# A Contemporary Novel Classification of Voltage Stability Indices
## 5 Simulation and Verification  
Simulation is carried out on WSCC 9 and IEEE 14, and 30-bus test systems [10; 55] to expose the merit and demerit of the voltage stability indices, which are mostly proposed and applied globally because of their simplicity in the formulation and broad application. Since the simulation of all 36 indices are not viable in a single study due to the requirement of specific hardware and software simulation tools (for real-time online application), the theoretical formulation of the rest of the indices is reviewed, and based on the indices formulation methodology, a precise classification is proposed. As a result, an exhaustive-coherent framework is proposed to qualify the merit and demerit of the indices. Moreover, it establishes a consistent relationship among indices in view of the index performance to identify the critical bus and line stability (or proximate the tended buses to collapse) in a power system. The idea of this study is to assess the indices theoretical formulation, functionality, applicability, and overall performances in each category through addressing the indices shortcomings. The study methodology is carried out in a systematic approach as follows: (a) The indices are studied in two categories, node and line indices, (b) such that, each simulated test system in a category is assessed separately with respect to the ranking of the three top sensitive critical lines, and three top critical buses identification in the system by means of each index, (c) then, the overall test systems results are concluded. All the analyzed indices in this section depend on two categories (from two classes, variable-based and Jacobian matrix-based), nodal and line indices. The critical buses and lines are sorted in descending order in Tables 2 and 3; that are named 1 to 3. From Table 2, it is noticed that the proposed line indices are comparatively agreed on the identification of the top three critical branches in the system. However, the WSCC 9-bus system results indicate that the L index appears different in ranking of the second and third critical feeders compared to the rest of indices. At the 14-bus system, almost all indices are in agreement at the first and second ranking orders; except, \(V_{\text{cr}}\) and LVSI. Whereas, the indices are varied in the third critical branch identification. Altogether, the 30-bus systems ranking results imply that except for the first three indices, all are enormously diverse. So far, a quick conclusion can be drawn that line indices are affected by the system configuration in an interconnected system. Table 3 illustrates the response for ranking of the three top critical weak buses by each index. Excluding from VSF and PSI, almost all the proposed bus indices have the same recognition ranking with dissimilarity in identification of the third critical bus at the 14-bus system and first and second weak buses recognition at the 30-bus system. In order to facilitate the calculation and preserve accuracy, the following are assumed: The angles ratio of the V and V\({}_{\rm o}\) in the V/V\({}_{\rm o}\) index calculation are neglected, due to their close prices and negligible impact on the index magnitude. To avoid ambiguity in the indices calculation, for some cases the magnitude of line parameters such as resistance (r), and reactance (x) are supposed as 0.00001, instead