# A Contemporary Novel Classification of Voltage Stability Indices
## 1 Introduction  
Day-by-day, increase in electricity demand and liberalization policy of the electricity markets persuade the power systems to operate close to their stability limits. Despite, voltage instability in a system can swiftly lead the power system to the voltage collapse. A blackout can take place in the entire power system or a part of a system due to voltage collapse that can appear abruptly. Instability prediction and continuous monitoring of power system performance are therefore known as exigent. Voltage stability involves both static and dynamic behaviors of a power system [1]. Regardless of the differences, both types of voltage stability are correlative to analyze the system stability mechanism. Investigation of steady-state operation is a prerequisite for initiating transient stability analysis. Therefore, the steady-state equilibrium is a necessary condition for stable transient operation [2; 3; 4]. The static voltage stability indices employ a measure of the distance from the current operating point to the voltage collapse point [5]. The static indices can either contribute to identifying the critical bus and stability of connected lines in the system along with evaluating the stability margin concerning the system loadability. Power system operation and voltage stability assessment are correlative to each other to ensure reliable and cost-effective operation. It is impelling to employ voltage stability indices to cognize the system performance behavior that show how close the system is to voltage collapse, loadability and security limits, and overall performance of the system. Over recent decades, valuable researches have been conducted with the concept of the comparative analysis and classification of voltage stability indices. From different standpoints, [PERSON] et al. [6] proposed a new voltage stability index (critical boundary index-CBI) based on active and reactive power deviations. The effectiveness of the proposed index is compared with the most worldwide accepted indices. However, the proposed index is time consuming. Still, it counted a novel index due to its high accuracy of prediction. [PERSON] et al. [7] examined some line voltage stability indices using IEEE 30-bus and 118-bus test systems under various operating conditions. This study pointed out a systematic methodology of applying parameters for the appropriate use of indices. [PERSON] et al. [8] proposed a new integrated transmission line transfer index (ITLTI) based on the radial topology that is known as suitable for power transferring situations including leading, lagging, or unity power factor. In [9], the authors introduced an improved voltage stability index using linear algebra techniques to predict a power system operating condition beyond the collapse point. The effectiveness of the proposed algorithm and the index performances are verified by comparing the existing indices in the literature. In other related studies [10; 11; 12], authors compared customary indices and recognized the most appropriate indices in terms of load shedding and optimum storage allocation in a critical situation. [PERSON] et al. [13] compared three voltage stability indices by testing on a real power system of the Italian HV transmission grid with a focus on the functionality of the indices. [PERSON] and [PERSON] [14] proposed an index (I\({}_{i}\)) based on active and reactive power deviation at the operating point and no-load values. The authors have compared the effectiveness of the proposed index by changing the line parameters and load power factor. To have an effectiveness comparison amongst the indices, [PERSON] and [PERSON] [15] investigated some original static voltage stability indices. Despite the promising works in the literature, still, there is a lack of a broad precise classification and comparison analysis of the voltage stability indices. However, [PERSON] and [PERSON] [15] performed a wrathful comparative analysis of line and nodal indices. [PERSON] et al.