Optimal Coordination of Directional Overcurrent Relays Using an Exponential-Based Non-Standard Characteristic and the Nutcracker Optimizer

Directional overcurrent relays (DOCRs) play a crucial role in protecting sub-transmission and distribution systems due to their simplicity and cost-effectiveness. For selective and rapid protection, proper coordination of these relays is essential. At this point, the coordination of DOCRs is formulated as an optimization problem. The primary objective of this problem is to minimize relay operating times without violating coordination constraints. However, considering the complex nature of power systems, solving this nonlinear problem with high-level constraints becomes challenging. Furthermore, achieving efficiency in such solutions using standard relay characteristics is also difficult under the presence of numerous coordination constraints. In this context, this study proposes the use of an exponential-based non-standard relay characteristic function for calculating relay operating times and employs the nutcracker optimizer, a recently developed metaheuristic optimization algorithm, for solving the problem. The performance of the proposed method is tested on the IEEE 9-bus and IEEE 15-bus test systems, which are widely used in this field. The results obtained with the proposed method are compared with those in the literature and show the effectiveness of the proposed approach. Especially, the results demonstrate that the exponential-based non-standard relay characteristic used in the proposed method achieves approximately a 67% reduction in relay operating times compared to the standard relay characteristic (normally inverse) for the IEEE 15-bus system.