Hybrid Methods in Solving Alternating-Current Optimal Power Flows

Optimisation problems in power systems employing alternating-current models of power flows have driven much recently interest in (convergent hierarchies of) convex relaxations for polynomial optimisation problems. Readily available second-order methods for solving the convex relaxations on real-world large-scale power systems often fail to perform even a single iteration within reasonable run-times. First-order methods have much lower per-iteration computational and memory requirements, but require many more iterations than second-order methods to converge within the same accuracy. We hence study means of switching from first-order methods for solving the convex relaxation to Newton method working on the original non-convex problem, which would allow for convergence under the same conditions as in solvers for the convex relaxation, but with an improved rate of convergence. We illustrate our approach on the alternating current power flows (ACPF) and alternating current optimal power flows (ACOPF).