1. Key Laboratory of Control of Power Transmission and Conversion of Ministry of Education Shanghai Jiao Tong University Shanghai 200240 China; 2. Shanghai Electric Power Company Shibei Power Supply Company Shanghai 200070 China; 3. Electric Power Research Institute of State Grid Henan Electric Power Company Zhengzhou 450052 China
Abstract:With increasing penetration of renewables to the electricity grid, commercialization of energy storage technology, diversification of demand side management resources type, and maturity of multi-energy complementation, more and more stakeholders are being progressively introduced into source-grid-load of power systems. However, due to trading volume and market position, the decision-makers have different priorities. The application of Stackelberg game theory, which has master-slave hierarchical structure, was investigated in this manuscript to solve sequential decision-making problems in investment and energy trading under the deregulated environment. Firstly, the mathematical structure of Stackelberg game was described, and it was classified according to the number of players in the master/slave problems; then, the application of Stackelberg game in power market was sorted out, and equivalent transformation skills, the advantages and disadvantages of various solving methods were summarized; finally, the key scientific problems still existing in the application of Stackelberg game in power market were refined. It is hoped that the work can provide a method reference for those stakeholders who participate in sequential decision-making in power market.
张衡, 张沈习, 程浩忠, 张希鹏, 谷青发. Stackelberg博弈在电力市场中的应用研究综述[J]. 电工技术学报, 2022, 37(13): 3250-3262.
Zhang Heng, Zhang Shenxi, Cheng Haozhong, Zhang Xipeng, Gu Qingfa. A State-of-the-Art Review on Stackelberg Game and Its Applications in Power Market. Transactions of China Electrotechnical Society, 2022, 37(13): 3250-3262.
[1] 李力行, 苗世洪, 孙丹丹, 等. 多利益主体参与下主动配电网完全信息动态博弈行为[J]. 电工技术学报, 2018, 33(15): 3499-3509. Li Lixing, Miao Shihong, Sun Dandan, et al.Dynamic games of complete information in active distribution network with multi-stakeholder participation[J]. Transactions of China Electrotechnical Society, 2018, 33(15): 3499-3509. [2] 刘念, 余星火, 王剑辉, 等. 泛在物联的配用电优化运行:信息物理社会系统的视角[J]. 电力系统自动化, 2020, 44(1): 1-12. Liu Nian, Yu Xinghuo, Wang Jianhui, et al.Optimal operation of power distribution and consumption system based on ubiquitous internet of things: a cyber-physical-social system perspective[J]. Automation of Electric Power Systems, 2020, 44(1): 1-12. [3] 郭通, 李永刚, 徐姗姗, 等. 考虑多主体博弈的火电机组灵活性改造规划[J]. 电工技术学报, 2020, 35(11): 170-181. Guo Tong, Li Yonggang, Xu Shanshan, et al.Planning of flexibility retrofits of thermal power units considering multi-agent game[J]. Transactions of China Electrotechnical Society, 2020, 35(11): 170-181. [4] 宋依群, 侯志俭, 文福拴, 等. 电力市场三种寡头竞争模型的市场力分析比较[J]. 电网技术, 2003, 27(8): 10-15. Song Yiqun, Hou Zhijian, Wen Fushuan, et al.Comparison of market power in three oligopoly models of elecetricity market[J]. Power System Technology, 2003, 27(8): 10-15. [5] 梅生伟, 魏韡. 智能电网环境下主从博弈模型及应用实例[J]. 系统科学与数学, 2014, 34(11): 1331-1344. Mei Shengwei, Wei Wei.Hierarchal game and its applications in the smart grid[J]. Journal of Systems Science and Mathematical Sciences, 2014, 34(11): 1331-1344. [6] 代业明, 高岩. 基于智能电网需求侧管理的多零售商实时定价策略[J]. 中国电机工程学报, 2014, 34(25): 4244-4249. Dai Yeming, Gao Yan.Real-time pricing strategy with multi-retailers based on demand-side management for the smart grid[J]. Proceedings of the CSEE, 2014, 34(25): 4244-4249. [7] Taheri S, Kazempour J, Seyedshenava S.Transmission expansion in an oligopoly considering generation investment equilibrium[J]. Energy Economics, 2017, 64: 55-62. [8] Kazempour J, Conejo A, Ruiz C.Strategic generation investment using a complementarity approach[J]. IEEE Transactions on Power Systems, 2011, 26(2): 940-948. [9] David P, Enzo E, Contreras J.A three-level static MILP model for generation and transmission expansion planning[J]. IEEE Transactions on Power Systems, 2013, 28(1): 202-210. [10] Yaser T, Mohammad R, Francois R.Sequential coordination of transmission expansion planning with strategic generation investments[J]. IEEE Transactions on Power Systems, 2017, 32(4): 2521-2534. [11] Isaac-Camilo G, Sonja W, Tomas G.Proactive transmission expansion planning with storage considerations[J]. Energy Strategy Reviews, 2019, 24: 154-165. [12] Lajos M, Trine K, Afzal S.Transmission and wind investment in a deregulated electricity industry[J]. IEEE Transactions on Power Systems, 2015, 30(3): 1633-1643. [13] Rafiei S, Mohammadi A.Bi-level model for generation expansion planning with contract pricing of renewable energy in the presence of energy storage[J]. IET Renewable Power Generation, 2019, 13(9): 1544-1553. [14] Wang Yifan, Liu Shixin, Wang Jianhui, et al.Capacity expansion of wind power in a market environment with topology control[J]. IEEE Transactions on Sustainable Energy, 2019, 10(4): 1834-1843. [15] Masoumzadeh A, Nekouei E, Alpcan T, et al.Impact of optimal storage allocation on price volatility in energy-only electricity markets[J]. IEEE Transactions on Power Systems, 2018. 33(2): 1903-1914. [16] Zhang Xiaohu, Shi Di, Wang Zhiwei, et al.Optimal allocation of series facts devices under high penetration of wind power within a market environment[J]. IEEE Transactions on Power Systems, 2018, 33(6): 6206-6217. [17] Li Tao, Shahidehpour M.Risk-constrained FTR bidding strategy in transmission markets[J]. IEEE Transactions on Power Systems, 2005, 20(2): 1014-1021. [18] Haghighat H, Seifi H, Kian A.Gaming analysis in joint energy and spinning reserve markets[J]. IEEE Transactions on Power Systems, 2007, 22(4): 2074-2085. [19] Fampa M, Barroso L, Candal D, et al.Bilevel optimization applied to strategic pricing in competitive electricity markets[J]. Computational Optimization and Applications, 2008, 39(2): 121-142. [20] Shafie-Khah M, Heydarian-Forushani E, Golshan M, et al.Strategic offering for a price-maker wind power producer in oligopoly markets considering demand response exchange[J]. IEEE Transactions on Industrial Informatics, 2015, 11(6): 1542-1553. [21] Cruz M, Finardi E, Matos V, et al.Strategic bidding for price-maker producers in predominantly hydroelectric systems[J]. Electric Power Systems Research, 2016, 140: 435-444. [22] 窦春霞, 贾星蓓, 李恒. 基于多智能体的微电网中分布式发电的市场博弈竞标发电[J]. 电网技术, 2016, 40(2): 579-586. Dou Chunxia, Jia Xingbei, Li Heng.Multi-agent-system-based market bidding strategy for distributed generation in microgrid[J]. Power System Technology, 2016, 40(2): 579-586. [23] 方燕琼, 甘霖, 艾芊, 等. 基于主从博弈的虚拟电厂双层竞标策略[J]. 电力系统自动化, 2017, 41(14): 61-69. Fang Yanqiong, Gan Lin, Ai Qian, et al.Stackelberg game based bi-level bidding strategy for virtual power plant[J]. Automation of Electric Power Systems, 2017, 41(14): 61-69. [24] Du Yan, Li Fangxing.A hierarchical real-time balancing market considering multi-microgrids with distributed sustainable resources[J]. IEEE Transactions on Sustainable Energy, 2020, 11(1): 72-83. [25] Naebi A, SeyedShenava S, Contreras J, et al. EPEC approach for finding optimal day-ahead bidding strategy equilibria of multi-microgrids in active distribution networks[J]. International Journal of Electrical Power & Energy Systems, 2020, 117: 105702. [26] 徐意婷, 艾芊. 考虑碳税策略的微网与常规机组协同运行[J]. 电力系统自动化, 2016, 40(14): 25-32. Xu Yiting, Ai Qian.Coordinated operation of microgrid and conventional generators considering carbon tax strategy[J]. Automation of Electric Power Systems, 2016, 40(14): 25-32. [27] Jay D, Swarup S.Game theoretical approach to novel reactive power ancillary service market mechanism[J]. IEEE Transactions on Power Systems, 2021, 36(2): 1298-1308. [28] Feng Changsen, Li Zhiyi, Shahidehpour M, et al.Stackelberg game based transactive pricing for optimal demand response in power distribution systems[J]. International Journal of Electrical Power & Energy Systems, 2020, 118: 105764. [29] Wu Hongbin, Liu Xin, Ye Bin, et al.Optimal dispatch and bidding strategy of a virtual power plant based on a Stackelberg game[J]. IET Generation, Transmission & Distribution, 2020, 14(4): 552-563. [30] Yin Shuangrui, Ai Qian, Li Zhouyu, et al.Energy management for aggregate prosumers in a virtual power plant: a robust Stackelberg game approach[J]. International Journal of Electrical Power & Energy Systems, 2020, 117: 105605. [31] Haghighat H, Kennedy S.A bilevel approach to operational decision making of a distribution company in competitive environments[J]. IEEE Transactions on Power Systems, 2012, 27(4): 1797-1807. [32] Kovács A.Bilevel programming approach to demand response management with day-ahead tariff[J]. Journal of Modern Power Systems and Clean Energy, 2019, 7(6): 1632-1643. [33] Qiu Dawei, Papadaskalopoulos D, Ye Yujian, et al.Investigating the effects of demand flexibility on electricity retailers’ business through a tri-level optimisation model[J]. IET Generation, Transmission & Distribution, 2020, 14(9): 1739-1750. [34] 孙峰洲, 马骏超, 于淼, 等. 含多端柔性多状态开关的主动配电网日前-日内协调能量管理方法[J]. 中国电机工程学报, 2020, 40(3): 778-790. Sun Fengzhou, Ma Junchao, Yu Miao, et al.A day-ahead and intraday coordinated energy management method for active distribution networks based on multi-terminal flexible distribution switch[J]. Proceedings of the CSEE, 2020, 40(3): 778-790. [35] 芮涛, 李国丽, 胡存刚, 等. 考虑电价机制的微电网群主从博弈优化方法[J]. 中国电机工程学报, 2020, 40(8): 2535-2545. Rui Tao, Li Guoli, Hu Cungang, et al.Stackelberg game optimization method for microgrid cluster considering electricity price mechanism[J]. Proceedings of the CSEE, 2020, 40(8): 2535-2545. [36] Bruninx K, Pandzic H, Cadre L, et al.On the interaction between aggregators, electricity markets and residential demand response providers[J]. IEEE Transactions on Power Systems, 2020, 35(2): 840-853. [37] Qiu Haifeng, Gu Wei, Wang Lu, et al.Trilayer stackelberg game approach for robustly power management in community grids[J/OL]. IEEE Transactions on Industrial Informatics: 1-10[2021-1-23].https://ieeexplore. ieee. org/stamp/stamp. jsp?tp= &arnumber=9165150. [38] 杨健维, 黄宇, 王湘, 等. 基于动态概率潮流的住宅区电动汽车代理商定价策略[J]. 中国电机工程学报, 2016, 36(21): 5822-5830. Yang Jianwei, Huang Yu, Wang Xiang, et al.A pricing strategy for electric vehicle aggregator in residential area based on dynamic probability power flow[J]. Proceedings of the CSEE, 2016, 36(21): 5822-5830. [39] Zhao Tianyang, Li Yuanzheng, Pan Xuewei, et al.Real-time optimal energy and reserve management of electric vehicle fast charging station: hierarchical game approach[J]. IEEE Transactions on Smart Grid, 2018, 9(5): 5357-5370. [40] 刘洪, 阎峻, 葛少云, 等. 考虑多车交互影响的电动汽车与快充站动态响应[J]. 中国电机工程学报, 2020, 40(20): 6455-6468. Liu Hong, Yan Jun, Ge Shaoyun, et al.Dynamic response of electric vehicle and fast charging stations considering multi-vehicle interaction[J]. Proceedings of the CSEE, 2020, 40(20): 6455-6468. [41] 林凯骏, 吴俊勇, 刘迪, 等. 基于双层Stackelberg博弈的微能源网能量管理优化[J]. 电网技术, 2019, 43(3): 973-983. Lin Kaijun, Wu Junyong, Liu Di, et al.Energy management optimization of micro energy grid based on hierarchical Stackelberg game theory[J]. Power System Technology, 2019, 43(3): 973-983. [42] 熊宇峰, 司杨, 郑天文, 等. 基于主从博弈的工业园区综合能源系统氢储能优化配置[J]. 电工技术学报, 2021, 36(3): 507-516. Xiong Yufeng, Si Yang, Zheng Tianwen, et al.Optimal configuration of hydrogen storage in industrial park integrated energy system based on stackelberg game[J]. Transactions of China Electrotechnical Society, 2021, 36(3): 507-516. [43] Kavousi-Fard A, Su Wencong, Jin Tao, et al.Two-stage stochastic operation framework for optimal management of the water-energy-hub[J]. IET Generation, Transmission & Distribution, 2019, 13(22): 5218-5228. [44] Yoon A, Kim Y, Moon S.Optimal retail pricing for demand response of HVAC systems in commercial buildings considering distribution network voltages[J]. IEEE Transactions on Smart Grid, 2019, 10(5): 5492-5505. [45] 王海洋, 李珂, 张承慧, 等. 基于主从博弈的社区综合能源系统分布式协同优化运行策略[J]. 中国电机工程学报, 2020, 17(5): 5435-5444. Wang Haiyang, Li Ke, Zhang Chenghui, et al.Distributed coordinative optimal operation of community integrated energy system based on Stackelberg game[J]. Proceedings of the CSEE, 2020, 17(5): 5435-5444. [46] 陈玥, 魏韡, 刘锋, 等. 基于CES型效用函数的热-电市场消费者最优决策[J]. 电力系统自动化, 2018, 42(13): 118-126. Chen Yue, Wei Wei, Liu Feng, et al.CES utility function based consumer optimal decision making in heat-power market[J]. Automation of Electric Power Systems, 2018, 42(13): 118-126. [47] Li Guoqing, Zhang Rufeng, Jiang Tao, et al.Security-constrained bi-level economic dispatch model for integrated natural gas and electricity systems considering wind power and power-to-gas process[J]. Applied Energy, 2017, 194: 696-704. [48] 卢强, 陈来军, 梅生伟. 博弈论在电力系统中典型应用及若干展望[J]. 中国电机工程学报, 2014, 34(29): 5009-5017. Lu Qiang, Chen Laijun, Mei Shengwei.Typical applications and prospects of game theory in power system[J]. Proceedings of the CSEE, 2014, 34(29): 5009-5017. [49] 唐博文, 孙元章, 徐箭, 等. 售电公司参与下的工业园区局域电网建设项目新模式探讨[J]. 电力系统自动化, 2020, 44(19): 185-193. Tang Bowen, Sun Yuanzhang, Xu Jian, et al.Discussion on new mode of construction project for regional power grid in industrial park with participation of electricity retailers[J]. Transactions of China Electrotechnical Society, 2020, 44(19): 185-193. [50] 杨丽君, 曹玉洁, 张子振. 基于博弈思想的主动配电网故障灵活分层恢复策略[J]. 电工技术学报, 2018, 33(6): 1410-1421. Yang Lijun, Cao Yujie, Zhang Zizhen.A flexible layered service restoration strategy for active distribution network based on game theory[J]. Transactions of China Electrotechnical Society, 2018, 33(6): 1410-1421. [51] 刘念, 赵璟, 王杰, 等. 基于合作博弈论的光伏微电网群交易模型[J]. 电工技术学报, 2018, 33(8): 1903-1910. Liu Nian, Zhao Jing, Wang Jie, et al.A trading model of PV microgrid cluster based on cooperative game theory[J]. Transactions of China Electrotechnical Society, 2018, 33(8): 1903-1910. [52] 叶畅, 苗世洪, 刘昊, 等. 联盟链框架下主动配电网电力交易主体合作演化策略[J]. 电工技术学报, 2020, 35(8): 141-155. Ye Chang, Miao Shihong, Liu Hao, et al.Cooperative evolutionary game strategy for electricity trading stakeholders in active distribution network under consortium blockchain framework[J]. Transactions of China Electrotechnical Society, 2020, 35(8): 141-155. [53] Salvador P, Morales J.Solving linear bilevel problems using Big-Ms: not all that glitters is gold[J]. IEEE Transactions on Power Systems, 2019, 34(3): 2469-2471. [54] Pandzic H, Conejo A, Kuzle I.An EPEC approach to the yearly maintenance scheduling of generating units[J]. IEEE Transactions on Power Systems, 2013, 28(2): 922-930. [55] Garces L, Conejo A, Garcia-Bertrand R, et al.A bilevel approach to transmission expansion planning within a market environment[J]. IEEE Transactions on Power Systems, 2009, 24(3): 1513-1522. [56] Tohid A, Saeed Z, Ehsan P, et al.Coordinated planning of generation capacity and transmission network expansion: a game approach with multi-leader-follower[J]. International Transaction on Electrical Energy Systems, 2017, 27: e2339. [57] Ruiz C, Conejo A, Yves S.Equilibria in an oligopolistic electricity pool with stepwise offer curves[J]. IEEE Transactions on Power Systems, 2012, 27(2): 752-761. [58] Zeng Qing, Zhang Baohua, Chen Zhe, et al.A bi-level programming for multistage co-expansion planning of the integrated gas and electricity system[J]. Applied Energy, 2017, 200: 192-203. [59] 包涛, 张孝顺, 余涛, 等. 反映实时供需互动的Stackelberg博弈模型及其强化学习求解[J]. 中国电机工程学报, 2018, 38(10): 2947-2955. Bao Tao, Zhang Xiaoshun, Yu Tao, et al.A Stackelberg game model of real-time supply-demand interaction and the solving method via reinforcement learning[J]. Proceedings of the CSEE, 2018, 38(10): 2947-2955.