Distributed Event-Triggered Communication Scheme for Economic Dispatch Problem in Power System With Uncoordinated Step-Sizes

Inspired by the distributed economic dispatch problem (EDP) in power system, this paper considers a problem of optimizing a sum of m local convex cost functions on an undirected network of m agents. Each agent in the network privately knows its own local convex objective function and is subjected to both coupling linear constraint and individual box constraints. To be able to reduce the requirements for information exchange among agents, we propose a novel fully event-triggered based distributed primal-dual algorithm for the convex optimization problem. Our algorithm allows the use of uncoordinated step-sizes and assumes that each agent communicates with its neighboring agents (the corresponding variables are updated) only at some independent event-triggered sampling time instants. Under some relatively standard assumptions (strong convexity and smoothness) on the objective functions, our theoretical analysis proves that the proposed algorithm can linearly seek the exact optimal solution when the upper bound of the uncoordinated step-sizes is smaller than a certain constant. We also conduct a clear estimate of the rate. Finally, a simple numerical example on distributed economic dispatch problem in power system is provided to illustrate the effectiveness of our event-triggered based optimization algorithm and validate the correctness of the analysis process.