A Linearized Transmission Model Based Market Equilibrium In Locational Pricing Environments

  • Joung, Man-Ho (Dept. of Electrical Computer Engineering, University of Texas at Austin) ;
  • Kim, Jin-Ho (Dept. of Electrical Engineering, Kyungwon University)
  • Published : 2007.12.31


In this paper, we have investigated how transmission network constraints can be modeled in an electricity market equilibrium model. Under Cournot competition assumption, a game model is set up considering transmission line capacity constraints. Based on locational marginal pricing principle, market clearing is formulated as a total consumers# benefit maximization problem, and then converted to a conventional optimal power flow (OPF) formulation with a linearized transmission model. Using market clearing formulation, best response analysis is formulated and, finally, Nash equilibrium is formulated. In order for illustration, a numerical study for a four node system with two generating firms and two loads are presented.


Cournot competition;Deregulated electricity markets;Electricity market equilibrium model;Game theory;Nash equilibrium;Power system network constraints


  1. H. Song, C. C. Liu, J. Lawarree, and R. W. Dahlgren, 'Optimal electricity supply bidding by Markov decision process,' IEEE Trans. Power Systems, Vol. 15, No. 2, pp. 618-624, May 2000
  2. F. Wen and A. K. David, 'Optimal bidding strategies and modeling of imperfect information among competitive generators,' IEEE Trans. Power Systems, Vol. 16, No. 1, pp. 15-21, Feb. 2001
  3. J. B. Park, B. H. Kim, J. H. Kim, M. H. Joung, and J. K. Park, 'A continuous strategy game for power transaction analysis in competitive electricity markets,' IEEE Trans. Power Systems, Vol. 16, No. 4, pp. 847-855, Nov. 2001
  4. A. Rudkevich, M. Duckworth, and R. Rosen, 'Modeling electricity pricing in a deregulated generation industry,' Energy Journal, Vol. 19, No. 3, pp. 19-48, 1998
  5. R. Baldick, R. Grant, and E. Kahn, 'Linear supply function equilibrium,' UC Energy Institute POWER PaperPWP-078, August 2000
  6. M. Shahidehpour and M. Almoush, Restructured Electrical Power Systems, New York: Marcel Decker, 2001
  7. S. Borenstein and J. Bushnell, 'Market power in electricity markets: Beyond the concentration measure,' Energy J., Vol. 20, No. 4, pp. 65-88, 1999
  8. S. Borenstein and J. Bushnell, E. Kahn, and S. Stoft, 'Market power in California electricity markets,' Utility Policy, Vol. 5, No. 3-4, pp. 219-236, 1995
  9. Y. Liu and F. F. Wu, 'Impacts of network constraints on electricity market equilibrium,' IEEE Trans. Power Systems, Vol. 22, No. 1, pp. 126-135, Feb. 2007
  10. J. D. Weber and T. J. Overbye, 'A two-level optimization problem for analysis of market biding strategies,' Proc. IEEE Power Eng. Soc. Summer Meeting, Vol. 2, pp 682-687, 1999
  11. T. S. Peng and K. Tomsovic, 'Congestion influence on bidding strategies in an electricity market,' IEEE Trans. Power Systems, Vol. 18, No. 3, pp. 1054-1061, Aug. 2003