An earlier study focused on the stochastic features of PD in terms of phase or time-resolved statistics and the mechanisms underlying the various phases of PD including inception, propagation and extinction in the movement of the low-frequency charge along the polymer, which exists during and after PD. This subsequent effect can account for in part the abnormal space charge accumulation, dielectric loss and electric field distortion. This paper presents a first attempt to observe the slow current flow induced by PD and describes its dynamics along different polymer films under AC electric field. We designed a measurement system to acquire the slow current component by cancelling the displacement current, intrinsic conduction current and the transferred PD current from the total current flow. It is shown that the PD-transferred charge is independent on the polymer material while the PD-induced slow current is the opposite and presents a stepped variation with applied electric field. To understand the findings, the trap depth, trap density and carrier mobility of each polymer film were measured, and the surface current is not measured through the grounded guard electrode. The bulk slow current is found to be closely related to the trap parameters and mobility of the dielectric. A preliminary model considering space charge and driven by electric field is proposed which may facilitate the understanding and analysis of the complicated charges dynamics during PD at AC electric field. The relationship between the heat by slow current and the degradation of dielectric is discussed.