Abstract
This study proposes an optimal coordination scheme for overcurrent relays (OCRs) with inverse-time characteristics. The primary objective is to minimize the total operating time of primary and backup relays while optimizing key parameters, including the Time Dial Setting (TDS) and Pick-up Current, subject to relay setting limits, operating time constraints, and the Coordination Time Interval (CTI). The proposed firefly optimization - based coordination strategy is tested on the IEEE 30-bus system and further validated using data from the Kampala North 33 kV Substation, Uganda, to assess its practical applicability. Pre-fault loading conditions were determined to identify heavily loaded lines, which were subsequently monitored for potential overloads. Results from the IEEE 30-bus system show that the optimized relays achieved an average 27% reduction in pickup currents, highlighting the improved coordination efficiency and selective responsiveness of the proposed FOA-based optimization approach. At Kampala North, the network employs two protection schemes; overcurrent and zonal protection, divided into three zones to enhance fault detection and isolation. Various fault scenarios were simulated to analyze phase current responses. Under fault conditions, significant current surges were observed, particularly for single-line-to-ground (SLG), line-to-line, and double-line-to-ground faults. For instance, on the Kawala feeder, where the pre-fault current was 182 A, an SLG fault on Phase A resulted in a peak current of 850 A, while Phases B and C rose to 520 A and 500 A, respectively. These findings emphasize the necessity of accurate relay coordination and proper protection settings, including backup overcurrent, earth fault, and instantaneous protection, to ensure rapid fault clearance, minimize equipment damage, and maintain overall system stability.

Key words: Coordination Time Interval, Firefly Optimization, Inverse Operating Time, Overcurrent Relays, Pick-up Current, Time Dial Settings.