Coordination of directional over-current relays in active distribution networks using generalised benders decomposition

Coordination of directional over-current relays (DOCRs) as the primary protection of meshed distribution networks is formulated as a mixed-integer non-linear programming (MINLP) problem. The coordination of DOCRs has been mainly accomplished using heuristic methods. Therefore, this study aims at proposing an efficient analytical tool for this problem. A two-stage analytical approach based on the generalised Benders decomposition is proposed to find the time and current settings of DOCRs with minimum operating time, while satisfying coordination constraints. The standard curves and the discrete current settings of DOCRs are determined in the first stage using a relaxed MINLP master problem. The obtained settings are then passed to the second stage to determine the time dial settings. In this stage, two linear sub-problems are solved to check feasibility and optimality of the solution. In each sub-problem another linear optimisation problem is developed to construct new constraints that are then backed to the first stage to remove the infeasibility and reduce the optimality gap, respectively. The iterative process continues till all the infeasibilities are removed and the optimality gap decreases below a given threshold. The obtained results on test cases are compared with two well-known MINLP solvers and some previous approaches.