Oligopolistic equilibrium analysis for electricity markets: a nonlinear complementarity approach

Oligopolistic equilibrium models are widely used in electricity market analysis, among which the supply function equilibrium model has been chosen as the basis of many power market models. A nonlinear complementarity approach has been proposed in this paper to calculate the Nash supply function equilibrium for a bid-based-pool generation market with a dc transmission model. A mixed nonlinear complementarity problem (NCP) is presented by combining the Karush-Kuhn-Tucker conditions of all strategic generating firms. Using a special nonlinear complementarity function, the mixed NCP is reformulated as a set of nonlinear algebraic equations and thus can be solved by an inexact Levenberg-Marquardt algorithm. Numerical examples are presented to verify the effectiveness of the proposed method. The results show that the generating firms could exercise their market power by over-production under congestion, or by capacity withholding in case of power shortage. The approach developed in this paper provides an efficient way to the solution of large-scale, complicated equilibrium models for electricity markets.