*4.3. Results*

Apart from the adaptive control approach, other frequency strategies have been simulated and compared for the sixty scenarios under consideration:


As was discussed in Section 4.1, sixty different scenarios are considered to evaluate the new frequency control approach for VSWTs. Results are focused on four different aspects for each scenario: (i) the minimum rotational speed *ωmin*; (ii) the maximum torque *Tmax*; (iii) the power shed due to the corresponding load shedding programs; (iv) number of cases in which VSWTs do not participate in frequency control with the adaptive proposed approach. Both *ωmin* and *Tmax* are expressed in % with regard to the pre-event values, which is equal to their values when they do not participate in frequency control.

Figure 9 depicts the range values of the rotational speed in % compared to the pre-event value. When VSWTs do not participate in frequency control, its *ω* variation is null, as they are providing *pMPP*(*sw*). According to these results, and depending on the frequency control strategy, important differences can be identified. With regard to the frequency control referred to as *previous approach*, and considering that the change from overproduction to recovery period is always with *<sup>ω</sup>*/*<sup>ω</sup>*0 < 0.9, all scenarios then give the same minimum *ω*, which represents more than a 7% variation. Based on the *adaptive approach*, *ωmin* variations range in between 0 (for those cases in which the frequency control is not activated) and 6.62%. In fact, the average *ωmin* variation with the proposed strategy is 2.15%. As a consequence, the new frequency control strategy technique does not only optimize those imbalances where VSWTs frequency control participation is required but also reduces the averaged variation of *ω* to more than half of the previous frequency control approaches.

Figure 10 compares the maximum torque during the VWST frequency response to the corresponding pre-event value. These results are in line with the previous rotational speed comparison, see Figure 9. The torque does not vary when VSWTs do not participate in frequency control, as both *ω* and *pe* remain constant. With the *previous approach* for VSWT frequency control, the maximum torque variation is always the same. Moreover, this variation is over a 30% increase—in comparison to the pre-event value, which can address relevant mechanical loads on the turbine shaft. In contrast, with the proposed *adaptive approach*, the maximum *Tmax* variation is 26.5% (only 9 out of 60 scenarios), with an average *Tmax* of 9.7%. It can be then deduced that the new frequency control approach does not only avoid the activation of the frequency control of VSWTs in most of imbalance scenarios but also that both *ω* and *Tmax* ranges are reduced significantly compared to previous approaches.

**Figure 9.** Minimum rotational speed (**a**) Largest power plant disconnection; (**b**) Second largest power plant disconnection.

**Figure 10.** Maximum torque variation (**a**) Largest power plant disconnection; (**b**) Second largest power plant disconnection.

Figure 11 shows the power shed by the load shedding program. As can be seen, it is reduced when wind power plants participate in frequency control, compared to the current case in which only thermal power plants are providing such ancillary service. Comparing the two different frequency control approaches analyzed, small differences are found. The *previous approach* gets better results in 4 out of 60 scenarios under study, whereas the *adaptive approach* obtained lower load shedding values in 2 out of 60 scenarios. In the other cases, both frequency controllers obtain the same load shedding.

**Figure 11.** Load shedding (**a**) Largest power plant disconnection; (**b**) Second largest power plant disconnection.

Finally, 57% of imbalances without any VSWTs frequency response participation have been identified. These results reduce significantly the mechanical and electrical VSWT efforts under imbalances, maintaining similar frequency excursions to the previous control strategies. More specifically, the VSWT frequency participation is not required to provide additional power in 11 out of 30 for the largest power plant loss and 23 out of 30 for the second largest power plant loss. These 34 scenarios where the adaptive frequency control is not triggered can be seen in Figures 9 and 10: imbalance scenarios will null variation of *ωmin* and *Tmax* for the proposed control strategy. Therefore, *pe* and *ω* values keep as constant during the imbalance and, subsequently, also maintain the torque. In addition, authors have checked that in 94% of the cases in which VSWTs are not participating in frequency control with the *adaptive approach*, the power shed was initially null, pointing out that their participation was not required within acceptable frequency excursion ranges.

As an additional result, Figures 12–14 depict the frequency evolution, load shedding, wind power, and rotational speed for scenarios 9, 16, and 27, respectively, for the loss of the largest power plant. Together with the aforementioned advantages of the new approach, authors also point out that the rotational speed of VSWTs is recovered in a lower time interval than with the previous frequency control approach. Moreover, the transition from overproduction to recovery period is also smoother, avoiding undesirable secondary frequency dips (refer to Figure 12).

**Figure 12.** Results for scenario 9 (**a**) Frequency (Hz). (**b**) Load shedding (MW) (**c**) Wind power (MW) (**d**) VSWTs rotational speed (pu).

**Figure 13.** Results for scenario 16 (**a**) Frequency (Hz); (**b**) Load shedding (MW); (**c**) Wind power (MW); (**d**) VSWTs rotational speed (pu).

**Figure 14.** Results for scenario 27 (**a**) Frequency (Hz); (**b**) Load shedding (MW); (**c**) Wind power (MW); (**d**) VSWTs rotational speed (pu).
