# Analyzing Six Indices for Online Short-Term Voltage Stability Monitoring in Power Systems
## 4 Comparison and Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Index name**} & \multicolumn{2}{c}{**Time Interval**} & \multicolumn{2}{c}{**Index Total Error in SVS**} & \multicolumn{2}{c}{**Number of Unstable Cases**} & \multicolumn{2}{c}{**Number of Stable Cases**} \\  & **(sec)** & **Assessment (\%)** & **Detected as Stable Cases** & **Detected as Unstable Cases** \\ \hline \multirow{4}{*}{LE} & 0.8 & 15 & 6 & 9 \\  & 1 & 35 & 3 & 32 \\  & 1.2 & 40 & 3 & 37 \\  & 1.5 & 36 & 3 & 33 \\  & 2 & 10 & 1 & 9 \\ \hline \multirow{4}{*}{CSI} & 0.8 & 15 & 15 & 0 \\  & 1 & 12 & 12 & 0 \\  & 1.2 & 9 & 9 & 0 \\  & 1.5 & 6 & 6 & 0 \\  & 2 & 6 & 6 & 0 \\ \hline \multirow{4}{*}{PI} & 0.8 & 25 & 25 & 0 \\  & 1 & 17 & 17 & 0 \\  & 1.2 & 11 & 11 & 0 \\  & 1.5 & 6 & 6 & 0 \\  & 2 & 4 & 4 & 0 \\ \hline \multirow{4}{*}{TVI} & 0.8 & 29 & 17 & 12 \\  & 1 & 25 & 12 & 13 \\ \cline{1-1}  & 1.2 & 24 & 9 & 15 \\ \cline{1-1}  & 1.5 & 12 & 0 & 12 \\ \cline{1-1}  & 2 & 7 & 0 & 7 \\ \hline \multirow{4}{*}{TVSI} & 0.8 & 23 & 23 & 0 \\  & 1 & 19 & 16 & 3 \\ \cline{1-1}  & 1.2 & 17 & 11 & 6 \\ \cline{1-1}  & 1.5 & 14 & 3 & 11 \\ \cline{1-1}  & 2 & 12 & 3 & 9 \\ \hline \multirow{4}{*}{VSRI} & 0.8 & 7 & 2 & 5 \\ \cline{1-1}  & 1 & 3 & 0 & 3 \\ \cline{1-1}  & 1.2 & 6 & 1 & 5 \\ \cline{1-1}  & 1.5 & 4 & 2 & 2 \\ \cline{1-1}  & 2 & 4 & 2 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: SVS indices performance in instability detection. decreased from 15% in time 0.8 s to 6% in time 1.5 s. The total error of this index in SVS assessment is generally due to unstable cases detected as stable cases. Although the CSI's total error is lower than LE, it is much worse than LE because it has worse performance in detecting the unstable cases which are very important to the power system operators. According to Table 2, PI ability in the detection of the short-term voltage instability is similar to CSI, and PI's detection total error is related to bad operation in terms of detecting unstable cases as stable cases. However, CSI's error in time intervals less than 1 s is lower than PI, but PI has slightly better performance with time intervals equal to 2 s.  
The TVI index performance in SVS assessment has also been shown in Table 2. It can be seen that TVI's total error is decreased from 29% in time 0.8 s to 7% in time 2 s and unstable cases' misdiagnosis is equal to zero with time intervals more than 1.5 s. Therefore, it can be identified that TVI has proper performance in SVS monitoring for time intervals close to 1.5 s. However, the main practical problem is related to the high amount of time needed for detecting the unstable cases, which limits its practicability. Based on the results introduced in Table 2, TVSI has an average performance in SVS assessment. However, TVSI error is mostly related to mistaken detection of stable cases as unstable cases, but, due to the number of misdiagnosed cases, this index is not suitable for SVS online monitoring. It is obvious from results presented in Table 2 that the proposed VSRI has proper performance and good ability for online SVS assessment. The VSRI total error in instability detection considering a time interval equal to 0.8 sec is less than 10% and most of this error is related to stable cases detected as unstable cases, which makes this index a proper one for practical implementations. For time intervals between 1.5 sec to 2 sec, the VSRI error has been reduced to less than 5% and only two misdiagnosed unstable cases exist. Therefore, it can be concluded that the proposed VSRI is a proper index for SVS online monitoring in modern power systems. To make clear comparison between the performance of the modified and the six indices in SVS assessment proposed, linear approximation of their total error in instability detection and their accuracy in unstable cases assessment for different time intervals from 0.8 s to 2 s are depicted in Figure 10(a),b, respectively.