A Newton Method-Based Distributed Algorithm for Multi-Area Economic Dispatch

In this paper, we propose a novel Newton method-based distributed algorithm (NMDA), which is also effective in solving the general single-area EDP (SAEDP), to deal with the multi-area economic dispatch problem (MAEDP), of which the focus is to minimize the total generation cost in the presence of system and generator constraints. To develop the NMDA, we first introduce a virtual SAEDP formulation to fit the framework of Newton method (NM), and then employ the average consensus protocol to obtain the global information needed to execute the NM and backtracking line search algorithm in a distributed manner. Compared with the centralized methods that can yield the optimal solution, the proposed NMDA provides a suboptimal solution with a very small relative error. The NMDA ensures the instantaneous system power balance throughout the iteration process while the centralized methods compared in this paper cannot do so. We also provide a rigorous theoretical analysis for the convergence of NMDA. Moreover, the advantage of NMDA in terms of the convergence speed is validated by comparing with other distributed methods such as the gradient-based ADMM (G-ADMM) and quasi Newton-based primal dual interior point (QN-PDIP) method. Finally, case studies demonstrate the effectiveness and scalability of the proposed distributed algorithm.