In this paper we derive an efficient optimization approach to calculate optimal controls of electric transmission lines. These controls consist of time-dependent inflows and switches that temporarily disable single arcs or whole subgrids to reallocate the flow inside the system. The aim is then to find the best energy input in terms of boundary controls in combination with the optimal configuration of switches, where the dynamics is driven by a coupled system of hyperbolic differential equations. Our optimization approach is a two-step heuristic based on the idea of partial outer convexification. We examine the applicability of a discrete approximation lemma and introduce a third step to improve the quality of the heuristic. A comparison with a direct solver yields very promising results.
University of Mannheim, Department of Mathematics, 68131 Mannheim, Germany; Preprint November 2017