Journal of Electrical Engineering and Technology

  • 제8권4호
  • /
  • Pages.675-685
  • /
  • 2013
  • /
  • 1975-0102(pISSN)
  • /
  • 2093-7423(eISSN)
대한전기학회 (The Korean Institute of Electrical Engineers)
권호 표지
DOI QR코드

DOI QR Code

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

  • Lee, Kwang-Ho (Department of Electrical Engineering, Dankook University)
  • 투고 : 2012.08.06
  • 심사 : 2013.02.14
  • 발행 : 2013.07.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  1. P. D. Klemperer and M. A. Meyer, "Supply function equilibria in oligopoly under uncertainty," Econometrica, Vol. 57, pp. 1243-1277, 1989. https://doi.org/10.2307/1913707
  2. 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. https://doi.org/10.1109/TPWRS.2005.857272
  3. 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. https://doi.org/10.1109/TPWRS.2004.831237
  4. 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. https://doi.org/10.1109/TPWRS.2004.835663
  5. 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.
  6. 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
  7. 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
  8. 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
  9. 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
  10. D. Fudenberg and J. Tirole, Game Theory. Cambridge, MA: MIT Press, 1991.
  11. 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. https://doi.org/10.1109/59.918286
  12. 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.
  13. 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. https://doi.org/10.1109/59.867153
  14. T.C. Price, "Using co-evolutionary programming to simulate strategic behavior in markets," J. Evol. Econ. Vol. 7, pp.219-254, 1997. https://doi.org/10.1007/s001910050042
  15. 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
  16. 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. https://doi.org/10.1109/59.630479
  17. C.E. Lemke and J.T. Howson, "Equilibrium points of bimatrix game," SIAM J. Appl. Math., Vol. 12, pp. 413-423, 1964. https://doi.org/10.1137/0112033
  18. 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. https://doi.org/10.1109/TPWRS.2003.820692
  19. 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. https://doi.org/10.1007/s10589-007-9145-6
  20. J. B. Krawczyk, Jacek and Zuccolo, NIRA-3: An improved MATLAB package for finding Nash Equilibriua in infinite games, in Working Paper, Dec. 2006.
  21. 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. https://doi.org/10.2307/2601042
  22. A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, New York: Wiley-Interscience, 1996.
  23. 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 https://doi.org/10.5370/JEET.2012.7.2.141
  24. Roy Gardner, Games for Business and Economics, John Wiley& Sons, Inc. 2003.

피인용 문헌

  1. Strategy Equilibrium in Stackelberg Model with Transmission Congestion in Electricity Market vol.9, pp.1, 2014, https://doi.org/10.5370/JEET.2014.9.1.090
  2. Modified penalty function method for optimal social welfare of electric power supply chain with transmission constraints vol.57, 2014, https://doi.org/10.1016/j.ijepes.2013.11.046