## 4 Results and Discussion
Several merit figures have been depicted to perform a comparative analysis in terms of the efficiency of the system's performance at different operating points, comparing the proposed controller and the conventional VSTLPC. Again, different sets of VVVs are used to extend the exhaustiveness of the analysis. The merit figures obtained include the number of switching commutations per cycle (NCPC), the root mean square error in the current tracking for the \(\alpha\beta\) plane (\(RMS_{\alpha\beta}\)), the root mean square error in the current tracking for the plane \(xy\) (RMSxy), and the total harmonic distortion of the currents (\(THD\)), which are defined as follows:  
\[RMS_{\alpha\beta}=\frac{1}{2}\sum\limits_{m=-\alpha,\beta}\sqrt{\frac{1}{N} \sum\limits_{j=1}^{N}\left(i_{sm}(j)-i_{sm}^{*}(j)\right)^{2}}\]  
\[RMS_{xy}=\frac{1}{2}\sum\limits_{m=x,y}\sqrt{\frac{1}{N}\sum\limits_{j=1}^{N} \left(i_{sm}(j)\right)^{2}}\]  
\[THD=\sqrt{\frac{\int_{0}^{\infty}\left(i_{s}(t)-i_{s}(t)\right)^{2}dt}{\int_{ 0}^{\infty}\left(i_{s}(t_{1})\right)^{2}dt}}\]  
The original VSTLP controller is compared with the proposal using ML-VVV, since LLL-VVV provides similar results and our interest in LL-VVV is limited to high  
Figure 8: Obtained figure of merits in different operating points (reference speed and load torque) using the conventional VSTLPC technique and the proposed control method with ML-VVV. speed/torque demanding operations. Figure 8 summarizes the results obtained. Regardless of the speed and torque demand, the proposed controller provides lower harmonic distortions in the stator currents due to the reduction in the _xy_ stator voltage components (lower \(RMS_{xy}\) values). In contrast, there are no important differences in the regulation of torque and flux, except in high-speed operations. Note that NCPC increases significantly in the proposed controller with the application of the VVV concept. This is a direct consequence of using VVV and two switching states of the 5p2L-VSI in the same sampling period, while only one switching state is applied in the case of the original VSTPLC method. This result can generate a disadvantage when using the proposed controller because it can force an increase in the switching losses of the power converter. Therefore, incorporating VVVs into the VSTLPC algorithm can improve the efficiency of the controlled system, reducing copper losses by limiting the injection of the _xy_ current. This is the case when ML-VVV or LLL-VVV is considered. This improvement is also complemented by a reduction in the computational burden of the controller due to the simplification of the predictive model using the VSTLPC algorithm. However, the use of two or three voltage vectors in a sampling period instead of only one can increase the switching losses in the power converter, limiting the interest of the proposal. Note also that the use of VVV leads to a reduction in DC link voltage utilization, which limits the operating range of the machine. This drawback can be mitigated using LL-VVV, which extends the operational range in the real system compared to using ML-VVV or LLL-VVV. As a general conclusion, the selection of the applied VVV should be carried out based on the required control performance and the operational point of the machine.