# Influence of the Flexible Tower on Aeroelastic Loads of the Wind Turbine
## 4 Flexible Tower Vibration Feedback Analysis  
### Tower Load Error Analysis  
Under the action of wind load, the tower will vibrate, which will cause the pitch and roll angle of the nacelle to change, and the change of attitude angle will in turn affect the load calculation of the rotating blade, which is a cyclic process. In this paper, we design a method to analyze the dynamics under the action of dynamic structural parameter feedback, and use MATLAB to prepare the corresponding program to explore the laws through numerical examples [9]. In analyzing the effect of flexible pylons on aeroelastic loads, the following assumptions are made first. 1. The nacelle and the tower have only yaw motion. 2. The center of mass of the nacelle coincides with the center of the tower top. The deflection of the tower top in downwind direction and crosswind direction will be equal to the fore-and-aft displacement and left-right displacement of the nacelle respectively, and the angle of rotation of the tower top in fore-and-aft direction and left-right direction will be equal to the pitch angle and cross-roll angle of the nacelle, respectively. The relationship between the tower top turning angle and the nacelle attitude angle is shown in Figure 7.  
\(\psi_{ty}\) and \(\psi_{tx}\) denote the angle of rotation of the top of the tower in the front-to-back direction and the left-to-right direction, respectively. Based on the assumptions of this paper, there are \(\psi_{y}=\psi_{ty}\), \(\psi_{x}=\psi_{tx}\) holds at the same time. The load calculation formula for any nacelle attitude angle derived in this paper is applied to the study of the effect of the flexible tower on the aeroelastic load of the wind turbine. In the steady-state yaw condition, when considering the effect of the flexible tower vibration feedback on the wind turbine aeroelastic load, it is necessary to calculate the large feedback effect of the tower top front-to-back and left-right directional turning angle and displacement at the same time, and it is also necessary to consider the two-way feedback effect of the nacelle's cross-roll angle, pitch angle, downwind tower top displacement, and cross-wind tower top displacement at the same time, and its calculation process is shown in Figure 6. At the same time, the calculation flow without considering the feedback effect is also incorporated into this procedure, only when the feedback is not considered, the influence of tower vibration on the structural parameters needs to be compensated. Figure 7: Relationship between tower turning angle and cabin attitude. (**a**) Forward and backward. (**b**) Left and right. To simulate the roll of tower vibration feedback in the dynamic response of flexible towers, simulation analysis is performed for towers with different flexibility. First, the other parameters of the towers are maintained consistent with the NREL 5 MW wind turbine; the geometric parameters of the wind turbine tower and the basic operating parameters of the wind turbine are shown in Table 3. The increase of its flexibility is simulated by increasing the height of the tower, and the parameters of the tower used for numerical simulation are shown in Table 4.  
The relative errors of the tower top load are calculated separately for the two cases of considering feedback and not considering feedback; the comparative analysis results of longitudinal thrust and transverse thrust are shown in Figure 8.  
As can be seen from Figure 8, when the tower stiffness is relatively large, the effect on the wind turbine pneumatic load is small when considering the tower bending-bending coupling vibration feedback. When the tower flexibility increases, its load relative error increases rapidly, especially the transverse thrust; for each flexible tower, its relative error amplitude is almost maintained at about two times the relative error of the longitudinal thrust, which will have a significant increase in impact for the more flexible tower, and cause a large impact on the power of the wind turbine.