# Analyzing Six Indices for Online Short-Term Voltage Stability Monitoring in Power Systems
## 4 Comparison and Results  
In order to compare the modified and proposed indices in this paper, the reliability and speed of different indices in SVS assessment are evaluated. For this purpose, a database of simulation data for many scenarios has been provided based on the basic operating point mentioned in [23], considering different disturbances, fault locations, portion of dynamic loads, and taking different consumed and generated power by loads and generators. The scenarios include 100 cases, where there are 66 stable and 34 unstable cases. The modified and proposed indices and their corresponding suggested instructions have been applied to determine unstable cases from an SVS point of view. With taking a different time interval from 0.8 s to 2 s, the performance of each of the six mentioned indices in SVS monitoring are provided in Table 1 using computation of their total error in instability detection. As shown in Table 1, using the Lyapunov exponent without phase rectification in SVS monitoring is not reliable in time 2 s. The \(CSI\) and \(TVI\) indices have average performance in SVS monitoring. They need at least 2 s for instability detection. \(VSRI\)'s error at short-term voltage instability detection is minimal and near 3%. Furthermore, SVS monitoring using \(VSRI\) needs 1 s for detecting instability. This research shows that the proposed \(VSRI\) has the best performance between the available and modified indices for short-term voltage stability monitoring. Figure 10: \(VSRI\) calculated for defined scenarios with \(N=60\): (**a**) Case a, (**b**) Case b, (**c**) Case c, (**d**) Case d, (**e**) Case e, (**f**) Case f.  
A further detailed comparison study between the modified and proposed indices considering the number of unstable cases detected as stable cases and conversely the stable cases detected as unstable cases is introduced in Table 2. It is worth mentioning that the ability to correctly detect unstable cases is more important compared to the detection stable cases. As presented in Table 2, LE's accuracy in instability detection for time intervals less than 2 s is not appropriate. Although the error is mostly because of detecting stable cases as unstable cases, there is a significant number of stable cases which are detected as unstable cases and cause incorrect operation of control systems. The comparison results clearly show that, by increasing the time interval, LE index performance can be enhanced, and it has acceptable performance if the time is set to 2 s. However, such time interval is long especially for online SVS monitoring, which identifies an LE index as an unsuitable index for online SVS monitoring applications. Likewise, the detailed performance of CSI in SVS assessment is inserted in Table 2. As expected by an increasing time interval, the performance of CSI in SVS assessment has been improved. It can be seen from the table that total detection error in CSI has been \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Time Interval (sec)**} & \multicolumn{4}{c}{**Index Error in Instability Detection (\%)**} \\ \cline{2-7}  & **LE** & **CSI** & **PI** & **TVI** & **TVSI** & **VSRI** \\ \hline
0.8 & 15 & 15 & 25 & 29 & 23 & 7 \\
1 & 35 & 12 & 17 & 25 & 19 & 3 \\
1.2 & 40 & 9 & 11 & 24 & 17 & 6 \\
1.5 & 36 & 6 & 6 & 12 & 14 & 4 \\
2 & 10 & 6 & 4 & 7 & 12 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: SVS indices performance in instability detection.