Utilization of plug-in electric vehicles (PEVs) is gaining popularity in recent years due to the growing concerns about fuel depletion and the increasing petrol price. Random uncoordinated charging of multiple PEVs in residential distribution feeders at moderate penetration levels are expected in the near future. The potential for stresses and network congestion is significant as PEV charging activities represent sizeable loads with unpredictable locations. Furthermore, the forthcoming smart grids will be unbalanced due to non-uniform distributions of PEVs in the three phases with unpredictable charging rates, times and durations. This paper explores the detrimental impacts of random PEV charging on the distribution transformer loading and bus voltage profiles of unbalanced smart grids. The impacts of non-uniform distributions of PEVs on the three phases, as well as deferred plugging of vehicles (encouraged by introducing higher electricity prices during the peak hours) are also explored. Simulation results will be generated and analyzed for an unbalanced three-phase 62 node residential network populated with PEV chargers using Matlab/Simulink software.