Mixed-Integer Optimization for Volt/VAr Control in Radial Networks

Due to the increase in load demand and capacity of distributed generation, radial distribution systems are exposed to voltage violation problems. Volt/VAr control (VVC) has a primary objective of removing voltage violations, and a secondary objective of minimizing the real power loss. Volt/VAr control operates on capacitor switches, transformer taps, and the reactive power set-points of distributed generation. In this paper, the VVC problem is solved using mixed-integer conic programming to establish a globally optimal benchmark. To improve computational performance, a discrete coordinate-descent algorithm is employed, starting from a solution to the continuous relaxation of the VVC mixed-integer conic program. Numerical results are reported on radial distribution networks with up to 3146 nodes. The results reveal that the discrete coordinate-descent algorithm, when initialized by solving a continuous conic program, can give solutions that are very close to the global optimum; these solutions are obtained within a very reasonable computing time and are superior to initiating the search from the current operating point.