Integrated Curve and Setting Optimization for DOCRs in Microgrid Environments with a BRKGA-MILP Matheuristic

Guaranteeing the effective coordination of directional overcurrent relays (DOCRs) within microgrids (MGs) is a complex nonlinear problem due to bidirectional power flows, varying fault current levels, and the need for adaptive operation across multiple grid configurations. To address this challenge, this paper proposes a hybrid matheuristic approach combining a Biased Random-Key Genetic Algorithm (BRKGA) with Mixed-Integer Linear Programming (MILP). This formulation treats the selection of relay characteristic curves as a decision variable, allowing for simultaneous optimization of time multiplier settings (TMS), plug setting multipliers (PSM), and curve types. The BRKGA handles the global search, while the embedded MILP decoder performs exact optimization under fixed conditions. The proposed BRKGA–MILP method was tested on the IEC benchmark microgrid under multiple operating modes. Compared with conventional MILP-based coordination, it achieved up to 18.31% reduction in total relay operating times (11.81% on average) while maintaining proper coordination time intervals (CTI). Relative to previous heuristic and hybrid approaches, the method improved protection speed by up to 14.87%. These results indicate that the proposed framework effectively enhances coordination performance in adaptive microgrid protection, particularly under bidirectional power flows and varying fault current levels.