Optimal Protection Coordination of Dual-Setting Relays With Inverse-Time and Definite-Time Characteristics

Optimal protection coordination (OPC) is a well-established problem with numerous solution methods, including mathematical optimization and genetic algorithms. Traditional OPC formulations for overcurrent relays typically optimize two parameters: the time dial setting (TDS) and the pickup current. However, modern relays offer additional curve characteristics, yet standard formulations do not fully utilize these additional settings. This paper introduces a novel OPC formulation for dual-setting relays that integrates inverse-time and definite-time curve characteristics. The optimization variables include TDS, pickup current, short-time delay (STD), and short-time pickup (STP) To ensure proper coordination, new constraints are developed for the interplay of these four settings per relay. The problem is formulated as a Mixed-Integer Nonlinear Programming (MINLP) task, solved using both a general-purpose MINLP solver and a Genetic Algorithm (GA). The approach is validated on the IEEE 123-bus network integrating inverter-based resources with limited fault current contributions under two switch configurations, which are selected to alter current flows and reassign backup roles among relays. Results demonstrate that incorporating dual-curve settings significantly reduces total relay operation time and improves discrimination times between primary and backup relays, compared to the standard OPC formulation.