Convergence Analysis of Demand Response in Smart Grids with Time Delays: A Networked Evolutionary Game Approach

Time delays can significantly affect the decision-making process of demand response in smart grids, bringing challenges to the convergence analysis of demand response scheduling. In this paper, the demand response in smart grids with time delays is investigated using Networked Evolutionary Game (NEG) theory. Firstly, a novel demand response model is established based on the NEG. The NEG-based demand response model presented in this paper effectively describes the dynamic characteristics of time delays in the strategic evolution of participants during demand response scheduling. With the help of semi-tensor product (STP), a necessary and sufficient condition is proposed for determining the convergence of the NEG-based demand response model. Then, an algorithm is proposed to calculate the game equilibrium set that corresponds to the stable energy prices. Finally, a numerical example is provided to illustrate the effectiveness of the results obtained.