## 5 Simulation Results
### Simulation of the ITSCF Model  
Based on the motor model in Figure 8, the a-phase ITSC architecture from Figure 2 is integrated into the Simscape block diagram, as shown in Figure 9. In this circuit, outlined in the red box in Figure 9 and detailed in Figure 10, \(V_{\mathit{gf}}\) represents the voltage across the phase-a coil during ITSCF, while \(V_{\mathit{gf}}\) denotes the ITSC voltage. The associated voltage drops include \(r_{\mathit{f}}\) for the parallel resistance of the short-circuited coil, \(\mu L\) for the ITSC inductance, \(\mu r_{\mathit{s}}\) for the ITSC resistance, and \(\mu M\) for the voltage generated by mutual inductance, as well as the induced back electromotive force (EMF) of the short-circuited coil, \(\mu\lambda^{{}^{\prime}}\)\(=\)\(\omega\)\(r_{\mathit{f}}\)cos(\(\theta_{\mathit{f}}\)). In this setup, \(r_{\mathit{f}}\) is set to represent the severity of ITSCFs and affects the magnitude of the circulating current generated in the ITSC. Additionally, the voltage generated by mutual inductance \(\mu M\) is calculated using the circuit model outlined in the orange box in Figure 9.  
Figures 11 and 12 show the voltage and current waveforms for the \(q\)-axis under conditions of 1500 rpm and 600 rpm, respectively, with \(r_{\mathit{f}}\) = 0 \(\Omega\) and \(\mu\) values of 0.3 and 0.7. It can be observed that both the \(q\)-axis voltage and current exhibit a  
Figure 8: Simscape block diagram for IPMSM model simulation. Figure 7: Simulink/simscape block diagram for IPMSM speed control simulation. response characteristic. Furthermore, as the internal short-circuit ratio \(\mu\) increases, the responses of the \(q\)-axis voltage and current become more pronounced. The reason is that as \(\mu\) increases, the back-EMF of the shorted coil also increases, leading to an increase in \(i_{f}\). This causes the waveforms of \(V_{q}\) and \(i_{q}\) to include the voltage and current characteristics of the shorted coil. Furthermore, it is evident that when \(r_{f}\) is set to 0 \(\Omega\), the influence of ITSCF on the \(q\)-axis voltage and current is less pronounced. This study will further analyze the responses of \(V_{q}\) and \(i_{q}\) under different conditions of \(r_{f}\) regarding this phenomenon. Figure 11: Voltage and current responses at 1500 RPM with \(r_{f}\) = 0 \(\Omega\) for \(\mu\) values of 0.3 and 0.7. (**a**) \(i_{q}\); (**b**) \(V_{q}\). Figure 9: Integrated ITSC model simulation block diagram for IPMSM. To investigate the influence of \(r_{f}\) on \(V_{q}\) and \(i_{q}\), simulations are conducted at 1500 rpm and 600 rpm with a fixed \(\mu\) of 0.7 and varying \(r_{f}\) values of 0 \(\Omega\), 10 \(\Omega\), and 100 \(\Omega\). The corresponding responses of \(V_{q}\) and \(i_{q}\) are presented in Figures 13 and 14, respectively. By comparing the two sets of waveforms, it is observed that a larger \(r_{f}\) value corresponds to a less severe ITSC. This is attributed to the significant increase in voltage drop across \(r_{f}\), which in turn leads to larger magnitudes of \(V_{q}\) and \(i_{q}\). Conversely, a smaller \(r_{f}\) value results in a more severe ITSC, as the reduced voltage drop across \(r_{f}\) causes \(V_{q}\) and \(i_{q}\) to decrease. These results indicate that varying the value of \(r_{f}\) can manifest different levels of ITSCF severity. Specifically, as the short-circuit condition becomes more severe, the responses of \(V_{q}\) and \(i_{q}\) become less pronounced compared to the simulation results in reference [8], which showed a smaller \(V_{q}\) response for a larger \(r_{f}\) and a larger \(V_{q}\) response for a smaller \(r_{f}\). However, the simulation results of this study exhibit an opposite trend. This discrepancy is attributed to the voltage drop caused by the interaction between the \(r_{f}\) and \(i_{f}\) currents, which is projected onto the phase voltage and subsequently transformed into the \(V_{q}\) component.