# Multi-Phase Stator Current Tracking with Gradual Penalization of Commutations
## 4 Experimental Results
### Steady State Results  
In order to assess the proposal, the operating range of the 5 pIM is discretized considering the electrical frequency \(f_{e}\) and the amplitude of the stator current reference in \(\alpha-\beta\) plane (\(I_{s}^{*}\)). For the comparisons, the following controllers are considered. Figure 4: Diagram of the laboratory setup used in the experiments. Signal \(i\) corresponds to stator currents for phases a to d obtained with Hall sensors. First, as a base-line method, a standard PSCC with \(\lambda_{xy}=0.08\), \(\lambda_{sc}=0\), and \(T_{s}=55\) (\(\upmu\)s) is applied. This controller is identified as STD-SV since it belongs to the single-vector family. This controller makes little use of commutations, even though \(\lambda_{sc}\) is set to zero. This controller uses an exhaustive search of (12) to attain the optimal VVs to be applied. The control set contains the 32 VVs that the five-phase VSI can produce. Second, a low-complexity multi-vector approach is considered. The VVVs are formed by a large and a medium VV applied for \(0.618\cdot T_{s}\) and \(0.382\cdot T_{s}\), respectively. As a result, the ASF is increased to almost double the value of STD-SV. The sampling period is adjusted so that the maximum switching frequency is not surpassed. This controller does not consider \(x-y\) regulation and uses as a control set just 10 VVV plus the zero configuration. Hence, a reduction in computation time is possible, resulting in \(T_{s}=50\) (\(\upmu\)s). This controller is identified as LC-VVV. Finally, the proposal is considered. Both \(x-y\) content and \(ASF\) are considered using the method indicated in Section III with \(\lambda_{xy}=0.12\). The sampling time need not be adjusted since ASF can be independently controlled using the \(J_{ap}\) values of Figure 2. This controller is identified as PRO-SV. The results are summarized in Table 4, where the experimental figures of merit for each controller are presented. It can be seen in said figure that \(E_{\alpha-\beta}\) values are notably reduced by the proposal. The reduction is more noticeable in operating points characterized by high speed and load. The \(ASF\) is kept below the VSI limit of 10 kHz in all cases. The reported values are in the range found in many applications using standard IGBT semiconductors. In Table 4, the operating points (points (A) to (D)) feature a percentage of rated mechanical speed and opposing load provided by the DC machine. Point (A) is characterized by high load and speed, point (B) is for high load at low speed, point (C) is for medium speed and load, and point (D) is for low speed and load. It can be seen that the proposal obtained the best results for all figures of merit as a consequence of the fast computation of the control signal and the limits imposed on \(x-y\) currents and the ASF by the weighted metric and the new control block, respectively. A quantitative measure of the improvement is presented in Table 5, where the improvement provided by the proposal is shown as a percentage. The improvement is measured against the multi-vector case. For the standard single-vector case, the improvements are more pronounced. Please notice that for this comparison, the ASFs for the various controllers were maintained equal by carefully tuning the WF; in this way, all controllers made a similar use of the power converter. In addition to the previous tables, Figure 5 presents the experimental trajectories of stator currents in \(\alpha-\beta\) plane, \(x-y\) plane, and phase currents \(a-b-c-d-e\). The correct behavior of the proposed method is clearly seen. Also, it is interesting to show that, unlike the multi-vector approach, the proposal has the flexibility to trade \(\alpha-\beta\) tracking with the other figures of merit, as discussed in [34]. For instance, if one is willing to obtain a slightly higher \(x-y\) content, a reduction in \(\lambda_{xy}\) can be made, producing improved results in the other figures of merit.