Across the world, the impact of increasing electric vehicle (EV) adoption requires a better understanding. The authors hypothesize that the introduction of EV’s will cause significant overloading within low voltage distribution grids. To study this, several low voltage networks were reconstructed based on the literature and modelled using DigSilent Powerfactory, taking into account the stochastic variability of household electricity consumption, EV usage, and solar irradiance. The study incorporates two distinct usage scenarios—residential loads with varying EV penetrations without and with distributed grid tied generation of electricity. The Monte-Carlo simulation took into account population demographics and showed that in urban networks, EV introduction could lead to higher cable loading percentages than allowed, and in rural networks, this could lead to voltage drops beyond the allowed limits. Distributed generation (DG) in the form of solar power could significantly offset both these overloading characteristics, as well as the active and reactive power demands of the network, by between 10–50%, depending on the topology of the network.