A double-sided non-cooperative game in electricity market with demand response and parameterization of supply functions

•A double-sided non-cooperative game can obtain great peak shaving results.•The (slope, intercept)-parameterization method has multiple Nash equilibrium.•The actual characteristics of shiftable loads should be considered in demand-side.•A gradient-based distributed iterative method has great convergence performance. In a competitive electricity market, the market flexibility will be greatly improved with demand response, but the self-optimizing behavior of each market participant will have a great impact on the market effectiveness and stability. In this paper, we model the electricity market as a double-sided non-cooperative game with multiple electricity firms and customers, based on the supply function equilibrium model and the demand response resources scheduling model. In the supply-side, four parameterization methods of the supply function equilibrium model are studied with a rigorous mathematical proof of the existence and uniqueness of Nash equilibrium. In the demand-side, instead of simplifying demand as a function of price as the usual way, we consider fixed loads and shiftable loads characteristics and propose a detailed model to benefit each customer and guide the electricity use in reality. A distributed iterative approach is proposed to obtain the Nash equilibrium solution with great convergence performance. Based on real data, the simulation results show that the proposed model has good performance in peak shaving and improving social welfare. The effect of parameterization on firms’ profit, customers’ payoff, social welfare is analyzed qualitatively, so as to guide firms to choose the appropriate parameterization method according to their own goals.