Performing accelerated convergence in decentralized economic dispatch over dynamic directed networks

Abstract

This article delves into the economic dispatch problem (EDP) within smart grids, specifically exploring it in time-varying directed networks. The objective is to allocate generation power efficiently among generators to fulfill load demands while minimizing the total generation cost, adhering to local capacity constraints. Each generator carries its unique local generation cost, and the total cost is calculated by summing these individual costs. To this aim, a novel algorithm (ADED-TVD) Accelerated Decentralized Economic Dispatch Algorithm is introduced, which is suitable for Time-Varying Directed networks well. ADED-TVD takes inspiration from the parameter momentum accelerated technique to improve the convergence with different parameters resulting in different momentum (Nesterov or heavy-ball) methods. In addition, ADED-TVD lies in time-varying directed communication networks, where theoretical evidence of linear convergence towards the optimal dispatch is offered. Also, explicit bounds for the step-size and momentum parameters are obtained. Finally, simulations that delve into various aspects of EDP in smart grids are presented.