Optimal coordination of directional overcurrent protections considering the occurrence probability of different configurations and the effect of grouping cases

This article shows the optimal coordination of directional overcurrent protections considering the occurrence probability of different system configurations and the effect of grouping cases. The optimization is formulated for specific subgroups of topologies to find the optimal Bundle of Protection Settings (BPS) for each subgroup. The number of BPS is limited by the available setting groups in the relays. The objective function is the average of main protection tripping times, taking the occurrence probability of each topology as weighting factor. A slowness index σ of each subgroup solution, regarding the optimal solution of a topology of reference, is computed. If σ is greater than a given threshold σ0, some topologies must be taken off the subgroup until obtaining σ less than σ0. Thus, the computed settings are optimal for that subset of configurations, without an inadmissible increment of delays for main protections. The most probable topology should be in the first subgroup, and the process is repeated for the next subgroups until covering the total number of topologies. Some topologies could remain out of the solved optimization problems if the number of available BPS is low, and the trade-off between selectivity and speed should be solved for them. Numerical results for an example are shown, as an efficient way to explain the analyzed problems and solutions.