## 1 Introduction
When multiple charging stations participate in the secondary power system frequency regulation, there are typically two critical steps: (a) assigning the total power command \(\Delta P_{\text{EV}}\) of EV centralized control center to each charging station and (b) assigning the power command of the charging station to each battery in the station. Nowadays, the studies on the participation of EV in power system frequency regulation are still insufficient, which means the majority of studies mainly focus on the AGC power allocation of EVs in the EV charging station. Besides, the relevant factors including frequency regulation price, charging cost, and charging demand are taken into consideration in the literature [24], in which an allocation model is proposed to maximize the benefits of an EV charging station. Moreover, the authors of [25] regarded the fairness of EV's participation in power system frequency regulation as the ultimate purpose, instead of maximizing the benefits of the EV charging station, upon which various optimization algorithms are proposed to fairly allocate the charging and discharging power of EV. Moreover, in order to avoid over-charging and over-discharging of batteries, the authors of [26] allocated frequency regulation power commands according to the proportional allocation method based on state-of-charge (SOC). However, none of the above studies involves the AGC power distribution among EV charging stations. At present, the most convenient and practical method is to allocate the total power instruction \(\Delta P_{\text{EV}}\) equally to each EV charging station according to the proportion of adjustable capacity. Because each EV charging station belongs to different agents and the cost of power system frequency regulation is various, the average distribution method of adjustable capacity cannot minimize the cost of power system frequency regulation. In addition, the method usually allocates the total power command \(\Delta P_{\text{EV}}\) to each EV charging station by centralized control, which requires collecting the information of each EV charging station in the real-time. When the scale of EV charging station participating in system frequency regulation increases, communication blockage and other problems will often occur. In order to adapt to the trend of distributed/centralized development of centralized AGC in a smart grid [27] with high-penetration renewables [28], a decentralized and autonomous intelligent power generation control framework [29] combined with multi-agent collaborative consensus algorithm [30] was proposed. Hence, the decentralized autonomous problem of AGC power allocation in interconnected power grid can be effectively solved, while EV is not involved as distributed generators to participate in the system frequency regulation. Particularly, a consensus algorithm can make the variables to reach a consensus through the cooperation between agents and adjacent agents in a multi-agent network, which has been widely used in formation control, unmanned aerial vehicle (UAV) control [31], cluster [32], robot swarm navigation [33], and stable flocking [34]. Hence, this paper applies the consensus algorithm to the AGC power allocation for each EV charging station. In order to avoid battery over-charging or over-discharging and to prolong the lifespan of the battery, a proportional allocation method based on SOC [21] is adopted to solve the AGC power redistribution. Finally, the model of the Hainan power grid in south China is utilized to evaluate the specific performance of the proposed method. Compared with the previous works, the main novelty of this paper can be summarized as follows:  
* The traditional AGC power allocation is implemented among the thermal and hydro power plants in a centralized manner. In contrast, this paper provides a framework of AGC power allocation with EV, while the control command of each EV charging station can be calculated in a decentralized way.