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In this paper, an aggregate game is adopted for the modeling and analysis of energy consumption control in smart grid. Since the electricity users' cost functions depend on the aggregate energy consumption, which is unknown to the end users, an average consensus protocol is employed to estimate it. By neighboring communication among the users about their estimations on the aggregate energy consumption, Nash seeking strategies are developed. Convergence properties are explored for the proposed Nash seeking strategies. For energy consumption game that may have multiple isolated Nash equilibria, a local convergence result is derived. The convergence is established by utilizing singular perturbation analysis and Lyapunov stability analysis. Energy consumption control for a network of heating, ventilation, and air conditioning systems is investigated. Based on the uniqueness of the Nash equilibrium, it is shown that the players' actions converge to a neighborhood of the unique Nash equilibrium nonlocally. More specially, if the unique Nash equilibrium is an inner Nash equilibrium, an exponential convergence result is obtained. Energy consumption game with stubborn players is studied. In this case, the actions of the rational players can be driven to a neighborhood of their best response strategies by using the proposed method. Numerical examples are presented to verify the effectiveness of the proposed methods.

Game Design and Analysis for Price-Based Demand Response: An Aggregate Game Approach