## 3 Frequency Response Analysis Considering the PFR Dead Zone
### The Modeling of the PFR Dead Zone  
In a practical power system, the setting of the PFR dead zone of the WTG is very important, which can avoid the frequent operation of the WTG when the frequency is disturbed in a small range and reduce the equipment life.  
In order to further directly analyze the influence of the PFR dead zone (\(d\)) on the frequency response characteristic of the power system, the frequency response characteristic curves under different dead zones are drawn as shown in Figure 4, according to the simulation parameters in Table 1.  
According to Figure 4, the frequency response curves of four cases are given. When there is no dead zone, the lowest frequency has the highest value, which is 49.66 Hz. When the dead zone is 0.05 Hz, the value of the lowest frequency is the smallest, which is 49.64 Hz. Compared with the response characteristic curves when considering the effect of the PFR dead zone of the WTG, the frequency response characteristic of the power system is better without the dead zone. In addition, the larger the dead zone of PFR is, the smaller the minimum value of system frequency response is.  
Therefore, if the influence of the PFR dead zone is not considered in the analysis of frequency response characteristics for the power system, the frequency deviation will be smaller than the actual value of the power grid. It will seriously affect the accurate evaluation of the frequency regulation ability of WTG. In the meantime, the PFR ability of the WTG cannot be fully utilized, which is not helpful to the coordinated and stable operation of the power system. As a result, it is of great significance to quantitatively analyze the influence of the PFR dead zone on the frequency response characteristics of the power system and synthetically evaluate the frequency regulation capacity of the WTG.  
When the WTG with the dead zone participates in the frequency regulation, if the frequency deviation is less than or equal to the dead zone PFR, the WTG will not participate in the PFR of the power system. On the contrary, if the frequency deviation is greater than the dead zone of PFR, the additional active power-frequency control for the WTG will be  
Figure 4: The frequency response characteristic curves of the power system.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(J_{\text{vsg}}\) & 0.98 pu \\ \(K_{\text{vsg}}\) & 7.54 pu \\ \(K_{\text{G}}\) & 20 pu \\ \(D_{\text{L}}\) & 0 pu \\ \(D_{\text{vsg}}\) & 4 pu \\ \(T_{\text{G}}\) & 5 s \\ \(H\) & 2.77 s \\ \(\Delta P_{\text{L}}\) & 0.1 pu \\ \hline \hline \end{tabular}
\end{table}
Table 1: The parameters of simulation.  
put into operation. In this case, the expression of the PFR power with a dead zone is shown in Equation (13):  
\[\begin{cases}\Delta P_{\text{f}}=-K_{\text{vsg}}(\Delta f-d)&\Delta f>d\\ \Delta P=0&-d\leq\Delta f\leq d\\ \Delta P_{\text{f}}=-K_{\text{vsg}}(\Delta f+d)&\Delta f<-d\end{cases} \tag{13}\]  
The expression of the PFR power without the dead zone is shown in Equation (14):  
\[\Delta P_{\text{f}}=-K_{\text{vsg}}\Delta f \tag{14}\]  
When the frequency drop is greater than the dead zone due to the sudden increase in load, after considering the quantization and modeling of the PFR dead zone, the control block diagram of the system frequency response can be considered to add the expression, which can be represented as \(K_{\text{vsg}}d\). This constant expression can be added to the transfer function block diagram as a disturbance quantity, and this disturbance quantity is in the same position as the load disturbance quantity in the block diagram.