## 2 Modeling the Electric Drive Transmission System
### Analysis of Simulation Results  
Figure 8 depicts the dynamic characteristics of the electric drive transmission system under normal operation, open-phase faults, and self-fault-tolerant control at the rated operating conditions (3000 r/min and 0.5 Nm). As shown in Figure 8a,b, following D-phase open fault, the self-fault-tolerant control strategy promptly transitions the system into a self-fault-tolerant mode. Subsequently, the current in the faulty D-phase rapidly decays to zero, while the E-phase and F-phase currents exhibit equal magnitude and a 180\({}^{\circ}\) phase difference, slightly lower than normal value. The current in the healthy phases all increase in magnitude. Based on the winding spatial arrangement depicted in Figure 6, phase A is spatially adjacent to the faulty phase D. According to the principle of stator magnetomotive force (MMF) conservation, phase A, being closest to the faulty phase, exhibits the most pronounced current increase, reaching nearly 1.4 p.u. the normal-state value. Phases B and C also demonstrate higher amplitudes compared to normal value. In contrast, during a D-phase open fault under conventional control (without fault tolerance), all phase currents exhibit significantly increased magnitudes, with the phase A current rising to approximately 1.9 p.u. its normal value. Figure 8c,d demonstrate that under D-phase open fault, both motor speed and electromagnetic torque experience a significant increase with conventional control. In contrast, the self-fault-tolerant control strategy results in only a momentary speed and torque fluctuation at the fault onset, swiftly recovering and stabilization near the rated setpoint. This behavior underscores the superior dynamic robustness of the self-fault-tolerant control strategy in effectively mitigating the impact of faults on output parameters. Additionally, as shown in Figure 8e, conventional control leads to violent oscillations in meshing force amplitude. Conversely, the self-fault-tolerant control strategy rapidly stabilizes the meshing force within the rated range following a brief transient impact. The dynamic response of the gear system corresponds closely to that of the electromagnetic torque, reflecting the strong coupling within the mechatronic system. These findings confirm the efficacy of the fault-tolerant control strategy in coordinating system dynamics and maintaining operational stability. Figure 7: Open-phase faults strategy. Figures 9 and 10 compare the spectral characteristics of the system under rated conditions in normal operation, open-phase faults, and self-fault-tolerant control. Figures 9a and 10a reveal that compared to the normal condition, the amplitudes of odd-order harmonics such as 3 rd, 5 th, and 7 th in the A-phase current spectrum increase during both the open-phase faults and the self-fault-tolerant control operation. However, under self-fault-tolerant control, the increase in these harmonic amplitudes is significantly  
Figure 8: Dynamic response of electric drive transmission systems at rated conditions open-phase faults and before and after self-fault-tolerant control: (**a**) ABC phase currents; (**b**) DEF phase currents; (**c**) motor speed; (**d**) electromagnetic torque; (**e**) sun–planet gear meshing force. smaller than that during open-phase faults. This trend aligns with the harmonic growth in phase currents after open-phase faults reported in Ref. [23], and validates conclusions from Ref. [10] that the self-fault-tolerant control strategy enables autonomous fault tolerance without additional active interventions. As shown in Figures 9b,c and 10b,c, open-phase faults induce a significant increase in the amplitude of even-order harmonic components such as 2 nd, 4 th, and 6 th harmonics in the motor speed and electromagnetic torque spectra. Specifically, the 2 nd harmonic component exhibits amplitude increments of approximately 51.4 dB in motor speed and 49.6 dB in torque. Under self-fault-tolerant control, the steady-state performance of speed and torque is effectively maintained.