An Accelerated Distributed Gradient-Based Algorithm for Constrained Optimization With Application to Economic Dispatch in a Large-Scale Power System

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 51; no. 4; pp. 2041 - 2053
• Main Authors: Guo, Fanghong, Li, Guoqi, Wen, Changyun, Wang, Lei, Meng, Ziyang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acceleration; Algorithms; Computational geometry; Constrained optimization; Constraints; Convergence; Convexity; Cost function; decentralized gradient; Distributed algorithms; economic dispatch (ED); Economics; Gradient methods; large-scale power system; Optimization; Power dispatch; Power systems; virtual agent
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2019.2936829

In this article, we consider a convex optimization problem which minimizes the sum of local agents' cost functions subject to certain local constraints. Besides, both the local cost function and local constraints are only known by the local agent itself. To solve this problem, a new accelerated distributed gradient-based algorithm is proposed, which is inspired by the "momentum" phenomena in nature and aims to accelerate the convergence speed of conventional distributed gradient algorithms. Sufficient conditions for the stepsizes and the acceleration gains are derived to ensure the convergence of the proposed algorithm. Furthermore, based on this proposed fast distributed algorithm, a new decentralized approach is proposed to solve economic dispatch problem, especially for a large-scale power system. Based on the idea of virtual agent, it is proved that this decentralized algorithm is equivalent to the original fast distributed gradient method. Several case studies implemented on IEEE 30-bus, IEEE 118-bus power systems, and a large-scale power system consisting of 1000 generators are conducted to validate the proposed method.