## 1 Introduction  
Recently, voltage stability has become a serious issue in modern power systems. As power systems are becoming increasingly complex and dynamic, uncertainty regarding their stability is increasing gradually. A monitoring system is required to control power systems that change hourly depending on the situation [1; 2]. The traditional method of monitoring a power system, i.e., supervisory control and data acquisition/energy management system (SCADA/EMS), involves technical limitations that cannot provide synchronized data. However, the development of the phasor measurement unit (PMU) has enabled the supervision of dynamic networks. The information obtained from a PMU is synchronized by a global positioning system (GPS), which can be transmitted in almost real time [3; 4]. Therefore, all the snapshot data indicate the same time, allowing for the representation of a dynamic situation across a wide area of the power system, thereby enabling a wide range of stability monitoring and control applications. For this reason, the research of real-time voltage stability monitoring has focused on developing new indices to detect voltage instability. To prevent blackouts such as a voltage collapse, an accurate and efficient real-time online voltage stability monitoring methodology is necessary [5; 6; 7; 8; 9; 10]. Hence, numerous online voltage stability indices have been researched. The estimation of a Thevenin equivalent (TE) impedance is beneficial for monitoring voltage stability in real time because of its simplicity. The primary idea of such a method is as follows: (i) Obtain the voltage and current from local phasor measurement; subsequently, calculate the TE impedance of the remaining systems; (ii) when the measured load impedance is equal to the TE impedance (i.e., the maximum power delivered point), voltage instability occurs to the power system; and (iii) convert the load observation and TE impedance to the system margin to monitor the voltage stability of the power system. Many researchers have applied this method and several applications have been developed because of its simplicity [11; 12; 13; 14; 15; 16]. Among the indicators, the voltage instability prediction (VIP) algorithm is a voltage stability monitoring method that predicts a voltage collapse by observing the Z-index [17; 18]. This method involves a time delay; thus, the results are not reliable if the PMU is not installed on a radial bus. Further, the corridor monitoring method measures both ends of the transmission corridor before establishing the voltage stability index (VSI). The primary advantage of this algorithm is that parameter estimation involving time delay is not required [19; 20]. A coupled single-port circuit [21] can be represented by TE circuit parameters using a concept that decouples a meshed network into an individual single generator versus a single bus network. Reference [22] proposed the estimation of impedance using the recursive least-squares estimation. This algorithm is based on using the PMU to identify the impedance parameters of a power grid. A general model was presented for investigating the TE impedance analytically in [23]. A virtual voltage source and an impedance method were proposed to approximate the TE impedance. In addition, the application methods calculating the voltage stability margin (VSM) using a synchronized phasor and the TE impedance were introduced in References [24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. Every method presents its own advantages and disadvantages for the monitoring of voltage stability. Recent studies have resulted in TE estimation methods for wide-area monitoring that utilizes synchrophasor measurement technology (SMT) attained based on PMUs. The authors of Reference [34] have developed a TE method according to a least-squares procedure to determine the parameters from local measurements. In the study by [PERSON] et al., an improved TE method for real-time voltage stability assessment using wide-area information from PMUs was proposed [35].