## 1 Introduction
To sum up, firstly, in most studies, VSG control systems are equipped with electrical energy storage, but the energy storage unit will increase the cost of wind farm construction. There are few studies on the frequency regulation control strategy of a VSG control system with limited frequency regulation capability. Therefore, for WTG based on VSG control with limited frequency regulation capacity, the study of a frequency regulation control strategy has significant practical engineering value. Next, there are a few parameter formulation principles that comprehensively consider the rotor speed constraint of the WTG and the converter capacity limit. Most of the existing literature only considers the rotor speed constraint, which ensures the safety of the operation of WTG, but ignores the converter capacity limit of WTG during the frequency regulation process. The inappropriate frequency regulation parameter tends to make the converter capacity exceed the limit, resulting in converter damage to the WTG. Lastly, the above literature does not quantitatively consider the influence of the PFR dead zone on the frequency regulation process of WTGs. The dead zone is one of the most important parameters of PFR. However, there are few literature studies that quantitatively consider the influence of the PFR dead zone during the frequency regulation process of WTG. The setting of the frequency regulation dead zone is related to the response speed and output of PFR. If the dead zone is set too small, even a slight frequency deviation may cause WTG to respond to the frequency issue, which will affect the service life of WTG and the stability of the power system. If the dead zone setting is too large, the WTG will not act when the system has a large, unbalanced power, which is not conducive to the rapid action of PFR to raise the frequency to the specifiedrange, and frequency accidents may occur. Additionally, the authors of [25] show that if the influence of the PFR dead zone is not considered, the frequency deviation obtained from analysis is smaller than the actual value, so the frequency regulation capability of WTGs cannot be accurately evaluated. Therefore, in the study of frequency regulation parameter optimization for WTG, the modeling of the PFR dead zone should be more carefully considered so as to accurately characterize the PFR capability of WTG, which can improve the capacity of renewable power systems to cope with sudden load changes and the frequency stability of the system. In order to fill the gaps, this paper proposes an optimization method for a virtual synchronous control parameter of WTG that takes into account the PFR dead zone and physical constraint boundary. The main contributions to this article are as follows:  
* Based on the WTG model controlled by VSG, in order to evaluate the frequency regulation capability of WTG more comprehensively and accurately, the primary frequency regulation dead zone is modeled. Then, the evaluation index expression of the whole process of frequency response after the load disturbance is derived through time domain analysis;
* Based on the frequency regulation capacity margin of WTG, this paper proposes a method of frequency regulation capability evaluation by considering both the speed limit of the rotor and the capacity limit of the converter. According to the proposed method, the real-time frequency regulation capacity of WTG is quantified by optimizing the frequency regulation coefficient.