## 1 Introduction  
The increased use of electronically controlled loads and the increasing induction motor (IM) loads make modern power systems more complex in terms of dynamic stability. The use of IM loads is continually evolving based on technological advances and economics, which changes the performance characteristics of the loads. The characteristics of IM-dominating loads have an important role in the dynamic behaviors of the systems. Recently, there has been an increasing concern on the load model of IMs, especially small single-phase IM loads for small appliances and some air conditioners (AC), and the portion of these is increasing. Systems with a large portion of inductive (IM) loads might face delayed voltage recovery (DVR) after the fault. The DVR phenomenon, observed and reported in various parts of the world, has been recognized as a voltage stability issue [1; 2; 3; 4]. The phenomenon is basically caused by stalling of IM loads, and it could in turn potentially result in the cascading effect on other IMs in the same feeder or in their vicinity. As dynamic reactive power consumption by the IM loads stalling increases during disturbances, the imbalance between the reactive power supply and demand is aggravated. This might eventually cause voltage collapse in the power system. Thus, the growing penetration of IM loads in power systems is the leading driving force of short-term voltage instability [5; 6; 7]. The research on the DVR problems in the literature can be categorized into the following three aspects: (i) the development of a load model to represent DVR in time-domain simulation, (ii) the method to mitigate IM stalling in power systems, and (iii) the influence of the increasing distributed energy source (DER) penetration on the power system. The literature related to the development of an IM load model can be reviewed as follows. The early studies on IM load modeling are summarized in [8; 9]. In [10] and [11], the frame transformation and detailed flux modeling were proposed. They developed a set of differential equations for single-phase IM models that can be used in transient simulation [12]. A deterministic performance model based on experimental data was produced in [13]. IM stalling was studied probabilistically within the cascade model in [14; 15]. The dynamic performance model for IM stalling and over-heat thermal tripping was developed in [16]. Generally, mitigation countermeasures against DVR events can be classified into supply side and demand side ones. As supply side countermeasures, utility applications include the implementation of flexible alternating current transmission system (FACTS) devices such as the static VAR compensator (SVC) and static synchronous compensator (STATCOM), for reactive power support [17; 18; 19; 20]. As demand side countermeasures, under voltage load shedding (UVLS) has been widely used to mitigate voltage related problems [21]. In recent years, various UVLS schemes have been proposed. Regardless of a specific mechanism, the key parameters always are the time, the location, and the amount of load shedding for UVLS schemes [22; 23; 24]. However, the existing adaptive schemes do not consider the dynamics of motors [25; 26]. The UVLS practices in the world [27] are as follows. In the North America, Puget Sound applies a distributed UVLS scheme using under-voltage relays as a safety net. New Mexico adopts the scheme preventing voltage collapse following loss of both 345 kV lines during peak loads. Energy's scheme is against voltage collapse following critical double contingencies, and BC Hydro's scheme considers loss of major transmission or reactive power support facilities. Hydro Quebec applies a centralized scheme considering extreme disturbances. For Asia, TEPCO (Tokyo Electric Power Company) is applying prevent voltage collapse following extreme contingencies. The scheme of Taiwan Power Company is to estimate the load shedding amount based on the WECC's UVLS guidelines.