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With the increase in the penetration of battery electric vehicles (BEVs) all over the world, utilities should start considering their increased demand as part of their electric demand. Generally, the literature lacks works that consider the impact of transportation electrification on the reliability of the power system. Thus, this paper proposes a new mechanism for reliability assessment including BEVs, with both grid-to-vehicle (G2V) and vehicle-to-grid (V2G) modes. Three charging strategies: uncontrolled, controlled unidirectional, and controlled bidirectional are considered in this paper to model the interactions between the transportation and electric power systems. A dynamic stochastic consumption model for a fleet of BEVs is developed to be used in the reliability assessment for the distribution networks. This dynamic model takes into consideration the variability and uncertainty of different trip purposes, starting and ending trip times, as well as the corresponding battery consumption in weather conditions. Furthermore, it is composed of two sequential submodels: travel behavior and battery depletion. The first submodel considers trip-related information while the second considers battery-depleted energy. Simulation results on a benchmark test system show the negative impacts of uncontrolled charging on the power system's reliability. However, they also show that controlled charging can significantly reduce or mitigate these impacts. [ABSTRACT FROM AUTHOR]