Based on the assumption that vehicles served by petrol stations will be replaced by Electric Vehicles (EV) in the future, EV public charging station facilities, with off-board fast chargers, will be progressively built. The power demand of these installations is expected to cause great impact on the grid, not only in terms of peak power demanded but also in terms of power quality, because most battery chargers behave as non-linear loads. This paper presents the proposal of a novel comprehensive global control strategy for the power electronic converters associated with bidirectional three-phase EV off-board fast chargers. The Charging Station facility Energy Management System (CS-EMS) sends to each individual fast charger the active and reactive power setpoints. Besides, in case the charger has available capacity, it is assigned to compensate a fraction of the harmonic current demanded by other loads at the charging facility. The proposed approach works well under distorted and unbalanced grid voltages. Its implementation results in improvement in the power quality of each fast charger, which contributes to improvement in the power quality at the charging station facility level, which can even provide ancillary services to the distribution network. Simulation tests are conducted, using a 100 kW power electronic converter model, under different load and grid conditions, to validate the effectiveness and the applicability of the proposed control strategy.