Branch Optimal Power Flow Model for DC Networks with Radial Structure: A Conic Relaxation

Abstract Objective: This work involves a convex-based mathematical reformulation for the optimal power flow problem in DC networks. The objective of the proposed optimization model corresponds to the minimization of the power losses through all the network branches considering a convex conic model that warranties finding the global optimal. Methodology: This is split into three stages: The first stage presents the mathematical model of optimal power flow for DC networks and all its geometric features that make it non-convex; the second stage presents the convex reformulation from a second order conic relaxation; the third stage shows the main characteristics of the DC system under study; and the fourth stage presents the optimal solution of the power flow problem and its comparisons with some methods reported in the specialized literature. Results: The numerical validations demonstrate that the model of proposed convex optimal power flow obtains the same solution as the exact model of the problem with an efficiency of 100%, which is in contrast with the variability of the results that are presented by the metaheuristic techniques reported as comparison methodologies. Conclusions: The proposed second-order conic relaxation warrantied the convexity of the solution space and therefore, the finding of the optimal solution at each execution; besides of this, demonstrated that for optimal power flow problems in DC networks, the numerical performance is better than most of the comparative metaheuristic methods; and the provided solution by the proposed relaxation is equivalent to that provided by the exact model. Keywords: Direct current networks, second-order conic relaxation, non-linear programming model, convex optimization.