Sequential quadratic programming models for solving the OPF problem in DC grids

•Two convex optimal power flow reformulations are proposed.•Sequential quadratic programming allows global convergence.•Radial and mesh dc grids with multiple generation nodes are included.•Nonlinear model does not guarantee reaching the optimal solution.•SQP proposed models are faster than the exact non-convex OPF model. 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.