Impedance Modeling for Quadrature-Axis Active Damping of PLL Dynamics

When grid-following voltage source converters (VSCs) operate in inverter mode, the phase-locked loop (PLL) dynamics introduce a negative-real-part impedance, which may lead to the instability of the closed-loop system, especially in a weak-grid connection. This undesirable property of the PLL may be offset by so-called active damping. Nevertheless, the interaction between the active damping and the adverse PLL impact is not fully understood. To this end, the properties of different active-damping methods are analyzed, with the focus on the q-to-q coupling of the input admittance. One important finding is that adding an integrator to the q-axis active damper can improve the system performance in a weak-grid connection. Simulations and experimental results verify the theoretical analysis.