## 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 phase currents and phase flux linkages of the stator in the steady-state mode were taken. Data were included into Table 3.  
The time diagrams of phase currents (Figure 5a) and stator flux linkages (Figure 5b) were designed for the mode with \(+2\%\) deviation of the phase A voltage amplitude in the case of symmetric stator windings in the steady-state mode. Figure 5 suggests a pattern for both phase currents and phase flux linkages: constant ratios of the stator current amplitude and the stator flux linkage amplitude of the phase with the deviation of the stator voltage amplitude and phases with the nominal value of the stator voltage amplitude, in steady-state mode. It should be noted that the phase flux linkages of the intact stator phases were the same, i.e., \(\psi_{\text{sb}}=\psi_{\text{sc}}\). The results in Table 3 were used to build the dependencies of currents (Figure 6a) and flux linkages of the stator (Figure 6b) 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. Figure 6 suggests that the dependency of the phase stator voltage with the deviation of amplitude from the normal value is linear, while the dependency of the stator currents with the nominal values of the voltage amplitudes is non-linear. It should also be noted that with the voltage amplitude exceeding the nominal value, the current of the respective phase increases and decreases in case of the voltage amplitude lower than the nominal value. Figure 5: Time diagrams of phase currents (**a**) and stator flux linkages (**b**) of the asynchronous motor in steady-state mode with \(+2\%\) deviation of the phase A voltage amplitude and symmetric windings of the stator. At the phase A voltage amplitude equal to the nominal value, the phase currents of other phases have the local maximum [45; 46]. With the phase A voltage amplitude increasing, the currents of other phases were decreasing non-linearly, and with the decrease in the phase A voltage amplitude, the currents of other phases were initially decreasing down to the local minimum and increasing afterwards. The flux linkages of all phases showed an upward trend at a higher than nominal value of the voltage amplitude. At the same time, the phase flux linkage accompanied by the deviation of the voltage from the nominal value was increasing faster than the stator flux linkages of other phases, and the phase flux linkages of the intact stator phases were the same, i.e., \(\psi_{\text{sb}}=\psi_{\text{sc}}\). The flux linkages of all phases showed a downward trend at a lower than the nominal value of the voltage amplitude. At the same time, the phase flux linkage accompanied by deviation of the voltage from the nominal value was decreasing faster than the stator flux linkages of other phases. Investigation of the Effect of Simultaneous Asymmetry of the Feed Voltage System and Motor Windings in the Same Phase  
In the investigation of the effect of asymmetry of the feed voltage system on the starting characteristics of the asynchronous motor under the conditions of asymmetry of the stator windings, the following adjustments were made in the simulation model. Adjustments of active resistance and inductance of leakage of the damaged phase equal to five turns of the phase A winding of the stator were introduced into the \"Unit for determining motor phase currents\". The number of turns of the damaged turns was reduced by five turns in the \"Block for calculating mutual inductances and total inductance of the magnetization circuit\". Respective variations of the amplitude were entered into the sinusoidal voltage source of phase A U\({}_{\text{s}\alpha}\).