Weighted matrix based distributed optimization method for economic dispatch of microgrids via multi-step gradient descent

Abstract

Due to the slow convergence rates and reliance on global information, distributed optimization methods, such as alternating direction method of multipliers (ADMM) and distributed gradient descent method (DGDM), have been difficult to meet the needs of solutions for the large-scale distributed system. In this paper, a distributed multi-step gradient descent method (DMGDM) combined with the allocation of upper bounds of second derivatives, has been proposed to tackle the economic dispatch problem (EDP) of microgrid (MG). At first, the agent assigns the reciprocal of its own upper bound of the second derivative according to the product of out-degree and upper bounds of second derivatives from the neighbors, which is the key to our method. Further, the weight matrix is constructed through the negotiation among neighbors in a distributed manner. Additionally, the distributed weight matrix relaxes the convergence conditions of the proposed method so that momentum parameters can be tuned without the need for global information. Numerical examples show that the convergence rate of our method is faster than the ADMM and the DGDM. Finally, a bi-layer optimization model of the EDP of MG is built via Matlab/Simulink, and the results show that the proposed method can realize the optimal dispatch of controllable distributed generators (DGs) in the MG.