## 1 Introduction
PMU measurements have been used in Reference [36] to estimate the relative VSM of the affected load buses. [PERSON] et al. [37] have proposed a method to compute the static TE voltage and reactance of a power system using measured data. In this research, TE parameters are used to compute the maximum power transfer capability of a wind hub that is constrained by voltage stability. In Reference [38], a method for the online determination of the TE parameters of a power system at a given node using local PMU measurements at that node was presented. The authors of Reference [39] developed a novel approach based on SMT to estimate the online TE impedance of a power system at a generator terminal. Furthermore, many applications exist for the theoretical evaluation of wide-area voltage stability monitoring. The authors of Reference [40] proposed the application of voltage stability monitoring based on the TE technique for online system loading margin estimation. [PERSON] et al. [41] deployed a measurement-based voltage stability monitoring method for a load area with boundary buses and a voltage source that represented the external system. In Reference [42], techniques have been proposed to assess the VSM in real time, which can facilitate in taking control actions to prevent an imminent voltage collapse. Studies on the VSI are being performed on various systems by varying the loads throughout the system and by increasing only the reactive loads [43]. In Reference [44], a method was proposed for monitoring the VSM using the regression technique. Load margin calculation for stressed buses was proposed in Reference [45] using particle swarm optimization. In Reference [46], a robust normalized voltage stability indicator based on solid theoretical foundations was proposed for monitoring power. Further, the applications of the VSI for estimating the distance to collapse and the amount of load to be shed were presented. Although these studies have motivated further improvements, the dynamic response of the system to practical applications must be studied further. The power systems undergo continuous variation, and the TE impedance from a particular bus cannot be fully represented by a constant value. Therefore, load modeling should be performed to capture the practical load dynamics of the power system. In addition, the network should be reconfigured using part of the calculating parameter to avoid computational burden in real time. Hence, this study proposes the real-time voltage stability assessment method using the TE impedance. This method presents the analytical process of the TE impedance estimation of a power system, and the procedure to convert the Thevenin impedances to the VSM. To estimate the TE impedance of the power system, a network reduction that converts a multiple bus system to a single bus system is implemented. Subsequently, the TE circuit is composed from virtual buses. Because the PMU can measure the voltage and current phasor, the active power and reactive power can be obtained; it is possible to calculate the voltage phasor of a virtual bus using the current phasor and complex power of each bus. For deriving the Thevenin voltage and impedance of the generation part, a parameter estimation method is essential. Estimating the parameters from data affected by continuously varying the parameters might yield a TE that does not reflect the actual stability. This paper details how this issue is addressed. The contributions of this paper are as follows: (i) Development of TE impedance estimation method; (ii) power system network remodeling for calculating TE impedances; (iii) composing a TE circuit from virtual buses; (iv) improving the accuracy of the estimated VSM by applying constant impedance-current-power (ZIP) load modeling; (v) using a least-squares method to account for errors in the model that arise from the time-varying TE and noise. In addition, the nose (power-voltage) curve is drawn based on theory using the TE voltages and impedances. To compare the operating and nose point, the VSM should be obtained.