## 1 Introduction  
With the increase of load, the transient voltage stability of a power system will deteriorate gradually [1; 2]. To ensure the safe and stable operation of a large-scale power system, it is necessary to first evaluate, quickly and accurately, its transient voltage stability. Transient voltage instability usually occurs after a severe voltage sag. The primary mechanism of transient voltage instability is due to the inability of the induction motor to accelerate after disturbance or to a block of the induction motor caused by weakening of the transmission system [3; 4; 5]. Therefore, the evaluation of transient voltage stability requires evaluating the transient stability of the induction motor. At present, there are many methods to judge transient voltage stability, including time domain simulation, the direct method, and the intelligent algorithm. Among them, the time domain simulation method is well developed and widely used in various commercial software [6]. Compared with the time domain simulation method, the direct method can avoid the heavy work of numerical integration. The most classical direct method is based on the Lyapunov theory [7; 8]. In recent years, some new direct methods have been applied to transient voltage stability analysis. Ref. [9] presents a voltage stability analysis method based on the holomorphic embedding theory. Ref. [10] analyzes the transient voltage stability by stability boundaries on the power-voltage plane. However, the direct method is difficult to be applied in a large-scale power system with high orders. With the development of intelligent algorithms, the application of the intelligent algorithm has gradually attracted the attention of scholars. Data-driven intelligent algorithms have been utilized [11; 12] to evaluate the transient voltage stability. However, data-driven intelligent algorithms are usually based on a large amount of accurate data, which requires a large-scale application of power management units. In some works, [13; 14], machine learning methods were applied to the transient voltage stability assessment. The intelligence algorithm can be applied to online monitoring to prevent transient voltage instability [15; 16]. Although the intelligent algorithm has good application prospects, it is difficult to widely apply it at present, due to high complexity and large amount of calculation it involves. The direct method and the intelligent algorithm are still far from engineering application. At present, in order to evaluate the transient voltage stability, bus voltage curves are usually obtained by the time domain simulation or the on-line monitoring first, and then a criterion is used to evaluate the voltage curves. Among various transient voltage stability criteria, there is a class of practical criteria based on voltage magnitude and sag duration that are widely used in practical engineering. For example, the technique specification of the State Grid Corporation of China (SGCC) stipulates that the voltage cannot remain below 0.8 pu for longer than 10 s [17]. The reliability guideline of the Western System Coordinating Council (WSCC) establishes that the voltage drop cannot exceed 20% of the normal value for longer than 0.33 s [18]. In addition to practical criteria, a transient voltage stability index was proposed [19], which considers both the voltage sag and the recovery. Ref. [20] presents a method for evaluating voltage sag severity, and this method is based on the scaling and wavelet coefficient energy function. A new voltage stability index was proposed by [PERSON] et al. [21]. In another study [22], a voltage sag index was put forward to evaluate the severity of the voltage sag. An index was proposed to evaluate the voltage stability margin [23], and this index can be applied to the formulation of the load shedding strategy. Although a variety of criteria have been proposed, the widely used transient voltage stability criteria in practical engineering are still the practical criteria based on voltage magnitude and sag duration.