## 1 Introduction  
With the development of electric vehicles (EVs), EVs have the potential to replace the traditional diesel locomotives and become the main means of transportation for people to travel in the future. However, the large-scale application of those battery-based electric vehicles will bring new problems to the operation and planning of existing power grids. Large-scale battery-based electric vehicle charging will result in a significant increase in grid load. If the charging behaviors occur during the peak period of the grid, it will Intensify the difference of peak-to-valley load of the current grid, hence reduces the efficiency of the current power system. For example, Reference [1] refers to a test of random charging of electric vehicles in 13 regional power grids in the United States. The results show that in order to accept high-penetrated unmanaged electric vehicles charging during early-evening, the power company needs to build an additional 160 new power stations to meet the power requirements of electric vehicles. What worse is, the peak load of traffic and power grid tends to be at the same time period, which means that there will be a large number of low-battery EVs need to be charged during the peak period of grid load. Studies used in Reference [2] show 7334 charging events of 64 EVs for a period of one year in Los Angeles, USA. It indicates that the 24 h charging energy distribution curve is pretty similar to the daily load curve in California. Hence, If the EV charging load is not well managed, once a large number of EVs that are connected to the grid at the peak time, the huge instantaneous power demand may suddenly crash the local grid. Therefore, how to control the orderly charge or discharge of a large number of EVs, so as to maintain the stability of power grids and meet the electricity needs of EV users is an important problem to be addressed and solved. In terms of how to reduce the impact of electric vehicle charging on the grid, Reference [3] points out that in the United States, if the charging load of EVs with 10% penetration is moved from daytime to the night, it will prevent the growth of a peak load of nearly 50%. Reference [4] points out that when a large number of EVs are connected to the power grid by bi-directional power electronics controller, they can be regarded as the backup storage for the power grid to deflate the energy fluctuations brought by the renewables, such as wind, solar, etc. The References [5,6] pointed out that when an EV is connected to the grid by power electronic devices with bidirectional power control capability, and when the capacity of the electric vehicle is large enough, it can be regarded as the backup energy storage for the grid, to be absorbed by the renewable energy power generation system. It can absorb the excess power generated by the power generation plant, supplement the shortage of the power supply system, and thus stabilize the frequency and voltage fluctuations of the power grid. The idea of utilizing the idle power in electric vehicle batteries to feed the grid is known as vehicle-to-gird (V2G) [7]. A V2G system can provide services, such as frequency regulation, reactive power support, spinning reserve, load balancing, etc. to the power grid [8, 9, 10, 11]. The purpose of frequency regulation to keep the grid frequency stable around the rated frequency point, so that the supply and demand balance of active power of the power system are met. As for frequency regulation, current power system mainly relies on large synchronous generators for frequency regulation by adjusting their active power output, which maintenance cost is expensive. With the increase in the number of EVs in the future, if the number is large enough, by controlling the charging and discharging behavior of the EVs group through a certain strategy, then the EVs group can be used instead of the large synchronous generators for frequency regulation.