Distributed optimization algorithms for game of power generation in smart grid

In this paper, we consider a problem of finding optimal power generation levels for electricity users in Smart Grid (SG) with the purpose of maximizing each user’s benefit selfishly. As the starting point, we first develop a generalized model based on the framework of IEEE 118 bus system, then we formulate the problem as an aggregative game, where its Nash Equilibrium (NE) is considered as the collection of optimal levels of generated powers. This paper proposes three distributed optimization strategies in forms of singularly perturbed systems to tackle the problem under limited control authority concern, with rigorous analyses provided by game theory, graph theory, control theory, and convex optimization. Our analysis shows that without constraints in power generation, the first strategy provably exponentially converges to the NE from any initializations. Moreover, under the constraint consideration, we achieve locally exponential convergence result via the other proposed algorithms, one of them is more generalized. Numerical simulations in the IEEE 118 bus system are carried out to verify the correctness of the proposed algorithms.