## 1 Introduction
Such inverters have been widely used in high-voltage and high-power applications, including high-voltage dc transmission, superconducting energy storage, and motor frequency control. However, applications, such as military equipment, power systems, steel mills, and electric vehicles have particularly high requirements for continuous equipment operation. Consequently, inverter failure during operation would engender severe economic losses and even casualties. Improving inverter system reliability is thus imperative. Fault-tolerant control is among the primary methods for improving inverter system reliability. However, after prolonged use, multilevel inverters may break down because of switch damage induced by overcurrent (or high temperature) operation [18], component aging, and drive circuit failure. Multilevel inverter systems must thus be equipped with fault detection mechanisms and fault-tolerant control capabilities to ensure continued operation in failure events [8; 20; 21]. The fault-tolerant control strategies proposed in [22; 23] showed that the maximum renewable energy capture can be achieved. However, these methods are only applicable to power systems. However, the purpose of the fault-tolerant control system for multilevel inverters is to ensure continued inverter operation in the event of power transistor failure. Therefore, to maintain the three-phase balance of the output voltage of the inverter, the power transistor switching state and the phase angle of the reference voltage in the pulse width modulation (PWM) control mechanism must be modified simultaneously. However, this process would increase the difficulty of designing and controlling the fault tolerance of a multilevel inverter in a failure event. In addition, the maximum output voltage amplitude of current fault-tolerant control systems is only 0.577 times that achieved under normal operation [6]. This study proposes a smart fault-tolerant control system for locating faults in a three-level T-type inverter; the system is based on an artificial intelligence algorithm incorporated with chaos theory [25] and extension theory [26]. First, the output phase voltage waveform observed during an event of power transistor failure is converted according to the dynamic states of Lorenz chaotic system; chaos eye coordinates are extracted from a scatter diagram of chaotic states and used as feature valuesfor fault detection. Extension theory is applied to locate a faulty power transistor. Subsequently, an external backup power transistor (leg) and 3 three-pole ac semiconductor switches (triode AC, TRAIC) are used for fault-tolerant control to maintain the three-phase balanced line voltage output, thereby maintaining the normal voltage amplitude if any power semiconductor switch of the inverter fails. Figure 1 illustrates the overall architecture of the proposed fault-diagnosis and fault-tolerant control system. This paper is organized as follows. In Section 2, the concepts of Chaos and Extension theory are described in detail, and how to use them for fault diagnosis of a three-level T-type inverter is explained. Then, the simulation is made in Section 3 to demonstrate the effectiveness of the proposed fault diagnosis method based on Chaos and Extension theory. Final, in Section 4, the fault-tolerant control in the event of any power switch failure in the three-level T-type inverter is analyzed, and then the simulation is used to prove its feasibility.