With the increasing penetration of photo-voltaic (PV) units into electrical grids, particularly in distribution networks (DNs), the concern of short-term voltage instability (STVI) are growing in the presence of induction motor (IM) loads. On the event of unsymmetrical faults, STVI issues could be more complicated as the next-generation PV systems would require negative sequence power injection into the grid in conjunction with positive one. Therefore, this paper comprehensively investigates the impact of negative sequence power on the short-term voltage stability (STVS) of DNs. The method of characterizing an unbalanced fault and supplementary controls for PV systems are developed. Different case studies are conducted on a balanced IEEE 4 bus and an unbalanced IEEE 13 bus system by injecting different level of negative sequence power considering with and without peak current limitation of the PV converters. It is observed that STVS is likely to be weakened in case of large negative sequence power penetration, while injecting high positive sequence power can cause excessive voltage swell resulting inverter disconnections. Therefore, both positive and negative sequence powers need to be injected optimally to ensure the system's security following a fault.