Exploring Damping Effect of Inner Control Loops for Grid-Forming VSCs

This paper presents an analytical framework to evaluate the damping contributed by inner control loops in grid-forming voltage-source converters. First, an impedance model is developed to characterize the dynamics of three types of inner loops, with the control-shaped resistive component indicating the damping for synchronous oscillations. Then, inner-outer loop interactions and interaction-induced oscillations are evaluated using the complex torque coefficient, with the damping torque used for stability assessment. The framework offers two benefits: (i) it yields intuitive physical insight into inner-outer loop interactions and oscillation mechanisms; and (ii) it enables inner-loop parameter tuning using electrical damping torque with minimal dependence on outer-loop operating points. The method is exemplified for virtual-admittance and current-control inner loops, where both synchronous and sub-synchronous oscillations are analyzed and mitigated. Time-domain simulations and hardware experiments validate the approach and its findings.