  This paper outlines reduced-order models for grid-forming
virtual-oscillator-controlled inverters with nested current- and
voltage-control loops, and current-limiting action for over-current protection.
While a variety of model-reduction methods have been proposed to tame
complexity in inverter models, previous efforts have not included the impact of
current-reference limiting. In addition to acknowledging the current-limiting
action, the reduced-order models we outline are tailored to networks with
resistive and inductive interconnecting lines. Our analytical approach is
centered on a smooth function approximation for the current-reference limiter,
participation factor analysis to identify slow- and fast-varying states, and
singular perturbation to systematically eliminate the fast states.
Computational benefits and accuracy of the reduced-order models are benchmarked
via numerical simulations that compare them to higher-order averaged and
switched models.
