In this paper, a new approach is presented to solve the electric vehicle charging coordination (EVCC) problem considering Volt-VAr control, energy storage device (ESD) operation and dispatchable distributed generation (DG) available in three-phase unbalanced electrical distribution networks (EDNs). Dynamic scheduling for the EVCC is proposed through a step-by-step methodology, which solves a mixed integer linear programming (MILP) problem for the whole time period. The objective is to minimize the total cost of energy purchased from the substation and DG units, the cost of energy curtailment on electric vehicles, the cost of energy injected from the ESDs, and the cost of energy curtailment on the ESDs. The Volt-VAr control considers the management of on-load tap changers, voltage regulators, and switchable capacitors installed along the grid. Furthermore, the formulation takes into account the voltage dependence of the loads, while the steady-state operation of the unbalanced distribution systems is modeled using linear constraints. The proposed model was tested in a 178-node three-phase unbalanced EDN considering a one-day time period.