Quadratic programming-based semi-deterministic approach to find optimal settings for the directional overcurrent relays with user-defined characteristics

This paper proposes a novel approach to solving the optimal protection relay coordination problem (PCP) involving directional overcurrent relays (DOC) with adjustable tripping characteristics. The inherent non-convexity of the PCP intensifies the intricacies, necessitating the utilization of global optimization solvers. The quadratic programming (QP) formulation, recognized for its ability to yield optimal solutions, encounters challenges in its direct application without presuming certain variables. The proposed two-stage optimization technique, heuristic phase and QP phase, addresses this challenge. In the initial heuristic phase, the Moth Flame Optimization algorithm with an acceleration coefficient (MFO- \(\alpha \) $\alpha$ ) is employed for its rapid convergence, generating a subset of variables. The subsequent QP phase formulates the optimization problem with the remaining variables, solved using a global optimization solver. The integration of the robustness of heuristic optimization (MFO- \(\alpha \) $\alpha$ ) with the precision of QP proves efficient by yielding optimal solutions for the PCP with minimal operating times for primary and backup DOCs. Testing on standard 8-bus, 15-bus, and 42-bus systems demonstrates remarkable reductions in operating times compared to recent literature: up to 58.6% for the 8-bus system, 61.48% for the 15-bus system, and 69.42% for the 42-bus system.