## 3 Impact of Yaw Operation on Wind Turbine Blades
### Prediction of the Blade Loads during Yaw Operation  
As mentioned earlier, it is very important to the control of hydraulic yaw brake if the blade loads during yaw operation can be predicted. To reach this purpose, mathematical models that reflect the relationship between the blade loads and wind speed, rotor speed, yaw angle, and pitch angle are developed by following the steps below:  
Figure 3: Aerodynamic loads acting on the blade during yaw operation. * Study the effects of individual factors on the blade loads. The factors include yaw angle, wind speed, rotor speed, and pitch angle;
* Conduct the orthogonal experiment, i.e., the study of some representative points that are selected from the overall experiment according to the orthogonality;
* Develop load models, i.e., the mathematical models of blade loads are developed, of which the variables are wind speed, rotor speed, yaw angle, and pitch angle. The orthogonal experimental design is a method to study multi-factors and multi-levels. In this method, some representative points are selected from the comprehensive experiments according to the orthogonality. These representative points are \"uniform dispersion, uniform comparison\". Renowned Japanese statistician [PERSON] tabulated the horizontal combinations chosen in the orthogonal experiment, called the orthogonal tables. For example, for a three-factor three-level experiment, according to the comprehensive experimental requirements, \(3^{3}=27\) combinations of the experiments are required, which has not yet taken into account the repetition number of each combination. If the experiment is arranged according to the L9 (\(3^{3}\)) orthogonal table, it only needs to be conducted nine times. To design the orthogonal experiment by referring to the orthogonal tables, the influences of individual factors are investigated first. Use the results obtained when yaw angle \(\gamma=0^{\circ}\), wind speed \(v=11.5\) m/s, rotor speed \(\omega=17\) r/min, and pitch angle \(\beta=0^{\circ}\) as the references, the influences of individual factors on blade loads are shown in Figure 4.  
From Figure 4, it is found that in the considered scenarios, blade loads will decrease with the increase of yaw angle and pitch angle, while they will increase with the increase of wind speed and rotor speed. According to the characteristic of the curve in Figure 4, the four factors of yaw angle, wind  
Figure 4: Influence of individual factors on the aerodynamic load. speed, rotor speed, and pitch angle are designed as six levels. Considering the influence of the yaw angle and pitch angle on the gradients of the blade load curves is relatively smooth, the yaw angle and pitch angle are designed as six levels based on a uniform distribution, while wind speed and rotor speed are designed as six levels obeying a non-uniform distribution because inflection points can be clearly observed from Figure 4b,c. The resultant factor levels for the orthogonal experiments are listed in Table 2.  
The level of every factor in Table 2 is divided into two stages in this paper. The first stage includes levels 1, 2, and 3, while the second stage includes levels 4, 5, and 6. A total of 16 sets of L9 (34) standard orthogonal experiments are designed. For example, when the levels of all four factors are in the first stage, it is the first standard orthogonal experiment table. When the level of pitch angle is in the first stage, and the other three factors are in the second stage, it is the second standard orthogonal experiment table. The design of the other orthogonal experiment tables is developed in the same way. For example, Table 3 gives the first orthogonal experiment table (\(T_{1}\) indicates edgewise moment and \(T_{2}\) indicates flapwise moment). Subsequently, use variables \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{4}\) to represent yaw angle, wind speed, rotor speed, and pitch angle, and use \(T_{1}\) to indicate edgewise moment and \(T_{2}\) flapwise moment, respectively.