基于双层Stackelberg博弈的微能源网能量管理优化
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摘要
提出了基于双层Stackelberg博弈的"供电公司–微能源网–用户"能源交易模型与求解算法。通过分析供电公司、微能源网和用户的博弈目标与策略,从理论上证明了该博弈存在唯一的Stackelberg均衡解,并求解了其均衡策略。在上层博弈中,供电公司作为领导者通过调整售电价格来刺激微能源网购电,微能源网作为跟随者,以最小化产能成本为目标,根据电价来决定购电量;在下层博弈中,作为领导者,微能源网根据用户的实际用能需求来制定售能价格,而用户作为跟随者,则调整用能策略以平衡购能支出和用能体验。经算例验证,所提的双层博弈方法可有效求解各参与者的均衡策略,并具有良好的收敛性和经济性。
In this paper, an energy trading model and solution algorithm of "power supply company, micro energy grid(MEG) and users" based on hierarchical Stackelberg game theory are proposed. By analyzing the game objectives and strategies of abovementioned participants, the unique Stackelberg equilibrium(SE) of the game is proved theoretically, and the equilibrium strategies are solved. In the upper-level game, power supply company as a leader stimulates MEG to purchase electricity by adjusting electricity selling price; as the follower, the MEG determines the amount of purchased electricity based on released selling price, to minimize production cost. In the lower-level game, the MEG leads the game by deciding energy selling prices based on actual energy demands of users, and users as followers adjust energy-using strategies to balance expenditure and experience of energy usage. Numerical studies demonstrate that the proposed hierarchical game method can obtain equilibrium strategies of each participant effectively and has good convergence and economy.
In this paper, an energy trading model and solution algorithm of "power supply company, micro energy grid(MEG) and users" based on hierarchical Stackelberg game theory are proposed. By analyzing the game objectives and strategies of abovementioned participants, the unique Stackelberg equilibrium(SE) of the game is proved theoretically, and the equilibrium strategies are solved. In the upper-level game, power supply company as a leader stimulates MEG to purchase electricity by adjusting electricity selling price; as the follower, the MEG determines the amount of purchased electricity based on released selling price, to minimize production cost. In the lower-level game, the MEG leads the game by deciding energy selling prices based on actual energy demands of users, and users as followers adjust energy-using strategies to balance expenditure and experience of energy usage. Numerical studies demonstrate that the proposed hierarchical game method can obtain equilibrium strategies of each participant effectively and has good convergence and economy.
引文
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[17]陆伟.城市能源环境中分布式功能系统优化配置研究[D].北京:中国科学院研究生院,2007.
[18]Peng Y,Gongguo T,Arye N.A game-theoretic approach for optimal time-of-use electricity pricing[J],IEEE Transactions on Power Systems,2013,28(2):884-892.
[19]Lin K J,Wu J Y,Liu D,et al.Energy management of combined cooling,heating and power micro energy grid based on leaderfollower game theory[J].Energies,2018,11(3),647.
[20]Nash J F.Non-cooperative games[J].Annals of Mathematics,1951,54(2):286-295.
[21]梅生伟,刘锋,魏韡.工程博弈论基础及电力系统应用[M].北京:科学出版社,2016:94-95.
[22]李旭.内燃机与直燃机联合的冷热电三联供系统优化设计研究[D].天津:天津大学,2012.
[23]Bao Z J,Zhou Q,Yang Z H,et al.A multi time-scale and multi energy-type coordinated microgrid scheduling solution-part I:model and methodology[J].IEEE Transactions on Power Systems,2015,30(5):2257-2266.
[2]Mei S W,Li R,Xue X D,et al.Paving the way to smart micro energy grid:concepts,design principles,and engineering practices[J].CSEEJournal of Power and Energy Systems,2017,3(4):440-449.
[3]刘凡,别朝红,刘诗雨,等.能源互联网市场体系设计、交易机制和关键问题[J].电力系统自动化,2018,42(13):108-117.Liu Fan,Bie Zhaohong,Liu Shiyu,et al.Framwork design,transaction mechanism and key issues of energy internet market[J].Automation of Electric Power Systems,2018,42(13):108-117(in Chinese).
[4]刘一欣,郭力,王成山.微电网参与下的配电侧电力市场竞价博弈方法[J].电网技术,2017,41(8):2469-2476.Liu Yixin,Guo Li,Wang Chengshan.Optimal bidding strategy for microgrids in electricity distribution market[J].Power System Technology,2017,41(8):2469-2476(in Chinese).
[5]张忠会,刘故帅,谢义苗.基于博弈论的电力系统供给侧多方交易决策[J].电网技术,2017,41(6):1779-1785.Zhang Zhonghui,Liu Gushuai,Xie Yimiao.A game theory approach to analyzing multi-party electricity trading on supply side[J].Power System Technology,2017,41(6):1779-1785(in Chinese).
[6]Li J,Liu Y K,Wu L.Optimal operation for community based multi-party microgrid in grid-connected and islanded modes[J].IEEETransactions on Smart Grid,2018,9(2):756-765.
[7]李晨迪,陈渊睿,曾君,等.基于非合作博弈的微电网能量管理系统优化算法[J].电网技术,2016,40(2):387-395.Li Chendi,Chen Yuanrui,Zeng Jun,et al.Research on optimization algorithm of microgrid energy management system based on noncooperative game theory[J].Power System Technology,2016,40(2):387-395(in Chinese).
[8]Ma L,Liu N,Zhang J H,et al.Energy management for joint operation of CHP and PV prosumers inside a grid-connected microgrid:a game theoretic approach[J].IEEE Transactions on Industrial Informatics,2016,12(5):1930-1942.
[9]Liu N,Yu X H,Wang C,et al.Energy sharing management for microgrids with PV prosumers:a Stackelberg game approach[J].IEEETransactions on Industrial Informatics,2017,13(3):1088-1098.
[10]Liu N,He L,Yu X H,et al.Multiparty energy management for grid-connected microgrids with heat and electricity coupled demand response[J].IEEE Transactions on Industrial Informatics,2018,14(5):1887-1897.
[11]马丽,刘念,张建华,等.基于主从博弈策略的社区能源互联网分布式能量管理[J].电网技术,2016,40(12):3655-3661.Ma Li,Liu Nian,Zhang Jianhua,et al.Distributed energy management of community energy internet based on leader-followers game[J].Power System Technology,2016,40(12):3655-3661(in Chinese).
[12]林凯骏,吴俊勇,郝亮亮,等.基于非合作博弈的冷热电联供微能源网运行策略优化[J].电力系统自动化,2018,42(6):25-32.Lin Kaijun,Wu Junyong,Hao Liangliang,et al.Optimization of operation strategy for micro-energy grid with CCHP systems based on non-cooperative game[J].Automation of Electric Power Systems,2018,42(6):25-32(in Chinese).
[13]吴利兰,荆朝霞,吴青华,等.基于Stackelberg博弈模型的综合能源系统均衡交互策略[J].电力系统自动化,2018,42(4):142-150.Wu Lilan,Jing Zhaoxia,Wu Qinghua,et al.Equilibrium strategies in integrated energy systems based on Stackelberg game model[J].Automation of Electric Power Systems,2018,42(4):142-150(in Chinese).
[14]Mengmeng Y,Hohong S.Incentive-based demand response considering hierarchical electricity market:a Stackelberg game approach[J].Applied Energy,2017,203:267-279.
[15]韩鑫.分布式能源系统构造及建模研究[D].太原:太原理工大学,2012.
[16]王成山,洪博文,郭力,等.冷热电联供微网优化调度通用建模方法[J].中国电机工程学报,2013,33(31):26-33.Wang Chengshan,Hong Bowen,Guo Li,et al.A general modeling method for optimal dispatch of combined cooling,heating and power microgrid[J].Proceedings of the CSEE,2013,33(31):26-33(in Chinese).
[17]陆伟.城市能源环境中分布式功能系统优化配置研究[D].北京:中国科学院研究生院,2007.
[18]Peng Y,Gongguo T,Arye N.A game-theoretic approach for optimal time-of-use electricity pricing[J],IEEE Transactions on Power Systems,2013,28(2):884-892.
[19]Lin K J,Wu J Y,Liu D,et al.Energy management of combined cooling,heating and power micro energy grid based on leaderfollower game theory[J].Energies,2018,11(3),647.
[20]Nash J F.Non-cooperative games[J].Annals of Mathematics,1951,54(2):286-295.
[21]梅生伟,刘锋,魏韡.工程博弈论基础及电力系统应用[M].北京:科学出版社,2016:94-95.
[22]李旭.内燃机与直燃机联合的冷热电三联供系统优化设计研究[D].天津:天津大学,2012.
[23]Bao Z J,Zhou Q,Yang Z H,et al.A multi time-scale and multi energy-type coordinated microgrid scheduling solution-part I:model and methodology[J].IEEE Transactions on Power Systems,2015,30(5):2257-2266.
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