# Seven-Phase PMSM Drives Operation Post Two Types of Faults
## 4 Saliency Position Tracking in the Seven-Phase Motor Post the Fault  
### Saliency-Tracking Algorithm Post the Failure  
The algorithm that has been developed in [38] to obtain the rotor speed and position in the seven-phase motor running without faults will not be applicable after losing phase 'A'. This is related to the fact that it depends on measuring the derivative of the stator currents due to the inverter switching actions to track the saliency position. While the derivative of the current in phase 'A' will be zero due to the open circuit. Moreover, the use of the new SVPWM post the fault as a part of the FTC technique will change the inverter switching actions, so it affects the algorithm to track the saliency. To solve these problems, a new algorithm to track the saliency in the seven-phase motor after losing phase 'A' is presented. The new algorithm is based on the new SVPWM technique introduced in this paper. Figure 13(a) shows how the adjacent active vectors in addition to the null vectors are used to synthesize V_ref in the first sector. While Figure 10(b) shows the PWM waveform associated with applying these vectors and it shows the sampling instant of the derivative of the stator currents. The dynamic circuits of the stator windings of the seven-phase motor after losing phase 'A' during the application of the vector V0, V3, V1, V5, V2, and V4 are shown in the Figure 15(a), Figure 15(b), Figure 15(c), Figure 15(d), Figure 15(e), and Figure 15(f) respectively. Using the circuits in these figures, the equations below hold true:  
\[[0]=r_{s}*\left[i_{B}{}^{(V0)}\right]+\left[l_{\sigma B}*\Delta\Big{(}i_{B}{}^ {(V0)}\Big{)}\right]+\left[e_{B}{}^{(V0)}\right] \tag{13}\]  
\[\left[ \begin{matrix}VDC\\ 0\end{matrix} \right]=r_{s}*\left[ \begin{matrix}i_{B}{}^{(V3)}\\ i_{G}{}^{(V3)}\end{matrix} \right]+\left[ \begin{matrix}l_{\sigma B}*\Delta \Big{(}i_{B}{}^{(V3)}\Big{)}\\ l_{\sigma G}*\Delta\Big{(}i_{G}{}^{(V3)}\Big{)}\end{matrix} \right]+\left[e_{B}{ }^{(V3)}\right] \tag{14}\]  
Figure 13: Simulation results of using the new SVPWM technique for the seven-phase motor drive after losing phase 'A’. \[ \begin{bmatrix}VDC\\ 0\end{bmatrix} =r_{s}* \begin{bmatrix}i_{G}{}^{(V1)}\\ i_{C}{}^{(V1)}\end{bmatrix} + \begin{bmatrix}l_{\sigma G}*\Delta\Big{(}i_{G}{}^{(V1)} \Big{)}\\ l_{\sigma C}*\Delta\Big{(}i_{C}{}^{(V1)}\Big{)}\end{bmatrix} + \begin{bmatrix}e_{G} {}^{(V1)}\\ e_{C}{}^{(V1)}\end{bmatrix}  \tag{15}\]  
\[ \begin{bmatrix}VDC\\ 0\end{bmatrix} =r_{s}* \begin{bmatrix}i_{C}{}^{(V5)}\\ i_{F}{}^{(V5)}\end{bmatrix} + \begin{bmatrix}l_{\sigma C}*\Delta\Big{(}i_{C}{}^{( V5)}\Big{)}\\ l_{\sigma F}*\Delta\Big{(}i_{F}{}^{(V5)}\Big{)}\end{bmatrix} + \begin{bmatrix}e_{C} {}^{(V5)}\\ e_{F}{}^{(V5)}\end{bmatrix}  \tag{16}\]  
\[ \begin{bmatrix}VDC\\ 0\end{bmatrix} =r_{s}* \begin{bmatrix}i_{F}{}^{(V2)}\\ i_{D}{}^{(V2)}\end{bmatrix} + \begin{bmatrix}l_{\sigma F}*\Delta\Big{(}i_{F}{}^{( V2)}\Big{)}\\ l_{\sigma D}*\Delta\Big{(}i_{D}{}^{(V2)}\Big{)}\end{bmatrix} + \begin{bmatrix}e_{F} {}^{(V2)}\\ e_{D}{}^{(V2)}\end{bmatrix}  \tag{17}\]  
\[ \begin{bmatrix}VDC\\ 0\end{bmatrix} =r_{s}* \begin{bmatrix}i_{D}{}^{(V4)}\\ i_{E}{}^{(V4)}\end{bmatrix} + \begin{bmatrix}l_{\sigma D}*\Delta\Big{(}i_{D}{}^{( V4)}\Big{)}\\ l_{\sigma E}*\Delta\Big{(}i_{E}{}^{(V4)}\Big{)}\end{bmatrix} + \begin{bmatrix}e_{D} {}^{(V4)}\\ e_{E}{}^{(V4)}\end{bmatrix}  \tag{18}\]  
\[ \begin{bmatrix}VDC\\ =r_{s}*\begin{bmatrix}i_{E}{}^{(V0)}\end{bmatrix}+\begin{bmatrix}l_{\sigma E}* \Delta\Big{(}i_{E}{}^{(V0)}\Big{)}\end{bmatrix}+\begin{bmatrix}e_{E}{}^{(V0)} \end{bmatrix}\end{bmatrix}  \tag{19}\]  
By subtracting each two adjacent equations from each other, the following equations can be derived. Figure 14: Active switching sequence and the associated PWM waveform of the seven-phase drive after losing phase ‘A’ when V_ref exists in the first sector. (**a**) active switching sequence. (**b**) sampling instants.