy system considering active demand response of residential heat loads[J].Power System Technology,2023,47(5):1989-2000.
• [39]Cao Wenzhi,Xiao Jiangwen,Cui Shichang,et al.An efficient and economical storage and energy sharing model for multiple multi-energy microgrids[J]. Energy,2022,244(PB):123124.