The Transactions of the Korean Institute of Electrical Engineers A (대한전기학회논문지:전력기술부문A)

The Korean Institute of Electrical Engineers (대한전기학회)
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Approach for Evaluating the Nash Equilibrium of Cournot Game Model for N-Gencos by Using Payoff Matrix in Wholesale Electricity Market

도매전력시장에서 N-발전사업자의 보수행렬을 이용한 꾸르노 모델의 내쉬균형점 도출을 위한 방법론

  • 박종배 (건국대학 공대 전기공학과) ;
  • 임정열 (건국대학 공대 전기공학과) ;
  • 이기송 (건국대학 공대 전기공학과) ;
  • 신중린 (건국대학 공대 전기공학과)
  • Published : 2005.02.01
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Abstract

This paper presents a method for evaluating the nash equilibrium of the Cournot model for N-Gencos in wholesale electricity market. In wholesale electricity market, the strategies of N-Gencos can be applied to the game model under the conditions, which the Gencos determine their strategies to maximize their benefit. Generally, the Lemke algorithm has known as the approach to evaluate the mixed nash equilibrium in the only two-player game model. In this paper, we have developed the necessary condition for obtaining the mixed nash equilibrium of N-player by using the Lemke algorithms. However, it is difficult to find the mixed nash equilibrium of two more players by using the analytic method since those have the nonlinear characteristics. To overcome the above problem, we have formulated the object function satisfied with the proposed necessary conditions for N-player nash equilibrium and applied the modified particle swarm optimization (PSO) method to obtain the equilibrium for N-player. To present the effectiveness the proposed necessary condition and the evaluation approach, this paper has shown the results of equilibrium of sample system and the cournot game model for 3-players.

Keywords

References

  1. 박만근, 김발호, 박종배, 정만호, '게임이론을 적용한 전력거래해석', 전기학회논문지A, 제49권, 제6호, pp.266-271, 2000.6.
  2. 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
  3. R. W. Ferrero, J. F. Rivera, and S. M. Shahidehpour, 'Application of Games with Incomplete Information for Pricing Electricity in Deregulated Power Pools', IEEE Trans. on Power Systems, Vol. 13, No. 1, pp. 184-189, Feb. 1998 https://doi.org/10.1109/59.651634
  4. J. B. Park, B. H. Kim, J. H. Kim, M. H. Jung, and J. K. Park, 'A Continuous Strategy Game for Power Transactions Analysis in Competitive Electrictiy Market', IEEE Trans. on Power Systems, Vol. 16, No. 4, pp. 847-855, Nov. 2001 https://doi.org/10.1109/59.962436
  5. J. H. Kim, J. B. Park, J. R. Shin, J. K. Park, 'Game Theory Based Quantity Constraint Analysis in the Uniform Price Auction', 12th Intelligent Systems Application to Power Systems Conference (ISAP 2003), Paper No. ISAP03-074, Greece Lemnos, August 31 - September 3, 2003
  6. L. B. Cunningham, R. Baldick, and M. L. Baughman, 'An Empirical Study of Applied Game Theory : Transmission Constrained Cournot Behavior,' IEEE Trans. on Power Systems, Vol_17 No_l, pp. 166-172, 2002 https://doi.org/10.1109/59.982209
  7. D. Chattopadhyay, 'Multicommodity Spatial Cournot Model for Generator Bidding Analysis', IEEE Trans. on Power Systems, Vol. 19, No. 1, Feb. 2004 https://doi.org/10.1109/TPWRS.2003.821436
  8. B. F. Hobbs, 'Linear Complementary Models of Nash-Cournot Competition in Bilateral and POOLCO Power Markets', IEEE Trans. on Power Systems, Vol. 16, No. 2, May, 2001 https://doi.org/10.1109/59.918286
  9. C.E LEMKE, J.T. HOWSON , 'Equilibrium Points of Bimatrix Games', J.SOC. INDUST. APPL. MATH, Vol_12 No_2, 413-423, 1964. 6. https://doi.org/10.1137/0112033
  10. K. W. Lee, and R. Baldick, 'Solving Three-Player Games by the Matrix Approach with Application to an Electric Power Market', IEEE Trans. on Power Systems, Vol. 18, No. 4, pp. 1573-1580, 2003 https://doi.org/10.1109/TPWRS.2003.818744
  11. J. Kennedy, and R. Eberhart, 'Particle swarm optimization,' Proceedings of IEEE International Conference on Neural Networks (ICNN' 95), Vol. IV, pp. 1942-1948, Perth, Australia, 1995
  12. J.B. Park, K..S. Lee, J.R. Shin, K.Y. Y, 'Economic Load Dispatch Based on a Hybrid Particle Swarm Optimization', 2003 IEEE Power Engineering Society General Meeting, Tronto, Ontario Canada, 13-17 July 2003, pp(Power NO.0-7803-7990-X/03) https://doi.org/10.1109/PES.2003.1270434