Fast distributed gradient descent method for economic dispatch of microgrids via upper bounds of second derivatives

Abstract

Distributed optimization algorithms, such as alternating direction method of multipliers (ADMM) and distributed gradient descent method (DGDM), can no longer meet the needs of the application in the large system due to their slow convergence rates. In this paper, based on the upper bounds of second derivatives, a fast distributed gradient descent method (FDGDM) has been proposed, where the upper bounds of second derivatives and out-degree information are exchanged among the neighbors, and the weight matrix used for iteration is completely distributedly formed. Especially, the objective function keeps declining monotonically during the iterative process, which is the key to accelerating the convergence rate of our method while maintaining the constraints. Numerical experiments are designed to verify the faster convergence rate of the FDGDM compared with the ADMM. Finally, a microgrid (MG) simulation platform based on Matlab/Simulink is established, and our method is applied to solve the economic dispatch problem (EDP) of MG. The results demonstrate that the proposed method can achieve the optimal economic dispatch while ensuring the operation stability.

Keywords

• Microgrid
• Economic dispatch problem
• Upper bounds of second derivatives
• Fast distributed gradient descent method