Solving three-phase distribution OPF with nonlinear programming

Three-phase optimal power flow (OPF) is a foundational mathematical optimization problem for power advanced distribution network management. In this work we study the application of nonlinear programming algorithms to a variety of state-of-the-art mathematical optimisation models for distribution OPF with 3 × 3 impedances on a library of 128 LV networks. We study numerical performance in terms of wall clock time as well as robustness. Specifically, we study a variety of voltage angle constraints, bounds and initialisation strategies that influence the performance significantly. Contrary to what has been observed for transmission networks, the power-voltage (polar) formulation is not necessarily the best formulation, and current-voltage is generally very competitive. We observe that power bases for per unit conversion need to be chosen small enough ( ≤ 1000 kW) to avoid inaccuracies. Numerical studies are performed for a set of 128 LV networks, using Ipopt and KNITRO.