DOCR Coordination in DG-Integrated Networks: Characteristic-Curve Selection Using a Hybrid Fractional-Entropy Metaheuristic–LP

The inverse-time characteristic of each relay is a degree of freedom in the coordination of directional overcurrent relays (DOCRs) that most studies leave fixed at standard inverse, optimising only the time multiplier setting (TMS) and plug setting (PS). This paper examined how the IEC 60255-151 characteristic assignment affected the sum of primary operating times on one static DG-integrated benchmark, the 33 kV section of the IEEE 30-bus network with 38 DOCRs and 62 primary/backup pairs. Six assignment rules, including a deterministic rule that selects each relay’s characteristic from its plug-setting multiplier (PSM), were compared under a common optimisation framework, in which a fractional-order, entropy-guided particle swarm–gravitational search from the authors’ earlier work explored the plug settings and a monotone relaxation solved the TMS linear programming problem. All the rules achieved zero coordination violations, and two separate findings emerged. First, characteristic-family selection had a large effect: the objective fell from 29.42 s with uniform standard-inverse settings to 9.16 s with uniform extremely inverse (EI) settings, a reduction of 68.9%. Second, the PSM-driven rule gave a smaller additional improvement, reaching 8.94 s, about 2.4% below uniform EI and the lowest value among the six rules. The relaxation agreed with a general linear programming solver on all the tested candidates, and in a preliminary quantisation check the PSM-driven rule kept a 1.5–2.0% advantage over uniform EI at the same plug settings. The findings were limited to this objective, dataset and static network configuration; implementation on protection hardware was not assessed.