## 3 Results and Discussion
### Identification and Verification of Dual Index in Power Grid Enterprises  
First, the index system was analyzed, and the element relation was constructed as per the relationship among indexes determined by expert grading. Next, an adjacency matrix was established based on this relationship (Figure 2), and a reachability matrix was calculated through the matrix operation (Figure 3). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Definition** & **Index** & **Definition** \\ \hline Power grid investment & S1 & Maintenance cost of power grid & S17 \\ Infrastructure investment & S2 & Industrial added value & S18 \\ Line length of per capita & S3 & Transmission and distribution cost & S19 \\ Total staff & S4 & Load rate & S20 \\ Technological transformation investment & S5 & Inventory turnover & S21 \\ Average price difference of power purchasing & S6 & Outage rate of power grid system & S22 \\ Marketing investment & S7 & Inventory material idle rate & S23 \\ Grid-connected installed capacity of new energy & S8 & Talent equivalent density & S24 \\ Electricity revere rate & S9 & Electricity sales & S25 \\ Market share & S10 & Per capita profit & S26 \\ Gross income & S11 & Economic value added & S27 \\ Reliability rate of power supply & S12 & Comprehensive line loss rate & S28 \\ Customer satisfaction rate & S13 & Voltage qualification rate & S29 \\ Power supply population & S14 & Return on equity & S30 \\ Emission reduction CO2\({}_{\text{2}}\) by generation & S15 & Total owners’ equity & S31 \\ Execution equilibrium rate of Electricity & S16 & Asset-liability ratio & S32 \\ Purchase Contracts & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Correspondence relation for index definition. Figure 2: Adjacency matrix. Finally, the reachability matrix was decomposed under the condition of \(R(S_{i})\cap Q(S_{i})=R(S_{i})\), and the relation diagram was constructed based on the result (Figure 1). As seen in Figure 4, the 32 indexes were distributed at two ends of the level, which meant that the element closer to the top was more likely to be affected, so had great dependence; and the element closer to the bottom was more likely to impact others, so had great driving force. Two core indicators were divided under different requirements: the achievement index group and the driving index group (specific indicators are shown in Table 2). The data was analyzed by SPSS, and to test whether 16 core indicators from the structural model could achieve a contribution rate of more than 85%. Based on the software results (Table 3), the contribution rate was more than 85%, which meant that the extracted index by the structural model could represent the operational monitoring index of a power grid. \begin{table}
\begin{tabular}{c c c} \hline
**Driving Index Group** & **Achievement Index Group** \\ \hline
**Number** & **Index** & **Number** \\ \hline
1 & Power grid investment & 1 & Comprehensive line loss rate \\
2 & Infrastructure investment & 2 & Voltage qualification rate \\
3 & Line length of per capita & 3 & Asset-liability ratio \\
4 & Total staff & 4 & Per capita profit \\
5 & Technological transformation investment & 5 & Economic value added \\
6 & Average price difference of power purchasing and selling & 6 & Electricity sales \\
7 & Marketing investment & 7 & Total owners’ equity \\
8 & Grid-connected installed capacity of new energy & 8 & Return on equity \\ \hline \end{tabular}
\end{table} 
Table 2: Achievement index group and driving index group. Figure 4: Relationship diagram of the operational monitoring index. Figure 3: Reachability matrix.