## 2 Decision Area Division and Decision Variable Determination of Virtual Power Plant
### Division of Decision Area  
In order to reduce the number of decision variables, we first divide the decision area of VPP, that is, according to some criteria, a region can be divided into several blocks. At this time, the numbers of decision variables are changed from the numbers of distributed power, controllable load and ES device before the division area to the numbers of distributed power, controllable load and ES device in the region. The main basis for determining the decision area of VPP is: regional load density, power consumption levels, administrative ranks, economic levels and user importance [26]. Then, we can choose whether to formulate appropriate service agreements for each area and participate in the construction of VPP. In this paper, the decision areas of VPP are divided according to the regional function, mixed resource power and regional area. According to the different functions of urban areas, they can be divided into residence, industry, commercial finance, administrative office, culture and entertainment, medical and health, education and scientific research, municipal facilities, warehousing, transportation and agriculture. Mixed resources include the DG, ES and controllable load, and the mixed resource power is the sum of these three resources. According to the regional function, the region is divided into \(K\) blocks, and the area \(j\) can be recorded as \(S_{j}\) (\(j=1,2,\ldots,K\)). Then, each area is carefully divided. The division criterion is to minimize the number of divided areas under certain constraints, that is, the regional area cannot exceed \(S_{\text{max}j}\), and the maximum power of the mixed resource in each area cannot exceed \(Q_{\text{max}j}\). The area \(S_{j}\) is divided according to the regional function, so the mixture resource density \(\rho_{j}\) is different. There is a negative function relationship between \(S_{\text{max}j}\) and \(\rho_{j}\). The steps for dividing the decision area of VPP are as follows:  
1. Determine the type and quantity of resources in different locations of the region. 2. Divide the region preliminary according to the regional function, and record the area as \(S_{j}\) (\(j=1\), \(2\),..., \(K\)). 3. Divide area \(S_{j}\) particularity, initialize division block number \(N_{j}\) in each area, determine the parameters \(S_{\text{max}j}\) and \(Q_{\text{max}j}\) in the constraints. 4. According to the number \(N_{j}\) of areas, make \(S_{j}\) divided into equal areas. Determine whether to meet the constraints; if satisfied, turn (5), and vice versa (6). 5. \(N_{j}=N_{j}+1\), return to (3). 6. Obtain the final detailed division result of regional \(S_{j}\), which is the corresponding division result of \(N_{j}=N_{j}-1\). The flow chart of the decision area of VPP is shown in Figure 2.  
This paper illustrates the steps of the decision area division of the VPP by the following figure. Firstly, a preliminary division is made according to the region function, which is shown in Figure 3. Then, each region is detailed divided according to the relevant criteria; for example, the area \(S_{1}\) is finally divided into 4 parts, which is shown in Figure 4.  
Figure 2: Flow chart of decision area division of VPP. Assuming that the area \(S_{j}\) can be divided into \(C_{j}\) sub-areas, the region is divided into \(m\) areas after the detailed division, which is as follows:  
\[m=\sum_{j=1}^{K}C_{j} \tag{9}\]  
The decision variables, which represent whether there are distributed power sources, ES devices and controllable loads in the area \(i\) (\(i\) = 1, 2,..., \(m\)), are represented by vector \(X_{i}\) which is made up of 0 and 1 elements and can be written as:  
\[X_{i}=\left[X_{i}^{DG},X_{i}^{ES},X_{i}^{DR}\right]^{T} \tag{10}\]  
The set of decision variables in the whole region is:  
\[(X_{1},X_{2},\ldots,X_{m-1},X_{m})=\left[ \begin{array}{cccc}X_{1}^{DG}&X_{2} ^{DG}&\ldots&X_{m-1}^{DG}&X_{m}^{DG}\\ X_{1}^{ES}&X_{2}^{ES}&\ldots&X_{m-1}^{ES}&X_{m}^{ES}\\ X_{1}^{DR}&X_{2}^{DR}&\ldots&X_{m-1}^{DR}&X_{m}^{DR}\end{array}