# Performance Analysis of Direct Torque Controllers in Five-Phase Electrical Drives
## 4 Results and Discussion
### Fault-Tolerant Capability  
In our work, the fault-tolerant capability of the system using the DTC controller is also analyzed. First, we consider an open-phase fault operation and later take into account the operation with two consecutive and nonconsecutive faults. Figures 14-16 show the performance of the mechanical speed and healthy stator currents when faults appear at \(t=0.2\) s. The system is operated as explained above with a load torque of 2.75 N\(\cdot\)m. Figure 14 summarizes the behavior when phase \(a\) is open, while Figures 15 and 16 show the performance when consecutive phases \(a\) and \(b\) and non-consecutive \(a\) and \(c\), respectively, are open. It is interesting to note that there is no degradation of the speed tracking in all cases; although, the stator phase currents show unequal peak values in the faulty system that becomes worse if the number of faulty phases increases.  
Figure 14: Experimental response of the controlled system when stator phase \(a\) is open at t = 0.2 s and the system is controlled at 500 rpm. The upper row shows the speed response and the lower one shows the stator current waveforms corresponding to phases \(b\), \(c\), \(d\), and \(e\) during the test.  
Figure 13: Experimental response of the controlled system in a speed reversal test. The reference speed is changed from 500 to \(-\)500 rpm at 0.2 s. The upper row shows the speed and torque responses. The lower row shows the stator current waveform and modulus of the stator flux during the test.  
Although the use of DTC is not habitual in the field of multiphase drives due to the intrinsic limitations of a method that only manages two degrees of freedom, it has been experimentally validated that it is possible to apply it to five-phase IM as long as a series of virtual voltage vectors is created to impose zero voltage in the non-controllable plane of \(x\)-\(y\). This allows DTC to be successfully applied when the machine does not have notable asymmetries in the design, where DTC can be considered as a quite competitive alternative to conventional and more complex field-oriented controllers. The results obtained, which can be summarized in Table 3, can be easily extended to multiphase drives with a higher number of phases, but the required virtual voltage vectors must be redefined to minimize stator voltage vectors in the \(x\)-\(y\) planes, which justifies considering the DTC technique as a stimulating strategy for the multiphase case.  
Figure 16: Experimental response of the controlled system when stator phase \(a\) and \(c\) are open at t = 0.2 s and the system is controlled at 500 rpm. The upper row shows the speed response, and the lower one depicts the stator current waveforms corresponding to phases \(b\), \(d\), and \(e\) during the test.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Closed-Loop System Performance** & **DTC** \\ \hline Speed tracking error when the fault appears & Negligible \\ \hline Torque tracking loss in control during the delay & No \\ \hline Robustness against fault detection delay & High \\ \hline Computational cost & Low \\ \hline Harmonic content in stator currents & High \\ \hline \hline \end{tabular}
\end{table}
Table 3: Qualitative analysis of the performance of the 5-phase IM drive using DTC.  
Figure 15: Experimental response of the controlled system when stator phases \(a\) and \(b\) are open at t = 0.2 s and the system is controlled at 500 rpm. The upper row shows the speed response, and the lower one depicts the stator current waveforms corresponding to phases \(c\), \(d\), and \(e\) during the test.