Fast Distributed Lagrange Dual Method Based on Accelerated Gradients for Economic Dispatch of Microgrids

Distributed optimization algorithms have long been criticized due to their slow convergence rates mostly caused by fixed step-sizes. In this paper, a fast distributed Lagrange dual method (FDLDM) has been proposed, where the Nesterov accelerated gradient is integrated and dynamic step-sizes are employed, which is the key to achieve the fast convergence rate of our method. However, the economic dispatch problem (EDP) of microgrids (MGs) is a thorny optimization problem because of a lot of distributed generators (DGs) in MGs. Fortunately, it can be modeled and solved by our method quickly and effectively. The results show that the convergence rate of our method is faster than that of the Distributed Lagrange dual method (DLDM), and the economic dispatch of an MG can be achieved, even if both loads and environmental conditions fluctuate significantly.