Distributed control for economic dispatch via saddle point dynamics and consensus algorithms

Abstract

In this paper, a fully distributed algorithm is proposed to solve the economic dispatch problem. Without a central control unit, the generators work collaboratively such that the total generation cost is minimized under the balance and capacity constraints. The proposed approach is based on consensus protocols and the saddle point dynamics. The consensus protocols are employed to estimate the global information in a distributed fashion, and the saddle point dynamics is leveraged to search for the optimal solution of the economic dispatch problem. When the capacity limits of the generators are not considered, exponential stability of the optimal solution is proved through Lyapunov stability analysis. With the capacity limits considered, practical stability of the optimal solution is proved by singular perturbation analysis. By the proposed method, no global information is needed, the initial condition of the variables is mild, and no private information is required to be communicated.