Power systems are being transformed to enhance the sustainability. This paper contributes to the knowledge regarding the operational process of future power networks by developing a realistic and stochastic charging model of electric vehicles (EVs).Large-scale integration of EVs into residential distribution networks (RDNs) is an evolving issue of paramount significance for utility operators. Unbalanced voltages prevent effective and reliable operation of RDNs. Diversified EV loads require a stochastic approach to predict EVs charging demand, consequently, a probabilistic model is developed to account several realistic aspects comprising charging time, battery capacity, driving mileage, state-of-charge, traveling frequency, charging power, and time-of-use mechanism under peak and off-peak charging strategies. An attempt is made to examine risks associated with RDNs by applying a stochastic model of EVs charging pattern. The output of EV stochastic model obtained from Monte-Carlo simulations is utilized to evaluate the power quality parameters of RDNs. The equipment capability of RDNs must be evaluated to determine the potential overloads. Performance specifications of RDNs including voltage unbalance factor, voltage behavior, domestic transformer limits and feeder losses are assessed in context to EV charging scenarios with various charging power levels at different penetration levels. Moreover, the impact assessment of EVs on RDNs is found to majorly rely on the type and location of a power network.