Commutation failure (CF) occurs frequently under inverter AC system faults. Around 70% of power system faults are Single-Line-to-Ground (SLG) faults that affect not only magnitudes but also phase angles of non-faulty phases. This has not been thoroughly analyzed in existing research. Therefore, this paper proposes a new commutation voltage calculation method where the commutation voltages under asymmetrical faults in Multi-Infeed LCC-HVDC systems are derived. The proposed method considers the impact of transformer connections, fault location, fault impedance, and voltage magnitude change and voltage phase shift of faulty and non-faulty phases that have not been considered in previous publications. Secondly, based on this proposed commutation voltage calculation method, CF prediction criteria based on the Voltage-Time Area (VTA) theory are proposed. Thirdly, a calculation method of the extra commutation voltage needed for each inverter to avoid CF is proposed to measure how close the commutations are to being successful under SLG faults. The effectiveness of the proposed methods is demonstrated by simulation results using the CIGRE LCC-HVDC Benchmark system and a six-machine-two-area (6M2A) test system simulated by the Real Time Digital Simulator (RTDS).