## 4 Fault-Tolerant Control of Three-Level T-Type Inverter
### Fault-Tolerant Control Simulation  
This study conducted a simulation of fault-tolerant control by using PSIM software. In the simulation, an open-circuit fault was considered to occur in \(S_{a1}{}^{+}\), \(S_{b2}{}^{-}\), and \(S_{c1}{}^{+}\). The simulation results revealed changes in the output line voltage under three conditions, namely conditions of normal inverter operation, faulty switch operation, and fault-tolerant control execution. As shown in Figure 13, at 0.06 s, an open-circuit fault occurred in switch \(S_{a1}{}^{+}\) and distorted the three-phase output line voltage. The fault-tolerant control system was launched at 0.12 s. The \(a\)-phase half-bridge switches (\(S_{a1}{}^{+}\) and \(S_{a2}{}^{-}\)) were deactivated, but the \(b\)-phase, \(c\)-phase, and neutral-point switches still operated normally. Switch \(T_{a}\) in the 3 three-pole ac semiconductor switches was activated to replace the faulty \(a\)-phase leg with the spare leg, and the spare leg adopted the switching mode of the original \(a\)-phase leg to maintain a balanced three-phase output voltage. As shown in Figure 13, after the execution of the fault-tolerant control system, the three-phase output line voltage remained to be five levels. Accordingly, after the occurrence of the fault, the balanced three-phase output line voltage remained unchanged, and the quality of the output voltage was not reduced. As presented in Figure 14, at 0.06 s, an open-circuit fault occurred in switch \(S_{b2}{}^{-}\) and distorted the three-phase output line voltage. The fault-tolerant control system was launched at 0.12 s. The \(b\)-phase half-bridge switches (\(S_{b1}{}^{+}\) and \(S_{b2}{}^{-}\)) were deactivated, but the \(a\)-phase, \(c\)-phase, and neutral-point switches still operated normally. Switch \(T_{b}\) of the 3 three-pole ac semiconductor switches was activated to replace the faulty \(b\)-phase leg with the spare leg, and the spare leg adopted the switching mode of the original \(b\)-phase leg to maintain a balanced three-phase output voltage. After the launching of the fault-tolerant control system, the three-phase output line voltage remained to be five levels. Hence, after the occurrence of the fault, the balanced three-phase output line voltage remained unchanged, and the quality of the output voltage was not reduced. Figure 13: The output voltage of \(S_{a1}{}^{+}\) after the occurrence of an open-circuit fault and the activation of fault-tolerant control. As illustrated in Figure 15, at 0.06 s, an open-circuit fault occurred in switch \(S_{c1}\)\({}^{+}\) and distorted the three-phase output line voltage. The tolerant control system was launched at 0.12 s. The \(c\)-phase half-bridge switches (\(S_{c1}\)\({}^{+}\) and \(S_{c2}\)\({}^{-}\)) were deactivated, but the \(a\)-phase, \(b\)-phase, and neutral-point switches still operated normally. Switch \(T_{c}\) of the 3 three-pole ac semiconductor switches was activated to replace the faulty \(c\)-phase leg with the spare leg, and the spare leg adopted the switching mode of the original \(c\)-phase leg to maintain the balanced three-phase output voltage. After the launching of the fault-tolerant control system, the three-phase output line voltage remained to be five levels. Accordingly, after the occurrence of the fault, the balanced three-phase output line voltage remained unchanged, and the quality of the output voltage was not reduced. Figure 14: The output voltage of \(S_{b2}\)\({}^{-}\) after the occurrence of an open-circuit fault and the activation of fault-tolerant control. Figure 15: The output voltage of \(S_{c1}\)\({}^{+}\) after the occurrence of an open-circuit fault and the activation of fault-tolerant control. As shown in Figure 13, at 0.06 s, an open-circuit fault occurred in switch \(S_{a1}{}^{+}\) and distorted the output line voltage \(v_{ab}\) and \(v_{ca}\). The fault-tolerant control system was launched at 0.12 s. As shown in Figure 13, after the execution of the fault-tolerant control system, the three-phase output line voltage waveforms remained to be five levels.