Abstract
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.
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References
J. von Neumann, O. Morgenstern. Theory of Games and Economic Behavior. Princeton: Princeton University Press, 1944.
J. F. Nash. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 1950, 36(1): 48–49.
J. F. Nash. Non-cooperative games. Annals of Mathematics, 1951, 54(2): 286–295.
J. M. Smith, G. R. Price. The logic of animal conflict. Nature, 1973, 246: 15–18.
J. M. Smith. Game theory and the evolution of behavior. Proceedings of the Royal Society of London–Series B: Biological Sciences, 1979, 205(1161): 475–488.
J. M. Smith. Evolution and the Theory of Games. Cambridge: Cambridge University Press, 1982.
X. Yang, B. Ye. Linear and Nonlinear H8 Control. Tabei: Chuan Hwa Publishing Ltd., 1997.
S. Mei, F. Liu, W. Wei. Foundations of Engineering Game Theory and its Applications in Power Systems (in Chinese). Beijing: Science Press, 2016.
N. Wiener. Cybernetics or Control and Communication in the Animal and the Machine. Cambridge: MIT Press, 1948.
H. S. Tsien. Engineering Cybernetics. New York: McGraw-Hill, 1954.
T. Basar, G. J. Olsder. Dynamic Noncooperative Game Theory. Philadelphia: SIAM, 1999.
S. A. Gabriel, A. J. Conejo, J. D. Fuller, et al. Complementarity Modeling in Energy Markets. New York: Springer, 2013.
D. B. Gillies. Solutions to general non-zero-sum games. A. W. Tucker & H. W. Kuhn (Eds.). Contributions to the Theory of Games. Annals of Mathematical Studies 40. Princeton: Princeton University Press: 47–85.
L. S. Shapley, M. Shubik. Quasi-cores in a monetary economy with nonconvex preferences. Econometrica: Journal of the Econometric Society, 1966, 34(4): 805–827.
L. S. Shapley. A value for n-person games. H. W. Kuhn & A. W. Tucker (Eds.). Contributions to the Theory of Games. Annals of Mathematical Studies 28. Princeton: Princeton University Press: 307–317.
D. Schmeidler. The nucleolus of a characteristic function game. SIAM Journal on Applied Mathematics, 1969, 17(6): 1163–1170.
J. F. Nash. The bargaining problem. Econometrica: Journal of the Econometric Society, 1950, 18(2): 155–162.
J. F. Nash. Two person cooperative games. Econometrica: Journal of the Econometric Society, 1953, 21(1): 128–140.
M. Smith. Evolutionary Genetics. New York: Oxford University Press, 1989.
A. Ben-Tal, A. Nemirovski. Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming, 2000, 88(3): 411–424.
R. Isaacs. Differential Games. Hoboken: Wiley, 1967.
T. Basar, P. Bernhard. H8 Optimal Control and Related Minimax Design Problems. Boston: Birkhauser, 2008.
H. von Stackelberg. Marktform und Gleichgewicht. Berlin: Springer, 1934. The Theory of the Market Economy (English translated). Oxford: Oxford University Press, 1952.
J. Bracken, J. McGill. Mathematical programs with optimization problems in the constraints. Operations Research, 1973, 21(1): 37–44.
S. Dempe, V. Kalashnikov, G. A. Perez-Valdes, et al. Bilevel Programming Problems: Theory, Algorithms and Applications to Energy Networks. Berlin: Springer, 2015.
J. S. Pang, M. Fukushima. Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games. Computational Management Science, 2005, 2(1): 21–56.
C. L. Su. Equilibrium Problems with Equilibrium Constraints: Stationarities, Algorithms, and Applications. Stanford: Stanford University, 2005.
W. Saad, Z. Han, H. V. Poor, et al. Game-theoretic methods for the smart grid: An overview of microgrid systems, demandside management, and smart grid communications. IEEE Signal Processing Magazine, 2012, 29(5): 86–105.
N. Singh, X. Vives. Price and quantity competition in a differentiated duopoly. Rand Journal of Economics, 1984, 15(4): 546–554.
B. F. Hobbs, C. B. Metzler, J. S. Pang. Strategic gaming analysis for electric power systems: An MPEC approach. IEEE Transactions on Power Systems, 2000, 15(2): 638–645.
X. Hu, D. Ralph. Using EPECs to model bilevel games in restructured electricity markets with locational prices. Operations Research, 2007, 55(5): 809–827.
M. Banaei, M. O. Buygi, H. Zareipour. Impacts of strategic bidding of wind power producers on electricity markets. IEEE Transactions on Power Systems, 2016, 31(6): 4544–4553.
S. J. Kazempour, H. Zareipour. Equilibria in an oligopolistic market with wind power production. IEEE Transactions on Power Systems, 2014, 29(2): 686–697.
T. Dai, W. Qiao. Optimal bidding strategy of a strategic wind power producer in the short-term market. IEEE Transactions on Sustainable Energy, 2015, 6(3): 707–719.
E. G. Kardakos, C. K. Simoglou, A. G. Bakirtzis. Optimal offering strategy of a virtual power plant: A stochastic bi-level approach. IEEE Transactions on Smart Grid, 2016, 7(2): 794–806.
A. S. Chuang, F. Wu, P. Varaiya. A game-theoretic model for generation expansion planning: Problem formulation and numerical comparisons. IEEE Transactions on Power Systems, 2001, 16(4): 885–891.
N. I. Voropai, E. Ivanova. Shapley game for expansion planning of generating companies at many non-coincident criteria. IEEE Transactions on Power Systems, 2006, 21(4): 1630–1637.
J. Wang, M. Shahidehpour, Z. Li, et al. Strategic generation capacity expansion planning with incomplete information. IEEE Transactions on Power Systems, 2009, 24(2): 1002–1010.
M. Jenabi, G. Fatemi, Y. Smeers. Bi-level game approaches for coordination of generation and transmission expansion planning within a market environment. IEEE Transactions on Power Systems, 2013, 28(3): 2639–2650.
S. Mei, Y. Wang, F. Liu, et al. Game approaches for hybrid power system planning. IEEE Transactions on Sustainable Energy, 2012, 3(3): 506–517.
Y. Wang, S. Mei, F. Liu. Imputation schemes for the cooperative game in the hybrid power system planning. Journal of Systems Science and Complexity, 2012, 32(4): 418–428 (in Chinese).
S. Mei, D. Zhang, Y. Wang, et al. Robust optimization of static reserve planning with large-scale integration of wind power: A game theoretic approach. IEEE Transactions on Sustainable Energy, 2014, 5(2): 535–545.
S. Mei, W. Guo, Y. Wang, et al. A game model for robust optimization of power systems and its application. Proceedings of the CSEE, 2013, 33(19): 47–56 (in Chinese).
R. Jiang, J. Wang, Y. Guan. Robust unit commitment with wind power and pumped storage hydro. IEEE Transactions on Power Systems, 2012, 27(2): 800–810.
L. Zhao, B. Zeng. Robust unit commitment problem with demand response and wind energy. IEEE Power and Energy Society General Meeting. San Diego: IEEE, 2012: DOI 10.1109/PESGM.2012.6344860.
D. Bertsimas, E. Litvinov, X. A. Sun, et al. Adaptive robust optimization for the security constrained unit commitment problem. IEEE Transactions on Power Systems, 2013, 28(1): 52–63.
W. Wei. Power System Robust Dispatch: Models and Applications. Beijing: Tsinghua University, 2013 (in Chinese).
W. Wei, F. Liu, S. Mei, et al. Robust energy and reserve dispatch under variable renewable generation. IEEE Transactions on Smart Grid, 2015, 6(1): 369–380.
B. Zeng, L. Zhao. Solving two-stage robust optimization problems using a column-and-constraint generation method. Operations Research Letters, 2013, 41(5): 457–461.
J. E. Falk. A linear maxmin problem. Mathematical Programming, 1973, 5(1): 169–188.
M. Zugno, A. J. Conejo. A robust optimization approach to energy and reserve dispatch in electricity markets. European Journal of Operational Research, 2015, 247(2): 659–671.
H. Konno. A cutting plane algorithm for solving bilinear programs. Mathematical Programming, 1976, 11(1): 14–27.
W. Wei, F. Liu, S. Mei. Nash bargain and complementarity approach based environmental/economic dispatch. IEEE Transactions on Power Systems, 2015, 30(3): 1548–1549.
W. Wei, J. Wang, S. Mei. Convexification of the Nash bargain based environmental-economic dispatch. IEEE Transactions on Power Systems, 2016, 31(6): 5208–5209.
W. Wei, F. Liu, J. Wang, et al. Robust environmental-economic dispatch incorporating wind power generation and carbon capture plants. Applied Energy, 2016, 183: 674–684.
Q. Lu, S. Mei, W. Hu, et al. Nonlinear decentralized disturbance attenuation excitation control via new recursive design for multimachine power systems. IEEE Transactions on Power Systems, 2001, 16(4): 729–736.
Q. Lu, S. Mei, W. Hu, et al. Decentralised nonlinearH8excitation control based on regulation linearization. IEE Proceedings Generation, Transmission and Distribution, 2000, 147(4): 245–251.
Q. Lu, S. Zheng, S. Mei, et al. NR-PSS (nonlinear robust power system stabilizer) for large synchronous generators and its large disturbance experiments on real time digital simulator. Science in China Series E: Technological Sciences, 2008, 51(4): 337–352.
S. Mei, W. Wei, S. Zheng, et al. Development of an industrial non-linear robust power system stabiliser and its improved frequency-domain testing method. IET Generation, Transmission and Distribution, 2011, 5(12): 1201–1210.
W. Guo, F. Liu, J. Si, et al. Online supplementary ADP learning controller design and application to power system frequency control with large-scale wind energy integration. IEEE Transactions on Neural Networks and Learning Systems, 2016, 27(8): 1748–1761
W. Guo, F. Liu, J. Si, et al. Approximate dynamic programming based supplementary reactive power control for DFIG wind farm to enhance power system stability. Neurocomputing, 2015, 170: 417–427.
W. W. Weaver, P. T. Krein. Game-theoretic control of small-scale power systems. IEEE Transactions Power Delivery, 2009, 24(3): 1560–1567.
N. C. Ekneligoda, W. W. Weaver. Game-theoretic cold-start transient optimization in DC microgrids. IEEE Transactions on Industrial Electronics, 2014, 61(12): 6681–6690.
H. Chen, R. Ye, X. Wang, et al. Cooperative control of power system load and frequency by using differential games. IEEE Transactions on Control Systems Technology, 2015, 23(3): 882–897.
J. Kim, J. Jeon, S. Kim, et al. Cooperative control strategy of energy storage system and microsources for stabilizing the microgrid during islanded operation. IEEE Transactions on Power Electronics, 2010, 25(12): 3037–3048.
Z. Wang, B. Chen, J. Wang, et al. Coordinated energy management of networked microgrids in distribution systems. IEEE Transactions on Smart Grid, 2015, 6(1): 45–53.
Z. Wang, B. Chen, J. Wang. Decentralized energy management system for networked microgrids in grid-connected and islanded modes. IEEE Transactions on Smart Grid, 2016, 7(2): 1097–1105.
Q. Wang, C. Zhang, J. Wang, et al. Real-time trading strategies of proactive DISCO with heterogeneous DG owners. IEEE Transactions on Smart Grid:: DOI 10.1109/TSG.2016.2597263.
W. Wei, F. Liu, S. Mei. Dispatchable region of the variable wind generation. IEEE Transactions on Power Systems, 2015, 30(5): 2755–2765.
W. Wei, F. Liu, S. Mei. Real-time dispatchability of bulk power systems with volatile renewable generations. IEEE Transactions on Sustainable Energy, 2015, 6(3): 738–747.
Y. Zhang, N. Gatsis, G. Giannakis. Robust energy management for microgrids with high-penetration renewables. IEEE Transactions on Sustainable Energy, 2013, 4(4): 944–953.
T. Ding, S. Liu, W. Yuan, et al. A two-stage robust reactive power optimization considering uncertain wind power integration in active distribution networks. IEEE Transactions on Sustainable Energy, 2016, 7(1): 301–311.
G. Asimakopoulou, A. Dimeas, N. Hatziargyriou. Leader-follower strategies for energy management of multi-microgrids. IEEE Transactions on Smart Grid, 2013, 4(4): 1909–1916.
W. Wei, F. Liu, S. Mei. Energy pricing and dispatch for smart grid retailers under demand response and market price uncertainty. IEEE Transactions on Smart Grid, 2015, 6(3): 1364–1374.
S. Mei, W. Wei. Hierarchal game and its applications in the smart grid. Journal of Systems Science and Mathematical Sciences, 2014, 34(11): 1331–1344 (in Chinese).
J. Lee, J. Guo, J. Choi, et al. Distributed energy trading in microgrids: A game-theoretic model and its equilibrium analysis. IEEE Transactions on Industrial Electronics, 2015, 62(6): 3524–3533.
N. C. Ekneligoda, W. W. Weaver. Game-theoretic communication structures in microgrids. IEEE Transactions on Smart Grid, 2015, 6(2): 1064–1072.
P. Chen, S. Cheng, K. Chen. Smart attacks in smart grid communication networks. IEEE Communications Magazine, 2012, 50(8): 24–29.
S. Backhaus, R. Bent, J. Bono, et al. Cyber-physical security: A game theory model of humans interacting over control systems. IEEE Transactions on Smart Grid, 2013, 4(4): 2320–2327.
M. Zugno, J. M. Morales, P. Pinson, et al. A bilevel model for electricity retailers’ participation in a demand response market environment. Energy Economics, 2013, 36: 182–197.
J. M. Lopez-Lezama, A. Padilha-Feltrin, J. Contreras, et al. Optimal contract pricing of distributed generation in distribution networks. IEEE Transactions on Power Systems, 2011, 26(1): 128–136.
P. Yang, G. Tang, A. Nehorai. A game-theoretic approach for optimal time-of-use electricity pricing. IEEE Transactions on Power Systems, 2013, 28(2): 884–892.
J. S. Vardakas, N. Zorba, C. V. Verikoukis. A survey on demand response programs in smart grids: pricing methods and optimization algorithms. IEEE Communications Surveys & Tutorials, 2015, 17(1): 152–178.
H. Mohsenian-Rad, V. Wong, J. Jatskevich, et al. Autonomous demand side management based on game-theoretic energy consumption scheduling for the future smart grid. IEEE Transactions on Smart Grid, 2010, 1(3): 320–331.
I. Atzeni, L. G. Ordonez, G. Scutari, et al. Noncooperative day-ahead bidding strategies for demand-side expected cost minimization with real-time adjustments: A GNEP approach. IEEE transactions on Signal Processing, 2014, 62(9): 2397–2412.
S. Maharjan, Q. Zhu, Y. Zhang, et al. Dependable demand response management in the smart grid: A Stackelberg game approach. IEEE Transactions on Smart Grid, 2013, 4(1): 120–132.
A. J. Holmgren, E. Jenelius, J. Westin. Evaluating strategies for defending electric power networks against antagonistic attacks. IEEE Transactions on Power Systems, 2007, 22(1): 76–84.
G. Chen, Z. Dong, D. J. Hill, et al. Exploring reliable strategies for defending power systems against targeted attacks. IEEE Transactions on Power Systems, 2011, 26(3): 1000–1009.
L. Zhao, B. Zeng. Vulnerability analysis of power grids with line switching. IEEE Transactions on Power Systems, 2013, 28(3): 2727–2736.
M. P. Scaparra, R. L. Church. A bilevel mixed-integer program for critical infrastructure protection planning. Computers & Operations Research, 2008, 35(6): 1905–1923.
J. M. Arroyo. Bilevel programming applied to power system vulnerability analysis under multiple contingencies. IET Generation, Transmission & Distribution, 2010, 4(2): 178–190.
G. Brown, M. Carlyle, J. Salmeron, et al. Defending critical infrastructure. Interfaces, 2006, 36(6): 530–544.
Y. Yao, T. Edmunds, D. Papageorgiou, et al. Trilevel optimization in power network defense. IEEE Transactions on Systems, Man, and Cybernetics–Part C: Applications and Reviews, 2007, 37(4): 712–718.
W. Yuan, L. Zhao, B. Zeng. Optimal power grid protection through a defender-attacker-defender model. Reliability Engineering & System Safety, 2014, 121: 83–89.
N. Alguacil, A. Delgadillo, J. M. Arroyo. A trilevel programming approach for electric grid defense planning. Computers & Operations Research, 2014, 41: 282–290.
X. Zhou, S. Chen, Z. Lu. Review and prospect for power system development and related technologies: a concept of three-generation power systems. Proceedings of the CSEE, 2013, 36(22): 2–11.
S. Mei, X. Zhang, M. Cao. Power Grid Complexity. Berlin: Springer, 2011.
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This work was supported by National Natural Science Foundation of China (No. 51621065).
Shengwei MEI is currently a Professor with Tsinghua University, Beijing, China. His research interests include power system complexity and control, game theory and its application in power systems.
Wei WEI is currently an Assistant Professor with Tsinghua University. His research interests include applied optimization, energy economics, and interdependent energy networks.
Feng LIU is an Associate Professor with Tsinghua University. His research interests include power system distributed control and optimization.
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Mei, S., Wei, W. & Liu, F. On engineering game theory with its application in power systems. Control Theory Technol. 15, 1–12 (2017). https://doi.org/10.1007/s11768-017-6186-y
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DOI: https://doi.org/10.1007/s11768-017-6186-y