# A Contemporary Novel Classification of Voltage Stability Indices
## 6 Result and Discussion
* Those indices which are initiated from the load flow Jacobian matrix, are not suitable for online application due to their prediction insufficiency of voltage collapse, nonlinearity properties at the collapse point, and a high computation requirement. * Sensitivity analysis applies to weak bus identification. The sensitivity index alone will not be sufficient to identify weak buses especially in an interconnected system [56]. Beyond the other methods, sensitivity analysis plays an important role in prediction of critical nodes in the system. It is important to investigate how this critical point is affected by changing system conditions [54]. * From the literature, it is found that for solving the instability phenomenon, there are dynamic factors involved that cause a high dimensional and multi-parameter system [57]. Therefore, it may be wise to consider the static or semi-dynamic behavior. Most indices that measure the stable margin from operating point to the voltage instability are based on static analysis using the power flow model [16]. * As in the indices' classification section mentioned, there is a partial argument between the scholars, and the terms of the static and dynamic indices are customarily used in the literature. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Characteristic**} & \multicolumn{2}{c}{**Voltage Stability Indices**} \\ \cline{2-3}  & **Jacobian Matrix-Based** & **System Variable-Based** \\ \hline
**Time** & More time consuming. & Less time consuming. \\ \hline \multirow{4}{*}{**Application**} & Power system voltage stability margin estimation. & Power system elements’ crucial state recognition (weak bus or stressed area and line identification). \\  & Measure of the distance from current operating point to the voltage collapse point. & Constraints that caused voltage instability phenomenon. \\ \hline \multirow{4}{*}{**Merit**} & It is very sensitive near the steady state boundary. & Response to the overall system load change. \\  & Assess the whole system and could count a centralized measurement. & \\  & Better performance in radial systems than interconnected systems. & \\  & Variety in application in power systems such as recognition of the optimum placement of FACTS (flexible AC transmission system) and distributed generator in the system. & \\ \hline \multirow{4}{*}{**Demerit**} & Mostly reactive power limits on generators are not considered during index formulation. & Often extracted based on two-bus system model. \\  & Due to the nonlinearity of the system, this method is not an accurate close vicinity of the actual voltage. & \\  & Some indices are based on the computation of path & \\  & matrix or RED (related electrical distance) method, & \\  & which are computationally expensive. & \\  & Some indices under this category show a nonlinear & \\  & profile due to change in loading parameters. & \\  & It does not accurately predict the collapse point & \\  & because of its nonlinear behavior when it nears the & \\  & collapse point. & \\ \hline \multirow{4}{*}{**Formulation**} & Collapse point. & Stability margin. \\  & Eigenvalue approach. & Maximum power capability. \\  & Stability margin. & Reactive power margin. \\ \cline{1-1}  & PV-PQ voltage. & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparative analysis of Jacobian matrix-based and system variable-based indices. While partially for the purpose of voltage stability indices formulation, the dynamic model was considered by the steady state operation based on the stable equilibrium operating point of the power system [32] that from reference [57] is called semi-dynamic analysis. Therefore, it is arduous to refer to static or dynamic classes. This study embraces the most used indices in the literature in order to identify the critical bus and line stability in a power system.