## 3 Impact of Yaw Operation on Wind Turbine Blades  
### Blade Loads during Yaw Operation  
When the wind blows a wind turbine, both edgewise and flapwise bending moments will be created at the root section of the blade. The former will drive the turbine rotor to rotate, while the latter will cause deflection to the blade. Both are not only dependent on wind speed and wind direction but are also influenced by the control parameters of the turbine, such as rotor speed, pitch angle, and yaw angle. To understand the blade loads during the process of yaw operation, both the edgewise and flapwise moments under various combined conditions of wind speed, rotor speed, yaw angle, and pitch angle are calculated. The calculation results are shown in Figure 3. In the subplots, \(\omega\) indicates the rotor speed, \(v\) is wind speed, \(\beta\) represents pitch angle, and yaw angle \(\gamma\) increases gradually from 0\({}^{\circ}\) to 18\({}^{\circ}\).  
Figure 3a,b show the influences of yaw operation on blade loads when rotor speed \(\omega=\)17 r/min, pitch angle \(\beta=0^{\circ}\), and wind speed \(v\) increases gradually from 3 m/s to 19 m/s. From Figure 3a,b it is found that when wind speed \(v=\)3 m/s, the edgewise moment is negative due to the mismatch of rotor speed and wind speed, and the flapwise moment decreases with the increase of the yaw angle. When wind speed \(v=\)5 m/s, it is interestingly found that with the increase of the yaw angle, both edgewise and flapwise moments increase first and then decrease. A similar phenomenon is also observed from the edgewise moment obtained when wind speed \(v=\)7 m/s. By contrast, the flapwise moment obtained at this wind speed decreases monotonously with the increase of the yaw angle. When wind speed varies in the range of [9 m/s, 13 m/s], both edgewise and flapwise moments show a decreasing trend with the increasing yaw angle. When the wind speed \(v>\)15 m/s, an obvious nonlinearly decreasing trend is observed from the moments in both directions.  
Figure 3c,d show the effect of yaw operation on blade loads when wind speed \(v=\)11.5 m/s, pitch angle \(\beta=0^{\circ}\), and rotor speed increases gradually from 3 r/min to 19 r/min. From Figure 3c,d, it is found that (1) both edgewise and flapwise moments generally decrease with the increase of yaw angle, and (2) increasing rotor speed will lead to the increase of the bending moments in both directions  
despite the value of yaw angle. Moreover, the faster the rotor speed, the more the bending moments will increase. The increase rate can be indicated by the gradients of the curves. Let \(x\) be the yaw angle, and let \(y\) be the bending moment in either edgewise or flapwise direction. Then a linear equation \(\hat{y}=ax+b\) can be used to describe the relationship between the yaw angle and the blade loads. After estimating the gradient of the equation using the least-squares method, it is found that when the rotor speed is 3 r/min, the gradient \(a=0.58\). The value of \(a\) increases to 0.95 when rotor speed \(v=\)11 r/min, 2.5 when \(v=\)13 r/min, and 6.8 when \(v=\)19 r/min.  
Figure 3e,f show the effect of yaw operation on blade loads when wind speed \(v=\)11.5 m/s, rotor speed \(\omega=\)17 r/min, and pitch angle \(\beta\) increases gradually from 0\({}^{\circ}\) to 16\({}^{\circ}\). From Figure 3e,f, it is found that when pitch angle \(\beta<\)8\({}^{\circ}\), both edgewise and flapwise moments decrease gradually with the increase of yaw angle. However, the edgewise and flapwise moments show negative values when \(\beta>\)8\({}^{\circ}\) due to the mismatch of wind speed, rotor speed, and pitch angle. In addition, it is found that with the increase of pitch angle, the influence of the yaw angle on the bending moments in both directions decreases. For example, when the pitch angle increases from 0\({}^{\circ}\) to 8\({}^{\circ}\), the value of gradient \(a\) decreases gradually from 7.0 to 5.0.