There is an existing problem in that assessment of simultaneous commutation failure (CF) risk is of inadequate accuracy based on the multi-infeed interaction factor (MIIF). Thus, first, the propagation mechanism of transient reactive power after an AC system fault in a multi-infeed HVDC (MIDC) system is clarified, and the complex interactions between reactive power and voltage that have a noticeable effect on MIIF are revealed. Secondly, an improved MIIF factor considering reactive power and voltage interactions is proposed to measure the interaction between MIDC systems. The voltage drops due to reactive power imbalance between AC and DC systems and the voltage variation due to reactive power transfer between DC converter stations are calculated. Then, based on the minimum extinction angle theorem and comprehensively considering the influence of transient reactive power and voltage characteristics, a critical simultaneous commutation failure factor (CSCFF) and its calculation expression are proposed. By comparing MIIF with CSCFF, a simultaneous commutation failure assessment method is proposed, which has higher accuracy in assessing the simultaneous commutation failure. Finally, double-infeed and three-infeed HVDC simulation models are constructed using the PSCAD/EMTDC platform. These verify the validity and applicability of the proposed method with different fault types, coupling impedances and fault severities.