A Distributed Convex Relaxation Approach to Solve the Power Flow Problem

Power flow is a fundamental problem for analyzing the power system. It is to solve a set of equations with quadratic terms. Procuring a reliable solution methodology for this problem is challenging as the feasibility region for this problem is nonconvex. Iterative approaches were employed to solve the problem, which may fail to provide a solution under certain circumstances such as bad initial point. In this paper, a solution methodology that is capable of providing a reliable solution to the power flow problem is presented. First, by exploiting sparsity in the power network, a convex relaxation for the problem is presented using the first order of the Lasserre hierarchy of moment relaxations. Then, a distributed approach using Jacobi-proximal alternating directions method of multipliers (JP-ADMM) is implemented to efficiently solve the power flow problem. To solve the sub-problems within JP-ADMM approach, the second order of the Lasserre hierarchy of moment relaxations is employed. To illustrate the effectiveness of the proposed approach, several case studies are presented.