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Rapid increase in the number of electric vehicles will likely deteriorate voltage profiles and overload distribution networks. Controlling the charging schedule of electric vehicles in a coordinated manner provides a potential solution to mitigate the issues and could defer reinforcement of network infrastructure. This work presents a method for robust, cost-minimising, day-ahead scheduling of overnight charging of electric vehicles in low voltage networks in a stochastic environment with minimal real-time adaptation. To reduce the computational complexity, a linear power flow approximation is utilised. The stochastic environment captures multiple uncertainties arising from the mobility behaviour including stochastic daily trip distances, arrival and departure times. Knowledge about the probability distributions of these parameters is used to hedge risks regarding the cost of charging, network overloading, voltage violation and charging reliability. The results on a test network provide an insight into the impact of uncertainty and the effectiveness of addressing aspects of risk during optimisation. In particular, planning with more conservative estimates of initial battery charge levels increases the reliability and technical feasibility of optimised schedules.