*4.2. Random Wind*

Figures 7 and 8 show the responses of the PMSG-WT to random wind. Figure 7a shows time-varying wind speed. It can be seen from Figure 7b,c that the VC, GSPI and FLC cannot provide high tracking performance of the mechanical rotation speed *ω*m under time-varying wind speed. However, the GSPI achieve better tracking performance than the FLC under random wind speeds. The NAC always keeps mechanical rotation speed *ω*m around its rated value. To limit the extracted wind power, the power coefficient *C*p varies with time-varying wind speed, shown in Figure 7d. During the whole operating period, the NAC can always keep consistent responses of *P*m and *Q*m shown in Figure 7e,f. The performances of the VC, GSPI and FLC are all affected by the time-varying wind speed. Figure 8 shows the designed observers can provide satisfactory estimations for the states and perturbations.

**Figure 7.** Responses of the PMSG-WT to random wind speed. (**a**) Wind speed V. (**b**) Mechanical rotation speed *ω*m. (**c**) Relative error of *ω*m. (**d**) Power coefficient *<sup>C</sup>*p. (**e**) Active generating power *P*m. (**f**) Reactive generating power *Q*m.

**Figure 8.** Estimations of states and perturbations. (**a**) Estimation of mechanical rotation speed *ω*m. (**b**) Estimation of perturbation term Ψ1. (**c**) Estimation of *i*md. (**d**) Estimation of perturbation term Ψ2. (**e**) Estimation of *<sup>i</sup>*mq. (**f**) Estimation of perturbation term Ψ3.
