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Low voltage ride through (LVRT) is one of the indispensable issues of recent decade in the context of grid codes. LVRT stands for the ability of a generation facility to stay connected during the voltage dip. Despite the numerous discussions in recent works, but they mostly concentrate on the LVRTbased control of distributed energy resources (DERs) integrated into a microgrid and its improvement. However, what has been hidden and not addressed any more yet is an index to measure the LVRT capability of a DER-penetrated distribution network (DPDN) under different voltage sags. This takes precedence when we want to evaluate the LVRT capability of DPDNs with consideration of various LVRT categories of DERs mandated in IEEE 1547 standard. This paper introduces a general framework for LVRT assessment of a DPDN by solving a system of differential algebraic equations (DAEs). Then expected LVRT capability of a DPDN is evaluated by a proposed LVRT index through the implementation of Monte Carlo simulation technique. INDEX TERMS Differential algebraic equation (DAE), Distributed energy resource (DER), Penetrated distribution network (DPDN), Low voltage ride through (LVRT), Monte Carlo