# Seven-Phase PMSM Drives Operation Post Two Types of Faults
## 3 Operation of the Seven-Phase Drive after Losing Phase 'A'
### SVPWM Techniques after Losing Phase 'A'  
The NSV-SVPWM technique that is used in the seven-phase inverter under healthy conditions cannot be applied post the failure, because, the reference currents post the failure will not be uniformly distributed according to the minimizing the inverter current optimization technique as shown in Figure 7. This paper is introducing a new SVPWM technique that will be utilized after the loss of phase 'A' to obtain the stator current based on the minimum inverter current optimization technique as illustrated in Equation (8) and Figure 7. The new SVPWM is considering the changes that are introduced to the healthy currents of the seven-phase drive when phase 'A' is lost. Hence a new vector diagram is  
Figure 7: Current distribution of seven-phase motor under minimizing inverter current optimization. (a) Phasor; (b) sinusoidal. considered as depicted in Figure 8. The new vectors are calculated by putting \(S_{A}=0\) in Equation (4). It should be mentioned here that the new space vector diagram contains 64 vectors, but only the vector that is used to synthesize the reference voltage is considered in Figure 8.  
The amplitude of the vectors whose arrows lies on the inner circle will be 0.2857*VDC, the amplitude of the vectors whose arrows lies on the next circle will be 0.4721*VDC, the amplitude of the vectors whose arrows lies on the third circle will be 0.4942*VDC. Finally, the vectors whose arrows lies one the outer circle will be 0.6039*VDC. It should be mentioned here that the vectors V5, V13, V20, and V28 (outer circle) are very close in direction to phase 'B', 'D', 'E', and 'G' respectively as the difference in angles between them is just 6.8\({}^{0}\) and hence, they will be approximated to be in the same direction in this paper (i.e., the direction of the phases 'B', 'D', 'E', and 'G'). The flowchart to implement the new SVPWM after losing phase 'A' in the seven-phase drive is depicted in Figure 9. The illustration of each part of the flow chart is given below. Firstly, outputs of the controllers (V_ref) are used to determine the sector no based on Table 1.  
Secondly, the time duration of each active vector is calculated. Figure 10a illustrates how the adjacent active vectors (V1, V2, V3, V4, V5) besides the null vectors are used to synthesize the V_ref when it exists in the first sector. While Figure 10b shows the PWM waveform associated with applying these vectors. Figure 8: Space vector diagram of the seven-phase PMSM after losing phase ’A’. The application time of the active vectors V1, V2, V3, V4, V5 and V0 i.e., (_t_0, \(t\)1, \(t\)3, \(t\)3, \(t\)4, and \(t\)5) can be deduced based on the assumption that the vectors V3, V5, and V4 are in the same direction while the vectors V1, V2 are in the same direction too. Hence, only, two vectors V3 and V1 can be used to calculate the total time duration in the direction of V3,V4, and V5 (i.e., _tx_), and the total time duration of the vectors V1, and V2 (i.e., _ty_) as shown in Figure 11. So, after calculating _tx_ and _ty_, the vector duration times \(t\)0, \(t\)1, \(t\)3, \(t\)3, \(t\)4, and \(t\)5 are obtained considering the length of the vectors as shown in the equations below:  
\[ \begin{bmatrix}V\alpha_{ref}\\ V\beta_{ref}\end{bmatrix} *\frac{T}{VDC}= \begin{bmatrix}0.2857*\cos(21.4^{\circ})&0.4721*\cos(0)\\ 0.2857*\sin(21.4^{\circ})&0.4721*\sin(0)\end{bmatrix} * \begin{bmatrix}tx\\ ty\end{bmatrix}  \tag{9}\]  
where \(V\alpha_{ref}\), \(V\beta_{ref}\) are the component of \(V_{ref}\) in the \(\alpha\beta\)\(T\) is the PWM period. Solving the above equation yields to:  
\[ \begin{bmatrix}tx\\ ty\end{bmatrix} =\frac{T}{VDC} \begin{bmatrix}0&7.41\\ 2.13&-3.954\end{bmatrix} * \begin{bmatrix}V\alpha_{ref}\\ V\beta_{ref}\end{bmatrix}  \tag{10}\]  
\[to=T-tx-ty \tag{11}\]  
Then vector duration times \(t\)1, \(t\)2, \(t\)3, \(t\)4, and \(t\)5 can be calculated according to the length of the vectors V1, V2, V3, V4, and V5 as follows:  
\[ \begin{bmatrix}t1\\ t2\\ t3\\ t4\\ t5\end{bmatrix} =