# Nonlinear Maximum Power Point Tracking Control Method for Wind Turbines Considering Dynamics
## 6 Performance Validation
### Dynamic Response of the Typical Turbulent Wind  
The turbulent wind profile contains wind components of various frequencies, which is suitable to simulate the real wind conditions. Therefore, a typical turbulent wind profile is used to test the wind turbine MPPT dynamic response under real wind conditions.  
As described in Section 6.2, the wind speed during periods of [0 s-50 s] and [200 s-250 s] are both set as the constant, 8 m/s. The analysis period is [50 s-200 s]. Figure 9a shows the turbulent wind profile and the estimated value. The black line and red line represent the simulating wind and the  
Figure 8: Simulation result of sinusoidal wind of several frequencies using the novel MPPT method and the conventional MPPT method: **(a)** wind-speed profile; **(b)** collective blade-pitch angle; **(c)** rotor speed; **(d)** electric energy errors of using novel MPPT method and using conventional MPPT method; **(e)** frequency spectrum of rotor speed. The black line in (**c,e**) with the legend of “ideal” means the ideal rotor speed to maintain the optimal TSR \(\lambda_{\text{opt}}\). The blue line with the legend of “conventional” and the red line with the legend of “novel” in (**c,e**) means the rotor speed using the conventional MPPT and using the novel MPPT method, respectively.  
estimated wind, respectively. Notably, the UKF-based estimator and the Newton-Raphson method work well to estimate the turbulent wind speed with high accuracy.  
Figure 9b depicts the blade-pitch angle. Obviously, the blade-pitch angle while using the novel MPPT method varies around \(-1^{\circ}\), corresponding to the value of using the conventional MPPT method.  
Figure 9c shows the dynamic response of rotor speed. During the period of [50 s 200 s], wind turbine tries to track, but seriously lag behind the wind components of low frequencies while using the conventional MPPT method. Figure 9d depicts the cumulative electric energy increment between using the novel MPPT method and using the conventional MPPT method. Obviously, the electric energy extracted from wind has significantly increased by 0.21 kW-h from 50 s to 250 s. That affirms the energy improvement of the novel MPPT method. Besides, wind turbines can hardly respond to  
Figure 9: Simulation result of typical turbulent wind using novel MPPT method and conventional MPPT method: (**a**) wind speed profile; (**b**) collective blade-pitch angle; (**c**) rotor speed; (**d**) electric energy errors of using novel MPPT method and using conventional MPPT method; (**e**) frequency spectrum of rotor speed. The black line in (**c**,**e**) with the legend of “ideal” means the ideal rotor speed to maintain the optimal TSR \(\lambda_{\text{opt}}\). The blue line with the legend of “conventional” and the red line with the legend of “novel” in (**c**,**e**) means the rotor speed using the conventional MPPT and the using novel MPPT method, respectively.  
the wind components of high frequencies. For the wind components of frequencies from 0.2 rad/s to 0.8 rad/s, wind turbines significantly track the wind variations better using the novel MPPT method than that using the conventional MPPT method, as shown in Figure 9e. That affirms the improved tracking bandwidth of the novel MPPT method.