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Stability studies in distribution smart grids (SGs) are very important due to the increased penetration of distributed energy resource making bidirectional flow of electric power. This paper presents two novel fast voltage stability indices (VSIs) applicable to the radial distribution SGs based on the real-time measured voltage data only, obtained by the SG infrastructures such as smart metering device. Each VSI depends on the system bus voltages and does not need additional calculations such as power flow solution, converting the actual distribution network into two-bus equivalent system etc. In other words, for a radial system with n-node, the voltage stability analysis is carried out by parallel n-microprocessor units independently. The concentrator units can collect and evaluate the computational results and decide about control actions directly or indirectly depending on the system requirements. The accuracy and efficiency of the proposed indicators are tested on a 41-node radial distribution system. Six load models including constant and composite types have been considered, and also SG in various states of operation and four types of distributed generation are analysed. The comparison results demonstrate that the proposed VSIs are fast and effective to identify the most sensitive node of the radial grids to the voltage collapse based on the smart infrastructures. [ABSTRACT FROM AUTHOR]