*5.3. Over-Voltage*

In over-voltage conditions the grid voltage is increased 50% of its rated value for 200 ms from 1 s to 1.2 s as shown in Figure 10b. The *Vdc* of the proposed controllers is robust, faster, and stable soon after the grid voltage recovers as shown in Figure 10a. *Id* for the PI, API and PR+RHC control controllers are clearly depicted in Figure 10c–e which prove that the proposed controllers are exactly following the reference value. Due to adaptiveness of the API and harmonic compensation of PR+RHC, both controllers are less sensitive to faults and the response is faster. *Ir* are also depicted in Figure 10f for all controllers. In case, the *Ig* responses in the API and PR+RHC controllers are fast and attain stability quickly after 1.2 s as shown in Figure 10g. Similarly *Iq*, the API and PR+RHC controller responses are fast and achieve stability soon after 1.2 s, while the PI controller responds after 1.5 s as elaborated in Figure 10h. The proposed controllers' responses in the case of *Pr* and *Ps* is less oscillatory and stable, which ensures stable performance is shown in Figure 10i,j. The proposed controllers' performances in the case of *Psreact*, *Tem* and *Vr* are also dominant and less harmonic as shown in Figure 10k–m. Finally, THD of *Ig* is calculated, which is 1046.10% using the PI controller while it reduces to 446.52% and 684.51% in the case of the API and PR+RHC controllers which makes the proposed controllers more reliable and efficient in over-voltage conditions as shown in Figure 10n–p. The performance indices of all the control schemes are evaluated in Tables 8–10 for *Vdc*, *Id*, and *Iq*, respectively. In the case of the API and PR+RHC controllers, all three parameters values are minimum compared with the PI controller, which validates the better performance of the proposed controllers.

**Figure 10.** *Cont.*

**Figure 10.** Comparison of PI and Proposed API and PR+RHC controller responses under overvoltage fault, considering: (**a**) Dc-link voltage *Vdc*; (**b**) Stator voltage *Vs*; (**<sup>c</sup>**–**<sup>e</sup>**) Active component of current *Id*; (**f**) Rotor current *Ir*; (**g**) Reactive current component *Iq*; (**h**) Grid current *Ig*; (**i**) Rotor active power *Pr*; (**j**) Stator active power *Ps*; (**k**) Electromagnetic torque *Tem*; (**l**) Stator reactive power *Psreact*; (**m**) Rotor voltage *Vr*; (**n**) PR+RHC controller THD; (**o**) PI controller THD; (**p**) API controller.



**Table 9.** Performance evaluation of the designed control strategies for *Id*.

**Table 10.** Performance evaluation of the designed control strategies for *Iq*.


#### *5.4. Single Phase Fault*

A single-phase fault is applied to evaluate the performance of the proposed controllers. The fault is applied for 200 ms from 1 s to 1.2 s as depicted in Figure 11b. The *Vdc* responses of the API and PR+RHC controllers are robust and attain stability soon after the fault is cleared, while the PI controller response is oscillatory and delayed in accomplishing stability after the fault is cleared as illustrated in Figure 11a. The *Id* responses for the PI, API and PR+RHC controllers are shown in Figure 11c–e.The API controller updates its parameters using fuzzy rules to track the reference abruptly and the PR+RHC controller, due to its harmonic compensation, effectively minimizes the error, in comparison to the PI controller. *Ir* values for the conventional and proposed controllers are illustrated in Figure 11f.The *Iq* and *Ig* responses of the proposed controllers are more stable and less oscillatory as shown in Figure 11g,h. The responses of *Ps* and *Pr* powers, *Tem*, *Psreact*, and *Vr* are shown in Figure 11i–m.Analyzing the controllers on the basis of the grid current *Ig* THD values, it clearly shows that the proposed API controller with 55.43% THD and PR+RHC with 60.91% THD show less harmonics with respect to the 76.35% THD of the PI controller with increased harmonics which shows that the proposed controllers' responses in case of a single-phase fault are robust and stable as compared to the PI controller as shown in Figure 11n–p. The performance indices of all the control schemes are evaluated in Tables 11–13 for *Vdc*, *Id*, and *Iq*, respectively. In the case of proposed API and PR+RHC controllers, all three parameter values are minimum compared with the PI controller, which guarantees the better performance of the proposed controllers under single-phase fault conditions.

**Figure 11.** *Cont.*

**Figure 11.** Comparison of PI and Proposed API and PR+RHC controller responses under Single-phase fault, considering: (**a**) Dc-link voltage *Vdc*, (**b**), Stator voltage *Vs*, (**<sup>c</sup>**–**<sup>e</sup>**) Active component of current *Id*, (**f**) Rotor current *Ir*, (**g**) Reactive component *Iq*, (**h**) Grid current *Ig*, (**i**) Stator active power *Ps*, (**j**) Rotor active power *Pr*, (**k**) Electromagnetic torque *Tem*, (**l**) Stator reactive power *Psreact*, (**m**) Rotor voltage *Vr*, (**n**) PR+RHC controller THD, (**o**) PI controller THD, (**p**) API controller.

**Table 11.** Performance evaluation of the designed control strategies for *Vdc*.



**Table 12.** Performance evaluation of the designed control strategies for *Id*.

**Table 13.** Performance evaluation of the designed control strategies for *Iq*.


## *5.5. Two-Phase Faults*

A two-phase fault is applied to evaluate the performance of the control strategies. The fault is applied for 200 ms from 1 s and cleared at 1.2 s, as shown in Figure 12b. The *Vdc* responses of the API and PR+RHC controllers are more stable, quickly tracking the reference value after the fault is cleared, as compared to the unstable response of the PI controller as presented in Figure 12a. A comparison of the *Id* of all controllers (Figure 12c–e) indicates that the API and PR+RHC controllers clearly track the reference value while PI goes unstable as it proceeds after 1.2 s. The API controller employs fuzzy rules adoptively with robust response and the PR+RHC due to its harmonic compensation effectively minimizes the error, in comparison to the PI controller. Figure 12f describes the *Ir* responses for all the controllers. Similarly, the *Iq* and *Ig* responses are more stable and robust in the API and PR+RHC controllers' case as elaborated in Figure 12g,h. The responses of other parameters of WTs i.e., *Ps*, *Pr*, *Tem*, *Psreact* and *Vr* are shown in Figure 12i–m. The grid current *Ig* THDs of all controllers are presented in Figure 12n–p.

**Figure 12.** *Cont.*

**Figure 12.** Comparison of PI and Proposed API and PR+RHC controller responses under two-phase fault, considering: (**a**) Dc-link voltage *Vdc*, (**b**) Stator voltage *Vs*, (**<sup>c</sup>**–**<sup>e</sup>**) Active component of current *Id*, (f) Rotor current *Ir*, (**g**) Reactive component *Iq*, (**h**) Grid current *Ig*, (**i**) Rotor active power *Pr*, (**j**) Stator active power *Ps*, (**k**) Electromagnetic torque *Tem*, (**l**) Stator reactive power *Psreact*, (**m**) Rotor voltage *Vr*, (**n**) PR+RHC controller THD, (**o**) PI controller THD and (**p**)API controller.

The API and PR+RHC controllers have THDs of 79.03% and 85.64% while the PI controller has 102.06% THD which demonstrates the effectiveness and dominance of the proposed (API & PR+RHC) controllers over PI. The performance indices of all the control schemes (PI, API & PR+RHC) are evaluated in Tables 14–16 for *Vdc*, *Id*, and *Iq*, respectively. In the case of the proposed (API & PR+RHC) controllers, all three parameter values are minimum compared with the PI controller, which authenticates the better performance of the proposed controllers under two-phase fault conditions.


**Table 14.** Performance evaluation of the designed control strategies for *Vdc*.



**Table 16.** Performance evaluation of the designed control strategies for *Iq*.

