Optimal Coordination of Directional Overcurrent Relays Using an Innovative Fractional-Order Derivative War Algorithm

Efficient coordination of directional overcurrent relays (DOCRs) is vital for maintaining the stability and reliability of electrical power systems (EPSs). The task of optimizing DOCR coordination in complex power networks is modeled as an optimization problem. This study aims to enhance the performance of protection systems by minimizing the cumulative operating time of DOCRs. This is achieved by effectively synchronizing primary and backup relays while ensuring that coordination time intervals (CTIs) remain within predefined limits (0.2 to 0.5 s). A novel optimization strategy, the fractional-order derivative war optimizer (FODWO), is proposed to address this challenge. This innovative approach integrates the principles of fractional calculus (FC) into the conventional war optimization (WO) algorithm, significantly improving its optimization properties. The incorporation of fractional-order derivatives (FODs) enhances the algorithm’s ability to navigate complex optimization landscapes, avoiding local minima and achieving globally optimal solutions more efficiently. This leads to the reduced cumulative operating time of DOCRs and improved reliability of the protection system. The FODWO method was rigorously tested on standard EPSs, including IEEE three, eight, and fifteen bus systems, as well as on eleven benchmark optimization functions, encompassing unimodal and multimodal problems. The comparative analysis demonstrates that incorporating fractional-order derivatives (FODs) into the WO enhances its efficiency, enabling it to achieve globally optimal solutions and reduce the cumulative operating time of DOCRs by 3%, 6%, and 3% in the case of a three, eight, and fifteen bus system, respectively, compared to the traditional WO algorithm. To validate the effectiveness of FODWO, comprehensive statistical analyses were conducted, including box plots, quantile–quantile (QQ) plots, the empirical cumulative distribution function (ECDF), and minimal fitness evolution across simulations. These analyses confirm the robustness, reliability, and consistency of the FODWO approach. Comparative evaluations reveal that FODWO outperforms other state-of-the-art nature-inspired algorithms and traditional optimization methods, making it a highly effective tool for DOCR coordination in EPSs.