Three-phase distribution OPF in smart grids: Optimality versus computational burden

Existing Mixed Integer Non-linear Programming (MINLP) solution methods and commercially available solvers lack computational efficiency and robustness in solving three-phase Distribution Optimal Power Flow (DOPF) programs, given the large number of continuous and integer variables encountered in practical sized systems. A heuristic approach to solve this problem was proposed by the authors, in which a compromise is made on optimality in order to reduce the computational burden. In the present work, a Genetic Algorithm (GA) based method is applied to determine the optimal solution to the three-phase DOPF problem, and is compared with the heuristic solution in terms of both optimality and computational burden. Two distribution feeders, namely, the IEEE 13-node feeder and a practical feeder from Hydro One are used for these comparisons. The results show that the GA-based method yields superior solutions in terms of optimality but at a rather large computational cost, making it unsuitable for practical implementation. The heuristic method is shown to yield solutions reasonably close to the global optima at a significantly reduced computational burden, demonstrating that the heuristic solution method has the potential to improve distribution system operation in practical real-time applications.