A new multi-infeed HVDC system that comprises inductive filtering device has been modeled on the basis of the CIGRE model. The definitions of Multi-infeed Effective Short Current Ratio (MESCR), Multi-infeed Interaction Factor (MIIF) and Commutation Failure Immunity Index (CFII) have been explained. The varying pattern of CFII in different fault types and different fault time has been analysed in comparison. The impact of the resisting capability on continuation commutation failure of multi-infeed HVDC systems by ac system strengths in the conditions of local commutation failure and concurrent commutation failure have also been studied in comparison. The theoretical calculation and simulation analysis shows that the inductive filtering device enhances the MESCR and CFII of the multi-infeed HVDC system and significantly decreases the risk of concurrent commutation failure and local concurrent commutation.