Mathematical Schemes to Linearize Operating Times of Overcurrent Relays by Sequentially Fixing Plug Settings and Time Multiplier Settings

Nowadays, many studies have been presented in the literature to solve various optimal relay coordination (ORC) problems. These highly constrained nonlinear nonconvex optimization problems are commonly solved using evolutionary algorithms (EAs). For online applications, where the processing speed is very crucial, some studies suggest using different types of linear programming (LP), including simplex and interior-point methods, while others suggest hybridizing both EAs and LPs. For these approaches, the ANSI/IEEE and IEC/BS standard models used to calculate the operating times of overcurrent relays (OCRs) are linearized by just fixing their plug settings (PS) and varying time multiplier settings (TMS). This study presents another way to linearize these models by doing the opposite where $TMS$ are fixed and $PS$ are varied for both standard models. These linearized models can be used to effectively tune the objective functions of ORC problems to achieve both performance criteria; the solution quality and the processing speed.