Optimal distribution systems reconfiguration for radial and meshed grids

In recent years, convex relaxations of the AC power flow equations have gained popularity. Their success is mainly due to the optimality guarantees they can provide. However, their use has mostly been limited to continuous problems. This paper extends the reach of relaxations to reconfiguration problems with binary decision variables, such as minimal power loss, load balancing and power supply restoration. This is achieved by extending the relaxations of AC power flow equations to bear on the on/off nature of constraints featured in reconfiguration problems. This leads to an approach producing AC feasible solutions with provable optimality gaps, on both radial and meshed grids. In terms of run time, the new models are competitive with state-of-the-art approximations which lack formal guarantees.