A Distributed Consensus-Based Algorithm for Optimal Power Flow in DC Distribution Grids

The optimal power flow problem over direct current (DC) grids is to minimize the cost of active power generation considering all power flow equations, the maximum capacitance of the lines, and voltage limited boundaries of all the buses. It is one of the famous non-convex problems in the power system area. In this paper, a new distributed consensus-based algorithm is proposed for solving optimal power flow for DC distribution systems. As this algorithm is based on semi-definite relaxation (SDR), a mathematical proof is provided to show the exactness of the SDR relaxation technique. Then, it is demonstrated that the proposed distributed method converges to the global optimal point while satisfying all system constraints. A detailed analysis of the proposed algorithm is provided by applying it to a modified version of the IEEE-30 bus system. Finally, this method is applied to different DC power flow case studies, such as 14, 30, 57, 118, 200-bus systems, to provide a strong performance assessment. The simulation results, when compared with the benchmark, are quite promising.