User Equilibrium Analysis of Aggregative Game in Demand Response

Demand response (DR) enables numerous small-scale users, as independent decision-makers, to minimize their costs while representing the real-time electricity consumption as an aggregative game. Consequently, the optimal power system operation would be determined by the equilibrium of small users. This paper leverages the user equilibrium (UE) concept based on the real-time electricity price to analyze the DR game for determining the grid load profile. First, the UE condition is introduced based on the aggregative DR game formulation, where no user can profit more by adjusting its consumption. Second, the UE state is proven to be the optimal solution of a convex programming problem, where an efficient solution is provided by the branch and price method. Finally, the properties and potential UE applications are discussed and illustrated by several numerical examples. Compared with the conventional Nash Equilibrium (NE) method, the proposed UE method can model flexible loads in terms of their types, where the proposed solution offers an advantage in terms of its fast computation and shows great potentials in large-scale DR analysis.