# Nonlinear Maximum Power Point Tracking Control Method for Wind Turbines Considering Dynamics
## 6 Performance Validation
### Dynamic Response of Step Wind  
In order to test the dynamic response between two steady states, wind speed profiles with a unit step at 5 m/s, 7 m/s, and 9 m/s are used, as shown in Figure 7a.  
Figure 7b depicts the blade-pitch angle. During the periods of stable wind conditions, there is only a little difference (less than 0.2\({}^{\circ}\)) of the blade-pitch angle at 5 m/s, 7 m/s, and 9 m/s. That phenomenon may result from the relatively imprecise calculation of the optimal blade-pitch angle. During the dynamic periods, the blade-pitch angle varies from \(-\)1.41\({}^{\circ}\) to \(-\)0.74\({}^{\circ}\) at 5 m/s, from \(-\)1.28\({}^{\circ}\) to \(-\)0.81\({}^{\circ}\) at 7 m/s and from \(-\)1.13\({}^{\circ}\) to \(-\)0.87\({}^{\circ}\) at 9 m/s. As analyzed in Section 3, the dynamic response of VSWTs tends to be slower, and TSR tends to vary in the wider range under lower-speed wind conditions, which can account for wider variations in the blade-pitch angle at 5 m/s.  
Figure 7c demonstrates the dynamic response of rotor speed. Obviously, during periods of stable wind conditions, there is no difference between the conventional method and the novel method. It takes about 30 s, 20 s, and 15 s for the transition process between two steady states at 5 m/s, 7 m/s, and 9 m/s, respectively, while using the conventional OT method. This result corresponds to the nonlinear performance as mentioned in Section 3. While using the novel MPPT method proposed in the paper, it only takes about 6 s for VSWTs to achieve the other steady-state, whatever at 5 m/s, 7 m/s, or 9 m/s. Thus, the novel MPPT method has assuredly shortened the dynamic transition process between two steady states.  
Figure 7d depicts the cumulative electric energy increment between using the novel MPPT method and using the conventional MPPT method. With the increasing unit step in wind velocity, higher wind energy is stored in rotating parts as the kinetic energy to accelerate the rotor speed by the novel method  
Figure 7: Simulation result using novel MPPT method and conventional MPPT method: (**a**) wind speed profile. (**b**) collective blade-pitch angle; (**c**) rotor speed; (**d**) electric energy increment of using novel MPPT method, and using conventional MPPT method. The red line, green line, and blue line show the unit step wind at 5 m/s, 7 m/s, and 9 m/s, respectively in (**a**). The black line in (**c**) 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**) means the rotor speed using conventional MPPT and using novel MPPT method, respectively.  
than that by the conventional OT method during the period of [100 s-105 s]. Hence, the electric energy output is first less, and then becomes more as the kinetic energy is released to the grid during the period of [105 s-140 s]. With the decreasing unit step in wind velocity, the kinetic energy releases faster to decelerate the rotor speed during the period of [140 s-d145 s]. Correspondingly, during the period of [60 s-180 s], the cumulative electric energy increment has significantly increased by 0.068 kw-h, 0.044 kw-h, and 0.028 kw-hat 5 m/s, 7 m/s, and 9 m/s, respectively. Therefore, the novel MPPT method shows more remarkable effects in the dynamic response of the rotor speed and the cumulative electric energy extraction than the conventional MPPT method, especially under lower-speed wind conditions.