This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Hobbs, B. F. Articles by Pang, J. S. Search for Related Content

Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints

Department of Geography and Environmental Engineering, The Johns Hopkins University, Baltimore, Maryland 21218-2682
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180-3590
bhobbs{at}jhu.edu
pangj{at}rpi.edu

Most previous Nash-Cournot models of competition among electricity generators have assumed smooth demand (price) functions, facilitating computation and proofs of existence and uniqueness. However, nonsmooth demand functions are an important feature of real power markets due, for example, to price caps and generator recognition of transmission constraints that limit exports. A more general model of Nash-Cournot competition on networks is proposed that accounts for these features by including (1) concave piecewise-linear demand curves and (2) joint constraints that include variables from other generating companies within the profit maximization problems for individual generators. The piecewise demand curves imply, in general, a nonmonotone multivalued variational inequality problem. Thus, for instance, imposition of a price cap can destroy the uniqueness properties found in previous models, so that distinct solutions can yield different sets of profits for market participants. The joint constraints turn the equilibrium problem into a quasi-variational inequality, which also can yield multiple solutions. The formulation poses computational challenges that can cause Lemke’s algorithm to fail; a restricted formulation is proposed that can be solved by that algorithm.

Subject classifications: games/group decisions; noncooperative; industries; electric; mathematics; piecewise linear; programming; complementarity.
History: Received September 2004; revision received June 2005; accepted January 2006.