*4.1. Ramp Wind*

Figures 5 and 6 show the responses of the PMSG-WT to ramp wind. Wind speed is shown in Figure 5a. As shown in Figure 5b,c, the proposed NAC provides the smallest tracking error of the mechanical rotation speed *ω*m, compared with the VC, GSPI and FLC. The VC has the biggest tracking error and requires the longest recovery time. It can be explained that the VC is adjusted for a specific operation point of the system and cannot ensure provision of a satisfactory dynamic performance for time-varying operation points. Although the FLC can provide a high tracking performance, the tracking error of *ω*m still exists. It is because that the FLC requires full state measurements, but the d*V* d*t* in Equation (9) is unknown in the FLC design. The GSPI also achieves better performance than the VC. This is because the GSPI can schedule PI gains frequently under time-varying wind speeds. However, it increases the burden of the controller.

**Figure 5.** Responses of the PMSG-WT to ramp wind speed. (**a**) Wind speed V. (**b**) Mechanical rotation speed *ω*m. (**c**) Relative error of *ω*m. (**d**) Required pitch angle. (**e**) Power coefficient *<sup>C</sup>*p. (**f**) Mechanical power *P*w. (**g**) Active generating power *P*m. (**h**) Reactive generating power *Q*m.

To keep the extracted wind power at the rated power, the required pitch angle *β*r should change with the varying wind speed, as shown in Figure 5d. In Figure 5e,f, to maintain the extracted wind power around its rated value, the power coefficient *C*p increases when wind speed decreases. The extracted wind power can be maintained around its rated value under the NAC even when wind speed varies, which the VC, GSPI and FLC cannot provide. The active generating power *P*m and reactive generating power *Q*m of the PMSG-WT are shown in Figure 5g,h, respectively.

**Figure 6.** 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.

In the previous section, it mentions that the proposed NAC can estimate the defined perturbation terms Equations (17) and (36) via the designed observers Equations (19), (38) and (39) to compensate the real perturbation. It can be seen from Figure 6 that both the states and perturbations can be well estimated by the designed SPO.
