Large‐scale integration of electric vehicles (EVs) into residential distribution networks (RDNs) is an evolving issue of paramount significance for utility operators. Similarly, electric load forecasting is an operational process permitting the utilities to manage demand issues for optimal energy utilization. Unbalanced voltages prevent the effective and reliable operation of RDNs. This study implements a novel framework to examine risks associated with RDNs by applying a residential forecasting model with a stochastic model of EVs charging pattern. Diversified EV loads require a stochastic approach to predict EVs charging demand; consequently, a probabilistic model is developed to account for several realistic aspects comprising charging time, battery capacity, driving mileage, state‐of‐charge, travelling frequency, charging power, and time‐of‐use mechanism under peak and off‐peak charging strategies. Peak‐day forecast of various households is obtained in summer and winter by implementing an optimum nonlinear auto‐regressive neural‐network (NN) with time‐varying external input vectors (NARX). Outputs of the EV stochastic model and residential forecasting model obtained from Monte‐Carlo simulations and the NARX‐NN model, respectively, are utilized to evaluate power quality parameters of RDNs. Performance specifications of RDNs including voltage unbalance factor (VUF) and voltage behavior are assessed in context to EV charging scenarios with various charging power levels under different penetration levels.