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In this paper, the impacts of residential Plug-In Electric Vehicles (PEVs) charging on a distribution grid are investigated. A stochastic charging model is developed and used to study the impacts on distribution transformer loading, hotspot temperature variation and Accelerated Aging Factor (AAF) of the transformer. Different penetration levels of PEVs are considered in a typical distribution system. Furthermore, distribution of State of Charge (SOC) is discussed which can be used to optimize battery capacity and required charging infrastructure. Distribution of parking time interval is also discussed which can be used to evaluate availability of PEVs for overnight charging. The merit of stochastic approach compared with deterministic approach is also illustrated. The main contribution of this paper is the stochastic approach to evaluate the impact of residential PEV charging on the distribution grid.