Sparsity-leveraging Reconfiguration of Smart Distribution Systems

A system reconfiguration problem is considered for three-phase power distribution networks featuring distributed generation. In lieu of binary line selection variables, the notion of group sparsity is advocated to re-formulate the nonconvex distribution system reconfiguration (DSR) problem into a convex one. Using the duality theory, it is shown that the line selection task boils down to a shrinkage and thresholding operation on the line currents. Further, numerical tests illustrate the ability of the proposed scheme to identify meshed, weakly-meshed, or even radial configurations by adjusting a sparsity-tuning parameter in the DSR cost. Constraints on the voltages are investigated, and incorporated in the novel DSR problem to effect voltage regulation.