On engineering game theory with its application in power systems

Due to its capability of solving decision-making problems involving multiple entities and objectives, as well as complex action sequences, game theory has been a basic mathematical tool of economists, politicians, and sociologists for decades. It helps them understand how strategic interactions impact rational decisions of individual players in competitive and uncertain environment, if each player aims to get the best payoff. This situation is ubiquitous in engineering practices. This paper streamlines the foundations of engineering game theory, which uses concepts, theories and methodologies to guide the resolution of engineering design, operation, and control problems in a more canonical and systematic way. An overview of its application in smart grid technologies and power systems related topics is presented, and intriguing research directions are also envisioned.

[1]  Gang Wang,et al.  NR-PSS (Nonlinear Robust Power System Stabilizer) for large synchronous generators and its large disturbance experiments on real time digital simulator , 2008 .

[2]  P.T. Krein,et al.  Game-Theoretic Control of Small-Scale Power Systems , 2009, IEEE Transactions on Power Delivery.

[3]  Jianhui Wang,et al.  Decentralized Energy Management System for Networked Microgrids in Grid-Connected and Islanded Modes , 2016, IEEE Transactions on Smart Grid.

[4]  Jose M. Arroyo,et al.  Bilevel programming applied to power system vulnerability analysis under multiple contingencies , 2010 .

[5]  J. Pang,et al.  Strategic gaming analysis for electric power systems: an MPEC approach , 2000 .

[6]  Masao Fukushima,et al.  Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games , 2009, Comput. Manag. Sci..

[7]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[8]  Jianhui Wang,et al.  Coordinated Energy Management of Networked Microgrids in Distribution Systems , 2015, IEEE Transactions on Smart Grid.

[9]  Shengwei Mei,et al.  Game Approaches for Hybrid Power System Planning , 2012, IEEE Transactions on Sustainable Energy.

[10]  J. Nash.  Two-Person Cooperative Games , 1953 .

[11]  Che-Lin Su,et al.  Equilibrium Problems with Equilibrium Constraints: Stationarities, Algorithms, and Applications in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy the Systems Optimization Laboratory Has Been a Great Working Environment. I Appreciate the Friendship of Kien , 2005 .

[12]  Osama A. Mohammed,et al.  Real-Time Implementation of Multiagent-Based Game Theory Reverse Auction Model for Microgrid Market Operation , 2015, IEEE Transactions on Smart Grid.

[13]  L. Shapley,et al.  QUASI-CORES IN A MONETARY ECONOMY WITH NONCONVEX PREFERENCES , 1966 .

[14]  Quanyan Zhu,et al.  Dependable Demand Response Management in the Smart Grid: A Stackelberg Game Approach , 2013, IEEE Transactions on Smart Grid.

[15]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Moshe Zukerman,et al.  Distributed Energy Trading in Microgrids: A Game-Theoretic Model and Its Equilibrium Analysis , 2015, IEEE Transactions on Industrial Electronics.

[17]  Russell Bent,et al.  Cyber-Physical Security: A Game Theory Model of Humans Interacting Over Control Systems , 2013, IEEE Transactions on Smart Grid.

[18]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[19]  J M Smith.  Game theory and the evolution of behaviour , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[20]  Nikos D. Hatziargyriou,et al.  Leader-Follower Strategies for Energy Management of Multi-Microgrids , 2013, IEEE Transactions on Smart Grid.

[21]  W. W. Weaver,et al.  Game-Theoretic Communication Structures in Microgrids , 2012, IEEE Transactions on Power Delivery.

[22]  Feng Liu,et al.  Online Supplementary ADP Learning Controller Design and Application to Power System Frequency Control With Large-Scale Wind Energy Integration , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Åke J. Holmgren,et al.  Evaluating Strategies for Defending Electric Power Networks Against Antagonistic Attacks , 2007, IEEE Transactions on Power Systems.

[24]  Daniel Pérez Palomar,et al.  Noncooperative Day-Ahead Bidding Strategies for Demand-Side Expected Cost Minimization With Real-Time Adjustments: A GNEP Approach , 2014, IEEE Transactions on Signal Processing.

[25]  Xu Andy Sun,et al.  Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem , 2013, IEEE Transactions on Power Systems.

[26]  Daniel Ralph,et al.  Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices , 2007, Oper. Res..

[27]  Kwang-Cheng Chen,et al.  Smart attacks in smart grid communication networks , 2012, IEEE Communications Magazine.

[28]  Wei Yuan,et al.  Optimal power grid protection through a defender-attacker-defender model , 2014, Reliab. Eng. Syst. Saf..

[29]  Feng Liu,et al.  Robust Energy and Reserve Dispatch Under Variable Renewable Generation , 2015, IEEE Transactions on Smart Grid.

[30]  Y. Smeers,et al.  Bi-Level Game Approaches for Coordination of Generation and Transmission Expansion Planning Within a Market Environment , 2013, IEEE Transactions on Power Systems.

[31]  Robert M. Glorioso,et al.  Engineering Cybernetics , 1975 .

[32]  F. F. Wu,et al.  Nonlinear Decentralized Disturbance Attenuation Excitation Control via New Recursive Design for Multimachine Power Systems , 2001, IEEE Power Engineering Review.

[33]  Anastasios G. Bakirtzis,et al.  Optimal Offering Strategy of a Virtual Power Plant: A Stochastic Bi-Level Approach , 2016, IEEE Transactions on Smart Grid.

[34]  Shengwei Mei,et al.  Development of an industrial non-linear robust power system stabiliser and its improved frequency-domain testing method , 2011 .

[35]  Long Zhao,et al.  Robust unit commitment problem with demand response and wind energy , 2012, 2012 IEEE Power and Energy Society General Meeting.

[36]  Ruiwei Jiang,et al.  Robust Unit Commitment With Wind Power and Pumped Storage Hydro , 2012, IEEE Transactions on Power Systems.

[37]  Shengwei Mei,et al.  Imputation schemes for the cooperative game in the hybrid power system planning , 2011, Proceedings of the 30th Chinese Control Conference.

[38]  Xiaodong Wang,et al.  Cooperative Control of Power System Load and Frequency by Using Differential Games , 2015, IEEE Transactions on Control Systems Technology.

[39]  M. Goto,et al.  Decentralised nonlinear H/sub /spl infin// excitation control based on regulation linearisation , 2000 .

[40]  Antonio J. Conejo,et al.  A robust optimization approach to energy and reserve dispatch in electricity markets , 2015, Eur. J. Oper. Res..

[41]  Anna Filomena Carbone,et al.  Power Grid Complexity , 2011 .

[42]  Hak-Man Kim,et al.  Cooperative Control Strategy of Energy Storage System and Microsources for Stabilizing the Microgrid during Islanded Operation , 2010, IEEE Transactions on Power Electronics.

[43]  Jianhui Wang,et al.  Real-Time Trading Strategies of Proactive DISCO With Heterogeneous DG Owners , 2018, IEEE Transactions on Smart Grid.

[44]  Jianhui Wang,et al.  Convexification of the Nash Bargaining Based Environmental-Economic Dispatch , 2016, IEEE Transactions on Power Systems.

[45]  E.Yu. Ivanova,et al.  Shapley Game for Expansion Planning of Generating Companies at Many Non-Coincident Criteria , 2006, IEEE Transactions on Power Systems.

[46]  Wei Wei.  A Game Model for Robust Optimization of Power Systems and Its Application , 2013 .

[47]  Shengwei Mei,et al.  Robust Optimization of Static Reserve Planning With Large-Scale Integration of Wind Power: A Game Theoretic Approach , 2014, IEEE Transactions on Sustainable Energy.

[48]  Derek P Molle,et al.  Defending Critical Infrastructure as Cyber Key Terrain , 2016 .

[49]  Nataliya I. Kalashnykova,et al.  Bilevel Programming Problems , 2015 .

[50]  Wei Wei,et al.  Energy Pricing and Dispatch for Smart Grid Retailers Under Demand Response and Market Price Uncertainty , 2015, IEEE Transactions on Smart Grid.

[51]  Lu Zongxiang,et al.  Review and Prospect for Power System Development and Related Technologies:a Concept of Three-generation Power Systems , 2013 .

[52]  Zhao Yang Dong,et al.  Exploring Reliable Strategies for Defending Power Systems Against Targeted Attacks , 2011, IEEE Transactions on Power Systems.

[53]  E. Robinson.  Cybernetics, or Control and Communication in the Animal and the Machine , 1963 .

[54]  Shengwei Mei,et al.  Real-Time Dispatchability of Bulk Power Systems With Volatile Renewable Generations , 2015, IEEE Transactions on Sustainable Energy.

[55]  Wei Yuan,et al.  A Two-Stage Robust Reactive Power Optimization Considering Uncertain Wind Power Integration in Active Distribution Networks , 2016, IEEE Transactions on Sustainable Energy.

[56]  H. Stackelberg,et al.  Marktform und Gleichgewicht , 1935 .

[57]  Felix Wu,et al.  A Game-Theoretic Model for Generation Expansion Planning: Problem Formulation and Numerical Comparisons , 2001, IEEE Power Engineering Review.

[58]  Wei Qiao,et al.  Optimal Bidding Strategy of a Strategic Wind Power Producer in the Short-Term Market , 2015, IEEE Transactions on Sustainable Energy.

[59]  Arkadi Nemirovski,et al.  Robust solutions of Linear Programming problems contaminated with uncertain data , 2000, Math. Program..

[60]  Jianhui Wang,et al.  Robust environmental-economic dispatch incorporating wind power generation and carbon capture plants , 2016 .

[61]  Shengwei Mei,et al.  Dispatchable Region of the Variable Wind Generation , 2015, IEEE Transactions on Power Systems.

[62]  P. Varaiya,et al.  Differential games , 1971 .

[63]  Nataliya I. Kalashnykova,et al.  Bilevel Programming Problems: Theory, Algorithms and Applications to Energy Networks , 2015 .

[64]  Walid Saad,et al.  Game-Theoretic Methods for the Smart Grid: An Overview of Microgrid Systems, Demand-Side Management, and Smart Grid Communications , 2012, IEEE Signal Processing Magazine.

[65]  Hiroshi Konno,et al.  A cutting plane algorithm for solving bilinear programs , 1976, Math. Program..

[66]  Hamidreza Zareipour,et al.  Equilibria in an Oligopolistic Market With Wind Power Production , 2014, IEEE Transactions on Power Systems.

[67]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[68]  Yu Zhang,et al.  Robust Energy Management for Microgrids With High-Penetration Renewables , 2012, IEEE Transactions on Sustainable Energy.

[69]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[70]  Hamidreza Zareipour,et al.  Impacts of Strategic Bidding of Wind Power Producers on Electricity Markets , 2016, IEEE Transactions on Power Systems.

[71]  L. S. Shapley,et al.  17. A Value for n-Person Games , 1953 .

[72]  Messaoud Bounkhel,et al.  Quasi-Variational Inequalities , 2012 .

[73]  Shengwei Mei,et al.  Nash Bargain and Complementarity Approach Based Environmental/Economic Dispatch , 2015, IEEE Transactions on Power Systems.

[74]  L. Shapley.  A Value for n-person Games , 1988 .

[75]  James E. Falk,et al.  A linear max—min problem , 1973, Math. Program..

[76]  J. Nash.  THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[77]  D. Schmeidler.  The Nucleolus of a Characteristic Function Game , 1969 .

[78]  Richard L. Church,et al.  A bilevel mixed-integer program for critical infrastructure protection planning , 2008, Comput. Oper. Res..

[79]  Henrik Madsen,et al.  A bilevel model for electricity retailers' participation in a demand response market environment , 2013 .

[80]  Jerome Bracken,et al.  Mathematical Programs with Optimization Problems in the Constraints , 1973, Oper. Res..

[81]  Donald B. Gillies,et al.  3. Solutions to General Non-Zero-Sum Games , 1959 .

[82]  R. Alvarez,et al.  Trilevel Optimization in Power Network Defense , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[83]  Christos V. Verikoukis,et al.  A Survey on Demand Response Programs in Smart Grids: Pricing Methods and Optimization Algorithms , 2015, IEEE Communications Surveys & Tutorials.

[84]  Feng Liu,et al.  Approximate dynamic programming based supplementary reactive power control for DFIG wind farm to enhance power system stability , 2015, Neurocomputing.

[85]  Nishantha C. Ekneligoda,et al.  Game-Theoretic Cold-Start Transient Optimization in DC Microgrids , 2014, IEEE Transactions on Industrial Electronics.

[86]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[87]  J.P. Hayes,et al.  Engineering cybernetics , 1976, Proceedings of the IEEE.

[88]  Gongguo Tang,et al.  A game-theoretic approach for optimal time-of-use electricity pricing , 2013, IEEE Transactions on Power Systems.

[89]  X. Vives,et al.  Price and quantity competition in a differentiated duopoly , 1984 .

[90]  M. Shahidehpour,et al.  Strategic Generation Capacity Expansion Planning With Incomplete Information , 2009, IEEE Transactions on Power Systems.

[91]  Natalia Alguacil,et al.  A trilevel programming approach for electric grid defense planning , 2014, Comput. Oper. Res..

[92]  Vincent W. S. Wong,et al.  Autonomous Demand-Side Management Based on Game-Theoretic Energy Consumption Scheduling for the Future Smart Grid , 2010, IEEE Transactions on Smart Grid.

[93]  D. E. Matthews.  Evolution and the Theory of Games , 1977 .

[94]  J. Nash,et al.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[95]  Long Zhao,et al.  Solving two-stage robust optimization problems using a column-and-constraint generation method , 2013, Oper. Res. Lett..

[96]  Ruben C. Arslan.  Evolutionary Genetics , 2014 .

[97]  J. I. Muñoz,et al.  Optimal Contract Pricing of Distributed Generation in Distribution Networks , 2011, IEEE Transactions on Power Systems.

[98]  B. Hobbs,et al.  Complementarity Modeling in Energy Markets , 2012 .

[99]  Bo Zeng,et al.  Vulnerability Analysis of Power Grids With Line Switching , 2013, IEEE Transactions on Power Systems.