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The increasing uptake of electric vehicles suggests that vehicle charging will have a significant impact on the electricity grid. Finding ways to shift this charging to off-peak periods has been recognized as a key challenge for integration of electric vehicles into the electricity grid on a large scale. In this paper, electric vehicle charging is formulated as a receding horizon optimization problem that takes into account the present and anticipated constraints of the distribution network over a finite charging horizon. The constraint set includes transformer and line limitations, phase unbalance, and voltage stability within the network. By using a linear approximation of voltage drop within the network, the problem solution may be computed repeatedly in near real time, and thereby take into account the dynamic nature of changing demand and vehicle arrival and departure. It is shown that this linear approximation of the network constraints is quick to compute, while still ensuring that network constraints are respected. The approach is demonstrated on a validated model of a real network via simulations that use real vehicle travel profiles and real demand data. Using the optimal charging method, high percentages of vehicle uptake can be sustained in existing networks without requiring any further network upgrades, leading to more efficient use of existing assets and savings for the consumer. [ABSTRACT FROM PUBLISHER]