Push-Based Distributed Economic Dispatch in Smart Grids Over Time-Varying Unbalanced Directed Graphs

Abstract

This paper is dedicated to solving the economic dispatch problem in smart grids, which aims at minimizing the total generation cost while satisfying the power supply-demand balance and generation capacity constraints. A distributed algorithm is proposed to solve the economic dispatch problem over directed communication topologies that are time-varying unbalanced. Its features are that the proposed algorithm is push-based, and the model of line losses is integrated into the problem of our interest to reduce the power losses. Resorting to geometric graph theory and convex analysis, it is proved that the incremental costs achieve consensus at a convergence rate O(1 / √t ) with t being the number of iterations. Furthermore, robustness of the proposed algorithm is investigated solving the EDP when the communication information undergoes arbitrary large but bounded constant delays and the local gradients involve observation noises with zero-mean and bounded variance. Finally, three case studies implemented on an islanded microgrid, the IEEE 30-bus system and the IEEE 118-bus system are tested to demonstrate the effectiveness of the proposed algorithm.