Type-2 Fuzzy C-Means-Based Clustering-Decomposed Coordination of Directional Overcurrent Relays

Optimal coordination of directional overcurrent relays (DOCRs) in medium-to-large power systems constitutes a computationally demanding, mixed-integer, nonlinear optimisation problem whose complexity escalates rapidly with system size, making the simultaneous minimisation of relay operating time and computational cost a critical open challenge. This study presents a two-level hierarchical framework in which Type-2 Fuzzy C-Means (T2FCM) clustering partitions 226 fault scenarios into subproblems at the upper level, while the Hybrid Fractional Entropy Evolution (HFEE) algorithm independently optimises relay settings for each cluster at the lower level. HFEE integrates fractional-order velocity updates—derived from the Grünwald–Letnikov formulation—with a Shannon entropy diversity-control mechanism to prevent premature convergence. T2FCM captures inherent fault-current uncertainty through interval-valued type-2 fuzzy memberships, yielding more robust cluster assignments near protection-zone boundaries than crisp partitioning methods. The framework is validated on the extended IEEE 30-bus system. An ablation study demonstrates that standalone HFEE achieves a 29.19% improvement in $T_{\mathrm{op}}$ over the prior best-reported result; however, a comprehensive parameter sweep over cluster counts $K\in \{2,\dots ,8\}$ and fractional orders $\alpha \in \{0.1,\dots ,0.9\}$ across 50 independent runs per configuration shows that the proposed clustering-decomposed method achieves 3.68–66.67% lower wall-clock computation time while maintaining zero CTI violations across all active relay pairs. The communicationless, entirely offline framework demonstrates scalability for simultaneous sub-transmission and distribution protection coordination and offers a practically deployable strategy for modern power networks.