In this work, a new methodology based on a mixed integer linear programming formulation is proposed to solve the optimal charging coordination of electric vehicles (EVs) in unbalanced electrical distribution systems (EDS) considering vehicle-to-grid (V2G) technology. The steady-state operation of the EDS is represented using the real and imaginary parts of voltages and currents at nodes and circuits respectively. Distributed generation (DG) and the imbalance of the system circuits and loads are taken into account. The developed method defines an optimal charging schedule for the EVs. This charging schedule considers the EVs' arrival and departure times and their arrival state of charge, along with the energy contribution of EVs equipped with V2G technology. The presented formulation was tested in a 123-node distribution system. The charging schedule obtained was compared in terms of V2G and DG scenarios, demonstrating the efficiency of the proposed method.