## 1 Introduction
### Selecting Direct Torque Control Imitation Model
As a result of the changes, the starting characteristics of the system of phase currents and phase flux linkages in the steady-state mode were taken for the intact stator windings and symmetric stator windings at different motor temperatures. The data were included into Table 6.  
The time diagrams of phase currents (Figure 9a) and stator flux linkages (Figure 9b) of the asynchronous motor were designed for 100 \({}^{\circ}\)C motor temperature mode in case of the symmetric feed voltage system and intact stator windings in steady-state mode. As suggested in Figure 9, the diagrams of both the phase currents and phase flux linkages of the stator were of the same nature as those of the motor with intact windings in the case of the asymmetric feed system at normal ambient temperature [62]. The amplitudes of phase currents were equal to 636 A only at the motor temperature equal to the normal ambient temperature (20 \({}^{\circ}\)C), and 617 A at 100 \({}^{\circ}\)C motor temperature. Subsequent investigations showed that where motor temperature variation took place in the case of stator winding damage and supply system asymmetry, phase currents and flux linkages of the stator demonstrated the same behavior as shown in the respective experiments with \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{5}{c}{**Motor Temperature (T, \({}^{\circ}\)C)**} \\ \cline{2-6}
**Parameter** & **20** & **60** & **100** & **140** & **160** \\ \hline Instantaneous value of the stator current of phase A \(I_{\rm s,\alpha}\), A & 636 & 619.7 & 617.8 & 617.1 & 616.4 \\ \hline Instantaneous value of the stator current of phase B \(I_{\rm s,\beta}\), A & 636 & 619.7 & 617.8 & 617.1 & 616.4 \\ \hline Instantaneous value of the stator current of phase C \(I_{\rm s,\gamma}\), A & 636 & 619.7 & 617.8 & 617.1 & 616.4 \\ \hline Instantaneous value of the stator flux linkage of phase A \(\psi_{\rm s,\alpha}\), A & 3.952 & 3.951 & 3.95 & 3.949 & 3.948 \\ \hline Instantaneous value of the stator flux linkage of phase B \(\psi_{\rm s,\beta}\), A & 3.952 & 3.952 & 3.951 & 3.95 & 3.949 \\ \hline Instantaneous value of the stator flux linkage of phase C \(\psi_{\rm s,\gamma}\), A & 3.952 & 3.952 & 3.951 & 3.95 & 3.949 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values of the phase currents and flux linkages of the stator at different motor temperatures with the intact stator windings and symmetric feed voltage system. Figure 9: Time diagrams of the stator phase currents (**a**) and stator flux linkages (**b**) of the asynchronous motor in the steady-state mode under the symmetry of feed and stator windings at 100 \({}^{\circ}\)C temperature of the windings. the motor temperature equal to the normal ambient temperature. The authors therefore consider that presentation of the diagrams of phase currents and flux linkages for similar experiments at higher motor temperatures would be unreasonable. Investigation of the Effect of Stochastic Change of the Feed Voltage under the Conditions of Symmetry of the Stator Windings and Feed Voltage System  
The analysis presented in Section 1 suggests that the specifics of operation of an electric rolling stock cause constant variation of the voltage at the input of autonomous voltage inverter U\({}_{\text{ds}}\) (Figure 1). At the same time, the process of variation of the voltage at the input of inverter U\({}_{\text{ds}}\) could be of a non-stationary, non-deterministic character. To put it otherwise, transient processes take place continuously at the autonomous voltage inverter input during the process of operation of the electric rolling stock. These transient processes move from the inverter input to its output. Moreover, thermal noise develops at the inverter output due to the theoretical processes in the traction drive system, such as motor heating as a result of current passing down the motor windings, heating of the autonomous voltage inverter caused by the processes of commutation, and passing of the currents through active resistances when transitioning between its active elements.