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

TLDR

The study introduces a two‑settlement electricity market model that incorporates flow congestion, demand uncertainty, system contingencies, and market power. The authors formulate the subgame‑perfect Nash equilibrium as an equilibrium‑with‑constraints problem, where each firm solves a mathematical‑program‑with‑equilibrium‑constraints model under linear demand, quadratic generation costs, and a lossless DC network, and they solve it iteratively using a quadratic‑program‑based MPEC algorithm with parametric LCP pivoting. Numerical experiments show that the proposed MPEC and EPEC algorithms are effective and that the model remains tractable for realistic‑size power systems.

Abstract

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.