It has been recognized that an increased penetration of electric vehicles (EVs) may potentially alter load profile in a distribution network. As EVs are regarded as a diversely distributed load so a deterministic method, to predict EV charging load, may not account for all possible factors that could affect the power system. Thus, a stochastic approach is applied that takes into account various realistic factors such as EV battery capacity, state of charge (SOC), driving habit/need, i.e., involving type and purpose of trip, plug-in time, mileage, recharging frequency per day, charging power rate and dynamic EV charging price under controlled and uncontrolled charging schemes. A probabilistic model of EVs charging pattern associated with residential load profile is developed. The probabilistic model gives an activity based residential load profile and EV charging pattern over a period of 24 h. Then, the model output is used to assess the power quality index such as voltage unbalance factor under different electric vehicle penetration levels at different nodes of the system. An uneven EV charging scenario is identified that could cause the voltage unbalance to exceed its permissible limit.