Low voltage reconfiguration: a comparison of metaheuristic and mathematical programming approaches

The distribution system reconfiguration problem, which involves optimizing the topology of a power distribution network by determining switch-states, is a challenging combinatorial optimization problem with a large, nonconvex search space. For low voltage (LV) distribution networks, a solid comparison of various alternative optimization methods is lacking in literature. This paper aims to address this gap by comparing two different reconfiguration methods: a metaheuristic optimization approach based on a genetic algorithm formulation, and a mathematical optimization approach based on a second order cone relaxation of the exact formulation. Additionally, the significance of exploiting the low meshedness in LV-networks, by decoupling the network into independently reconfigurable subnetworks, is highlighted. The comparative analysis is done for a real European LV network which decouples into 164 subnetworks of varying combinatorial size. In addition to this, two medium voltage (MV) networks are also included in the comparison. The results robustly show the computational advantage of the genetic algorithm approach over the relaxed second order cone approach for networks with large combinatorial sizes, though the relaxed approach has the advantage of providing a lower bound to the global optimum.