Feeder Reconfiguration in Distribution Networks Based on Convex Relaxation of OPF

The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed-integer nonlinear program and, hence, hard to solve. In this paper, we propose a heuristic algorithm that is based on the recently developed convex relaxation of the ac optimal power flow problem. The algorithm is computationally efficient and scales linearly with the number of redundant lines. It requires neither parameter tuning nor initialization for different networks. It successfully computes an optimal configuration on all four networks we have tested. Moreover, we have proved that the algorithm solves the feeder reconfiguration problem optimally under certain conditions for the case where only a single redundant line needs to be opened. We also propose a more computationally efficient algorithm and show that it incurs a loss in optimality of less than 3% on the four test networks.