This paper deals with different active damping approaches for PI-based current control of grid-connected PWM converters with LCL filters which are based on one additional feedback. Filter capacitor current as well as voltage feedback for purpose of resonance damping are analyzed and compared. Basic studies in continuous Laplace domain show that either proportional current feedback or derivative voltage feedback yield resonance damping. Detailed investigations of these two approaches in discrete z-domain taking into account the discrete nature of control implementation, sampling, and PWM are carried out. Several ratios of LCL resonance frequency and control frequency are considered. For high resonance frequencies only current feedback stabilizes the system. For medium resonance frequencies both approaches show good performance. For low resonance frequencies stability gets worse even if voltage feedback offers slighly better damping properties. Measurement results validate the theoretical results.