Capacitor-current-feedback (CCF) active damping has proven to be an effective solution for mitigating resonance in inductive-capacitive-inductive (LCL)-type grid-interactive power converters. However, the performance of active damping can be compromised by time delay in digitally controlled systems. To address this issue, this work introduces two delay compensation methods: model-based and model-free extended-state observer (ESO)-based prediction. Both methods involve predicting the variables of interest one sampling period ahead and incorporating these predictions into the active damping loop. Consequently, the proportional CCF effectively emulates a positive virtual resistor over a wider frequency range, preventing the occurrence of unstable open-loop poles. Both techniques have demonstrated their effectiveness in expanding the stable region of the active damping feedback gain. Furthermore, the ESO-based scheme is robust on LCL parameters and easily incorporates state observer techniques, reducing hardware complexity. Experimental results validate the proposed methods, confirming their effectiveness as per the theoretical analysis.