## 1 Introduction
### Selecting Direct Torque Control Imitation Model
The flux linkages of all phases showed an upward trend at higher values than the nominal value of the phase B voltage amplitude. At the same time, the flux linkage value of the damaged phase was lower than the flux linkage values of other phases, and the flux linkage of the phase with the voltage deviation was increasing faster than that of the intact phase and the phase of the nominal value of phase voltage. Investigation of the effect of phase C voltage deviation in the case of the damaged phase A stator winding demonstrated that the starting characteristics of the phase currents and flux linkages of the stator were the same as in the case of phase B voltage deviation at the damaged phase A winding. However, it should be noted that the current and flux linkage curves of phases B and C switched places, and the current and flux linkage curves of phase A did not change. Therefore, the authors consider that presentation of the data for this case would be unreasonable. Investigation of the Effect of Temperature under the Conditions of Symmetry of the Stator Windings and Feed Voltage System  
In the investigation of the effect of temperature on the starting characteristics of the asynchronous motor under the conditions of symmetry of the feed voltage system and the stator windings, the following adjustments were made in the simulation model. The respective variations of the active resistance of the stator and rotor calculated for the following motor temperatures were introduced into the \"Unit for determining motor phase currents\": 20 \({}^{\circ}\)C, 60 \({}^{\circ}\)C, 100 \({}^{\circ}\)C, 140 \({}^{\circ}\)C, and 160 \({}^{\circ}\)C. The papers [60; 61] provide that the process of temperature variation is inertial. It takes more than 30 min for the traction motor to reach the required temperature within the temperature range from the normal ambient temperature (20 \({}^{\circ}\)C) to the maximum value of the nominal mode (160 \({}^{\circ}\)C). Hence, a hypothesis was proposed to determine the starting characteristics, namely, that the motor was preheated to the required temperature. Active resistance of the stator and rotor windings was recalculated under Equation [70]:  
\[\mathrm{r_{T}=r_{0}.(1+\alpha.(T_{i}-T_{0}))} \tag{1}\] \begin{table}
\begin{tabular}{l c c c c c} \hline  & \multicolumn{5}{c}{**Deviation of Phase B Voltage from the Nominal**} \\ \cline{2-7}
**Parameter** & \multicolumn{5}{c}{**Value (\(\gamma\), \%)**} \\ \cline{2-7}  & **+2** & **+1** & **0** & **\(-\)1** & **\(-\)2** \\ \hline Instantaneous value of the stator current of phase A \(\mathrm{I_{s\alpha}}\), A & 666.92 & 673.689 & 693.393 & 677.543 & 681.536 \\ \hline Instantaneous value of the stator current of phase B \(\mathrm{I_{s\beta}}\), A & 685.42 & 666.927 & 667.747 & 631.045 & 612.953 \\ \hline Instantaneous value of the stator current of phase C \(\mathrm{I_{s\gamma}}\), A & 642.125 & 648.536 & 667.625 & 652.425 & 655.983 \\ \hline Instantaneous value of the stator flux linkage of phase A \(\mathrm{\psi_{s\alpha}}\), A & 3.929 & 3.92 & 3.912 & 3.902 & 3.893 \\ \hline Instantaneous value of the stator flux linkage of phase B \(\mathrm{\psi_{s\beta}}\), A & 4.004 & 3.987 & 3.969 & 3.951 & 3.934 \\ \hline Instantaneous value of the stator flux linkage of phase C \(\mathrm{\psi_{s\gamma}}\), A & 3.988 & 3.979 & 3.969 & 3.959 & 3.95 \\ \hline \end{tabular}
\end{table} 
Table 5: Values of phase currents and flux linkages of the stator at different degrees of damage of the phase B winding of the stator and 5 damaged turns of the phase A winding of the stator. where \(r_{0}\)--active resistance of the phase of stator (\(r_{\rm s}\)) or rotor (\(r_{\rm r}\)) at the respective temperature, \(\Omega\) 20 \({}^{\circ}\)C (Table 1); \(\alpha\) = 3.86\(\cdot\)10\({}^{-3}\), \({}^{\circ}\)C\({}^{-1}\)--temperature coefficient of copper resistance (Table 1); \(T_{\rm i}\)--current temperature value, \({}^{\circ}\)C; \(T_{0}\) = 20 \({}^{\circ}\)C--normal ambient temperature value.