# A Maximum Power Point Tracking Control Method Based on Rotor Speed PDF Shape for Wind Turbines
## 4 Simulation and Results
### Performance Validation  
For the turbulent wind speed signals as shown in Figure 6, the corresponding PDF-MPPT control is applied in the established 1.5 MW direct-drive wind power generation system and compared with the conventional OT control method named \"conventional (method)\" and the ideal condition named \"ideal\". The novel MPPT control based on PDF control is named the \"PDF-MPPT (method)\", which can be verified and analyzed by simulation results. For the turbulent wind speed as shown in Figure 6a, the response effect can be observed by applying the 2-order control law to the wind power generation system, as shown in Figure 7.  
Figure 7a shows the change of power coefficient of conventional and novel MPPT methods under the same wind condition. The power coefficient of this system controlled by the novel MPPT control method is always higher than that of the conventional MPPT control when wind speed changes, especially at high wind speeds. In addition, since wind power is not only related to \({C_{p}}\), but also specific wind speed, comprehensive factors. These comprehensive factors make novel MPPT control have better energy capture performance than conventional MPPT control. Figure 6: The variation of turbulent wind speed with time: (**a**) when the goal function of rotor speed is unimodal Gaussian distribution; (**b**) when the goal function of rotor speed is variable weight multi-Gaussian distribution. Figure 7b describes the dynamic response of rotor speed. It can be found that when the wind speed changes too fast, novel MPPT control can make the system reduce the frequent fluctuation of rotor speed and respond to the stochastic change of wind speed more quickly. Figure 7c also shows that, compared with the conventional MPPT method, the fluctuation of the rotor speed and the electromagnetic torque under novel MPPT control is reduced. This is because the characteristic of PDF control is to reduce the fluctuation range of various variables in the system. It is this characteristic that makes novel MPPT control reduce the mechanical damage to a certain extent. Figure 7: Simulation results using PDF-MPPT method and conventional MPPT method for the turbulent wind speed with constant average value: (**a**) power coefficient; (**b**) rotor speed; (**c**) electrical power generated; (**d**) cumulative generation increment of using PDF-MPPT method compared with conventional MPPT method. The green line with the legend of “ideal”, the blue line with the legend of “conventional” and the red line with the legend of “PDF-MPPT” in (**a**–**c**) means the corresponding performance index in ideal operation state, using the conventional MPPT method and using the novel MPPT method, respectively. Figure 7d shows the change of cumulative power generation increment of the novel MPPT control compared with conventional MPPT control. Between 50 s and 250 s, PDF-MPPT control makes the wind energy captured by wind turbines always greater than the conventional MPPT method, which confirms the impact of that the novel MPPT method on energy improvement. This novel method can improve the power generation of the system over a while to a certain extent. Similarly, for another turbulent wind speed shown in Figure 6b, the system response performance under the application of the 7-order control law is shown in Figure 8.  
Figure 8a shows the dynamic response of rotor speed. It can be found that the difference in rotor speed response between the two MPPT control methods is not obvious. However, it can be seen from Figure 8b that the novel MPPT method reduces the fluctuation degree of electrical power generated. This indicates that the fluctuation range of each variable under the control of the novel method is small, which can reduce the mechanical damage to a certain extent.