## 1 Introduction  
Under the pressure of environmental pollution and an energy crisis, the development and utilization of renewable energies have received more and more attention in the modern power system [1, 2]. As WTGs are connected to the power grid through power electronic converters, they are decoupled from the power system and cannot provide frequency support. Therefore, replacing traditional synchronous generators with WTGs will inevitably reduce inertia and weaken the frequency regulation ability of the power system [3, 4, 5]. In the case of interference, the power system with a high proportion of renewable energies is more prone to grid frequency accidents [6, 7]. On the one hand, in order to solve the problem of low inertia and weak damping in the modern system, many scholars have proposed the control strategy of a virtual synchronous generator, that is, by simulating the rotor characteristics of a synchronous generator, the inverter can have inertia and damping [8, 9]. The fluctuation of the output frequency and power can be suppressed. In addition, the system's stability can be improved by using VSG control, which has a broad prospect of application [10, 11]. On the other hand, the WTGs participate in frequency regulation mainly through load reduction control [12; 13] and rotor kinetic energy control [14; 15]. The control of decreasing load is divided into pitch angle control and rotor over-speed control, so that the WTG cannot operate in maximum power point tracking (MPPT) mode. Meanwhile, it reduces the amount of wind energy captured and decreases the economic benefits of the wind farm. Moreover, frequent pitch angle actions will increase the mechanical wear degree of WTG. The rotor kinetic energy control enables the WTG to operate at the MPPT point during normal operation without additional investment. Therefore, this paper focuses on using rotor kinetic energy to realize frequency support for WTG. A too small frequency regulation coefficient with rotor kinetic energy control is not helpful to fully release the frequency regulation capability of WTGs; on the contrary, a too large frequency regulation coefficient will easily lead to the rotor speed exceeding the constraint value. Therefore, the selection of frequency regulation coefficients for rotor kinetic energy control of WTGs has been further studied. The authors of [16; 17] adapted the fixed PFR coefficient control, which results in limitations in the frequency response capability of renewable energy units under different wind speed conditions. Therefore, the variable droop coefficient control method is developed in [18] by adapting to different wind speed conditions. However, the WTG is in a state of load reduction and does not operate at the optimal working point, which reduces the economy of the wind farm. The authors of [19] use the joint control method combining fuzzy control and predictive control to improve the frequency response, supporting the performance of participating systems for VSG. However, the VSG control system is equipped with electrical energy storage, and the control strategy is not applied to WTGs with limited frequency regulation capability, so the practical engineering application value is limited. The authors of [20; 21] proposed a modified virtual rotor mechanism, including virtual inertia and virtual damping, to improve the frequency stability of the power system. The authors of [22] studied the comprehensive control strategy of adaptive inertia and damping but did not explain the parameter formulation principle of the inertia and damping coefficients. The authors of [23] proposed a coordinated control method between a wind energy conversion system and a small hydro-generator by modified notch filters without considering the rotor speed constraint of the WTG and the converter capacity limit. The authors of [24] studied the adaptive primary frequency regulation approach with turbine limitations, but they ignored the influence of the primary frequency regulation dead zone.