*5.2. Under-Voltage*

The grid voltage is dropped to 50% of its rated value for 200 ms from 1 s to 1.2 s during the under-voltage case, as illustrated in Figure 9b. The proposed controller *Vdc* response, shown in Figure 9a, is less oscillatory, fast, and robust for the API and PR+RHC algorithms, as compared to PI's response which is unstable and out of limits. Figure 9c–e clearly shows that *Id* completely traces the

reference value which indicates the robustness of the proposed (API & PR+RHC) strategies. The API controller updates its parameters using fuzzy rules to track the reference abruptly and the PR+RHC, due to its harmonic compensation, effectively minimizes the error, in comparison to the PI controller. The proposed controller responses in the case of *Ir* is shown in Figure 9f. Figure 9g depicts *Iq* having smooth response for the proposed controllers which gain stability soon after voltage the reaches a normal value. Figure 9h illustrates the *Ig* response for the API & (PR+RHC) controllers with respect to the PI controller which ensures grid stability. The *Pr* and *Ps* responses are described in Figure 9i,j which show that the API & (PR+RHC) controller responses are less oscillatory, and more stable as compared to the PI controller which reduces mechanical stress y as well as stress on drives.

**Figure 9.** *Cont.*

**Figure 9.** Comparison of PI and Proposed API and PR+RHC controller responses under undervoltage 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; (**p**) API controller THD.

The *Psreact*, *Tem* and *Vr* responses for both the proposed and conventional strategy are shown in in Figure 9k–m. Finally, the robustness of the proposed controllers over the PI conventional controller was proved by harmonic spectrum analysis of *Ig*, The THD value for the PI controller was 90.22% which is reduced to 61.20% and 66.16% in the case of the API and PR+RHC, respectively, and demonstrated in Figure 9n–p. The performance indices of all the control schemes are evaluated in Tables 5–7 for *Vdc*, *Id*, and *Iq*, respectively. In the case of the API & PR+RHC controllers, all three parameter values are the minimum compared with the PI controller, which proves the better performance of the proposed controllers in under-voltage conditions.



**Table 6.** Performance evaluation of the designed control strategies for *Id*.



**Table 7.** Performance evaluation of the designed control strategies for *Iq*.
