## 2 Kernel Extreme Learning Machine Model
### Electric Vehicle Model  
The charging demand of an electric vehicle is usually related to the battery characteristics of the vehicle, the travel habits of the owner, and the charging mode. The battery characteristics are usually expressed by the state of charge (SOC), and the charging mode is mainly divided into fast and slow charging mode. Combined with the travel habits of car owners, private cars are the main research object in this paper. Two indicators are introduced to express the charging demands of electric vehicles: the location and capacity of the charging stations.  
The location information can reflect the convenience and the charging mode of the vehicle owner. The locations of the charging stations are divided into two types, one is the commercial or tourism centers, which usually adopt the fast charging mode, and the other is the residential centers or enterprises and institutions, which usually adopt the slow charging mode. The capacity information can reflect the rationality and economy of the charging station. If the capacity and number of charging piles are too large, the investment cost of the charging station will be too high. If the capacity and the number of charging piles are too small, the charging demand cannot be satisfied. Therefore, it is important to properly plan and design the location and capacity of electric vehicle charging stations.  
According to the 2017 global traditional energy power report [21], per capita annual electricity consumption in 2017 was about 4309 kWh, which can be used to estimate the population within the selected network's power supply area. Set the population within the power supply area as \(P_{s}\), the annual electricity consumption within forecasting area as \(A_{cc}\), and the per capita electricity consumption as \(P_{ccc}\), the Equation for \(P_{s}\) is as follows:  
\[P_{s}=A_{cc}/P_{ccc} \tag{22}\]  
According to the calculated number of cars per 100 people in developed regions, 32 vehicles/100 people, electric vehicle occupancy was calculated to be 40%. Among this, the fast charging mode accounted for 20% of the total number of electric vehicles, and the slow charging mode accounted for 80%. The availability rate of electric vehicles with fast charging modes is setting as 0.6. The slow charging mode vehicles, the rate is setting as 0.3. Thus, an estimated value of the charging powers of the electric vehicles is derived:  
\[P_{EVC}=N_{EV}\times 80\%\times 0.3\times P_{EVin}+N_{EV}\times 20\%\times(1-0.6) \times P_{EVin} \tag{23}\]  
\[N_{EV}=P_{s}\times 40\% \tag{24}\]  
where, \(P_{EVin}\) represents one electric vehicle charging power. \(P_{EVC}\) represents the charging power of all the electric vehicles in the network.  
So according Equations (5)-(7), using the actual data from some wind field and photovoltaic power stations, the power ranges of fast and slow charging modes needed by the electric vehicle can be derived, and the charging power can be derived by a Monte Carlo method. The electric vehicle charging power obeys a normal distribution. The distribution curve of electric vehicle charging power is presented in Figure 3. The X-axis indicates the charging power of electric vehicle and the Y-axis indicates the probability value of the electric vehicle charging power, and this value has no unit. \(\mu\) represents the average value of the electric vehicle charging power when its probability value is the largest, and its unit is MW.