## 2 Decision Area Division and Decision Variable Determination of Virtual Power Plant  
### Distributed Energy Resource Output Model  
The distributed DERs of a certain area constitute a VPP; therefore, the whole VPP is not restricted by the geographical area, and the control mode can be decentralized or centralized. The VPP is proposed to integrate all kinds of DER, including the DG, ES and DR, which is shown in Figure 1.  
By referring to the relevant references, most of authors take the DERs widely distributed in the city as research objectives in the study of VPP, such as the WP, PV, ES and flexible load [12; 13; 14; 21]. First of all, the mathematical model of these DERs is briefly introduced according to the relevant references. 1. Wind power Generation Model  
The output of WP is mainly affected by the wind speed and direction, and the wind speed and direction of different fans can be the same as those in the same power plant. Therefore, the output power \(P_{t}\) of a single fan is obtained according to the power characteristic curve of the wind turbine,  
Figure 1: The illustration of the constitution of virtual power plant. the product of the sum of all the fan power and the coefficient representing the output power [13], and can be described as:  
\[P_{t}=\left\{ \begin{array}{ccc}0&0\leq SW_{t}\leq V_{ci}\\ A+B\times SW_{t}+C\times SW_{t}^{2}&V_{ci}\leq SW_{t}\leq V_{r}\\ P_{r}&V_{r}\leq SW_{t}\leq V_{co}\\ 0&V_{co}\leq SW_{t}\end{array} \right. \tag{1}\]  
where \(A=\frac{1}{(V_{ci}-V_{r})^{2}}\bigg{[}V_{ci}(V_{ci}+V_{r})-4(V_{ci}V_{r})\bigg{(} \frac{V_{ci}+V_{r}}{2V_{r}}\bigg{)}^{3}\bigg{]}\), \(B=\frac{1}{(V_{ci}-V_{r})^{2}}\bigg{[}4(V_{ci}+V_{r})\bigg{(}\frac{V_{ci}+V_{r} }{2V_{r}}\bigg{)}^{3}-3(V_{ci}+V_{r})\bigg{]}\), \(C=\frac{1}{(V_{ci}-V_{r})^{2}}\bigg{[}2-4\bigg{(}\frac{V_{ci}+V_{r}}{2V_{r}} \bigg{)}^{3}\bigg{]}\), \(SW_{t}\) is the wind speed at the location of the fan, \(V_{ci}\) is the threshold wind velocity of the fan, \(V_{r}\) is the rated wind speed of the fan, \(V_{\alpha}\) is the resection wind speed of the fan, and \(P_{r}\) is the rated power of the fan. 2. Photovoltaic Generation Model  
The PV generation system is mainly constituted by power generation and conversion systems, which is composed of PV panels, controllers, ESs and conversion devices. The output power of PV generation system is directly related to the light intensity, and its power output model is [14]:  
\[P_{PV}=\left\{ \begin{array}{ccc}P_{sn}R^{2}/R_{r}R_{c}&0\leq R<R_{c}\\ P_{sn}R/R_{r}&R_{c}\leq R<R_{r}\\ P_{sn}&R\geq R_{r}\end{array} \right. \tag{2}\]  
where \(P_{PV}\) is the actual output power of PV generation system, \(P_{sn}\) is the rated power of the PV generation system, \(R_{c}\) is the characteristic intensity of solar irradiance which is generally 150 W/m\({}^{2}\), and \(R_{r}\) is the solar radiation intensity when the PV power generation system just reaches the rated power (generally 1000 W/m\({}^{2}\)). 3. Energy Storage Model  
ES technologies can be classified into mechanical ES, electrical ES, electrochemical ES, thermal ES, and chemical ES, according to the different storage media. As an application form of ES, electric vehicles have the characteristics of flexible regulation and widely exist on the user side. Therefore, the ES devices in this paper mainly consider electric vehicles. The main factors affecting the charging curve of electric vehicles include the quantity, type, charging characteristics and user behavior of electric vehicles [22]. The initial charge state of a single electric vehicle battery is related to mileage, which is shown as follows:  
\[SOC_{0}=1-D/L \tag{3}\]  
where \(SOC_{0}\) is the initial charging state, \(D\) is the actual mileage number, and \(L\) is the maximum mileage number. According to the initial charge state of electric vehicle battery, the charging duration time and charging power of single vehicle can be obtained, and then the daily charging curve of all the electric vehicles can be obtained. Taking Toyota RAV4 electric vehicle as an example.