## 4 Case Studies  
### System Model  
According to the literature [39], from 2015 to 2020, China will give priority to the construction of more than 12,000 centralized charging stations for public transportation, sanitation, and logistics. Besides, more than 4.8 million decentralized charging piles will be established to meet the charging demand of public vehicles and private vehicles. In particular, EVs in the public services own the priority of changing electricity mode. On the basis of the load frequency control model of the Hainan power grid in southern China, the parameters of eight AGC units are tabulated in Table 1. According to the gross domestic product (GDP) ranking of each city and county in Hainan province in 2015, it is assumed that the top ten cities and counties (Haikou, Sanya, Chengmai, Danzhou, Qionghai, Wanning, Wenchang, Dongfang, Lingao, Lingshui) possess a large bus charging station, denoted by CS1-CS10, respectively. Each bus charging station can charge 120 bus batteries at the same time, and the models and parameters of all bus batteries are identical, with a battery capacity of 96 kWh. The communication topology of CS1-CS10 is demonstrated in Figure 3, and the adjustment cost coefficient is reasonably set according to the unit electricity price range [\(\lambda_{\text{bid,min}}\), \(\lambda_{\text{bid,max}}\)] corresponding to the lowest and highest expected income of EV agents, as given in Table 2. Besides, considering the influence of time-of-use electricity price, buses are charged twice a day. During the daytime, buses are charged for supplementary charging, while the charging period is 10:00-16:30 with a rated charging power of 135 kW. In addition, night charging is for unified centralized charging, while the charging period is 23:00-05:30 with a rated charging power of 21 kW. Therefore, it can be assumed that the total adjustable capacity of CS1-CS10 changes every 15 min [40] when participating in AGC power allocation, such that 96 periods are formed in a day, as illustrated in Figure 4. The maximum and minimum regulation capacity of CS1-CS10 under one period is shown in Table 2.  
Figure 2: Flow chart of the proposed algorithm. SOC, state of charge.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Unit** & **Class** & \begin{tabular}{c} **Maximum Regulation** \\ **Capacity (MW)** \\ \end{tabular} & \begin{tabular}{c} **Minimum Regulation** \\ **Capacity (MW)** \\ \end{tabular} & \
\begin{tabular}{c} **Rate** \\ **(MW-min\({}^{-1}\))** \\ \end{tabular} &
\begin{tabular}{c} **Cost** \\ **(yuan-(MWh)\({}^{-1}\))** \\ \end{tabular} \\ \hline G1 & Coal-fired unit & 70 & –70 & 3.5 & 132.83 \\ G2 & Coal-fired unit & 210 & –210 & 10.5 & 127.64 \\ G3 & Coal-fired unit & 735 & –735 & 36.75 & 181.42 \\ G4 & Liquefied Natural Gas unit & 140 & –140 & 14 & 226.78 \\ G5 & Liquefied Natural Gas unit & 60 & –60 & 6 & 233.91 \\ G6 & Hydropower unit & 232 & 0 & 232 & 75.16 \\ G7 & Hydropower unit & 52 & 0 & 52 & 73.67 \\ G8 & Hydropower unit & 80 & 0 & 80 & 70.17 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model parameters of automatic generation control (AGC) units in the Hainan power grid.  
Figure 4: Total capacity power for regulation up and down of electric vehicle charging stations in one day.  
Figure 3: Communication network of charging stations (CSs) allocated in the Hainan power grid.