A Novel Distributed Optimization Algorithm With Linear Convergence for Economic Dispatch Under Compressed Communication

Abstract

This article addresses the distributed economic dispatch (ED) issue of microgrids. The primary objective of this study is to derive a distributed optimization algorithm with a compressed communication scheme over directed networks. Specifically, the algorithm aims to solve the ED problem, where the total power generation of distributed energy resources (DERs) is dispatched to meet the overall demand at the minimum operational cost under DER capacity constraints. To improve communication efficiency, a novel data compressed transmission mechanism is introduced into the consensus-based distributed algorithm by constructing estimator-like equations. Furthermore, by resorting to the property of matrix norms and system theory, a sufficient condition is derived to ensure that the proposed algorithm linearly converge to the optimal solution under arbitrary compression rate. This condition explicitly depends on the communication topologies and the algorithm parameters but is independent of the compression rate. Finally, simulated examples are provided to validate the theoretical claims and demonstrate the performance of the proposed algorithm.