## 1 Introduction
### Selecting Direct Torque Control Imitation Model
As a result of the variations for phase A voltage amplitude equal to the nominal value, +2%, +1%, -1%, and -2% deviations from the nominal value, the starting characteristics of the phase current system, and phase flux linkages of the motor in the steady-state mode were taken. The data are included in Table 4. The following was determined during the previous experiment: the pattern was observed both for the phase currents and phase flux linkages featuring a constant ratio of the amplitude of the instantaneous value of the stator current and amplitude of the instantaneous value of the phase stator flux linkage with the deviation of the stator voltage amplitude and phases with the nominal value of the stator voltage amplitude, in the steady-state mode. The pattern  
Figure 6: Dependencies of currents (**a**) and flux linkages (**b**) of the stator on the degree of deviation of the phase A voltage amplitude of the stator in case of the symmetry of stator windings in the steady-state mode. was maintained in the experiment considered. Hence, the diagrams of the instantaneous values of currents and flux linkages are not presented here. The results in Table 4 were used to build the dependencies of the currents (Figure 7a) and flux linkages of the stator (Figure 7b) on the degree of deviation of the phase A voltage amplitude of the stator in the case of asymmetry of the stator windings in steady-state mode. As suggested by Figure 7a, the dependencies of the stator currents of all phases on the degree of deviation of the phase A voltage amplitude were non-linear. The currents of intact phases were equal to each other. In case the phase A voltage amplitude equaled the nominal value, the phase currents of all phases had the local maximum, and the current of the damaged phase was higher than the currents of intact phases. With the phase A voltage amplitude increasing, the currents of the intact phases were decreasing non-linearly, and the current of the damaged phase was initially decreasing down to the local minimum and increasing afterwards. With the phase A voltage amplitude decreasing, the currents of the intact phases were initially decreasing down to the local minimum and increasing afterwards, while the current of the damaged phase was decreasing. Variation of the flux linkages caused by the deviation of the voltage on one of the phases (Figure 7b) was linear. This evidence is explained by the fact that the flux capacitance is determined by the relationship \(\psi=\mathrm{U}/\omega\), where \(\mathrm{U}\) is the phase supply voltage and \(\omega\) \begin{table}
\begin{tabular}{l c c c c c} \hline  & \multicolumn{5}{c}{**Deviation of Phase A Voltage from the Nominal**} \\ \cline{2-7}
**Parameter** & \multicolumn{2}{c}{**+2**} & \multicolumn{2}{c}{**+1**} & \multicolumn{1}{c}{**0**} & \multicolumn{1}{c}{\(\mathbf{-1}\)} & \multicolumn{1}{c}{\(\mathbf{-2}\)} \\ \hline Instantaneous value of the stator current of phase A \(\mathrm{I}_{\mathrm{sa}}\), A & 710.768 & 691.462 & 693.393 & 655.014 & 636.977 \\ \hline Instantaneous value of the stator current of phase B \(\mathrm{I}_{\mathrm{s}\beta}\), A & 642.125 & 647.936 & 667.625 & 652.225 & 655.983 \\ \hline Instantaneous value of the stator current of phase C \(\mathrm{I}_{\mathrm{s}\gamma}\), A & 642.125 & 647.936 & 667.625 & 652.225 & 655.983 \\ \hline Instantaneous value of the stator flux linkage of phase A \(\psi_{\mathrm{sa}}\), A & 3.946 & 3.928 & 3.912 & 3.893 & 3.876 \\ \hline Instantaneous value of the stator flux linkage of phase B \(\psi_{\mathrm{s}\beta}\), A & 3.989 & 3.979 & 3.969 & 3.959 & 3.949 \\ \hline Instantaneous value of the stator flux linkage of phase C \(\psi_{\mathrm{s}\gamma}\), A & 3.989 & 3.979 & 3.969 & 3.959 & 3.949 \\ \hline \end{tabular}
\end{table} 
Table 4: Values of phase currents and flux linkages of the stator at different degrees of deviation of phase A voltage and 5 damaged turns of the phase A winding of the stator.