The precise control of output power by grid-connected converters relies on the correct identification and tracking of a grid voltage’s phase at the converter terminal. During severe grid faults, large disturbances cause the converter’s operating point to move away from the stable equilibrium point during normal operation. This leads to oscillations of both the active and reactive power fed into the grid. Using large-signal modelling, this study investigated the converter’s dynamic processes during and after such fault situations. The investigation considered the influence of the converter’s phase-locked loop (PLL), responsible for phase tracking, as well as that of the DC link on the converter-grid system, which has a major influence on the active power exchange with the grid. On this basis, this study also focused on the reactive current reference’s influence during and after fault clearing. Furthermore, an easily implementable strategy for reactive current injection, leading to minimum power oscillations, was presented. The results and the optimized strategies were validated via controller hardware-in-the-loop tests.