# Analyzing Six Indices for Online Short-Term Voltage Stability Monitoring in Power Systems
## 1 Introduction  
In recent years, due to the ever-increasing electrical demand and the limitations associated with financial resources, power systems are usually operated near their transmission capability limits [1]. Therefore, new real-time monitoring and control techniques are necessary to guarantee secure operation of modern power systems. One of the main stability issues in modern power system is the voltage stability that needs to be monitored for keeping the system operation in safe mode. Based on time frame of appearance instability, voltage stability problem can be classified into long-term and short-term voltage stability studies [2]. Due to increase of amounts of dynamic loads, especially induction motors, which led to increasing the reactive power demand under reduced-voltage conditions, power systems have become more vulnerable to short-term voltage stability (SVS) problems. Therefore, the monitoring of short-term voltage stability (SVS) has become necessary to be taken into consideration especially for modern power systems and future smart grids [3; 4; 5]. Short-term voltage instability should be identified to prevent significant voltage drop which might lead to damage of equipment and disruption of power balance and finally might cause a system's collapse. In [6], an SVS analysis from the perspective of active and reactive power balancing has been proposed. In the last few decades, model-based methods have been utilized for analyzing short-term voltage stability, in which these methods have focused on the dynamic modeling and aggregation of fast acting load components like induction motor loads [7]. However, model-based methods for SVS monitoring have some difficulties in modeling dynamic loads and setting load parameters. It has been clearly demonstrated that the application of model-based methods in reality might encounter infeasibility due to reasons such as the wide diversity of the used components of the system loads and their different characteristics, and the unavailability of the required load information of all areas in the control center in real-time [4; 8]. Therefore, the effectiveness of model-based methods is limited in real-time applications. With the introduction of a phasor measurement unit (PMU) that acquires time-synchronized measurements at a much higher sampling rate rather than conventional measurement devices, wide-area measurement systems (WAMS) have been widely deployed in reality. Due to deployment of WAMS, the real-time voltage and current phasors become available in control centers which helps in improving the online monitoring and control of modern power systems [9; 10]. Therefore, data-based or model-free methods can be adopted and developed for online stability monitoring in modern and future power systems. In data-based methods, PMUs data are used to calculate indices for voltage instability detection. In [11; 12], long term voltage stability indicators based on PMU data have been proposed for stability monitoring and can identify critical loads in a system. Recently, Lyapunov exponents (LE) have been extensively used in literature for short-term voltage instability prediction. In [7], a data-driven method based on the voltage magnitude measured by PMUs has been explained for LE calculation. In [13], the authors have discussed the influence of oscillations and improper parameter settings in instability detection with LE; they proposed an improved phase rectification (PR)-based SVS monitoring method which removes that weakness using modal analysis. In [14], the authors have introduced a framework which uses the PMUs data for calculating LEs. They significantly improved their framework performance under noisy measurements by averaging the latest data packages received in the control center. Some voltage indices have been suggested in literature and used for dynamic VAR planning based on describing the integration of voltage deviation or the voltage violation time span.