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

• Published in: Operations research Vol. 56; no. 1; pp. 34 - 47
• Main Authors: Yao, Jian, Adler, Ilan, Oren, Shmuel S
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.01.2008; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Applied sciences; Cournot equilibrium; Economic aspects; Electric utilities; Electrical engineering. Electrical power engineering; Electrical power engineering; Electricity; electricity market; Equilibrium; Equilibrium (Economics); equilibrium problem with equilibrium constraints; Evaluation; Exact sciences and technology; Forward contracts; Game theory; linear complementarity problem; Market equilibrium; Market prices; Mathematical functions; mathematical program with equilibrium constraints; Modeling; Nash equilibrium; noncooperative games; Oligopolies; Oligopoly; Operational research and scientific management; Operational research. Management science; Power networks and lines; programming; Reorganization and restructuring; Spot market; Studies; Transmission lines; two settlements; Function generation; Pivoting method; Nash equilibrium; Iterative method; Equilibrium condition; Linear complementarity problem; Quadratic programming; equilibrium problem with equilibrium constraints; Modeling; Linear model; Demand(contract); Constrained optimization; noncooperative games: Cournot equilibrium; electricity market; two settlements; programming: mathematical program with equilibrium constraints; Uncertain system; Electrical network; Non cooperative game; Cost function; Demand function; Game equilibrium; Quadratic cost; Quadratic function; Oligopoly; Mathematical programming
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1070.0416

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.