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Battery charging of electric vehicles (EVs) will increase the power demand in distribution networks. It is anticipated that this will cause voltage drops, thermal overloads and an increase in losses. The severity of the impact will depend on the EV owners' behaviour. A generic three-phase low voltage (LV) residential distribution network model was used to evaluate the effects of EV battery charging on distribution networks, the effect of a smart charging regime for EVs as well as the contribution of dispersed micro-generation (mGen) sources. The uncertainties associated with the residential loads, m-Gen and EV owners' behaviour, were addressed with a probabilistic approach. A case study was performed for the year 2030 using both deterministic and probabilistic approaches. The probabilistic assessment showed the importance of the above uncertainties.