In this paper, we address the optimal power flow problem in dc grids (OPF-DC). Our approach is based on sequential quadratic programming which solves the problem associated with non-convexity of the model. We propose two different linearizations and compare them to a non-linear algorithm. The first model is a Newton-based linearization which takes the Jacobian of the power flow as a linearization for the optimization stage, and the second model uses the nodal currents as auxiliary variables to linearize over the inequality constraints. Simulation results in radial and meshed grids demonstrate the efficiency of the proposed methodology and allow finding the same solution given by the exact nonlinear representation of the OPF-DC problem. © 2018 Elsevier B.V.