Reformulation for Nash-Cournot equilibrium in pool-based electricity market supported by introducing the potential function

Equilibrium analysis of electricity market is of great importance not only for market operator and regulator to investigate the market power and other relevant issues, but also vital for market participants to determine the bidding strategies to maximize their own profits. Among different equilibrium models, Cournot model is widely used due to its explicit economic meaning and relatively high computation efficiency. However, finding equilibrium point for Cournot model is essentially a bi-level optimization problem, which might become computation intractable and lack of robustness with the current solution approaches. Therefore, this paper proposes a new method to reformulate the Nash-Cournot model as a single-level optimization model by introducing the potential function. With the potential function, the first-order optimal conditions (KKTs) of the reformulated single-level problem could theoretically be proved to be identical with those of the original bi-level problem. Finally, the numerical results validate the effectiveness of this reformulation method and testify the computation efficiency as well as robustness of the proposed approach.