In 2013, the University of Sheffield commissioned a 1 MWh lithium-titanate (LTO) battery energy storage system (BESS), directly connected to the grid through an 11 kV feed. With a view to later on develop a comprehensive model structure for the whole battery packkey to many online battery management system (BMS) operationsin this paper, an in-depth frequencydomain analysis is performed on one of the constituent 2.3 V 20 Ah LTO cells, using a potentiostatic sine-swept method. A first-order resistor-capacitor (RC) equivalent-circuit model is put forward, capable of representing the LTO cell's impedance magnitude with an error of less than 0.1 mΩ. Thereafter, the performance of the proposed one-RC model structure for online SOC estimation is experimentally verified using the Extended Kalman Filter (EKF). The verification test is performed on a dynamic pulsed-power profile, derived from a real grid frequency-support service that is offered by several BESSs in the UK.