The Transactions of The Korean Institute of Electrical Engineers (전기학회논문지)

The Korean Institute of Electrical Engineers (대한전기학회)
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Effect of Generation Capacity Constraints on a Mixed Strategy Nash Equilibrium in a Multi-Player Game

다자게임에서 발전력제약이 복합전략 내쉬균형에 미치는 영향

  • Published : 2008.01.01
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Abstract

Nash Equilibrium(NE) is essential to investigate a participant's bidding strategy in a competitive electricity market. Congestion on a transmission line makes it difficult to compute the NE due to causing a mixed strategy. In order to compute the NE of a multi-player game, some heuristics are proposed with concepts of a key player and power transfer distribution factor in other studies. However, generation capacity constraints are not considered and make it more difficult to compute the NE in the heuristics approach. This paper addresses an effect of generation capacity limits on the NE, and suggest a solution technique for the mixed strategy NE including generation capacity constraints as two heuristic rules. It is reported in this paper that a role of the key player who controls congestion in a NE can be transferred to other player depending on the generation capacity of the key player. The suggested heuristic rules are verified to compute the mixed strategy NE with a consideration of generation capacity constraints, and the effect of the generation constraints on the mixed strategy NE is analyzed in simulations of IEEE 30 bus systems.

Keywords

References

  1. Roy Gardner, Games for Business and Economics, John Wiley& Sons, Inc. 2003
  2. 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 https://doi.org/10.1109/TPWRS.2003.818692
  3. 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 https://doi.org/10.1109/TPWRS.2002.807067
  4. 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 https://doi.org/10.1109/TPWRS.2003.818744
  5. 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 https://doi.org/10.1109/TPWRS.2002.800899
  6. D. Fudenberg and J. Tirole, Game Theory. Cambridge, MA: MIT Press, 1991
  7. 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
  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 https://doi.org/10.1109/59.651644
  9. K.H. Lee "Solving mixed strategy equilibria of multi-player games with a transmission congestion," Transaction of KIEE, Vol. 55A, No.11, pp.492-497, Nov. 2006
  10. R. Baldick, "Electricity market equilibrium models: the effect of parametrization," IEEE Trans. Power Syst, Vol.17, No.4, pp.1170-1176, Nov. 2002 https://doi.org/10.1109/TPWRS.2002.804956
  11. (전기학회 심사중) "Supply Function Nash Equilibrium Considering Stochastic Demand Function," available at http://user.dankook.ac.kr/~gradelec/
  12. Paul D. Klemperer and Margaret A. Meyer, "Supply function equilibria in oligopoly under uncertainty," Econometrica, vol.57, no. 6, pp. 1243-1277, November 1989 https://doi.org/10.2307/1913707