A Gossip-Based Distributed Algorithm for Economic Dispatch in Smart Grids With Random Communication Link Failures

Motivated by the fact that gossip algorithms are asynchronous and suitable for the sensor networks with random link failures, a gossip-based distributed algorithm for the economic dispatch problem in smart grids is addressed in this paper. Random communication link failure phenomena is very common in a realistic communication network. By modeling a network as a Bernoulli network, the proposed algorithm can solve the economic dispatch problem in the imperfect communication network. Mean square consensus and almost sure consensus are adopted to analyze the convergence of the algorithm. Using matrix theory and perturbation theory, we prove that the algorithm can achieve mean square consensus and almost sure consensus. Therefore, the proposed algorithm converges to the optimal solution of the economic dispatch problem with probability 1. The convergence speed of the algorithm is discussed and simulation results show that the convergence rate is governed by the second largest eigenvalue of the system matrix. Case studies are designed to illustrate the effectiveness and plug-and-play capability of the algorithm.