Lyapunov optimization method to regulate PEVs to charge with on-grid power or renewable energy. Moreover, this paper further considers that each charging station is equipped with non-ideal energy storage with inefficient charging and discharging to store extra renewable energy. Thus, the framework of the algorithm designed for ideal storage in the aforementioned articles cannot be applied to this paper directly.

In this paper, a distribution network is considered, where there are multiple charging stations. Also many non-EV loads are connected to every transformer and transmission line in this distribution network. It is supposed that each charging station is equipped with a renewable energy generator and a non-ideal storage, which will absorb the abundant renewable energy. If the energy generated by renewable source is insufficient, charging stations are supposed to draw energy from the local storage or gain energy from the power grid. Hence this paper tries to minimize the time average non-renewable energy cost in a distribution network by coordinating the charging of PEVs and renewable energy management, while satisfying the safety of distribution networks by limiting the overload probability under a certain permitted bound. The contribution of this paper are threefold:

1.  A stochastic optimization problem is formulated to 