# Numerical Study on the Yaw Control for Two Wind Turbines under Different Spacings
## 4 Results
### Turbulent Inflow  
In previous sections, we analyzed the overall performance of two turbines for different yaw angles and turbine spacing in uniform inflow. There is also the atmospheric background turbulence effect in a real wind farm [29], which will affect the wake field development, especially in the far field region. Therefore, in this section, the wake fields of two turbines with a spacing of 7D in the ABL wind field are investigated to analyze the effects of the turbulent intensity on the yaw control.  
In this section, the precursor simulation of the wind field is carried out, similar to that in Section 2.4. The ground roughness \(z_{0}\) is still set as 0.001. In order to compare with the results of uniform inflow, we set the reference speed at the hub height to 11.4 m/s. With the  
Figure 16: Three-dimensional vortices structure in the vicinity of the turbines with 7D spacing for yaw angle from 0\({}^{\circ}\) to 30\({}^{\circ}\).  
inflow boundaries generated by the precursor wind field simulation, the wake fields of two turbines with yaw angles of 0\({}^{\circ}\), 10\({}^{\circ}\), 20\({}^{\circ}\) and 30\({}^{\circ}\) are simulated. The instantaneous velocity contour in a horizontal plane at hub height is given in Figure 17. It shows that the trend of the velocity deficit corresponding to the neutral ABL inflow is the same as that of uniform inflow. The distribution of velocity in the region far away from the turbine is still uneven, and the wake meandering is quite distinct. In contrast to the uniform inflow, the wind velocity recovers faster after the flow goes over wind turbines. Figure 18 shows the contour of turbulence intensity in the corresponding horizontal plane. The regions with high turbulence intensity are still induced by the wake deflection and interference. The quantity of the turbulence intensity due to the background turbulence is more significant than that of the uniform inflow.  
The average output power of turbines in the ABL wind field is compared with those of the uniform inflow in Figure 19. It can be found that when there is background turbulence, the power of WT1 is about 5 MW at 0\({}^{\circ}\) yaw angle and about 3.8 MW at the yaw angle of 30\({}^{\circ}\). The output power of WT1 does not obviously change in different inflow conditions. However, the output power of WT2 considering the background turbulence is quite different from that in the uniform inflow.  
Under ABL inflow, the power of WT2 is 2.631 MW for 7D and 0\({}^{\circ}\) yaw angle, but only 1.098 MW in the uniform inflow. The ambient inflow turbulence intensity makes the power of  
Figure 17: Contours of instantaneous velocity in the horizontal plane at hub height: (**a**) yaw = 0\({}^{\circ}\); (**b**) yaw = 10\({}^{\circ}\); (**c**) yaw = 20\({}^{\circ}\); (**d**) yaw = 30\({}^{\circ}\).  
WT2 increase by 139.5%, which is obviously due to faster recovery for the wake velocity of WT1. For 7D and 30\({}^{\circ}\) yaw angle, the power of WT2 is 4.112 MW, which has exceeded that of WT1. The output power of WT2 is 3.693 MW at uniform inflow, which increases by 11.3%.  
In general, the output power of two turbines in the ABL wind farm is higher than that of the uniform inflow. The background turbulence has little impact on the output power of WT1. However, it will interfere the wake of WT1 to make wake velocity recover faster. Thus, the output power of WT2 is improved due to the increase in the inflow wind speed of WT2. This improvement is particularly obvious in the case of small yaw angles. The optimal yaw angle corresponding to the maximum output power does not vary after considering the background turbulence.  
Figure 18: Contours of instantaneous turbulence intensity in the horizontal plane at hub height: (a) yaw = 0\({}^{\circ}\); (b) yaw = 10\({}^{\circ}\); (c) yaw = 20\({}^{\circ}\); (d) yaw = 30\({}^{\circ}\).