The installation of battery energy storage systems (BESSs) with various shapes and capacities is increasing due to the continuously rising demand for renewable energy. To prepare for potential accidents, a study was conducted to select the optimal location for installing an input BESS in terms of frequency stability when the index assumes the backup input of the BESS. This study builds on the premise that installing a BESS on a bus in an area where active power absorption and transmission are the most active can significantly contribute to increasing the frequency recovery of the power system. Based on this premise, the magnitude of the active power flow and the proportional characteristics of the phase difference between buses were mathematically confirmed. This study also calculated the effective power sensitivity index of a bus with 13 FR-ESSs installed in a domestic system and reviewed the frequency output by establishing a table for each failure scenario. The results indicated that the effect of frequency rise can be estimated at the level of tidal current calculation. Thus, the study suggested a direction for subsequent studies to improve the sensitivity index.