Permutation-based optimization for the load restoration problem with improved time estimation of maneuvers

After the occurrence of faults in a radial distribution system, the load restoration problem consists in implementing a sequence of switch opening and closing operations such that the resulting network configuration restores services to the most loads in the shortest possible time. We formulate this optimization problem in terms of two complementary objectives, minimizing simultaneously the energy not supplied and the power not restored. The search space is encoded as a set of permutation vectors containing all maneuverable switches, and the decoding mechanism always guarantees feasibility and allows for multiple solutions per vector. In order to cope with the possibly large search space, an efficient reduction mechanism is proposed to decrease the number of allowed permutations. The resulting optimization problem is solved using Simulated Annealing followed by a local search refinement. The time taken to perform the maneuvers is estimated using a scheduling approach, which takes into account the existence of multiple dispatch teams and thus provides a more reliable computation than the usual approach of using the number of switch operations. The proposed method is validated using known optimal results in small problem instances, and is able to return significantly better results when compared against a Branch and Bound method with a pruning heuristic in a more complex scenario.