## 1 Introduction  
Ensuring the stability of an operating grid system that includes high integration levels of wind power generation is a crucial challenge because of the unpredictable fluctuation of wind as an alternative energy source [1; 2; 3]. Furthermore, the inertia of the system has declined owing to the performance of the maximum power point tracking (MPPT) mechanism by dynamic speed wind power generators (WPCs) [4; 5; 6]. Variable-speed WPGs operated with MPPT control do not react to the frequency control support of a system in case any fault occurs within the electrical power network [7]; thus, challenges arise in maintaining the frequency of the grid system within a constricted range when the integration level of the wind power increases [8; 9]. To reduce these problems, a frequency control support scheme is required for a WPG operating within a grid system. To incorporate traditional frequency control techniques in a power system, the MPPT control loop is accompanied by a supplementary control loop [10; 11; 12; 13]. There are two groups of traditional frequency control techniques. The techniques include one which uses a fixed gain and the other which uses a variable gain. The authors in [14] proposed a releasable kinetic-energy-based inertial control system strategy to increase the frequency nadir by utilizing the releasable energy in a WPG. To achieve this frequency control, two additional loops for the inertial control are implemented in each DFIG controller: the rate of change of frequency and droop loops. In [15], to control wind farms providing a primary frequency response, synthetic inertia with a novel frequency-dependent multi-gain droop control approach is proposed. For comparison, a proportional and proportional-integral-type pitch angle controller is combined with the suggested multi-gain droop control. The simulation results demonstrate that the suggested multi-gain droop control system can provide the best frequency control performance. A novel virtual inertia control technique for wind turbines to enhance the rotor angle's first swing stability in the power grid is proposed in [16]. The stability of the power grid's frequency and rotor angle features that are closely related to the inertia can be improved by controlling their variables. The study of [17] suggests a rotor-speed-based frequency-droop control technique for wind turbines. The major frequency regulation employed by the wind turbine is accomplished by modifying its power tracking curve rather than by adding droop control signals to the wind turbine's power tracking reference, and the proposed control system is unaffected by rotor deceleration. The varying control method gains are accepted for the frequency deviance and rate of change of frequency (ROCOF) loops which are the supplementary control loops used as the frequency control technique. In [18], the primary frequency control loop was incorporated into the ROCOF loop. During the primary frequency response, the supplementary power is generated by using the ROCOF loop to prevent severe frequency drop; however, its magnitude decreases over time. Furthermore, the ROCOF loop causes a negative impact after the frequency recovery. The authors in [19] proposed a fast-frequency control technique for converter-interface energy storage systems. The approach optimizes the performance of the controller by combining droop and ROCOF regulation channels. The suggested technique enables full control of the storage device during both the inertial response and the primary frequency control periods. To control for system frequency violations caused by unforeseen events, a unique dynamic model is developed which incorporates large-scale wind farms and utility-scale batteries with frequency-sensitive active power reference schemes [20]. The power electronic interface model, its related control loops, and a brand-new controller based on fuzzy logic are also included in the proposed frequency control model.