Weak-Grid Stability Analysis of Quasi-PR Controlled LCL-Type Grid-Connected Inverters with Capacitor-Current Active Damping

Abstract

Three-phase grid-tied inverters built around an LCL filter exhibit two intertwined difficulties under weak-grid conditions: resonance-driven instability and inadequate harmonic rejection. This paper develops a joint tuning procedure in which a quasi-proportional-resonant (Q-PR) current regulator is paired with capacitor-current feedback acting as active damping (CCF-AD). The model retains the full third-order LCL dynamics together with the 1.5-sample computation delay of the digital controller, all expressed in the stationary alpha-beta frame. Filter component values are selected for a 10 kW / 750 V / 10 kHz prototype, yielding an LCL resonance near 2.43 kHz. Two candidate gain pairs are then put forward—one (Kp = 0.8, Kr = 80) biased toward fast transient response and the other (Kp = 0.5, Kr = 150) biased toward fundamental tracking accuracy. After comparing their gain and phase margins in the frequency domain, time-domain sweeps over Kp, Kr, and the equivalent grid inductance Lg map out THD, step overshoot, and the onset of instability. An apparently paradoxical result emerges: the parameter set with the larger strong-grid gain margin (6.29 dB versus 3.10 dB) is the first to lose stability when the grid becomes weak, failing already at Lg approximately 22 mH while the other set survives until approximately 25 mH. The mechanism turns out to be straightforward—the resonance migrates downward as Lg grows and eventually crosses into the loop bandwidth—and yields a quantitative robustness rule for Q-PR tuning when the line impedance is uncertain.