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Modeling and Computing Two-Settlement Oligopolistic Equilibrium in a Congested Electricity Network

Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720
jianyao{at}cal.berkeley.edu
adler{at}ieor.berkeley.edu
oren{at}ieor.berkeley.edu

A model of two-settlement electricity markets is introduced, which accounts for flow congestion, demand uncertainty, system contingencies, and market power. We formulate the subgame perfect Nash equilibrium for this model as an equilibrium problem with equilibrium constraints (EPEC), in which each firm solves a mathematical program with equilibrium constraints (MPEC). The model assumes linear demand functions, quadratic generation cost functions, and a lossless DC network, resulting in equilibrium constraints as a parametric linear complementarity problem (LCP). We introduce an iterative procedure for solving this EPEC through repeated application of an MPEC algorithm. This MPEC algorithm is based on solving quadratic programming subproblems and on parametric LCP pivoting. Numerical examples demonstrate the effectiveness of the MPEC and EPEC algorithms and the tractability of the model for realistic-size power systems.

Subject classifications: noncooperative games; Cournot equilibrium; electricity market; two settlements; programming; mathematical program with equilibrium constraints; equilibrium problem with equilibrium constraints; linear complementarity problem.
History: Received December 2005; revision received October 2006; accepted December 2006.