## 1 Introduction  
Over the past few years, wind energy has received significant attention as one of the most promising renewable energy sources given the adverse environmental impacts of conventional energy sources [1; 2]. Both permanent magnet synchronous generator (PMSG) wind turbines and doubly fed induction generator (DFIG) wind turbines have been widely used. PMSG wind turbines are advantageous over DFIG wind turbines due to their highly reliable operation, lower maintenance expenses, and smaller weight with a simpler structure. Moreover, the PMSG can connect to the turbine without the use of a gearbox [3; 4]. Therefore, many recent studies have focused on PMSG wind turbines. In power systems with high wind power penetration, frequency control is a critical issue from the viewpoint of stable system operation. The wind power system is required to provide a reliable frequency response to support the grid and reduce costs associated with reserve power. Variable-speed wind turbines are commonly operated to achieve optimal efficiency for the maximum power output using maximum power point tracking (MPPT) control technology [5]. As a result, wind turbines do not have an inherent frequency regulation capability to supply additional reserves [6]. A sufficient reserve margin is an important requirement to participate in frequency regulation, which is absent in a wind turbine generator. Many researchers have investigated the frequency support capability of wind turbine generators to supply the power margin. To provide an inertial response, the authors of [7; 8; 9] proposed an additional power control loop for variable-speed wind turbines. Further, the research in [10; 11] has helped develop a concept that directs a portion of the rotational energy and blade to short-term active power support, which could aid in reducing the system frequency drop after a generation deficit. Another option is to utilize a de-loaded control operation to provide the primary frequency response. In [12], the authors suggested an operation at the de-loaded power curve of a wind turbine to supply the power margin. Various methods are available for de-loaded operations; for example, a combination of pitch angle control and rotational speed control [13; 14; 15; 16; 17]. However, increasing dynamic characteristics could affect the life of the pitch angle controller and increase the system cost. The authors of [18; 19; 20] considered a fixed percentage of wind turbine de-loading. De-loaded control decreases the power output of the wind turbine generator but increases the primary frequency support capability during frequency disturbances. However, de-loading is restricted to between 10% and 20%, depending on the available wind speed and rotor speed limit constraints [18]. In [21; 22], the authors addressed the kinetic energy (KE) discharge control that incorporated a wind farm to supply additional reserves for frequency support. Two options have been reported in previous studies for the participation of wind turbines during a frequency event: de-loaded control and inertial response for primary frequency control. The inertial control utilizes the KE in the rotating mass of the wind turbine to provide a temporary frequency response. The de-loaded control allows the wind turbine to run in de-loaded operation mode to reserve partial wind power for the primary and secondary frequency regulations. However, an unsuitable margin of power would rapidly decrease the rotational speed of the wind turbine. In addition, improper control of the energy regained during acceleration may cause another frequency disturbance [23]. Overall, the main focus of the previous studies has been on the frequency support capabilities of wind turbine generators.