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A revolutionary approach to modeling oligopolistic electricity markets is presented in this paper. Two different market models: the Cournot model and the supply function equilibrium (SFE) model are used for analysis. Different parametrization cases of the supply function are investigated and the results are compared with the Cournot-Nash equilibrium. An example based on the cost data from the actual electricity industry is used to validate the approach presented in this paper. Simulation results show that the revolutionary approach converges to the Nash equilibria rapidly in all cases and is highly efficient in market simulation. The approach shows great potentials for practical electricity market analysis.