Smart Fault-Tolerant Control System Based on Chaos Theory and Extension Theory for Locating Faults in a Three-Level T-Type Inverter

Abstract

This study proposes a smart fault-tolerant control system based on the theory of Lorenz chaotic system and extension theory for locating faults and executing tolerant control in a three-level T-type inverter. First, the system constantly monitors the fault states of the 12 power transistor switches of the three-level T-type inverter; if a power transistor fails, the corresponding output phase voltage waveform is converted by a Lorenz chaotic system. Chaos eye coordinates are then extracted from a scatter diagram of chaotic dynamic states and considered as fault characteristics. The system then executes fault diagnosis based on extension theory. The fault characteristic value is used as the input signal for correlation analysis; thus, the faulty power transistor can be located and the fault diagnosis can be achieved for the inverter. The fault-tolerant control system can maintain the three-phase balanced output of the three-level T-type inverter, thereby improving the reliability of the motor drive system. The feasibility of the proposed smart fault-tolerant control system was assessed by conducting simulations in this study, and the results verified its feasibility. Accordingly, after the occurrence of the fault in power switches, the balanced three-phase output line voltage remained unchanged, and the quality of the output voltage was not reduced by using the integration of the proposed fault diagnosis system and fault-tolerant control system for a three-level T-type Inverter.

1. Introduction

Recent advances in renewable energy and electric vehicle technology have prompted the development of multilevel inverters [1,2,3,4,5]. Compared with that of a two-level inverter, the switch of a multilevel inverter is subjected to lower voltage stress and is associated with a lower output voltage change rate (dv/dt). Accordingly, multilevel inverters are suitable for applications requiring high power consumption. Such applications require a relatively high number of power transistors, thus increasing the difficulty of fault detection in inverters. The traditional fault diagnosis procedure for inverters entails the use of information (numeric or waveform) directly measured by instruments. The information is examined by on-site personnel, who subsequently conduct fault diagnosis for the inverters, repair the inverters, and replace components on the basis of their experience. However, this traditional fault diagnosis procedure is prone to erroneous fault point detections, causing unnecessary waste of labor and time for component repair and replacement [6,7,8]. To improve the reliability of equipment using motor drive systems, researchers have invested considerable effort in exploring fault detection mechanisms [9,10,11,12,13,14,15,16,17,18,19] and fault-tolerant control strategies [20,21,22,23] for multilevel inverters in order to enable early fault detection when inverter power semiconductor components fail; this can thus maintain the inverter operation and minimize damage.

Currently, primary techniques for smart fault diagnosis in inverters include model-based methods, expert systems, and machine learning systems. Although model-based methods are useful [9], they require the establishment of various fault-state models in advance. Moreover, such models should consider the values of snubber capacitance and balance resistor in inverters, which are difficult to obtain. The models comprise various parasitic elements that would inevitably require some assumptions and thus impose limitations to the general applicability of the models [10,11]. In addition, expert systems can modify themselves. Nevertheless, the entire systems should still be established by experts; therefore, such systems are associated with relatively high costs [12]. Finally, machine learning systems [13] notably mimic the neural network of the human brain. Through such neural connections, data models can be updated using backpropagation, and hidden layers can reduce the dependence of machine learning algorithms on feature engineering. However, a large body of data is required for neural network learning to make accurate judgments, and the corresponding operating time is long [14,15,16,17]. Therefore, developing new smart fault diagnosis systems with high accuracy, easy implementation, and fast response is imperative. The first author has previously used the extension theory to diagnose the type and number of fault modules in a photovoltaic module array [24]. This method measures the voltages, currents and powers of the photovoltaic module array at each moment, and then accordingly estimates the type and number of faulted modules in the photovoltaic module array. Although its fault diagnosis accuracy is very high, the input of this evaluation method must be a fixed single point value. Therefore, this method is not suitable for fault diagnosis where the input variables are continuous functions or waveforms. Based on this, we must first use another intelligent method like chaos theory to convert the three-phase voltage waveforms obtained in T-type multilevel inverters into equivalent characteristic values (chaos eye coordinates), where the fault diagnosis can be made by the extension theory.

Multilevel inverters exhibit numerous advantages, such as various control modes, relatively low transistor withstand voltage levels, low current harmonics, and high frequency conversion efficiency. 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 values for 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.

2. Materials and Methods

2.1. Fault Characteristics of Three-Level Inverter

To explore inverter fault diagnosis, this study considered a three-level T-type inverter, as shown in Figure 2. The faults of such an inverter can be divided into three types: Short-circuit fault, open-circuit fault, and an erroneous trigger signal. A short-circuit fault occurs when switching elements break down, due to excessive voltages across the switch. Moreover, an open-circuit fault occurs when switches cannot be activated, due to the lack of trigger signals for the power transistor. Finally, an erroneous trigger signal occurs when switching elements receive incorrect trigger signals.

This study established a simulation environment for the three-level T-type inverter by using PSIM software and monitored the failure of the inverter switches constantly. Consider, for example, an output voltage frequency of 60 Hz. The simulated waveform for a normally operating inverter should exhibit a three-phase balanced structure, and the output voltage waveform of each phase is presented in Figure 3. The voltage waveforms of the three phases have the same shape and size, and the phase difference between them is 120°, which is an inherent characteristic of a three-phase balanced structure. This balanced structure would be distorted in the event of inverter switch failure. For example, if the inverter switch S_a1⁺ fails, the waveform of the a-phase output voltage (v_ao) is distorted (Figure 4). Similarly, if the inverter switch S_b2⁻ or S_c1⁺ fails, the waveforms of the phase voltage v_bo and v_co would substantially differ from those observed under normal inverter switch operation. According to these observations, the output voltage waveform would be distorted when a fault occurs in an inverter.

2.2. Theory of the Lorenz Chaotic System

A Lorenz chaotic system is considered in the proposed system [25], which is presented in Equation (1).

$$S_{cs}=\left\{\begin{array}{l}{\dot{x}}_1=\alpha (x_2-x_1)\\ {\dot{x}}_2=\beta x_1-x_1{x}_3-x_2\\ {\dot{x}}_n=x_1{x}_2-\gamma x_3\end{array}\right\},$$

(1)

where $x$ represents the initial value of the system and can be used as the input value to be tested. $\alpha$, $\beta$, and $\gamma$ represent adjustment coefficients.

The three-phase voltage waveforms shown in Figure 3 and Figure 4 are measured with voltage sensors. At the same time, the sampling time is 5 us and 10,000 data have been obtained within 0.05 s and then input into the Lorenz chaotic system in Equation (1). The adjustment coefficients $\alpha$, $\beta$, and $\gamma$ in Equation (1) are set to 10, 28, and 8/3, respectively. Through the aforementioned Lorenz chaotic system, ${\dot{x}}_1$, ${\dot{x}}_2$, and ${\dot{x}}_3$ can be obtained. In the proposed system, ${\dot{x}}_1$ and ${\dot{x}}_2$ are used to generate a chaotic states scatter diagram, as illustrated in Figure 5, with the two centroid points in the scatter diagram serving as chaos eyes. The coordinates of the chaos eyes can serve as feature values for inverter fault diagnosis.

For the conditions described in Figure 3 and Figure 4, the corresponding waveforms can be converted through the Lorenz chaotic system to yield the chaotic scatter states diagrams displayed in Figure 6 and Figure 7, respectively. The chaos eye coordinates in Figure 6a are $C_1$ (−0.0462, −6.0298) and $C_2$ (0.0464, −7.0853), whereas those in Figure 7a are $C_1$ (−0.0493, −39.9884) and $C_2$ (0.0456, −42.5835). After the occurrence of a fault, the Y-axis coordinates of the chaos eye are considerably different from those (v_ao) observed before the fault; thus, S_a1⁺ can be suspected to be faulty. The proposed system can consider values of voltage waveforms of equal frequencies as the input for fault detection. After the use of the Lorenz chaotic system to convert the waveforms, the chaos eye coordinates ($C_1$ and $C_2$) in the resulting chaotic states scatter diagrams can be considered as the fault characteristic values. However, because of the failure of other transistors, chaos eye coordinates of v_ao observed before the occurrence of a fault might differ from those observed after the occurrence of the fault. The chaos eye coordinates are not fixed values; instead, they are distributed in a range. Therefore, the extension method is used for fault diagnosis to locate a fault in transistor switches.

2.3. Inverter Fault Diagnosis Based on Extension Theory

In 1983, the Chinese scholar Wen Cai proposed extension theory. The concept is to investigate the extension and contradictions of a matter from qualitative and quantitative perspectives. Matter element theory and extension mathematics constitute the two core components of extension theory. Matter element theory primarily describes the extension and transformation characteristics of matter elements, whereas extension mathematics comprises the core concepts of extension set and correlation function for calculation [26]. Extension theory expresses the information of matter through the matter element model and illustrates the relationship between matter quality and quantity through matter element transformation. Subsequently, the effects of quality and quantity on the matter are investigated using the correlation function to demonstrate the degree of influence of matter characteristics.

2.3.1. Concept of Extension Matter

In extension theory, a matter-element R contains three fundamental elements: matter name (N), matter characteristic (C), and values of matter characteristic (V). The model can be mathematically represented as follows:

R = (N, C, V),

(2)

where R is the basic element describing the matter (i.e., the matter element); N, C, and V are three elements that constitute the matter element. N represents the name of the matter, C represents the characteristic of the matter, and V represents the characteristic value of the matter. In extension matter element theory, if the matter element characteristic is not a single item, it is represented by x characteristics and x corresponding characteristic values. Accordingly, the characteristic can be expressed in vector form as C = [c₁, c₂, …, c_x], and the corresponding characteristic value can be expressed as V = [v₁, v₂, …, v_x]. Therefore, Equation (2) can be rewritten as follows.

$$R=\left[\begin{array}{c}{R}_1\\ R_2\\ ⋮\\ R_x\end{array}\right]=\left[\begin{array}{ccc}N,& c_1& v_1\\ & c_2& v_2\\ & ⋮& ⋮\\ & c_x& v_x\end{array}\right].$$

(3)

If the characteristic value is in a certain interval, the interval is defined as a classical domain and is included in a neighborhood domain. Assume the following intervals: F₀ = <a, b>, F = <d, e>, and $F_0\in F$; point f is any point in the interval F. Therefore, the matter element corresponding to F₀ = <a, b> can be expressed as follows:

$$\begin{array}{ll}{R}_0& =(F_0,C_i,V_i)\\ & =\left[\begin{array}{ccc}{F}_0,& c_1,& <a_1,b_1>\\ & c_2,& <a_2,b_2>\\ & ⋮& ⋮\\ & c_x,& <a_x,b_x>\end{array}\right]\end{array},$$

(4)

where C_i is the characteristic of $F_0$, and V_i is the characteristic value of C_i (i.e., its classical domain). The matter element R_F corresponding to F is presented in Equation (5), where C_j is the characteristic value of F and V_j is the characteristic value of C_j (i.e., its neighborhood domain).

$$\begin{array}{ll}{R}_F& =(F_{},C_j,V_j)\\ & =\left[\begin{array}{ccc}{F}_{},& c_1,& <d_1,e_1>\\ & c_2,& <d_2,e_2>\\ & ⋮& ⋮\\ & c_x,& <d_x,e_x>\end{array}\right]\end{array}.$$

(5)

2.3.2. Distance and Position Value

Classical mathematics explores the distance relationship between points, and extension theory describes the relationship between a point and an interval in the real domain, as expressed in the following equation:

$$\mathsf{\Phi }(f,F_0)=\left|f-\frac{v_a+v_b}{2}\right|-\frac{v_b-v_a}{2}.$$

(6)

In addition to considering the relationship between a point and an interval, the relationship between a point and two intervals or between intervals should be considered. Therefore, if F₀ = <v_a, v_b> and F = <v_d, v_e> are assumed to constitute two intervals in the real domain, and F₀ is in F, the position values of point f, F₀, and F can be expressed as follows:

$$D(f,F_0,F)=\{\begin{array}{ll}\mathsf{\Phi }(f,F)-\mathsf{\Phi }(f,F_0)\hfill & ,f\notin F_0\\ -1\hfill & ,f\in F_0\end{array}.$$

(7)

2.3.3. Correlation Function

The correlation function, derived by dividing the distance by the position value, can be expressed as follows:

$$K(f)=\frac{\mathsf{\Phi }(f,F_0)}{D(f,F_0,F)}.$$

(8)

If f = (v_a + v_b)/2, the correlation function has a maximum value and is called an elementary correlation function (Figure 8). In addition, if K(f) < −1, point f is outside the interval F. If K(f) > 0, point f is within the interval F₀. If −1 < K(f) < 0, point f is within the extension domain.

The fault diagnosis steps involved in the extension method are described as follows.

Step 1.

For each transistor failure, the chaos eye coordinates C₁ and C₂ on the chaos scatter diagram are used to establish the matter element model.

$$R_g=(F,C,V_p)=\left[\begin{array}{ccc}{F}_0& C_1& \langle x_1,y_1\rangle \\ & C_2& \langle x_2,y_2\rangle \end{array}\right],g=1,2,\cdots ,12$$

(9)

Step 2.

The chaos eye coordinates of the faulty transistor to be determined, namely C₁ and C₂, are input into the model, and the resulting matter element model can be expressed as follows:

$$R_{new}=\left[\begin{array}{ccc}{F}_{new}& C_1& V_{new1}\\ & C_2& V_{new2}\end{array}\right]$$

(10)

Step 3.

The characteristics (C₁ and C₂) and their corresponding weights W₁ and W₂ (representing the relative importance of the characteristics) are determined. Here, W₁ = W₂ = 0.5.

Step 4.

The degree of correlation between the fault categories of characteristics to be tested is calculated.

$${\lambda }_g={\displaystyle \sum _{j=1}^2{W}_j{K}_{gj}},g=1,2,\cdots ,12$$

(11)

Step 5.

The largest correlation value of each fault category derived from the calculation represents the fault category to which a fault characteristic belongs. Therefore, the faulty transistor can be determined according to the category.

3. Simulation Results

To identify faulty power transistors, fault states were divided into nine categories in this study: Failure of S_a1⁺; S_a2⁻; S_b1⁺; S_b2⁻; S_c1⁺; S_c2⁻; (S_a1⁻ or S_a2⁺); (S_b1⁺ or S_b2⁺); and (S_c1⁺ or S_c2⁺). The principles underlying the categorization are described as follows. When S_a1⁻ or S_a2⁺ is faulty, the current path and voltage waveform are considered to be the same; thus, S_a1⁻ and S_a2⁺ are categorized under the same category. The same principle applies to the categories S_b1⁺ or S_b2⁺ and S_c1⁺ or S_c2⁺.

Table 1. Power transistor fault categories.

Fault State	Category
Switch Sa1+ fails	F1
Switch Sa1− or Sa2+ fails	F2
Switch Sa2− fails	F3
Switch Sb1+ fails	F4
Switch Sb1− or Sb2+ fails	F5
Switch Sb2− fails	F6
Switch Sc1+ fails	F7
Switch Sc1− or Sc2+ fails	F8
Switch Sc2− fails	F9

lists the fault categories.

Table 2. Feature values of chaos eyes under various fault states (inverter frequency = 60 Hz).

Phase	Fault Category	C1X axis	C1Y axis	C2X axis	C2Y axis
a-phase chaos eye feature value	F1	−0.049	−39.988	0.046	−42.584
	F2	−0.046	32.789	0.049	30.448
	F3	−0.068	−1.429	0.075	17.557
	F4	−0.074	−36.222	0.067	−11.218
	F5	−0.079	15.843	0.069	13.017
	F6	−0.07	−24.913	0.08	−31.164
	F7	−0.06	−8.153	0.057	−4.901
	F8	−0.08	15.631	0.07	13.255
	F9	−0.052	−6.24	0.051	−6.531
b-phase chaos eye feature value	F1	−0.08	−0.08	−0.08	−0.08
	F2	−0.07	−0.07	−0.07	−0.07
	F3	−0.049	−0.049	−0.049	−0.049
	F4	−0.045	−0.045	−0.045	−0.045
	F5	−0.067	−0.067	−0.067	−0.067
	F6	−0.075	−0.075	−0.075	−0.075
	F7	−0.052	−0.052	−0.052	−0.052
	F8	−0.058	−0.058	−0.058	−0.058
	F9	−0.053	−0.053	−0.053	−0.053
c-phase chaos eye feature value	F1	−0.068	−0.068	−0.068	−0.068
	F2	−0.075	−0.075	−0.075	−0.075
	F3	−0.08	−0.08	−0.08	−0.08
	F4	−0.069	−0.069	−0.069	−0.069
	F5	−0.049	−0.049	−0.049	−0.049
	F6	−0.046	−0.046	−0.046	−0.046
	F7	−0.052	−0.052	−0.052	−0.052
	F8	−0.052	−0.052	−0.052	−0.052
	F9	−0.058	−0.058	−0.058	−0.058

presents the feature values of the chaos eyes for each phase under the switch failure state at an operating frequency of 60 Hz. The data in Table 2 were used as inputs in the established fault diagnosis system to execute fault detection.

Table 3. Fault detection results under the failure of different switches in a-phase (inverter frequency = 60 Hz).

Fault Category	Output Weight Value			Detection Result
	F1	F2	F3
F1	0.782085	−0.564565	−0.591532	F1
F2	−0.544865	0.861617	−0.629411	F2
F3	−0.037735	−0.378546	0.553326	F3

,

Table 4. Fault detection results under the failure of different switches in b-phase (inverter frequency = 60 Hz).

Fault Category	Output Weight Value			Detection Result
	F4	F5	F6
F4	0.780133	−0.549192	−0.594745	F4
F5	−0.572378	0.872429	−0.648071	F5
F6	−0.225007	−0.346686	0.701689	F6

and

Table 5. Fault detection results under the failure of different switches in c-phase (inverter frequency = 60 Hz).

Fault Category	Output Weight Value			Detection Result
	F7	F8	F9
F7	0.813761	−0.569932	−0.600617	F7
F8	−0.549737	0.884781	−0.62921	F8
F9	−0.253144	−0.351958	0.521521	F9

present the fault detection results, indicating that all faults could be correctly detected by the system. Consider, for example, the category F₂ (Table 2): The output weight determined for F₂ was the highest weight value (0.861617) (Table 3); thus, the fault was correctly identified to belong to F₂. To demonstrate the robustness of the proposed diagnostic system against interference, erroneous ($\pm 5\%$) test samples were considered at an operating frequency of 60 Hz, and the corresponding fault detection results are presented in

Table 6. Fault detection results under the failure of different switches in a-phase and addition of ±5% erroneous data (inverter frequency = 60 Hz).

Fault Category	Error Percentage	Output Weight Value			Detection Result
		F1	F2	F3
F1	5%	0.227338	−0.577322	−0.589176	F1
F1	−5%	0.563368	−0.512827	−0.593788	F1
F2	5%	−0.554998	0.442223	−0.617735	F2
F2	−5%	−0.514244	0.598609	−0.653885	F2
F3	5%	0.0491609	−0.39636	0.37029	F3
F3	−5%	−0.124961	−0.361071	0.709824	F3

,

Table 7. Fault detection results under the failure of different switches fail in b-phase and addition of ±5% erroneous data (inverter frequency = 60 Hz).

Fault Category	Error Percentage	Output Weight Value			Detection Result
		F4	F5	F6
F4	5%	0.225285	−0.581416	−0.59255	F4
F4	−5%	0.565218	−0.498222	−0.59684	F4
F5	5%	−0.555554	0.510485	−0.629454	F5
F5	−5%	−0.542088	0.536848	−0.665188	F5
F6	5%	−0.147346	−0.362908	0.727323	F6
F6	−5%	−0.30369	−0.331795	0.639154	F6

and

Table 8. Fault detection results under the failure of different switches in c-phase and addition of ±5% erroneous data (inverter frequency = 60 Hz).

Fault Category	Error Percentage	Output Weight Value			Detection Result
		F7	F8	F9
F7	5%	0.281603	−0.581739	−0.598714	F7
F7	−5%	0.51428	−0.517926	−0.602419	F7
F8	5%	−0.551061	0.455688	−0.617525	F8
F8	−5%	−0.522304	0.586427	−0.654039	F8
F9	5%	−0.17552	−0.367097	0.50828	F9
F9	−5%	−0.330461	−0.336816	0.514661	F9

. The results indicated that after the consideration of errors, the proposed system could still correctly detect the fault category. Therefore, regardless of whether accurate or erroneous test data are used, the proposed system can correctly detect the fault category.

4. Fault-Tolerant Control of Three-Level T-Type Inverter

Most applications have particularly high requirements for equipment reliability. Accordingly, the reliability of inverter systems can be improved by equipping such systems with fault-tolerant control mechanisms that can enable them to maintain a stable output voltage. Figure 9 presents the architecture of the three-level T-type inverter proposed in this study. Compared with conventional three-level T-type inverters, the proposed inverter includes two additional insulated gate bipolar transistors and 3 three-pole ac semiconductor switches (Triode AC, TRIAC). The spare leg comprises the insulated gate bipolar transistors (IGBT) S_x⁺ and S_x⁻, which can be used to replace those in the faulty phase to maintain circuit operation. The 3 three-pole ac semiconductor switches T_a, T_b, and T_c connect the spare legs and a-, b-, and c-legs. When a fault occurs, the spare leg is connected with the faulty leg so that the spare leg can replace the function of the faulty leg, thus achieving fault tolerance.

4.1. Fault-Tolerant Control Analysis

The proposed fault-tolerant control system deactivates the a-phase half-bridge switches (S_a1⁺ and S_a2⁻) when an open-circuit fault occurs in S_a1⁺ or S_a2⁻. The b-phase, c-phase, and neutral-point switches still operate normally, and switch T_a in the three three-pole ac semiconductor switches are activated to replace the faulty a-phase leg with the spare leg. The spare leg adopts the switching mode of the original a-phase leg to maintain the three-phase balanced output voltage. If an open-circuit fault occurs in S_b1⁺ or S_b2⁻, the b-phase half-bridge switches (S_b1⁺ and S_b2⁻) are deactivated. The a-phase, c-phase, and neutral-point switches still operate normally, and switch T_b in the three three-pole ac semiconductor switches are activated to replace the faulty b-phase leg with the spare leg. The spare leg adopts the switching mode of the original b-phase leg to maintain the three-phase balanced output voltage. Similarly, if an open-circuit fault occurs in S_c1⁺ or S_c2⁻, the c-phase half-bridge switches (S_c1⁺ and S_c2⁻) are deactivated. The a-phase, b-phase, and neutral-point switches still operate normally, and switch T_c of the three three-pole ac semiconductor switches are activated to replace the faulty c-phase leg with the spare leg. The spare leg adopts the switching mode of the original c-phase leg to maintain the three-phase balanced output voltage. Consider, for example, the occurrence of an open-circuit fault in S_a1⁺, S_b2⁻, and S_c1⁺; the corresponding switching states induced by the fault-tolerant control system for the three-level inverter are shown in Figure 10, Figure 11 and Figure 12, respectively.

4.2. 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.

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.

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. 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. The same results are obtained by using the proposed fault-tolerant control system for an open-circuit fault occurred in switch S_b2⁻ and S_c1⁺. As shown in Figure 14 and Figure 15, when the occurrence of the fault, by using the proposed fault-tolerant control system, the balanced three-phase output line voltage still remained unchanged, and the quality of the output voltage was not reduced.

The fault-tolerant control system can replace the faulty leg of any switch with a spare leg. Thus, after the occurrence of a fault, the three-phase output voltage is unaffected and a loading reduction is not required. The operating mode of the fault-tolerant control system is simple. Therefore, if a fault occurs, apart from changing the switching state of the switches, it is not necessary to adjust the phase angle of the reference voltage signal in a pulse width modulation (PWM) mechanism to maintain a balanced three-phase system. The proposed fault-tolerant control system can prevent economic losses and even casualties caused by faults and can substantially increase system utilization rates and expand system applications. In order to make the process of the proposed fault-tolerant control clearer, use the flow chart, shown in Figure 16, to explain.

5. Conclusions

This study proposes a fault-tolerant diagnosis system based on chaos theory and extension theory for locating a faulty power transistor in a three-level T-type inverter. The proposed system not only obviates the necessity of learning but also has the capability of generating fault tolerance. Therefore, it can reduce the influence of interference signals. In addition, the proposed system can perform control procedures immediately after any inverter switch fails, thus providing continuous power supply to and improving the power supply reliability of the three-level T-type inverter. The test results showed that the proposed fault diagnosis method can detect open-circuit faults in 12 power transistor switches by using only low-cost voltage sensors, and the final accuracy rate is 100%, demonstrating that the proposed fault diagnosis method has a good effect on three-level T-type inverters. The results also indicated that after the consideration of errors, the proposed fault diagnosis system could still correctly detect the fault category. Therefore, regardless of whether accurate or erroneous test data are used, the proposed system can correctly detect the fault category. After the failure of any switch, the proposed fault-tolerant control system can still control the output line voltage and maintain the three-phase balance; this thus verifies the feasibility of the proposed system. Therefore, the proposed fault-tolerant control system can prevent economic losses and even casualties caused by faults and can substantially increase system utilization rates and expand system applications.