Distributed economic dispatch via a predictive scheme: Heterogeneous delays and privacy preservation

Abstract This paper studies distributed economic dispatch problems for smart grids, in which a quadratic generation cost is to be minimized over a feasible set that is determined jointly by an equality constraint and a box constraint. Our primary objective is to seek a distributed design that can handle heterogeneous time-delays, while preserving agents’ privacy—a fundamental prerequisite that has become gradually important for cyber–physical systems. For this purpose, we design a state predictor for each agent to compensate for the effect of heterogeneous time-delays, which allows the agents to predict the missing states between two consecutive update times. Based upon the predictor, we present a distributed gradient-descent algorithm to locally update the outputs of the generators, which guarantees that the optimal solution is attained in an asymptotic manner. Among other things, we incorporate a privacy preservation scheme to the proposed algorithm in order to preserve agents’ privacy and delicately characterize its convergence, differential privacy properties, as well as accuracy.