전력시장 해석을 위한 3연 참여 게임의 해법 연구

A Solution Method of a Three-Player Game for Application to an Electric Power Market

  • 이광호 (단국대 전기전자컴퓨터공학부)
  • 발행 : 2003.06.01

초록

In models of imperfect competition of deregulated electricity markets, the key task is to find the Nash equilibrium(NE). The approaches for finding the NE have had two major bottlenecks: computation of mixed strategy equilibrium and treatment of multi-player games. This paper proposes a payoff matrix approach that resolves these bottlenecks. The proposed method can efficiently find a mixed strategy equilibrium in a multi-player game. The formulation of the m condition for a three-player game is introduced and a basic computation scheme of solving nonlinear equalities and checking inequalities is proposed. In order to relieve the inevitable burden of searching the subspace of payoffs, several techniques are adopted in this paper. Two example application problems arising from electricity markets and involving a Cournot and a Bertrand model, respectively, are investigated for verifying the proposed method.

키워드

참고문헌

  1. B.F. Hobbs, C.B. Metzler, and J.S. Pang, 'Strategic Gaming Analysis for Electric Power Systems : An MPEC approach,' IEEE Trans. on Power Systems, Vol.15, No.2, pp. 638-645, May 2000 https://doi.org/10.1109/59.867153
  2. Z.Q. Luo, J.S. Pang, and D. Ralph, Mathematical Programs with Equilibrium Constraints, N.Y.: Cambridge Univ. Press, 1996
  3. X. Guan, Y.C. Ho, and D.L. Pepyne, 'Gaming and Price Spikes in Electric Power Markets,' IEEE Trans. on Power Systems, Vol.16, No.3, pp. 402-408, August 2001 https://doi.org/10.1109/59.932275
  4. X. Bai, S.M. Shahidehpour, V.C. Ramesh, and E. Yu, 'Transmission Analysis by Nash Game Method,' IEEE Trans. on Power Systems, Vol. 12, No. 3, pp. 1046-1052, August 1997 https://doi.org/10.1109/59.630442
  5. C. Silva, B.F. Wollenberg, and C.Z. Zheng, 'Application of Mechanism Design to Electric Power Markets,' IEEE Trans. on Power Systems, Vol.16, No.1, pp.1-8, February 2001 https://doi.org/10.1109/59.910774
  6. J.D. Weber and T.J. Overbye, 'A Two-Level Optimization Problem for Analysis ofcPES Summer Meeting, Vol.2, pp.682-687, 1999 https://doi.org/10.1109/PESS.1999.787399
  7. B.F. Hobbs, 'Linear Complementarity Models of Nash-Cournot Competition in Bilateral and POOLCO Power Market,' IEEE Trans. on Power Systems, Vol.16, No.2, pp.194-202, May 2001 https://doi.org/10.1109/59.918286
  8. S.Stoft, 'Using Game Theory to Study Market Power in Simple Networks,' IEEE Tutorial on Game Theory in Electric Power Markets, IEEE Press TP-136-0, pp.33-40, 1999
  9. R.W. Ferrero, S.M. Shahidehpour, and V.C. Ramesh, 'Transaction Analysis in Deregulated Power Systems Using Game Theory,' IEEE Trans. on Power Systems, Vol.12, No.3, pp.1340-1347, August 1997 https://doi.org/10.1109/59.630479
  10. K.H. Lee and R. Baldick, 'Tuning of Discretization in Bimatrix Game Approach to Power System Market Analysis,' IEEE Trans. on Power Systems, Vol.18, No.2, pp.830-836, May 2003 https://doi.org/10.1109/TPWRS.2002.807067
  11. T.Curzon Price, 'Using Co-evolutionary Programming to Simulate Strategic Behavior in Markets,' Journal of Evolutionary Economics, Vol.7, pp.219-254, 1997 https://doi.org/10.1007/s001910050042
  12. L.B. Cunningham, R. Baldick, and M.L.Baughman, 'An Empirical Study of Applied Game Theory: Transmission Constrained Cournot Behavior,' IEEE Transactions on Power Systems, 17(1), pp166-172, February 2002 https://doi.org/10.1109/59.982209
  13. C.E. Lemke and J.T. Howson, 'Equilibrium Points of Bimatrix Games,' SIAM Journal of Applied Mathematics 12, pp.413-423, 1964 https://doi.org/10.1137/0112033
  14. 이광호, '전력시장 해석을 위한 Bimatrix 게임의 이산화 알고리즘,' 전기학회논문지, 52A권 1호, pp.62-67, January, 2003
  15. N.N. Vorob'ev, 'Equilibrium Points in Bimatrix Games,' Theory of Probability and its Applications, Vol.Ⅲ, pp.297-309, 1958 https://doi.org/10.1137/1103024
  16. D.W. Carlton, J.M. Perloff, Modern Industrial Organization, Addison-Wesley, 2000
  17. D. Fudenberg and J. Tirole, Game Theory, The MIT Press , 1991
  18. A. Mas-Collel, M.D. Whinston, J.R. Green, Microeconomic Theory, Oxford, 1995