  When grid-forming (GFM) inverter-based resources (IBRs) face severe grid
disturbances (e.g., short-circuit faults), the current limitation mechanism may
be triggered. Consequently, the GFM IBRs enter the current-saturation mode,
inducing nonlinear dynamical behaviors and posing great challenges to the
post-disturbance transient angle stability. This paper presents a systematic
study to reveal the fault recovery behaviors of a GFM IBR and identify the risk
of instability. A closed-form expression for the necessary condition that a GFM
IBR returns from the current-saturation mode to the normal operation mode is
presented. Based on these analyses, it has been inferred that the angle of the
magnitude-saturated current significantly affects the post-fault recovery and
transient stability; with different angle selection, the system may follow
multiple post-fault trajectories depending on those conditions: 1) Convergence
to a normal stable equilibrium point (SEP), 2) convergence to a saturated
stable equilibrium point (satSEP), or 3) divergence (instability). In this
paper, the circumstances under which a GFM IBR cannot escape from the
current-saturation mode are thoroughly investigated. The theoretical analyses
are verified by dynamic simulations.
