Modeling and computing two-settlement oligopolistic equilibrium in a congested electricity network

A model of two-settlement electricity markets is introduced, which accounts for flow con-gestion, demand uncertainty, system contingencies and market power. We formulate the sub-game perfect Nash equilibrium for this model as an equilibrium problem with equilibrium con-straints (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 complementar-ity 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 pro-gramming sub-problems 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.