## 1 Introduction
The authors of [12] minimized the electricity purchase costs of the aggregators by scheduling the charging loads of plug-in electric vehicles (PEVs) with normal charging at home, and the charging power was at the level of several kW. An energy management scheme for an off-board EV smart charger was proposed in order to support the grid against disturbances, for the application of vehicle-to-grid (V2G) or grid-to-vehicle (G2V) in [13]. A general model was proposed for the charging/discharging control of EVs in the procedure of vehicle-to-anything (V2A) in [14]. V2G technology can support the power demand of the grid, and the peak power of the station can be reduced by vehicle-to-vehicle (V2V). Reference [15] proposed an optimal decentralized protocol for electric vehicle charging using valley-filling, which contained an optimal decentralized charging algorithm, asynchronous optimal decentralized charging algorithm, and a real-time optimal decentralized charging algorithm. However, it is only suitable for private EVs charging at night, as the charging control of PEBs running without interruption cannot apply that protocol. A coordinated charging strategy for electric taxis in a temporal and spatial domain was presented in [16], where the PSO algorithm was used to balance the charging load distribution at different stations, as well as the times for the electric taxis. The authors in [17] proposed two real-time coordinated charging strategies to improve the charging costs of an electric bus fast-charging station responding to the time-of-use electricity prices. However, the research and simulation only considered five electric buses on one route, so the simulated bus operation and charging power could not accurately represent the conditions of actual PEB fast-charging stations. The authors of [18] proposed a novel decentralizedvalley-filling charging strategy, where a day-ahead pricing scheme that varied in both time and power forms was designed by solving a minimum-cost optimization problem at a device-level. A DC bus concept is proposed and validated for PEVs in [19], where the charging topology was established with a bipolar DC bus, based on a central neutral-point clamped (NPC) converter. This provided flexibility to the connection of the loads and electrical storage systems (ESSs), and had higher voltage and power handling capabilities. As is well known, the alternative locations of charging stations are limited by the bus lines. If the distribution capacity is extremely limited, the charging power demand needs to be further decreased [20]. The battery energy storage system (BESS) is widely used to shave the peak power in many scenarios. The BESS was used as a buffer to reduce the charging load fluctuation and to shave peak power [21]. The authors in [22] applied electrical storage systems as a way to reduce the operational costs of the station and to alleviate the negative impacts of the station operation on the power grid in the fast-charging stations of the PHEVs. Through the load prediction of the PHEVs, the size of the ESSs of many different types of energy storage were compared. However, the comprehensive revenue of the BESS may be less than the investment, because the peak charging power of the station was usually up to a megawatt level and the total charging electricity was only several kilo kWh. The research has focused on the charging optimization of private EVs or taxis, using the probability method to describe the charging characteristic based on the gasoline vehicle data. The main methods are as follows. 1. Using the charging price incentive mechanism to guide the charging behaviors of EV, owners can reduce the electricity cost, and the charging power is reduced during the peak duration of the distribution network. 2. Control the charging power through valley-filling to reduce the impact on the basic distribution load, and the total charging load level is less than hundreds of kilowatts. 3.