The dynamic electrochemical impedance spectroscopy (DEIS) of a three-electrode pouch type lithium-ion battery is measured using a series of sine wave perturbations super-imposed on pulse charge and discharge. The DEIS reveals noticeable differences between charge and discharge at frequencies corresponding to the charge transfer reaction. The charge transfer resistance during intercalation is generally found to be larger than that during deintercalation for the battery chemistry in this study. This result is mainly attributed to the decreased Li ion concentration in the electrolyte during intercalation. At low frequencies, an abnormal inductive behavior is also observed. Such abnormality is found to result from the violation of stationary condition, i.e. the state of the battery under pulse charge or discharge deviates significantly from its initial condition for the perturbation of low frequencies. To analytically define the stationary condition, we develop electrochemical models of a single active particle in both time and frequency domain, which describes the transport of lithium ions in both active particle and electrolyte phase and the interfacial charge transfer reactions at their interface. The lower frequency limit is a key parameter to ensure a quasistationary state during the DEIS measurement. An explicit formulation of the stationary condition predicts a positive correlation between the lower frequency limit and the DC pulse current.