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http://dx.doi.org/10.5370/JEET.2013.8.4.675

Solving Mixed Strategy Nash-Cournot Equilibria under Generation and Transmission Constraints in Electricity Market  

Lee, Kwang-Ho (Department of Electrical Engineering, Dankook University)
Publication Information
Journal of Electrical Engineering and Technology / v.8, no.4, 2013 , pp. 675-685 More about this Journal
Abstract
Generation capacities and transmission line constraints in a competitive electricity market make it troublesome to compute Nash Equilibrium (NE) for analyzing participants' strategic generation quantities. The NE can cause a mixed strategy NE rather than a pure strategy NE resulting in a more complicated computation of NE, especially in a multiplayer game. A two-level hierarchical optimization problem is used to model competition among multiple participants. There are difficulties in using a mathematical programming approach to solve a mixed strategy NE. This paper presents heuristics applied to the mathematical programming method for dealing with the constraints on generation capacities and transmission line flows. A new formulation based on the heuristics is provided with a set of linear and nonlinear equations, and an algorithm is suggested for using the heuristics and the newly-formulated equations.
Keywords
Cournot model; Electricity market; Generation capacity; Mixed strategy; Nash equilibrium (NE); Power transfer distribution factor (PTDF); Transmission congestion;
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1 K. H. Lee and R. Baldick, "Solving three-player games by the matrix approach with application to an electric power market," IEEE Trans. Power Syst., Vol. 18, No. 4, pp. 1573-1580, Nov. 2003.   DOI   ScienceOn
2 J. D. Weber and T.J. Overbye, "An individual welfare maximization algorithm for electricity markets," IEEE Trans. Power Syst., Vol. 17, No. 3, pp. 590-596, Aug. 2002.   DOI   ScienceOn
3 D. Fudenberg and J. Tirole, Game Theory. Cambridge, MA: MIT Press, 1991.
4 B.F. Hobbs, "Linear complementarity model models of Nash-Cournot competition in bilateral and POOLCO power market," IEEE Trans. Power Syst., Vol. 16, No. 2, pp. 194-202, May 2001.   DOI   ScienceOn
5 A. L. Motto and F. D. Galiana, "Coordination in markets with nonconvexities as mathematical program with equilibrium constraints-part I: a solution procedure," IEEE Trans. Power Syst., Vol. 19, No. 1, Feb. 2004.
6 B.F. Hobbs, "Strategic gaming analysis for electric power systems: an MPEC approach," IEEE Trans. Power Syst., Vol. 15, No. 2, pp. 638-645, May 2000.   DOI   ScienceOn
7 T.C. Price, "Using co-evolutionary programming to simulate strategic behavior in markets," J. Evol. Econ. Vol. 7, pp.219-254, 1997.   DOI
8 C. Richter and G. Sheble, "Genetic algorithm evolution of utility bidding strategies for the competitive marketplace," IEEE Trans. Power Syst., Vol.13, No.1, pp.256-261, Feb. 1998.   DOI   ScienceOn
9 R.W. Ferrero, S.M. Shahidehpour, and V.C. Ramesh, "Transaction analysis in deregulated power systems using game theory," IEEE Trans. Power Syst., Vol.12, No. 3, pp. 1340-1347, Aug. 1997.   DOI   ScienceOn
10 C.E. Lemke and J.T. Howson, "Equilibrium points of bimatrix game," SIAM J. Appl. Math., Vol. 12, pp. 413-423, 1964.   DOI   ScienceOn
11 J. Contreras, M. Klusch, and J. B. Krawczyk, "Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets," IEEE Trans. Power Syst., Vol. 19, No. 1, pp. 195-206, Feb. 2004.   DOI   ScienceOn
12 A. V. Heusinger and C. Kanzow, "Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions," Computational Optimization and Applications, Vol. 43, No. 2, pp. 353-377, 2009.   DOI   ScienceOn
13 J. B. Krawczyk, Jacek and Zuccolo, NIRA-3: An improved MATLAB package for finding Nash Equilibriua in infinite games, in Working Paper, Dec. 2006.
14 Severin Borenstein, James Bushnell, and Steven Stoft, "The Competitive effects of transmission capacity in a deregulated electricity industry," RAND Journal of Economics, Vol. 31, No. 2, pp. 294-325, Summer 2000.   DOI   ScienceOn
15 A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, New York: Wiley-Interscience, 1996.
16 S. Song, J. Jeong, Y. T. Yoon and S. Moon, "Model of Information Exchange for Decentralized Congestion Management," Journal of Electrical Engineering & Technology, Vol .7, No. 2, pp. 141-150, 2012   과학기술학회마을   DOI   ScienceOn
17 Roy Gardner, Games for Business and Economics, John Wiley& Sons, Inc. 2003.
18 P. D. Klemperer and M. A. Meyer, "Supply function equilibria in oligopoly under uncertainty," Econometrica, Vol. 57, pp. 1243-1277, 1989.   DOI   ScienceOn
19 H. Nui and R. Baldick, "Supply function equilibrium bidding strategies with fixed forward contracts," IEEE Trans. Power Syst., Vol. 20, No. 4, pp. 1859-1867, Nov. 2005.   DOI   ScienceOn
20 W. Xian, L. Yuzeng, and Z. Shaohua, "Oligopolistic equilibrium analysis for electricity market: a nonlinear complementarity approach," IEEE Trans. Power Syst., Vol. 19, No. 3, pp. 1348-1355, Aug. 2004.   DOI   ScienceOn
21 V. P. Gountis, and A. G. Bakirtzis, "Efficient determination of Cournot eqilibria in electricity markets," IEEE Trans. Power Syst., Vol. 19, No. 4, pp. 1837-1844, Nov. 2004.   DOI   ScienceOn
22 F.A. Wolak and R. H. Patrick, "The Impact of market rules and market structure on the price determination process in the England and Wales electricity market," Univ. California Energy Inst., Berkeley, PWP-047, Apr. 1997.
23 P. F. Correica, T. J. Overbye, and I. A. Hiskens, "Searching for noncooperative equilibria in centralized electricity markets," IEEE Trans. Power Syst., Vol. 18, No. 4, pp. 1417-1424, Nov. 2003.   DOI   ScienceOn
24 K.H. Lee and R. Baldick, "Tuning of discretization in bimatrix game approach to power system market analysis," IEEE Trans. Power Syst., Vol. 18, No. 2, pp. 830-836, May 2003.   DOI   ScienceOn