To address the issue of system oscillation and instability caused by a lack of damping during deep voltage sag and fault recovery at the Point of Connection (POC) of an energy storage system in a weak grid, this paper studies the zero-voltage ride-through (ZVRT) of a 125 MW energy storage system at the POC. Using a quasi-static model, the instability mechanism during faults is analyzed, at once the impact of phase-locked loop (PLL) parameters on system equivalent damping. The paper proposes a fault ride-through strategy that freezes the phase-locked loop by zeroing the q-axis component and setting the phase-locked loop PI controller integral coefficient to zero with delayed recovery. The feasibility of this approach is verified through an electromagnetic transient simulation model built with Fortran and the PSCAD platform.