  In this paper, we investigate the transient stability of a state-of-the-art
grid-forming complex-droop control (i.e., dispatchable virtual oscillator
control, dVOC) under current saturation. We quantify the saturation level of a
converter by introducing the concept of degree of saturation (DoS), and we
propose a provably stable current-limiting control with saturation-informed
feedback, which feeds the degree of saturation back to the inner
voltage-control loop and the outer grid-forming loop. As a result, although the
output current is saturated, the voltage phase angle can still be generated
from an internal virtual voltage-source node that is governed by an equivalent
complex-droop control. We prove that the proposed control achieves transient
stability during current saturation under grid faults. We also provide
parametric stability conditions for multi-converter systems under
grid-connected and islanded scenarios. The stability performance of the
current-limiting control is validated with various case studies.
