## 5 Validation of the Proposed Method by Comparing Inductance and Fault Current
### Inductance Comparisons  
#### 5.1.1 Inductances Identification of Faulty Coils in the Slot  
ITSCF in the Same Layer  
Table 2 shows the self-inductance of the faulty part in the finite-element model. It can be seen from Table 2 that the self-inductance of the faulty part is at a minimum when the faulty turns are located in layer 2 and the self-inductance of the faulty part are maximum when the faulty turns are located in layer 4. That is to say, when the same number of turns is short-circuited, the fault that occurred in layer 2 has the weakest effect on the motor performance. Therefore, different kinds of faults located on layer 2 are studied by using the NAM. Additionally, the results calculated by the FEM, NAM, and SAM are compared to verify the accuracy of the proposed method. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layer**Turns** & **2 Turns (Y = 1–2)** & **6 Turns (Y = 1–6)** & **10 Turns (Y = 1–10)** \\ \hline Layer1 & 5.07339 \(\times\) 10\({}^{-6}\) & 3.842 \(\times\) 10\({}^{-5}\) & 8.76368 \(\times\) 10\({}^{-5}\) \\ Layer2 & 4.89856 \(\times\) 10\({}^{-6}\) & 3.7532 \(\times\) 10\({}^{-5}\) & 8.6111 \(\times\) 10\({}^{-5}\) \\ Layer3 & 4.89909 \(\times\) 10\({}^{-6}\) & 3.75409 \(\times\) 10\({}^{-5}\) & 8.62187 \(\times\) 10\({}^{-5}\) \\ Layer4 & 5.07488 \(\times\) 10\({}^{-6}\) & 3.84441 \(\times\) 10\({}^{-5}\) & 8.79202 \(\times\) 10\({}^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The self-inductance of the faulty part in the finite element model. Figure 8 shows the flux density distributions when there are two turns shorted in layer 2 at the positions from the bottom of the slot to the slot opening. Figure 9 describes the flux density distributions when different numbers of turns are shorted in layer 2. It can be seen that all the flux density distributions mentioned above are different. When the fault occurs on the same layer, the inductances of the faulty coil are shown in Figures 10-12. Figure 10 analyzes the inductances of fault coil when there are two turns shorted in layer 2. Figure 11 describes the variation of the inductances in the faulty coil when there are six turns shorted in layer 2. And the inductances of fault coil, when there are 10 turns shorted in layer 2, are presented in Figure 12. It can be seen from Figures 10-12 that, as the fault position changes from the bottom of the slot to the slot opening, the self-inductance of the faulty part gradually decreases while the self-inductance of the healthy part tends to increase, and the mutual inductance between the faulty and healthy parts gradually decreases. The comparisons among Figures 10-12 reveals that, as the number of the shorted turns increased, the self-inductance of the faulty part is increased while the self-inductance of the healthy part tends to decrease, and the mutual inductance between the faulty and healthy parts gradually increases. Furthermore, Figures 10-12 indicates that the error between the finite-element result and the result calculated by the NAM is smaller than one between the finite-element result and the result obtained by the simplified method. In addition, it is verified that the simplified inductance calculation method does not consider the spatial position. Figure 8: The flux density distributions when there are two turns shorted in layer 2: (**a**) no. 13, 14; (**b**) no. 18, 19; (**c**) no. 23, 24. Figure 9: The flux density distributions when different numbers of turns are shorted in layer 2: (**a**) two turns shorted; (**b**) six turns shorted; (**c**) 10 turns shorted. ITSCF in the Different Layers  
Figure 13 compares the flux density distributions when the fault with different shorted turns is located on different layers. It can be seen that all the flux density distributions mentioned above are different. Figure 11: The inductances of the faulty coil when there are six turns shorted in layer 2: (**a**) self-inductance in faulty part; (**b**) self-inductance in healthy part; (**c**) mutual inductance.