Simultaneous Maximization of Speed and Sensitivity in the Optimal Coordination of Directional Overcurrent Protections

This paper presents the simultaneous maximization of speed and sensitivity in the Optimal Coordination of Directional Over-Current Protections (OC-DOCP), considering that maximum selectivity is maintained in all solutions. Only these three desirable features of the protection system were considered in the multi-objective approach; thus, the problem can be simply formulated as the weighted sum of speed and sensitivity as goals to be maximized, and the Pareto frontiers correlating speed and sensitivity are easily found in this way. These Pareto frontiers had not been shown in the literature about this topic, and they properly show the compromise solutions for the optimal solutions (i.e., speed improvements imply sensitivity deterioration while sensitivity improvements imply speed degradation). The simplest OC-DOCP formulation, applied to a well-known sample system, is taken as an example to show the Pareto frontiers for different time–current curve types. Another OC-DOCP formulation, which considers different topologies and their probability of occurrence, is also solved and the corresponding Pareto frontiers are also shown. The main findings of this work are the following: (a) in general, the results show that the variation in the speed in the Pareto frontier is more notorious for the less inverse curve types, whose optimal solutions are slower; (b) in the case of extremely inverse curves, the optimal solutions are faster and the effect of changes in sensitivity on the protection speed is very low in the Pareto frontiers; (c) it is also herein shown that the knowledge of this topic is also useful to solve some possible cases of unfeasibility related to the upper bound of time dial settings.