## 3 Algorithm and Scheme of Diagnostics of Asymmetric Emergency Modes
### Diagnostic Scheme for Asymmetric Emergency Modes
\tag{21}\]  
where, \(\mathrm{r_{\mathrm{sa}}}\), \(\mathrm{r_{\mathrm{sb}}}\), \(\mathrm{r_{\mathrm{sc}}}\)--current value of active resistances of the respective phases, \(\Omega\); \(\mathrm{U_{\mathrm{sa}}}\), \(\mathrm{U_{\mathrm{sb}}}\), \(\mathrm{U_{\mathrm{sc}}}\)--amplitudes of phase voltages of the stator of the respective phases, V.  
Amplitudes of phase voltages of the stator are calculated under Equation:  
\[\left\{ \begin{array}{l}\mathrm{U_{\mathrm{sa}}}=\mathrm{U_{\mathrm{ds}}} \cdot\mathrm{V_{\mathrm{a}}}\\ \mathrm{U_{\mathrm{sb}}}=\mathrm{U_{\mathrm{ds}}}\cdot\mathrm{V_{\mathrm{b}}}\\ \mathrm{U_{\mathrm{sc}}}=\mathrm{U_{\mathrm{ds}}}\cdot\mathrm{V_{\mathrm{c}}} \end{array} \right. \tag{22}\]  
where \(\mathrm{V_{\mathrm{a}}}\), \(\mathrm{V_{\mathrm{b}}}\), \(\mathrm{V_{\mathrm{c}}}\)--functions of switching of the inverter phase voltages. Then, the obtained values of phase flux linkages of the stator are transformed to stationary two-phase coordinates [62]:  
\[\left\{ \begin{array}{l}\psi_{\mathrm{sc}}=\psi_{\mathrm{sa}}-\frac{1}{2} \cdot(\psi_{\mathrm{sb}}+\psi_{\mathrm{sc}})\\ \psi_{\mathrm{s}\beta}=-\frac{\sqrt{3}}{2}\cdot(\psi_{\mathrm{sb}}+\psi_{ \mathrm{sc}})\end{array} \right. \tag{23}\]  
The scalar value of the module of the flux linkage vector is calculated as follows:  
\[\left.\left|\overset{\rightarrow}{\psi_{\mathrm{s}}}\right|=\sqrt{\left(\psi _{\mathrm{sc}}\right)^{2}+\left(\psi_{\mathrm{s}\beta}\right)^{2}}\right. \tag{24}\]The values obtained for the stator phase currents are converted to two-phase stationary coordinates using the following Equation [63]:  
\[\left\{ \begin{array}{l}\mathrm{I_{s\alpha}}=\mathrm{I_{sa}}-\frac{1}{2}\cdot( \mathrm{I_{sb}}+\mathrm{I_{sc}})\\ \mathrm{I_{s\beta}}=-\frac{\sqrt{3}}{2}\cdot(\mathrm{I_{sb}}+\mathrm{I_{sc}}) \end{array} \right. \tag{25}\]  
Then, the torque value calculated in the \"Observer of torque and flux\" is as follows:  
\[\mathrm{T}=\frac{3}{2}\cdot\mathrm{p}\cdot\left(\psi_{\mathrm{s\alpha}}\cdot \mathrm{I_{s\beta}}-\psi_{\mathrm{s\beta}}\cdot\mathrm{I_{s\alpha}}\right), \tag{26}\]  
where p--number of motor pole pairs. On one hand, this kind of approach to the determination of the module of spatial flux linkage of the stator would help increase the accuracy of control of the DTC system in the presence of asymmetric modes caused by transient processes in the traction drive system. On the other hand, it would help obtain the values of modules of phase flux linkages of the stator in order to diagnose asymmetric emergency modes in the traction drive system. In the implementation of the diagnostic system, the fact that the transient processes in the traction drive system also cause asymmetric modes even in normal (non-emergency) mode of the drive (Sections 2.7 and 2.8), but the frequency of the transient processes is lower than the feed voltage frequency, should be taken into account. Hence, in order to separate the emergency asymmetric modes from the normal asymmetric modes, the average position calculation of the amplitudes of phase currents and flux linkages of the stator is calculated for the time equal to five periods of variation of the feed voltage. In view of the above, to diagnose the asymmetric emergency modes in the DTC traction drive system, the following adjustments were introduced into the original scheme (Figure 1). In block \"Observer of torque and flux\", the amplitude of the space vector of the stator flux linkage and the torque on the motor shaft are calculated under Formula (21)-(26). The \"Block of coordinate transformations\" has been removed as the transformation of stator currents from the three-phase coordinate system to the stationary two-phase coordinate system in relation to the stator is implemented in the \"Observer of torque and flux\".