Objective:

This work involves a convex-based mathematical reformulation of the optimal power flow problem in DC networks. The objective of the proposed optimization model corresponds to the minimization of the power losses throughout all the network branches considering a convex conic model that ensures finding the global optimum solution.

Methodology:

This work is split into three stages. The first stage presents the mathematical model of optimal power flow for DC networks and all the 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, as well as 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 proposed convex optimal power flow model 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 ensured the convexity of the solution space and, therefore, the finding of the optimal solution at each execution, in addition to demonstrating that, for optimal power flow problems in DC networks, the numerical performance is better than most of the comparative metaheuristic methods and that the solution provided by the proposed relaxation is equivalent to that provided by the exact model.