Distributed DC Optimal Power Flow for radial networks through partial Primal Dual algorithm

In a smart grid platform, where more distributed resources are joining everyday and each of them wills to keep its own privacy and shares as less information as possible with the grid management, there is a motivation for transition from the current centralized structures to more distributed ones. In this paper, a distributed method is presented to solve DC Optimal Power Flow (DC-OPF) for radial networks based on partial Primal-Dual algorithm. The algorithm development process starts from an economic dispatch (ED) problem, derives a distributed ED, and finally makes a bridge from the distributed ED formulation to a distributed algorithm for DC-OPF. It is proved in the paper that the optimal solution of the distributed algorithm complies with the necessary and satisfactory KKT conditions of DC-OPF problem. The algorithm is tested on a radial power network with and without network congestion, where the results converge to the optimal solution.