## 4 Results and Discussion  
The effectiveness and efficiency of the proposed controller are explored, and the sets of VVVs are detailed in Table 2. Note that the selection of the parameters used in the experiments is based on heuristic adjustment and empirical observation. In all tests, maximum and minimum values are imposed for the sampling time \(T_{a}\) to consider limitations in the efficiency of the control algorithm and in the 5p2L-VSI switching frequency. In our case, the maximum value is set at 150 us, while the minimum value is forced to be 32.5 us using the conventional VSTLPC method and the proposed controller, and the advanced time \(t_{L}\) is set to \(T_{amin}\). A group of tests was conducted to compare the performance in the steady state of the original VSTLPC and the proposed one once the machine was close to the achievable limits. Figures 5-8 summarize the results obtained. In the first experiment (see Figure 5), a reference speed of 300 rpm (\(\omega_{m}\)) is imposed, and a load torque (\(T_{L}\)) equal to 50% of the nominal is applied. The regulation of speed and the control of the stator current in the \(\alpha\beta\) plane are achieved effectively in all cases. However, interesting comments regarding the stator current's performance in the \(xy\) subspace must be made. Considering VSTLPC with virtual ML and LLL vectors, a reduction in the \(xy\) current components is observed relative to the original VSTLPC technique. This leads to a reduction in the harmonic content of the stator currents and, consequently, to a higher system efficiency, thanks to the use of virtual voltage vectors themselves, which produce an effective open-loop regulation of the \(xy\) plane. However, a different situation is observed with the LL virtual vectors, where a non-zero-average \(xy\) voltage is imposed and higher \(xy\) stator current components appear, as expected. A reference speed of 500 rpm (\(\omega_{m}\)) is imposed, and a load torque (\(T_{L}\)) equal to 85% of the nominal is applied in a second batch of tests (see Figure 6). Again, the regulation of speed and control of the stator current in the \(\alpha\beta\) plane are achieved effectively in all cases, and the main conclusions achieved in the first experiment are confirmed. Figure 5: Steady-state response at 300 rpm and 50% of the nominal torque using conventional VSTPLC (**a**) and the proposed controller with ML-VVV (**b**), LL-VVV (**c**), and LLL-VVV (**d**). From left to right: mechanical speed and \(\alpha\beta\) and \(xy\) stator currents. Figure 6: _Cont_. Figure 6: Steady-state response at 500 rpm and 85% of the nominal torque using conventional-VSTPLC (**a**) and the proposed controller with ML-VVV (**b**), LL-VVV (**c**), and LLL-VVV (**d**). From left to right: mechanical speed and \(\alpha\beta\) and \(xy\) stator currents. Figure 7: Steady-state response at 600 rpm and 85% of the nominal torque using the proposed controller with ML-VVV (**a**), LL-VVV (**b**), and LLL-VVV (**c**). From top to bottom: mechanical speed and \(\alpha\beta\), \(xy\), and \(dq\) stator currents. A second batch of experiments is then considered, where higher speed and torque conditions are imposed, and the optimal usage of the DC link voltage becomes essential. Figure 7 shows the results obtained when a speed reference of 600 rpm and 85% of the nominal torque is forced. In this case, VSTLPC with ML and LL-VVV is not capable of effectively controlling the machine's speed. This is the main consequence of their limited DC link utilization because of the reduced magnitude of these VVVs. This situation produces the saturation of the \(q\)-current reference generated by the PI regulator, which achieves the maximum admissible value. In contrast, when LL-VVV vectors are applied, the speed can be regulated because of the extended DC link utilization provided by this set of virtual vectors, at the expense of suboptimal current quality. Then, LL-VVV provides higher voltage magnitudes compared to other virtual vector groups.