Resonant poles of LCL filters may challenge the entire system stability especially in digital-controlled pulse width modulation (PWM) inverters. In order to tackle the resonance issues, many active damping solutions have been reported. For instance, a notch filter can be employed to damp the resonance, where the notch frequency should be aligned exactly to the resonant frequency of the LCL filter. However, parameter variations of the LCL filter as well as the time delay appearing in digital control systems will induce resonance drifting, and thus break this alignment, possibly deteriorating the original damping. In this paper, the effectiveness of the notch filter-based active damping is first explored, considering the drifts of the resonant frequency. It is revealed that when the resonant frequency drifts away from its nominal value, the phase lead or lag introduced by the notch filter may make itself fail to damp the resonance. Specifically, the phase lag can make the current control stable despite of the resonant frequency drifting, when the grid current is fed back. In contrast, in the case of an inverter current feedback control, the influence of the phase lead or lag on the active damping is dependent on the actual resonant frequency. Accordingly, in this paper, the notch frequency is designed away from the nominal resonant frequency to tolerate the resonance drifting, being the proposed robust active damping. Simulations and experiments performed on a 2.2-kW three-phase grid-connected PWM inverter verify the effectiveness of the proposed design for robust active damping using digital notch filters.