## 1 Introduction  
Voltage stability is a major concern and is the main factor that limits power transfers in today's grid operations. For this reason, significant research efforts have been devoted to understanding the voltage instability phenomenon and proposing corresponding countermeasures [1; 2; 3]. Voltage stability is an essential dynamic phenomenon. If analysis targets system load margin, critical bus identification, or reactive power compensation, then the use of static model is adequate. A large portion of studies have focused on the steady-state aspects of voltage stability. While static analysis is simple, it still provides some practical advantages over dynamic analysis, providing results with acceptable accuracy and little computational effort [4; 5]. In several recent large-scale blackout events, such as in Scandinavia (2003), the northeastern United States (2003), southern Sweden (2003), eastern Denmark (2003), Italy (2003), Athens (2004), and Brazil (2009), voltage collapse has played a major role [6; 7; 8]. In view of this, it is essential for system operators to identify whether a current operating state is prone to voltage collapse or not. In order to measure system long-term voltage stability, the concept of voltage stability margin (VSM) has been proposed to demonstrate the closeness of current operating point to voltage collapse point [9; 10]. A review of literature reveals that various VSM evaluation approaches are based on different kinds of techniques, such as sensitivity techniques [11; 12], singular value decomposition techniques [13; 14], machine learning techniques [15; 16], impedance-based techniques [17; 18; 19; 20], continuation techniques [21; 22; 23; 24], and line voltage stability indices [25; 26]. It is noteworthy that different voltage stability indices may give different results, i.e., they may not show the true distance to voltage collapse. An extensive comparison study on voltage stability indices can be found in the works [27; 28]. In fact, voltage stability is related to saddle-node bifurcation, which corresponds to the maximum loading point [23]. When the generation-transmission system is unable to meet the continuous increase in load demand, voltage instability and even voltage collapse situations are more likely to take place. In this regard, load power margin is often associated with VSM, as illustrated in Figure 1. Indeed, a number of methods proposed in works [21; 22; 23; 24] utilize this kind of measure as a monitoring index of voltage stability. To determine load power margin under a certain load level, _P-V_ curves are widely utilized by power companies. Generally, such curves are generated by means of a series of power flow solutions for different load levels. However, successive computation using the traditional power flow approach may lead to a divergence problem near the voltage stability boundary. Thus, continuation power flow (CPFLOW)-based methods have been used to cope with the numerical difficulties caused by the singularity of the power-flow Jacobian matrix at and around the critical point [21; 22; 23; 24]. Although CPFLOW based methods are able to track the exact voltage collapse point, these methods are time-consuming, especially for a large power grid model. Recently, some impedance match methods [17; 18; 19; 20] have been proposed to determine the voltage collapse point. To the author's knowledge, most of these can quickly provide the results with acceptable accuracy. The main contribution of this paper is the development of a new method for fast and accurate VSM computation in a large-scale power system. To this end, an efficient framework based on the impedance match-based technique and the model-based technique is proposed. In the proposed framework, the Thevenin equivalent (TE) network approach with cubic spline extrapolation technique and continuation technique are employed to determine the voltage collapse point. In addition, the developed approach is capable of dealing with the cases that cause generators to reach the \(Q\) limits.