  In this paper, a hierarchical distributed method consisting of two iterative
procedures is proposed for optimal electric vehicle charging scheduling (EVCS)
in the distribution grids. In the proposed method, the distribution system
operator (DSO) aims at reducing the grid loss while satisfying the power flow
constraints. This is achieved by a consensus-based iterative procedure with the
EV aggregators (Aggs) located in the grid buses. The goal of aggregators, which
are equipped with the battery energy storage (BES), is to reduce their
electricity cost by optimal control of BES and EVs. As Aggs' optimization
problem increases dimensionally by increasing the number of EVs, they solved
their problem through another iterative procedure with their customers. This
procedure is implementable by exploiting the mathematical properties of the
problem and rewriting Aggs' optimization problem as the \textit{sharing
problem}, which is solved efficiently by the alternating direction method of
multipliers (ADMM). To validate the performance, the proposed method is applied
to IEEE-13 bus system.
