Modern grid codes demand the integration of voltage support capability with photo-voltaic (PV) generators to ensure a secure operation of power systems. On the other hand, short-term voltage instability (STVI) of distribution networks (DNs) is one of the key issues to be addressed. It can occur due to high proportion of induction motor loads. However, the existing literature lacks a thorough analysis of short-term voltage stability (STVS) of DNs following an asymmetrical fault. Furthermore, an effective voltage-support strategy for PV units, which can improve the STVS while mitigating the excessive voltage swell, is essential for secure operation. Hence, firstly this paper thoroughly investigates the STVS of DNs subjected to asymmetrical faults. It is perceived that voltage support through conventional methods can increase the risk of STVI and excessive voltage swell. Secondly, a new voltage-support strategy is proposed based on the negative sequence voltage at point of common coupling (PCC) aimed at mitigating the STVI and regulating the phase voltages within the margins. The key features of the proposed strategy are, fast and accurate estimation of the network's impedance at PCC is not required and it can be easily re-designed considering the network's dynamic behaviors. The efficacy of the proposed method is validated on two IEEE benchmark test systems, and the results demonstrate the effectiveness in improving the STVS and alleviating over voltage issues.