## 4 Aerodynamic Performance Enhancements
### Optimal Position of Nacelle Anemometer and Flow Angle  
The nacelle anemometer of the wind turbine is used for the yaw angle control, which makes the wind flow perpendicular to the rotating blade plane. The yaw angle has a significant effect on the aerodynamic performance [19]. If a yaw error of 15\({}^{\circ}\) occurs, the aerodynamic performance decreases about 6.7%. The several candidate locations of nacelle anemometer are shown in Figure 14.  
Additionally, velocity time history at suggested six points are computed as shown in Figure 15 according to the varying azimuth angle. The periodic fluctuation apparently indicates the effect of interaction of rotating blades with a hub and nacelle. The velocity components (\(V_{a}\), \(V_{r}\), \(V_{\theta}\)) in the polar coordinate were transformed from the Cartesian velocity components (\(V_{x}\), \(V_{y}\), \(V_{z}\)) as follow.  
\[V_{a}=V_{x} \tag{5}\]  
\[V_{r}=-V_{y}\sin(\theta)+V_{z}\cos(\theta) \tag{6}\]  
\[V_{\theta}=V_{y}\cos(\theta)+V_{z}\sin(\theta) \tag{7}\]  
where \(V_{a}\) is axial component, \(V_{r}\) is radial component, \(V_{\theta}\) is tangential component, and \(\theta\) is the azimuth angle of rotor blade 1. As shown in Figure 15, all velocity components have the remarkable fluctuation with 3P frequency.  
Figure 14: Possible locations of nacelle anemometer.  
Figure 15: Cont.  
The flow angle (FA) and turbulence intensity (\(T_{i}\)) normalized by the rotor tip speed on the nacelle anemometer points are computed by Equations (8) and (9), and the time history of flow angle (FA) on each location is shown in Figure 16.  
\[FA=\text{atan}(V_{\theta}/V_{a}) \tag{8}\]  
\[T_{i}=\sqrt{\frac{\vv^{\prime}_{a}+\vv^{\prime}_{r}+\vv^{\prime}_{\theta}}{3V^{ \prime}_{t}}} \tag{9}\]  
where \(\vv^{\prime}_{a}\), \(\vv^{\prime}_{r}\), and \(\vv^{\prime}_{\theta}\) denote the velocity fluctuation components in the axial, radial, and tangential directions, respectively, and \(V_{t}\) is the rotor tip speed.  
Figure 15: Velocity time history with varying azimuth angle. (**a**) Axial velocity time history, (**b**) radial velocity time history (**c**) tangential velocity time history.  
The FA is dominated by the fluctuation with 3P frequency and is defined negative for the clockwise rotating when viewed from upstream. The FA has the strong relationship with anemometer positions. Table 4 lists the time averaged FA and \(T_{i}\) level at the different positions of nacelle anemometer. As the distance between the vortex shedding area of the rotor hub and the nacelle anemometer position becomes closer, the higher the FA fluctuation and turbulence intensity become. Regardless of the nacelle anemometer position, the time averaged FA values are little different. It means that the inlet free-stream flowing with theoretically \(0^{\circ}\) yaw angle error will be deflected to \(11.43^{\circ}\) in average, due to the interaction of rotating blades with a hub and nacelle. Based on Table 4, it is recommended that the nacelle anemometer position should be placed at the point 6 due to the lowest turbulence intensity level. Additionally, analysis results show that the intrinsic yaw error should be considered for wind turbine control to avoid the loss of aerodynamic performance.