电力系统控制与决策中的博弈问题—–工程博弈论初探
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摘要
由于在处理多主体、多目标与复杂决策时序等方面具有的独特优势,博弈论从其诞生至今半个多世纪以来,已经对经济学、社会学、军事学、政治学以及工程科学等诸多领域产生深远的影响,成为分析研究策略相互作用的主流理论和控制与决策领域不可或缺的辅助设计工具.由于存在多个决策主体以及竞争与合作等多种利益关系,工程系统优化决策问题往往可归结为某种特殊形式的博弈问题.本文从电力系统中的控制与决策问题出发,阐述了工程博弈论的建模思想和主要方法,并以笔者团队近年来在相关领域的科研工作为主线,对工程博弈论在电力系统中的应用进行总结与展望.
Game theory has far-reaching influences on many fields such as economics, sociology, military science, political science, and engineering science since its birth more than half a century ago due to its unique advantages in dealing with multi-subjects, multi-objectives and sequential actions. It becomes an indispensable design tool for the analysis and research on strategy interactions in many key theories and fields of control and decision making. Because there exist multiple decision-making entities with interactive relationships which could be either competitive or cooperative, the optimal decision-making problems of engineering system can often boil down to some special form of game problem. This article focuses on the control and decision-making problems in the power system and illustrates the modeling concepts and main methods of engineering game theory. In addition, based on authors' research work in related fields, this article summarizes applications and prospects of engineering game theory in power systems.
Game theory has far-reaching influences on many fields such as economics, sociology, military science, political science, and engineering science since its birth more than half a century ago due to its unique advantages in dealing with multi-subjects, multi-objectives and sequential actions. It becomes an indispensable design tool for the analysis and research on strategy interactions in many key theories and fields of control and decision making. Because there exist multiple decision-making entities with interactive relationships which could be either competitive or cooperative, the optimal decision-making problems of engineering system can often boil down to some special form of game problem. This article focuses on the control and decision-making problems in the power system and illustrates the modeling concepts and main methods of engineering game theory. In addition, based on authors' research work in related fields, this article summarizes applications and prospects of engineering game theory in power systems.
引文
[1]Von NEUMANN J,MORGENSTERN O.Theory of Games and Economic Behavior[M].Commemorative Edition.Princeton:Princeton University Press,2007.
[2]NASH J F.Equilibrium points in n-person games[J].Proceedings of the National Academy of Sciences,1950,36(1):48–49.
[3]NASH J F.Non-cooperative games[J].Annals of Mathematics,1951,54(2):286–295.
[4]SMITH J M,PRICE G R.The logic of animal conflict[J].Nature,1973,246:15.
[5]SMITH J M.Evolution and the Theory of Games[M].Cambridge:Cambridge University Press,1982.
[6]LU Qiang,MEI Shengwei.Review of modern power system controlepitome and prospect of related research in state key lab of power systems,Tsinghua University[J].Journal of System Science and Mathematics Science,2012,32(10):1207–1225.(卢强,梅生伟.现代电力系统控制评述—–清华大学电力系统国家重点实验室相关科研工作缩影及展望[J].系统科学与数学,2012,32(10):1207–1225.)
[7]WEI Wei,MEI Shengwei,ZHANG Xuemin.Review of advanced control theory and application in power system[J].Power System Protection and Control,2013,41(12):143–153.(魏韡,梅生伟,张雪敏.先进控制理论在电力系统中的应用综述及展望[J].电力系统保护与控制,2013,41(12):143–153.)
[8]WIENER N.Cybernetics:Control and Communication in the Animal and the Machine[M].New York:Wiley,1948.
[9]TSIEN H S.Engineering Cybernetics[M].New York:Mcgraw-Hill Book Company,1954.
[10]CHEN Daizhan,XIA Yuanqing,MA Hongbin,et al.Matrix Algebra Control and Game Theory[M].Beijing:Beijing Institute of Technology Press,2016.(程代展,夏元清,马宏宾,等.矩阵代数控制与博弈[M].北京:北京理工大学出版社,2016.)
[11]HARSANYI J C.Games with incomplete information played by Bayesian players,part I:the basic model[J].Management Science,1967,14(3):159–182.
[12]HARSANYI J C.Games with incomplete information played by Bayesian players,part II:Bayesian equilibrium points[J].Management Science,1968,14(5):320–334.
[13]HARSANYI J C.Games with incomplete information played by Bayesian players,part III:The basic probability distri-bution of the game[J].Management Science,1968,14(7):486–502.
[14]SMITH J M,PRICE G R.The logic of animal conflict[J].Nature,1973,246:15–18.
[15]MEI Shengwei,WEI Wei.Hierarchal game and its applications in the smart grid[J].Journal of Science and Mathematics Science,2014,34(11):1331–1344.(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.)
[16]SCUTARI G,PALOMAR D P,FACCHINEI F,et al.Convex optimization,game theory,and variational inequality theory[J].IEEE Signal Processing Magazine,2010,27(3):35–49.
[17]LU Qiang,MEI Shengwei,SUN Yuanzhang.Nonlinear Control of Power System[M].Beijing:Tsinghua University Press,2008.(卢强,梅生伟,孙元章.电力系统非线性控制[M].清华大学出版社,2008.)
[18]SHAPLEY L S.A value for n-person games[R].Santa Monica,CA:Rand Corporation,1952.
[19]NASH J F.The bargaining problem[J].Econometrica,1950,18(2):155–162.
[20]SONG Meiping,GU Guochang,ZHANG Guoyin.Survey of multiagent reinforcement learning in Markov games[J].Control and Decision,2005,20(10):1081–1090.(宋梅萍,顾国昌,张国印.随机博弈框架下的多agent强化学习方法综述[J].控制与決策,2005,20(10):1081–1090.)
[21]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.(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.)
[22]MEI Shengwei,LIU Feng,WEI Wei.Basic Introduction of Engineering Game Theory and Its Applications in Power System[M].Beijing:Scientific Press,2016.(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.)
[23]WANG Yingying,MEI Shengwei,LIU Feng.Imputation schemes for the cooperative game in the hybrid power system planning[J].Journal of Science and Mathematics Science,2012,32(4):418–428.(王莹莹,梅生伟,刘锋.混合电力系统合作博弈规划的分配策略研究[J].系统科学与数学,2012,32(4):418–428.)
[24]MEI S,WANG Y,LIU F,et al.Game approaches for hybrid power system planning[J].IEEE Transactions on Sustainable Energy,2012,3(3):506–517.
[25]MEI Shengwei,GUO Wentao,WANG Yingying,et al.A game model for robust optimization of power systems and its application[J].Proceedings of the CSEE,2013,33(19):47–56.(梅生伟,郭文涛,王莹莹,等.一类电力系统鲁棒优化问题的博弈模型及应用实例[J].中国电机工程学报,2013,33(19):47–56.)
[26]WEI Wei,LIU Feng,MEI Shengwei.Robust and economical scheduling methodology for power systems,part one:theoretical foundations[J].Automation of Electric Power System,2013,37(17):37–43.(魏韡,刘锋,梅生伟.电力系统鲁棒经济调度(一):理论基础[J].电力系统自动化,2013,37(17):37–43.)
[27]WEI Wei,LIU Feng,MEI Shengwei.Robust and economical scheduling methodology for power systems,part two:application foundations[J].Automation of Electric Power System,2013,37(18):60–67.(魏韡,刘锋,梅生伟.电力系统鲁棒经济调度(二):应用实例[J].电力系统自动化,2013,37(18):60–67.)
[28]WEI W,LIU F,WANG J,et al.Robust environmental-economic dispatch incorporating wind power generation and carbon capture plants[J].Applied Energy,2016,183:674–684.
[29]YANG Xiandong,YE Fangbo.Linear and Nonlinear H-infinity Control Theory[M].Taipei:Quanhua Science and Technology Books Corporation,1997.(杨宪东,叶芳柏.线性与非线性H∞控制理论[M].台北:全华科技图书股份有限公司,1997.)
[30]Gui Xiaoyang,MEI Shengwei,LU Qiang.Nonlinear coordinated robust governor control of hydro-turbine generator sets in multimachine power systems[J].Automation of Electric Power System,2006,30(3):29–33.(桂小阳,梅生伟,卢强.多机系统水轮机调速器鲁棒非线性协调控制研究[J].电力系统自动化,2006,30(3):29–33.)
[31]LU Qiang,ZHENG Shaoming,MEI Shengwei,et al.Experimental study on large disturbance of NR–PSS and RTDS in large aynchronous generator sets[J].Science in China Journal E,2008,38(7):979–992.(卢强,郑少明,梅生伟,等.大型同步发电机组NR–PSS及RTDS大扰动实验研究[J].中国科学E辑,2008,38(7):979–992.)
[32]LU Q,MEI S,ZHENG S.Field experiments of NR-PSS for large synchronous generators on a 300 MW machine in Baishan Hydro Plant[J].Science in China Journal E(English Version),2007,50(4):516–520.
[33]MEI S,WEI W,ZHENG S,et al.Development of an industrial nonlinear robust power system stabilizer and its improved frequency domain testing method[J].IET Generation,Transmission,Distribution,2011,5(12):1201–1210.
[34]LI N,MARDEN J.Designing games for distributed optimization[J].IEEE Journal of Selected Topics in Signal Processing,2013,7(2):230–242.
[35]WANG Z,LIU F,CHEN Y,et al.Unified distributed control of standalone dc microgrids[EB/OL].IEEE Transactions on Smart Grid,2017,https://ieeexplore.ieee.org/document/8052512/.
[36]WANG Z,LIU F,LOW S H,et al.Distributed frequency control with operational constraints,Part I:Per-node power balance[EB/OL].IEEE Transactions on Smart Grid,2017,https://ieeexplore.ieee.org/document/7990543/.
[37]WANG Z,LIU F,LOW S H,et al.Distributed frequency control with operational constraints,Part II:Network power balance[EB/OL].IEEE Transactions on Smart Grid,2017,https://ieeexplore.ieee.org/document/7990367/.
[38]MEI Shengwei,GONG Yuan,LIU Feng.The evolution model of three-generation power systems and characteristic analysis[J].Proceedings of the CSEE,2014,34(7):1003–1012.(梅生伟,龚媛,刘锋.三代电网演化模型及特性分析[J].中国电机工程学报,2014,34(7):1003–1012.)
[39]ZHOU Xiaoxin,CHEN Shuyong,LU Zongxiang.Review and prospect for power system development and related technologies:a concept of three-generation power systems[J].Proceedings of the CSEE,2013,33(22):1–11.(周孝信,陈树勇,鲁宗相.电网和电网技术发展的回顾与展望—–试论三代电网[J].中国电机工程学报,2013,33(22):1–11.)
[40]LIU Nian,YU Xinghuo,ZHANG Jianhua.Coordinated cyber-attack:influence and thinking of inciden on Ukarinian power grid[J].Automation of Electric Power System,2016,40(6):144–147.(刘念,余星火,张建华.网络协同攻击:乌克兰停电事件的推演与启示[J].电力系统自动化,2016,40(6):144–147.)
[41]GUO Lei.Some thoughts on the development of control theory[J].Journal of Science and Mathematics Science,2012,31(9):1014–1018.(郭雷.关于控制理论发展的某些思考[J].系统科学与数学,2012,31(9):1014–1018.)
[2]NASH J F.Equilibrium points in n-person games[J].Proceedings of the National Academy of Sciences,1950,36(1):48–49.
[3]NASH J F.Non-cooperative games[J].Annals of Mathematics,1951,54(2):286–295.
[4]SMITH J M,PRICE G R.The logic of animal conflict[J].Nature,1973,246:15.
[5]SMITH J M.Evolution and the Theory of Games[M].Cambridge:Cambridge University Press,1982.
[6]LU Qiang,MEI Shengwei.Review of modern power system controlepitome and prospect of related research in state key lab of power systems,Tsinghua University[J].Journal of System Science and Mathematics Science,2012,32(10):1207–1225.(卢强,梅生伟.现代电力系统控制评述—–清华大学电力系统国家重点实验室相关科研工作缩影及展望[J].系统科学与数学,2012,32(10):1207–1225.)
[7]WEI Wei,MEI Shengwei,ZHANG Xuemin.Review of advanced control theory and application in power system[J].Power System Protection and Control,2013,41(12):143–153.(魏韡,梅生伟,张雪敏.先进控制理论在电力系统中的应用综述及展望[J].电力系统保护与控制,2013,41(12):143–153.)
[8]WIENER N.Cybernetics:Control and Communication in the Animal and the Machine[M].New York:Wiley,1948.
[9]TSIEN H S.Engineering Cybernetics[M].New York:Mcgraw-Hill Book Company,1954.
[10]CHEN Daizhan,XIA Yuanqing,MA Hongbin,et al.Matrix Algebra Control and Game Theory[M].Beijing:Beijing Institute of Technology Press,2016.(程代展,夏元清,马宏宾,等.矩阵代数控制与博弈[M].北京:北京理工大学出版社,2016.)
[11]HARSANYI J C.Games with incomplete information played by Bayesian players,part I:the basic model[J].Management Science,1967,14(3):159–182.
[12]HARSANYI J C.Games with incomplete information played by Bayesian players,part II:Bayesian equilibrium points[J].Management Science,1968,14(5):320–334.
[13]HARSANYI J C.Games with incomplete information played by Bayesian players,part III:The basic probability distri-bution of the game[J].Management Science,1968,14(7):486–502.
[14]SMITH J M,PRICE G R.The logic of animal conflict[J].Nature,1973,246:15–18.
[15]MEI Shengwei,WEI Wei.Hierarchal game and its applications in the smart grid[J].Journal of Science and Mathematics Science,2014,34(11):1331–1344.(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.)
[16]SCUTARI G,PALOMAR D P,FACCHINEI F,et al.Convex optimization,game theory,and variational inequality theory[J].IEEE Signal Processing Magazine,2010,27(3):35–49.
[17]LU Qiang,MEI Shengwei,SUN Yuanzhang.Nonlinear Control of Power System[M].Beijing:Tsinghua University Press,2008.(卢强,梅生伟,孙元章.电力系统非线性控制[M].清华大学出版社,2008.)
[18]SHAPLEY L S.A value for n-person games[R].Santa Monica,CA:Rand Corporation,1952.
[19]NASH J F.The bargaining problem[J].Econometrica,1950,18(2):155–162.
[20]SONG Meiping,GU Guochang,ZHANG Guoyin.Survey of multiagent reinforcement learning in Markov games[J].Control and Decision,2005,20(10):1081–1090.(宋梅萍,顾国昌,张国印.随机博弈框架下的多agent强化学习方法综述[J].控制与決策,2005,20(10):1081–1090.)
[21]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.(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.)
[22]MEI Shengwei,LIU Feng,WEI Wei.Basic Introduction of Engineering Game Theory and Its Applications in Power System[M].Beijing:Scientific Press,2016.(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.)
[23]WANG Yingying,MEI Shengwei,LIU Feng.Imputation schemes for the cooperative game in the hybrid power system planning[J].Journal of Science and Mathematics Science,2012,32(4):418–428.(王莹莹,梅生伟,刘锋.混合电力系统合作博弈规划的分配策略研究[J].系统科学与数学,2012,32(4):418–428.)
[24]MEI S,WANG Y,LIU F,et al.Game approaches for hybrid power system planning[J].IEEE Transactions on Sustainable Energy,2012,3(3):506–517.
[25]MEI Shengwei,GUO Wentao,WANG Yingying,et al.A game model for robust optimization of power systems and its application[J].Proceedings of the CSEE,2013,33(19):47–56.(梅生伟,郭文涛,王莹莹,等.一类电力系统鲁棒优化问题的博弈模型及应用实例[J].中国电机工程学报,2013,33(19):47–56.)
[26]WEI Wei,LIU Feng,MEI Shengwei.Robust and economical scheduling methodology for power systems,part one:theoretical foundations[J].Automation of Electric Power System,2013,37(17):37–43.(魏韡,刘锋,梅生伟.电力系统鲁棒经济调度(一):理论基础[J].电力系统自动化,2013,37(17):37–43.)
[27]WEI Wei,LIU Feng,MEI Shengwei.Robust and economical scheduling methodology for power systems,part two:application foundations[J].Automation of Electric Power System,2013,37(18):60–67.(魏韡,刘锋,梅生伟.电力系统鲁棒经济调度(二):应用实例[J].电力系统自动化,2013,37(18):60–67.)
[28]WEI W,LIU F,WANG J,et al.Robust environmental-economic dispatch incorporating wind power generation and carbon capture plants[J].Applied Energy,2016,183:674–684.
[29]YANG Xiandong,YE Fangbo.Linear and Nonlinear H-infinity Control Theory[M].Taipei:Quanhua Science and Technology Books Corporation,1997.(杨宪东,叶芳柏.线性与非线性H∞控制理论[M].台北:全华科技图书股份有限公司,1997.)
[30]Gui Xiaoyang,MEI Shengwei,LU Qiang.Nonlinear coordinated robust governor control of hydro-turbine generator sets in multimachine power systems[J].Automation of Electric Power System,2006,30(3):29–33.(桂小阳,梅生伟,卢强.多机系统水轮机调速器鲁棒非线性协调控制研究[J].电力系统自动化,2006,30(3):29–33.)
[31]LU Qiang,ZHENG Shaoming,MEI Shengwei,et al.Experimental study on large disturbance of NR–PSS and RTDS in large aynchronous generator sets[J].Science in China Journal E,2008,38(7):979–992.(卢强,郑少明,梅生伟,等.大型同步发电机组NR–PSS及RTDS大扰动实验研究[J].中国科学E辑,2008,38(7):979–992.)
[32]LU Q,MEI S,ZHENG S.Field experiments of NR-PSS for large synchronous generators on a 300 MW machine in Baishan Hydro Plant[J].Science in China Journal E(English Version),2007,50(4):516–520.
[33]MEI S,WEI W,ZHENG S,et al.Development of an industrial nonlinear robust power system stabilizer and its improved frequency domain testing method[J].IET Generation,Transmission,Distribution,2011,5(12):1201–1210.
[34]LI N,MARDEN J.Designing games for distributed optimization[J].IEEE Journal of Selected Topics in Signal Processing,2013,7(2):230–242.
[35]WANG Z,LIU F,CHEN Y,et al.Unified distributed control of standalone dc microgrids[EB/OL].IEEE Transactions on Smart Grid,2017,https://ieeexplore.ieee.org/document/8052512/.
[36]WANG Z,LIU F,LOW S H,et al.Distributed frequency control with operational constraints,Part I:Per-node power balance[EB/OL].IEEE Transactions on Smart Grid,2017,https://ieeexplore.ieee.org/document/7990543/.
[37]WANG Z,LIU F,LOW S H,et al.Distributed frequency control with operational constraints,Part II:Network power balance[EB/OL].IEEE Transactions on Smart Grid,2017,https://ieeexplore.ieee.org/document/7990367/.
[38]MEI Shengwei,GONG Yuan,LIU Feng.The evolution model of three-generation power systems and characteristic analysis[J].Proceedings of the CSEE,2014,34(7):1003–1012.(梅生伟,龚媛,刘锋.三代电网演化模型及特性分析[J].中国电机工程学报,2014,34(7):1003–1012.)
[39]ZHOU Xiaoxin,CHEN Shuyong,LU Zongxiang.Review and prospect for power system development and related technologies:a concept of three-generation power systems[J].Proceedings of the CSEE,2013,33(22):1–11.(周孝信,陈树勇,鲁宗相.电网和电网技术发展的回顾与展望—–试论三代电网[J].中国电机工程学报,2013,33(22):1–11.)
[40]LIU Nian,YU Xinghuo,ZHANG Jianhua.Coordinated cyber-attack:influence and thinking of inciden on Ukarinian power grid[J].Automation of Electric Power System,2016,40(6):144–147.(刘念,余星火,张建华.网络协同攻击:乌克兰停电事件的推演与启示[J].电力系统自动化,2016,40(6):144–147.)
[41]GUO Lei.Some thoughts on the development of control theory[J].Journal of Science and Mathematics Science,2012,31(9):1014–1018.(郭雷.关于控制理论发展的某些思考[J].系统科学与数学,2012,31(9):1014–1018.)