## 2 Model and Method
### Load Calculation  
The optimization of the DES based on a single set load cannot reflect the influence of the annual hourly load fluctuation on the optimization results. It is difficult to obtain multiple sets of annual hourly loads with different volatilities through the existing methods. Therefore, the discretization method is used to solve this problem. In addition, the variance of the annual load is quoted to describe the fluctuation. Finally, the typical daily load of the discrete load is obtained using a clustering algorithm. The specific steps are as follows:  
Step 1: The type, location, heat transfer coefficient of the maintenance structure, and the structure of the building are obtained to calculate the initial cooling, heating, and power loads by DeST (a software for building environment simulations and HVAC system simulation). Figure 1: The typical structure of the DES and SP. Step 2: Multiple sets of discrete loads are obtained by discretizing the initial load using MATLAB. Firstly, due to the load data of the building meeting the normal distribution [32], the ratio of two normal distribution functions (\(f_{1}\)(x) and \(f_{2}\)(x)) with different variances is defined as an index function (\(f\)(x)). Secondly, the range of the independent variable (\(-\)a, a) of the normal distribution functions with a confidence interval of 0.99 is solved. Thereafter, the index coefficients (\(f\)(x)) are obtained by the index function \(f\)(x) and the independent variables (\(0=x_{1}\), \(x_{2}\), \(x_{3}\)... \(x_{n}=\) a). Finally, the discrete load is obtained by multiplying the index coefficients and the sorted initial load [33]. Taking the cooling load as an example, the processes of discretization are shown in Figure 3. Where \(C_{i}\) is the cooling load at time \(i\), \(C^{\prime}{}_{i}\) and \(CD^{\prime}{}_{i}\) are the descending order and discretization of \(C_{i}\), and \(n\) is the number of hours in a year. Step 3: The fluctuation of the load is quantitatively described by the variance of hourly cooling, heating, and power load. The proportion of the variance of the discrete load deviating from the initial load data is defined as the fluctuation change rate \(\theta\). A positive  
Figure 3: The process of discretization for the initial cooling load. Figure 2: The flow chart of the optimization model. \(\theta\) denotes a higher fluctuation of the set of discrete loads than the initial load, while a negative \(\theta\) denotes a lower fluctuation. The equations are shown as follows:  
\[S=\sum_{i=1}^{n}((C_{i}-C_{mean})^{2}+(H_{i}-H_{mean})^{2}+(E_{i}-E_{mean})^{2}) \tag{1}\]  
\[\theta=\frac{S_{dl}-S_{il}}{S_{dl}} \tag{2}\]  
where \(S\) is the variance of load; \(n\) is the number of hours in a year (=8760); \(C_{i}\), \(H_{i}\), and \(E_{i}\) are the cooling, heating, and power load of the building at time \(i\), respectively; \(C_{mean}\), \(H_{mean}\), and \(E_{mean}\) are the annual mean value of cooling, heating, and power load, respectively; and \(S_{dl}\) and \(S_{il}\) are the variances of discrete load and initial load, respectively. Step 4: An agglomerative clustering algorithm is used to cluster the building loads [34]. Taking summer as an example, according to the different hours in each day, the cooling and power load of the building are divided into the 24 load matrixes (L\({}_{1}\) to L\({}_{24}\)). Columns 1-24 of the matrixes refer to the hourly cooling of the building in the summer, while columns 24-48 represent the hourly power load of the building in the summer. \[\text{L}_{1}= \begin{bmatrix}l_{1,1}&l_{1,25}\\ \vdots&\vdots\\ l_{i,1}&l_{i,25}\\ \vdots&\vdots\\ l_{m,1}&l_{m,25}\\ \end{bmatrix} \text{, L}_{2}= \begin{bmatrix}l_{1,2}&l_{1,26}\\ \vdots&\vdots\\ l_{i,2}&l_{i,26}\\ \vdots&\vdots\\ l_{m,2}&l_{m,48}\\ \end{bmatrix} \ldots\text{ L}_{24}= \begin{bmatrix}l_{1,24}&l_{1,48}\\ \vdots&\vdots\\ l_{i,24}&l_{i,48}\\ \vdots&\vdots\\ l_{m,24}&l_{m,48}\\ \end{bmatrix}  \tag{3}\]  
The hourly agglomerating points (\(W_{p},M_{p}\)) are obtained by clustering the matrix (\(L_{p}\)).