## 4 Numerical Results and Discussion
### Fatigue Analysis
#### 4.2.2 Effect of the BCS on DELs  
The DELs of the four load components were calculated from the load's cycles with an alpha version of Mlife, a damaging loads assessment code developed at NREL [43]. In Equation (16), we also find that the load amplitude has a great effect on the DEL. In order to quantify the amount of variation or dispersion of a set of data values, the coefficient of variation (COV) is used. Therefore, the COVs of the four load components were also calculated to analyze the results of the structural dynamic responses in the two cases. Figure 14 shows the DEL and COV calculation results in different wind scenarios for two cases and compared with No. 1 data as reference values. It can be seen that the values of DEL and COV in No. 2 are larger than that in No. 1 in most conditions, especially for TBFX and TBMY around the cut-in speed. The variation trend of fatigue loads and the related COV as wind speed increase in the region of below-rated wind speed range is consistent, a low COV results in a low DEL and a high COV results in a high DEL. In the region of above-rated wind speed range, because that the volatility in No. 2 is greater than in No. 1 and the mean value of dynamic response in No. 2 is smaller than in No. 1, the normalized COV is significantly larger in DEL in the same wind condition. Figure 14a,b show that the DELs of BFX and BMY in both cases are approximately the same in the region of below-rated wind speed range. However, when the wind speed exceeds the rated speed,  
Figure 11: Comparison of the binned range rainflow cycles of BMY between the two cases: (**a**) \(V_{\text{hub}}\) is 3 m/s, (**b**) \(V_{\text{hub}}\) is 11.4 m/s, (**c**) \(V_{\text{hub}}\) is 17 m/s, and (**d**) \(V_{\text{hub}}\) is 25 m/s. the DELs of BFX and BMY in No. 1 are smaller than that in No. 2, which achieves DELs decrease of more than 34% in the cut-out wind speed compared to the No. 2. The changing rotor speeds and blade-pitch angles along time in No. 2 lead to an oscillation increase of aerodynamic loads on the blade which in turn increase the COVs of load components in blade and the load amplitudes in rainflow cycle counting, and then affects the DELs of wind turbine blade. Figure 14c,d shows that the DELs of TBFX and TBMY in No. 2 are greatly larger than that in No. 1 when the wind speeds are around the cut-in speed. The phenomenon is also caused by the reason that the first tower FA natural frequency is close to the 3P of the rotor speed in these wind ranges. When the wind speeds exceed rated speed, the DELs of TBFX in No. 2 are slightly less than that in No. 1 (Figure 14c), while the DELs of TBMY in No. 2 are slightly larger than that in No. 1 (Figure 14d). Figure 12: Comparison of the binned range rainflow cycles of TBFX between the two cases: (**a**) \(V_{\rm hub}\) is 3 m/s, (**b**) \(V_{\rm hub}\) is 11.4 m/s, (**c**) \(V_{\rm hub}\) is 17 m/s, and (**d**) \(V_{\rm hub}\) is 25 m/s. The dynamics are generated from the rotation of the blades in the azimuth direction and the vibrations in the flap-wise and edge-wise directions. Considering that blade's azimuth position is of great influence on the sinusoidal behavior of blade's loads and deflections [53], and in order to further analyze the effect of BCS on fatigue loads of blades and tower, the comparison of BFX and TBFX are shown with the azimuth position of the blade in Figures 15 and 16. It can be seen from the figures that under normal operation, the responses of the wind turbine with different azimuth angles in No. 2 fluctuates greatly, which clearly clarify the obvious influence of BCS on fatigue loads of blades and tower. Frequency analysis had been made for BFX and TBFX, and the results are shown in Figures 17 and 18. The pictures show the frequency distribution characteristics under different wind speeds for two cases. And the resonance can be checked in No. 2 from Figure 18a. It is concluded that the BCS should be considered when calculating the fatigue loads of wind turbine blades and support structure subjected to external loads.