The penetration of electric vehicle (EV) charging stations (CSs), along with the progressive connection of stochastic distributed generation, is increasing the probability of violating the power distribution grid operational constraints and deteriorate the quality of power supply. To this end, the paper proposes a real-time control scheme for allocating power set-points to EV CSs while accounting for the grid operational requirements. In the proposed problem formulation the grid and the power injections are modelled accounting for their unbalanced 3-phase nature, thus enabling to formulate the problem objective and its constraints adopting the sequence decomposition. The EVs’ users need, along with the stochastic nature of other uncontrollable injections (e.g. loads and generation from photovoltaic generation units), are also taken into account. A distributed control scheme, with a minute-scale control horizon, is proposed where local controllers, operating at EV aggregation level, compute EV battery-secure power set-points. These controllers send their set-points to a central controller operating at the grid aggregation level. The central controller solves a scenario-based linearised optimal power flow accounting for grid operational and power quality constraints. Then, it sends back its solution to the respective local controllers. The obtained iterative algorithm is efficiently solved until convergence. We analyse the performance of the proposed control scheme via a simulation ran on the IEEE-34 feeder. Comparisons with two other control algorithms, a grid-unaware local controller and a myopic maximum power controller, are included to benchmark the proposed control scheme.