**6. Conclusions and Future Work**

A convex reformulation of the voltage stability margin determination in DC networks with constant-power loads was proposed in this paper based on a second-order cone formulation. This model guarantees a global optimum for the problem by approximating the hyperbolic constraints related to the power flow problem. Numerical results, in comparison with those of the Newton–Raphson, SDP, and interior-point approaches, show the efficiency of the proposed SOCP formulation in terms of the objective function calculation and processing times required.

An analysis of voltage stability margin in DC grids enabled the determination of the maximum range of load increments before the collapse of the network. This is important because utilities can use these results for planning and grid reposition procedures (changes in the size of conductors, substations, grid topology) to avoid blackouts when new users are interconnected.

In future work, it will be possible to extend the convex SOCP formulation presented in this paper for optimal power flow analysis, i.e., economic dispatch, in DC networks considering daily operation with a high penetration of renewable energy resources and batteries.

**Author Contributions:** Conceptualization, O.D.M., W.G.-G., and A.M.-C.; methodology, O.D.M., W.G.-G., and A.M.-C.; formal analysis, O.D.M., W.G.-G., and A.M.-C.; investigation, O.D.M., W.G.-G., and A.M.-C.; resources, O.D.M., W.G.-G., and A.M.-C.; writing—original draft preparation, O.D.M., W.G.-G., and A.M.-C. All authors have read and agreed to the published version of the manuscript. These authors contributed equally to this work.

**Funding:** This work was partially supported by the National Scholarship Program Doctorates of the Administrative Department of Science, Technology, and Innovation of Colombia (COLCIENCIAS), by calling contest 727-2015.

**Acknowledgments:** The authors want to thank Vicerrectoria de Investigación, Innovación y Extensión from Universidad Tecnológica de Pereira for the support provided in this investigation.

**Conflicts of Interest:** The authors declare no conflicts of interest.
