Distributed optimal power flow of DC microgrids: A penalty based ADMM approach

The popularity of direct current (DC) networks have made their optimal power flow (OPF) problem a hot topic. With the proliferation of distributed generation, the many problems of centralized optimization methods, such as single point failure and slow response speed, have led to utilization of measures such as distributed OPF methods. The OPF problem is non-convex, which makes it difficult to obtain an optimal solution. The second-order cone programming (SOCP) relaxation method is widely utilized to make the OPF problem convex. It is difficult to guarantee its exactness, especially when line constraints are considered. This paper proposes a penalty based ADMM approach using difference-of-convex programming (DCP) to solve the non-convex OPF problem in a distributed manner. The algorithm is composed of distributed x iteration, z iteration and λ, μ iteration. Specifically, in the distributed z iteration, the active power flow injection equation of each line is formulated as a difference of two convex functions, and then the SOCP relaxation is given in a different form. If the SOCP relaxation is inexact, a penalty item is added to drive the solution to be feasible. Then, an optimal solution can be obtained using a local nonlinear programming method. Finally, simulations on a 14-bus system and the IEEE 123-bus system validate the effectiveness of the proposed approach.