## 4 Numerical Results and Discussion
### Dynamic Analysis
#### 4.1.2 Effect of the BCS on Maximum Values of Dynamic Response  
Figure 8 shows the maximum values of the six components from the 23 wind speeds between the two cases and the fitted curves for No. 2. We also found that the maximum values in No. 1 are always larger than those in No. 2 with the same wind condition. The fixed \(\beta\) and rotor speed in No. 1 lead to the aerodynamic loads increase as wind speed, which causes the same trend for maximum results with the mean values. Because of the action of BCS, the maximum values in No. 2 increase first and then decrease with the increase of wind speed. The maximum values of the six parameters in cut-in, rated, and cut-out wind speed and Table 4 shows the difference between the two cases. It is observed that the BCS in No. 2 achieves reduction of maximum values by more than 42% in the cut-out wind speed compared to No. 1. The six fourth order polynomial fits are used to calculate the corresponding maximum values with respect to different wind speeds and they are shown in Equations (23)-(28). From the Figure 8 and Table 4, it is can be seen that the maximum values of the displacement and load components in tower with the wind speed around cut-in speed in No. 1 are smaller than that in No. 2. To find the reason of this phenomenon, the Campbell diagram of the wind turbine was calculated and shown in Figure 9. And the green shaded zone indicates the normal operating design range of the rotor speed. It should be noted that the Campbell diagram of a rotating machine consists of a plot of the natural frequencies of the system as functions of the spin speed on which the frequencies of the forcing excitation functions are superimposed, and is one of the most important tools for understanding the dynamic behavior of the rotating machine [49]. For the wind turbine with three blades, the first side-to-side and fore-aft tower frequencies are designed between the 1P (the frequency of rotor speed) and 3P during the total operational range in the Campbell diagram avoid \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Wind Speed** & **Cases** & **BSX** & **BFX** & **BMY** & **TTSX** & **TBFX** & **TBMY** \\
**(m/s)** & **Cases** & **(m)** & **(kN)** & **(10\({}^{3}\) kN\(\cdot\)m)** & **(m)** & **(kN)** & **(10\({}^{3}\) kN\(\cdot\)m)** \\ \hline \multirow{3}{*}{3} & No. 1 & 2.64 & 126.2 & 4.49 & 0.09 & 220 & 16.73 \\  & No. 2 & 1.98 & 93.45 & 3.38 & 0.19 & 399.8 & 32.7 \\  & Difference (\%) & +25 & +25.95 & +24.72 & \(-\)111.11 & \(-\)81.73 & \(-\)95.46 \\ \hline \multirow{3}{*}{11.4} & No. 1 & 8.42 & 426.8 & 14.87 & 0.54 & 1080 & 92.14 \\  & No. 2 & 7.76 & 368.9 & 13.43 & 0.47 & 1007 & 81.01 \\  & Difference (\%) & +7.84 & +13.57 & +9.68 & +12.96 & +6.76 & +12.08 \\ \hline \multirow{3}{*}{25} & No. 1 & 12.05 & 642.7 & 20.95 & 0.89 & 1680 & 147.2 \\  & No. 2 & 4.42 & 369.1 & 10.11 & 0.41 & 769.8 & 67.08 \\ \cline{1-1}  & Difference (\%) & +63.32 & +42.57 & +51.74 & +53.93 & +54.18 & +54.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum values and difference between the two cases in cut-in, rated, and cut-out wind speed. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Wind Speed** & **Cases** & **BSX** & **BFX** & **BMY** & **TTSX** & **TBFX** & **TBMY** \\
**(m/s)** & **Cases** & **(m)** & **(kN)** & **(10\({}^{3}\) kN\(\cdot\)m)** & **(m)** & **(kN)** & **(10\({}^{3}\) kN\(\cdot\)m)** \\ \hline \multirow{3}{*}{3} & No. 1 & 1.93 & 83.65 & 3.05 & 0.05 & 123.04 & 9.63 \\  & No. 2 & 1.02 & 50.64 & 1.74 & 0.03 & 78.59 & 5.80 \\  & Difference (\%) & +47.15 & +39.46 & +42.95 & +40.00 & +36.13 & +39.77  
the risk of resonance related to rotor speed harmonics [31; 50; 51; 52]. In Figure 9, we find that in No. 2 the rotor speeds are around 7 rpm around the cut-in wind speed, which causes resonance with the 3P of the rotor speed closing to the first tower FA natural frequency. This is the reason of the phenomenon. It is also concluded that the BCS has a great effect on the maximum values of modern wind turbine structural dynamic responses.