## 3 Example Analysis
### Using Analytic Hierarchy Process (AHP) to Calculate Subjective Weight  
The first-level indicator judgment matrix is as follows:  
\[C_{1}=\left( \begin{array}{cccc}1&1&1&2\\ 1&1&1&2\\ 1&1&1&3\\ 1/2&1/2&1/3&1\end{array} \right)\]  
The calculation results show that \(\lambda_{1 max}=4.0206\). The corresponding weight vector is [0.2804, 0.2804, 0.3120, 0.1272]\({}^{T}\). \(CR_{1}=0.0076<0.1\). It passes consistency verification. The judgment matrix of the secondary indicator corresponding to reliability is as follows:  
\[C_{2}=\left( \begin{array}{cc}1&2\\ 1/2&1\end{array} \right)\]  
The calculation results show that \(\lambda_{2 max}=2.0000\). The corresponding weight vector is [0.6667, 0.3333]\({}^{T}\). \(CR_{2}=0<0.1\). It passes consistency verification. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**First-Level Indicators** & **Secondary Indicators** & **Scheme 1** & **Scheme 2** & **Scheme 3** & **Scheme 4** \\ \hline \multirow{3}{*}{The reliability indicators (A1)} & Average service availability & \multirow{3}{*}{99.9784} & \multirow{3}{*}{99.9630} & \multirow{3}{*}{99.9911} & \multirow{3}{*}{99.9863} \\  & index (B1)/\% & & & & \\ \cline{2-6}  & System average interruption duration index (B2)/(h/year) & & & & \\ \hline \multirow{3}{*}{The economic indicators (A2)} & Initial investment cost (B3)/ & \multirow{3}{*}{6270} & \multirow{3}{*}{5982} & \multirow{3}{*}{7990} & \multirow{3}{*}{7476} \\  & (RMB 10,000) & & & & \\ \cline{2-6}  & Operation and maintenance cost & & & & \\ \cline{2-6}  & (B4)/(RMB 10,000) & & & & \\ \cline{2-6}  & Network loss cost (B5)/ & \multirow{3}{*}{15.768} & \multirow{3}{*}{11.038} & \multirow{3}{*}{15.768} & \multirow{3}{*}{12.614} \\  & (RMB 10,000) & & & & \\ \hline \multirow{3}{*}{The power quality indicators (A3)} & Voltage offset (B6)/\% & 0.42 & 0.51 & 0.42 & 0.33 \\ \cline{2-6}  & Frequency deviation (B7) & Excellent & Good & Excellent & Excellent \\ \cline{2-6}  & Harmonic distortion rate (B8) & Good & Fair & Good & Excellent \\ \hline \multirow{3}{*}{The environmental Protection Indicators(A4)} & Emissions of polluted gases (B9) & Excellent & Good & Excellent & Excellent \\ \cline{2-6}  & Land occupation area (B10)/m\({}^{2}\) & & & & \\ \cline{1-1} \cline{2-6}  & \multirow{3}{*}{1/2} & \multirow{3}{*}{1/2} & \multirow{3}{*}{1/3} & \multirow{3}{*}{1} & \multirow{3}{*}{1} \\ \cline{1-1} \cline{2-6}  & & & & & \\ \cline{1-1} \cline{2-6}  & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Scheme parameters. Figure 3: Power grid structure diagram. The judgment matrix of the secondary indicator corresponding to economy is as follows:  
\[C_{3}=\left( \begin{array}{ccc}1&2&3\\ 1/2&1&2\\ 1/3&1/2&1\end{array} \right)\]  
The calculation results show that \(\lambda_{3 max}\) = 3.0092. The corresponding weight vector is [0.5396, 02970, 0.1634]\({}^{T}\). \(CR_{3}\) = 0.0046 \(<\) 0.1. It passes consistency verification. The judgment matrix of the secondary indicator corresponding to power quality is as follows:  
\[C_{4}=\left( \begin{array}{ccc}1&1&3\\ 1&1&3\\ 1/3&1/3&1\end{array} \right)\]  
The calculation results show that \(\lambda_{4 max}\) = 3.0000. The corresponding weight vector is [0.4286, 0.4286, 0.1429]\({}^{T}\). \(CR_{4}\) = 0 \(<\) 0.1. It passes consistency verification. The judgment matrix of the secondary indicator corresponding to environmental protection is as follows:  
\[C_{5}=\left( \begin{array}{ccc}1&2\\ 1/2&1\end{array} \right)\]  
The calculation results show that \(\lambda_{5 max}\) = 2.0000. The corresponding weight vector is [0.6667, 0.3333]\({}^{T}\). \(CR_{5}\) = 0 \(<\) 0.1. It passes consistency verification. Using the Equation (15), we can check the consistency of hierarchical total ranking. \(CR\) = 0.0046 \(<\) 0.1. It passes consistency verification. Therefore, the subjective weight of each evaluation indicator is shown in Table 5 and Figure 4.