Solving Mixed Strategy Equilibria of Multi-Player Games with a Transmission Congestion

다자게임 전력시장에서 송전선 혼잡시의 복합전략 내쉬균형 계산

  • Published : 2006.11.01

Abstract

Nash Equilibrium (NE) is essential to investigate a participant's bidding strategy in a competitive electricity market. The transmission line constraints make it difficult to compute the NE due to causing a mixed strategy NE instead of a pure strategy NE. Computing a mixed strategy is more complicated in a multi-player game. The competition among multi-participants is modeled by a two-level hierarchical optimization problem. A mathematical programming approach is widely used in finding this equilibrium. However, there are difficulties to solving a mixed strategy NE. This paper presents two propositions to add heuristics to the mathematical programming method. The propositions are based on empirical studies on mixed strategies in numerous sample systems. Based on the propositions a new formulation is provided with a set of linear and nonlinear equations, and an algorithm is suggested for using the prepositions and the newly-formulated equations.

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References

  1. H. Nui and R. Baldick, 'Supply function equilibrium bidding strategies with fixed forward contracts,' IEEE Power Syst., Vol.20, No.4, pp.1859-1867, Nov. 2005 https://doi.org/10.1109/TPWRS.2005.857272
  2. W. Xian, L. Yuzeng, and Z. Shaohua, 'Oligopolistic equilibrium analysis for electricity market: a nonlinear complementarity approach,' IEEE Trans. Power Syst., Vol.l9, No.3, pp.1348-1355, Aug. 2004 https://doi.org/10.1109/TPWRS.2004.831237
  3. Roy Gardner, Games for Business and Economics, John Wiley& Sons, Inc. 2003
  4. 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
  5. 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
  6. 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
  7. J.D. Weber and T.J. Overbye, 'An individual welfare maximization algorithm for electricity markets,' IEEE Power Syst., Vol.17, No.3, pp.590-596, Aug. 2002 https://doi.org/10.1109/TPWRS.2002.800899
  8. D. Fudenberg and J. Tirole, Game Theory. Cambridge, MA: MIT Press, 1991
  9. 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. 9, No.1, Feb. 2004 https://doi.org/10.1109/TPWRS.2003.820709
  10. 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
  11. R.W. Ferrero, S.M. Shahidehpour, and V.C. Ramexh, 'Transaction analysis in deregulated power systems using game theory,' IEEE Trans. Power Syst., Vol.12, No.3, pp.1340-1347, Aug. 1997 https://doi.org/10.1109/59.630479
  12. A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, New York: Wiley, 1996
  13. X. Cheng, T.J. Overbye, 'PTDF-based power system equivalents,' IEEE Trans. Power Syst., Vol. 20, No.4, Nov. 2005 https://doi.org/10.1109/TPWRS.2005.857013