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In the paper, we consider delay-optimal charging scheduling of the electricvehicles (EVs) at a charging station with multiple charge points. The chargingstation is equipped with renewable energy generation devices and can also buyenergy from power grid. The uncertainty of the EV arrival, the intermittence ofthe renewable energy, and the variation of the grid power price are taken intoaccount and described as independent Markov processes. Meanwhile, the chargingenergy for each EV is random. The goal is to minimize the mean waiting time ofEVs under the long term constraint on the cost. We propose queue mapping toconvert the EV queue to the charge demand queue and prove the equivalencebetween the minimization of the two queues' average length. Then we focus onthe minimization for the average length of the charge demand queue under longterm cost constraint. We propose a framework of Markov decision process (MDP)to investigate this scheduling problem. The system state includes the chargedemand queue length, the charge demand arrival, the energy level in the storagebattery of the renewable energy, the renewable energy arrival, and the gridpower price. Additionally the number of charging demands and the allocatedenergy from the storage battery compose the two-dimensional policy. We derivetwo necessary conditions of the optimal policy. Moreover, we discuss thereduction of the two-dimensional policy to be the number of charging demandsonly. We give the sets of system states for which charging no demand andcharging as many demands as possible are optimal, respectively. Finally weinvestigate the proposed radical policy and conservative policy numerically.

Charging Scheduling of Electric Vehicles with Local Renewable Energy under Uncertain Electric Vehicle Arrival and Grid Power Price