A coevolutionary approach to analyzing supply function equilibrium model

This paper presents a coevolutionary approach to analyzing supply function equilibrium (SFE) models of an oligopolistic electricity market. Both the affine supply function model and the piece-wise affine supply function model are considered. Different parametrization cases of the affine supply function model are analyzed. The piece-wise affine supply functions that have a large number of pieces are used to numerically estimate the equilibrium supply functions of any shapes. Simulation cases of the piece-wise affine supply function model with different peak loads, nonquadratic and nonconvex costs, and different demand elasticities are studied. An example based on the cost data from the real-world electricity industry is used to validate the approach presented in this paper. Simulation results show that the coevolutionary approach rapidly converges to SFE in the affine supply function model simulation and robustly converges to SFE in all cases of the piece-wise affine supply function model simulation. The approach is robust and flexible and has the potential to be used to solve the complicated equilibrium problems in real-world electricity markets.