## 3 Algorithm and Scheme of Diagnostics of Asymmetric Emergency Modes
### Diagnostic Scheme for Asymmetric Emergency Modes  
In view of the algorithm for diagnosing the asymmetric emergency modes in the DTC traction drive system presented in the previous subsection, its implementation requires the following data:  
* Values of the stator phase currents;
* Values of the stator phase flux linkages;
* Value of the stator flux linkage at intact stator windings and symmetric feed voltages for the specified operation mode of the traction drive;
* Value of the stator current at intact stator windings and symmetric feed voltages for the specified operation mode of the traction drive. Value of the stator flux linkage at intact stator windings and symmetric feed voltages for the specified operation mode of the traction drive is formed by the \"Flux setting block\". The output signal \(\,|\psi_{\text{sset}}|\,\) of the block corresponds to the value of the stator flux linkage amplitude at intact stator windings and symmetric feed voltages for the specified operation mode of the traction drive. The value of the stator current at intact stator windings and symmetric feed voltages for the specified operation mode of the traction drive may be calculated using Equation [62]:  
\[|\mathrm{I_{\mathrm{sset}}}|=\frac{\mathrm{U_{\mathrm{ds}}}}{\mathrm{r_{\mathrm{s }}}}-\frac{|\mathrm{\psi_{\mathrm{sset}}}|}{\mathrm{L_{\mathrm{s}}}}, \tag{19}\]  
where \(\mathrm{U_{\mathrm{ds}}}\)--voltage at inverter input, V; \(\mathrm{L_{\mathrm{s}}}\)--full inductance of the stator phase with the intact windings, H; \(\mathrm{r_{\mathrm{s}}}\)--active resistance of the stator phase with the intact windings, \(\Omega\) (Table 1). Full inductance of the stator phase with the intact windings was determined using Equation:  
\[\mathrm{L_{\mathrm{s}}}=\mathrm{L_{\mathrm{\sigma s}}}+\mathrm{L_{\mathrm{u}s}}, \tag{20}\]  
where \(\mathrm{L_{\mathrm{\sigma s}}}\)--inductance of leakage of the stator phase with the intact stator windings, H (Table 1); \(\mathrm{L_{\mathrm{u}s}}\)--inductance of magnetic circuit with the intact stator windings, H (Table 1). It is also necessary to transform the \"Observer of torque and flux\". The classical DTC scheme (Figure 1) does not account for the possibility of occurrence of asymmetric modes in the motor windings. In this case, the module of space vector of the stator flux linkage is calculated under the condition that active resistances of the stator windings of all phases are equal. Therefore, at first, the system of stator phase currents is transformed from three-phase coordinates to the stationary \(\alpha\)-\(\beta\) two-phase coordinates (\"Block of coordinate transformations\"). Afterwards, the module of space vector of the stator flux linkage is calculated (\"Observer of torque and flux\"). Under this kind of approach to the determination of the module of space vector of the stator flux linkage, an error in the control system operation arises when there are asymmetric modes of the stator windings. To account for the asymmetric modes in the stator windings, it has been proposed that the module of space vector of the stator flux linkage is determined using the following algorithm. Current values of active resistances of all three stator windings are entered into the \"Observer of torque and flux\". Phase flux linkages of the stator are calculated under Equation [62]:  
\[\left\{ \begin{array}{l}\frac{\mathrm{d}\mathrm{\psi_{\mathrm{sa}}}}{\mathrm{ d}\mathrm{t}}=\mathrm{U_{\mathrm{sa}}}-\mathrm{I_{\mathrm{sa}}}\cdot\mathrm{r_{ \mathrm{sa}}}\\ \frac{\mathrm{d}\mathrm{\psi_{\mathrm{sb}}}}{\mathrm{d}\mathrm{t}}=\mathrm{U_{ \mathrm{sb}}}-\mathrm{I_{\mathrm{sb}}}\cdot\mathrm{r_{\mathrm{sb}}}\\ \frac{\mathrm{d}\mathrm{\psi_{\mathrm{sc}}}}{\mathrm{d}\mathrm{t}}=\mathrm{U_{ \mathrm{sc}}}-\mathrm{I_{\mathrm{sc}}}\cdot\mathrm{r_{\mathrm{sc}}}\end{array} \right.