# A Contemporary Novel Classification of Voltage Stability Indices
## 1 Introduction
[16] inexact static indices based on the load flow model, applied the small signal and dynamic analysis to evaluate the accuracy of the indices based on the power law model. [PERSON] et al. [17] investigated four original voltage stability indices, which include various categories based on different formulation and techniques. This study is performed in light of the indices' performance with respect to the load factor change under different operating situations. The RTDS(r) a (Real-Time Digital Simulator) is used to estimate the real-time behavior of the indices. Finally, the authors found that the voltage collapse point indicators (VCPIs) have the best performance of the studied indices. In [18], the authors compared the suitability of the two indices (L\({}_{mn}\) and VCPI) to find the most suitable index for the control application. In [19], the mathematical terminologies and application are reviewed, which mostly relies on quasi-steady state and dynamic analysis such as voltage sensitivity factor (VSF), singular values, eigenvalue decomposition, second-order, voltage instability proximity index (VIPI), loading margin, direct methods, P and Q angles, test functions, etc. [PERSON] et al. [20] compared the power transfer stability index (PTSI) derived by considering the two-bus Thevenin equivalent system with line index (L index is known as a traditional index for voltage stability) and VCPI. In [21], a quantitative measure based on the operating point of load flow for an online application is proposed with a range of 0 (no load) and 1.0 (voltage collapse point). This index is formulated by using two-bus system power flow equations. Then, the index is generalized for a multi-bus system in the view of PQ and PV categories. In [22], the L index is denoted as a nonabsolute indicator of voltage stability in the system. In 2013, [PERSON] et al. [23] extended this index based on an alternative generator equivalent model (GEM) instead of an ideal constant voltage source. The generalizability of previous research efforts in this context implies that the efforts do not cover all aspects or have been limited. Most studies in voltage stability indices comparison and classification have only been carried out in a small domain or focused on dynamic analysis. It is manifested that the adequate picture of voltage stability indices' classification is still ambiguous due to behavioral similarity and intervention of their behavior in the system, as well as the variety in an application. Nevertheless, this study aims to define comprehensively and compare the performance of the original indices, which are proposed and applied globally. With the embrace of literature, a detailed classification of these indices (mainly based on the formulation) is transpired. Meanwhile, we take the distinguish between merit and demerit of the proposed indices as an essence, because these indices scale the power system behavior with respect to the system parameters changes, in the form of voltage variations. This study reveals an extensive-unified perspective from various classes as the most outstanding indices from each category. The rest of the paper is organized as follows; in Section 2, the proposed classification method and classification of the voltage stability indices are presented. Section 3 describes a broad classification of voltage stability indices along with proposing a novel method. The theoretical analysis of indices of different categories is defined in Section 4. In Section 5, the simulation results and verifications are discussed. Finally, Section 6 concludes the preference of the study through originality, significance, and practical value of the topic by summarizing the advantages and disadvantages of the indices in each category.