## 1 Introduction  
In recent years, renewable energy generation made great progress worldwide to meet the challenge of drastic climate changes and increasing energy demands [1]. Among various renewable energy sources, wind energy is the most rapidly growing one around the world [2; 3]. In 2018, the 51.3 GW of new installations brought total cumulative installations of wind power up to 591 GW, and the Global Wind Energy Council (GWEC) expects that more than 55 GW of new capacity will be added each year until 2023. In 2019, with the 25.7 GW of new wind power installations, the cumulative wind power installations of China increased by 14% to 210 GW. With the development of wind energy, wind turbines (WTs) are more widely used in electrical power systems. WTs can be classified into four basic categories based on the ways of speed control: fixed-speed wind turbines, limited variable-speed-controlled wind turbines, doubly fed induction generator (DFIG)-based wind turbines (DFIG-WTs), and full variable-speed-controlled wind turbines [4; 5]. Among these four types of wind turbines, DFIG-WTs are mostly preferred in practical applications due to their advantages including simple installation, low cost, variable-speed constant frequency, and independent control of active and reactive power [6]. Figure 1 shows the schematic diagram of a DFIG. The stator is connected to the power grid directly, and the rotor is linked to the power grid through a back-to-back voltage source converter, which comprises a rotor-side converter (RSC) and a grid-side converter (GSC). RSC is used to control the active power and reactive power delivered and to achieve the maximum power capture. GSC is used to control the active power and reactive power delivered, as well as maintain the direct current (DC)-link voltage [1; 7]. DFIG-WTs are susceptible to grid voltage dips and disturbances. During grid voltage dips, the stator and GSC are influenced directly by the sudden change in DFIG bus voltage. Stator perturbations will induce large voltages in rotor windings and lead to uncontrolled rotor current. The rotor overcurrent may cause a large increase in DC-link voltage. Both rotor inrush current and DC-link overvoltage can damage wind turbines [8] and may lead to tripping of DFIG-WTs. The ability to ensure continuous operation during voltage dips, as well as minimize re-synchronization problems after the clearance of faults, is stated as low-voltage ride-through (LVRT) capability. In the past, the penetration level of wind energy was extremely small compared with conventional generation systems [9]. Therefore, wind turbines were allowed to disconnect from the power grid during voltage dips to avoid overcurrent. However, with the penetration of wind energy in electrical power systems increasing, a sudden loss of wind power during voltage dips can result in control problems of system frequency and voltage, which leads to a system collapse in the worst case [10; 11]. Hence, it is ideal to make wind turbines stay connected to the power grid and provide support during transient periods. Therefore, the LVRT capability in wind turbines is now mandatory. With emphasis on the LVRT capability of DFIG-WTs, many countries updated their grid code requirements (GCRs). The German LVRT grid criteria are mostly preferred over other GCRs in practical applications [1]; they require that (1) wind turbines shall remain connected to grid for at least 0.65 s after fault inception, (2) the permitted fault voltage is 15% of its rated voltage, and (3) the voltage should recover to 90% of its rated voltage within 3 s after the clearance of faults. According to the GCR for LVRT, wind turbines should have the ability to ensure continuous operation during voltage dips, and the voltage should be kept above the curve shown in Figure 2. In addition, most GCRs require reactive current injection during voltage dips.