Topology-Driven Global Optimization of Directional Overcurrent Relay Settings in ADNs via Graph-Theoretic Coordination-Pair Generation and MINLP

The integration of distributed energy resources transforms passive radial distribution networks into active systems characterized by bidirectional fault currents and dynamic topologies, significantly complicating directional overcurrent relay coordination. While existing adaptive optimization methods improve efficiency, they frequently rely on manually predefined primary-backup pairs and scenario-dependent modeling. Consequently, scalability, reproducibility, and topology consistency remain limited under varying network conditions. To address these limitations, this paper proposes a topology-driven, reproducible coordination workflow tailored to directional overcurrent relays (DOCRs). Specifically, graph theory is used to model network topologies and switch states, thereby automatically generating topology-consistent primary-backup constraints. A unified mixed-integer nonlinear programming (MINLP) model is constructed to evaluate coordination time intervals and jointly optimize discrete directional overcurrent relay variables, including time dial settings and time-current characteristic curve indices. A genetic algorithm (GA) global search framework is then employed to derive engineering-feasible settings. Furthermore, the method exports standardized setting tables and statistical indicators for operating times and coordination margins, significantly improving traceability and comparability. Validation on the IEEE 123-node test feeder demonstrates the method's ability to automatically construct valid coordination constraints, eliminate reliance on manual modeling, and ensure strict coordination correctness alongside competitive operating speeds. Under a common 100-generation comparison budget, the GA improved the mean objective value by approximately 14%, 9%, and 5% relative to particle swarm optimization (PSO), differential evolution (DE), and grey wolf optimizer (GWO), respectively, while maintaining a 100% feasibility rate; coefficient sensitivity checks supported the selected penalty weights. Ultimately, this approach enhances the automation, reproducibility, and practical applicability of relay protection optimization in modern distribution networks.