A Distributed Randomized Gradient-Free Algorithm for the Non-Convex Economic Dispatch Problem

Abstract

Abstract:In this paper, a distributed randomized gradient-free algorithm (DRGF) is employed to solve the complex non-convex economic dispatch problem whose non-convex constraints include valve-point loading effects, prohibited operating zones, and multiple fuel options. The DRGF uses the Gauss approximation, smoothing parameters, and a random sequence to construct distributed randomized gradient-free oracles. By employing a consensus procedure, generation units can gather local information through local communication links and then process the economic dispatch data in a distributed iteration format. Based on the principle of projection optimization, a projection operator is adopted in the DRGF to deal with the discontinuous solution space. The effectiveness of the proposed approach in addressing the non-convex economic dispatch problem is demonstrated by simulations implemented on three standard test systems.

Recent progress on the study of distributed economic dispatch in smart grid: an overview

“…For the valve-point loading effects, the cost functions of generators are usually approximated by adding the sine function after the quadratic function (Binetti et al, 2014a;Xie et al, 2018;Li FY et al, 2019). Some more distributed ED algorithms under various operational constraints, like ramp rate limits, prohibited operating zones, and valve-point loading effects, have been designed (Binetti et al, 2014a;Xu et al, 2015;Xie et al, 2018;Zhou et al, 2018;Li FY et al, 2019). Binetti et al (2014a) designed a distributed algorithm based on auction technology and the consensus algorithm to solve non-convex EDP in the SG, including valve-point loading effects, multi-fuel selection, prohibited operating zones, and other constraints.…”

“…Zhou et al (2018) reported a distributed consensus-based EDP with ramp rate limits. Xie et al (2018) proposed a distributed stochastic gradient-free method to solve non-convex EDP with practical operational constraints. Considering the valve-point loading effects, Li FY et al (2019) studied EDP on strongly connected digraphs using the distributed pattern search algorithm.…”