Distributed Optimal Power Flow for Distribution System Using Second Order Cone Programming and Consensus Alternating Direction Method of Multipliers

In this paper, the distributed method for alternating current optimal power flow (AC OPF) based on second order cone programming (SOCP) and consensus alternating direction method of multipliers (ADMM) is proposed. Due to recent trend toward distributed energy resources in distribution systems, the AC OPF problem has become a difficult challenge to distribution market operators. The difficulties of the AC OPF problem are non-convex and long computational time. To secure the convexity, the SOCP is introduced when formulating the problem. The performance of the SOCP is verified by comparing with the direct current optimal power flow, which is a widely known method to secure convexity, in terms of the dispatch and cost of generation. To shorten the computational time, the consensus ADMM is introduced when solving the problem. The OPF problem is decomposed into sub-problems, which account for the power flow of a single bus. Then, the sub-problems are solved using the consensus ADMM, which consists of parallel computing and communication. Finally, the performance of the SOCP and consensus ADMM is verified by a three-bus radial test system. By using the SOCP, the AC OPF becomes a convex problem while maintaining its modeling rigorousness. By using the consensus ADMM, the OPF problem is solved in distributed manner while having the same result of the centralized method. Furthermore, the effect of the ADMM parameter on the convergence speed is verified.