Optimal AC distribution systems reconfiguration

Convex power flow relaxations have become popular to alleviate difficulties with embedding the non-convex AC power flow equations into optimisation models, and to provide guarantees on the quality of feasible solutions generated by heuristic approaches. However, their use has almost universally been limited to purely 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 flows 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, and to global optimal solutions in some cases. In terms of run time, the new models are competitive with state-of-the-art approximations which lack formal guarantees.