# The Diagnostic Method for Open-Circuit Faults in Inverters Based on Extended State Observer

Authors: Chaobo Chen; Ying Yang; Binbin Zhang; Song Gao
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

To reduce the influence of unknown disturbance on open-circuit fault diagnosis of inverters in the motor drive system, an open-circuit fault diagnosis method, which is based on extended state observer, is proposed for inverters. A mixed logic dynamic model of the inverters is established by analyzing the current flow path when the system works normally and there are open-circuit faults. A voltage extended state observer is designed for the mixed logic dynamic model. The open-circuit faults are detected according to the phase voltage residual between the observed voltage and the actual voltage. The position of the faulty switches is determined by querying the voltage residual information table. Finally, the simulation results show that the method can effectively reduce the influence of the unknown interference on the inverter faults diagnosis, improve the fault diagnosis rate, and verify the effectiveness and feasibility of the method.


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## Body

## 1. Introduction

With the rapid development of power electronics technology, motors are widely used in industry, military, aviation, and so on, and many motors are driven by inverters. In reality, if the inverter fault cannot be detected in time, it will directly affect the operation of the motor drive system and even the safety of the whole system. Therefore, fast fault diagnosis of the inverter is of great significance to improve the reliability of the system.Inverter faults are mainly caused by power electronic fault, and 38% of the inverter faults are IGBT (Insulated Gate Bipolar Transistor) fault [1]; there is short-circuit or open-circuit fault about IGBT fault. Short-circuit fault occurs for a short period and cannot be diagnosed by software algorithms. Inverter short-circuit fault can transform into an open-circuit fault due to the break of the connecting fast fuses in the circuit, so the short-circuit fault can be diagnosed by the open-circuit faults diagnostic method [2]. At present, the diagnostic methods of IGBT open-circuit fault are classified into the current-based method, the voltage-based method, and the intelligent algorithm methods. The intelligent inverter fault diagnosis methods are mainly the neural network method [3–5], the fuzzy logic method [6], spectrum analysis method [7], and so on. Due to these intelligent fault diagnosis methods which rely on experience and the fact that they are subjective, they are less used in inverter fault diagnosis. The current-based inverter fault diagnosis methods are mainly the current vector trajectory slope method [8], the current vector instantaneous frequency method [9], average current Park’s vector approach [10], and so forth. However, the current vector trajectory slope method is susceptible to load changes, the current vector instantaneous frequency method only detects the open-circuit fault, and average current Park’s vector approach will be misdiagnosed if the threshold is unsuitable. The inverter fault voltage-based methods are mainly the voltage analytical model method [11], switching function model-based method [12], mixed logic dynamic model method [13–15], and so forth. In [12], the switching function model-based method is studied, but it is easy to cause misdiagnosis because the dead time of the switch devices is not considered. Moreover, this method requires a high-speed optocoupler or comparator when diagnosing the fault of the inverter. References [13–15] established the mixed logic dynamic model of motor and inverter, using the coordinate transformation to diagnose and locate IGBT fault.Compared with the current-based inverter fault diagnosis methods, the inverter fault voltage-based methods have many advantages, such as simple use and low cost, and, in order to reduce the influence of unknown disturbance in motor driven system, extended state observer, which is based on the mixed logic dynamic model, is used to improve robustness of fault diagnostic method.The remainder of this paper is organized as follows. The mixed logic model of the motor and inverter is introduced in Section2. The schematic of inverter IGBT open-circuit fault diagnosis is analyzed in Section 3, as well as obtaining the output phase voltage of the circuit under normal working and fault conditions. The feasibility and effectiveness of the proposed method are verified by the simulation test in Section 4. Finally, a conclusion and some perspectives are proposed.


## 2. The Mixed Logic Dynamic Model of the Inverter

The topology diagram of the motor driving system is shown in Figure1. The inverter circuit is composed of six IGBTs T1∼T6 and six reverse diodes D1∼D6. Udc is the voltage of the DC side, (ia, ib, ic) are the three-phase winding current. (ea, eb, ec) are opposite electromotive forces, R is the stator winding resistor, and L is the stator inductor. F1∼F6 are fast fuses that convert short-circuit fault into open-circuit fault [2], so this paper only studies the diagnostic method of open-circuit fault.Figure 1
The topology diagram of the motor driving system.In the motor drive system, the motor is equivalent to a circuit consisting of a series of resistorR, inductor L, and opposite electromotive forces e. The formula of the phase voltage of the motor is shown as(1)uan=Ria+Ldiadt+ea,ubn=Rib+Ldibdt+eb,ucn=Ric+Ldicdt+ec,where uan, ubn, and ucn are the voltage between the three-phase winding of the motor and the hypothetical midpoint n of the circuit.According to the characteristics of the circuit, the formulas are shown as(2)uan=uao+uon,ubn=ubo+uon,ucn=uco+uon,(3)ia+ib+ic=0,(4)ea+eb+ec=0.Based on (1)–(4), the phase voltage is shown as(5)uanubnucn=132−1−1−12−1−1−12uaoubouco.In practice, three or more IGBTs fault of the inverter will not occur at the same time. This paper discusses the diagnosis method of a single IGBT or two IGBTs open-circuit fault. Taking thec-phase as an example, the model of the inverter is established by the operating state of uco when IGBTs work normally or abnormally.Due to the change of current flow direction and the on/off signals change of IGBTs in the motor driving system, the operating state ofuco can be affected. The normal current flow path of the c-phase IGBT is shown in Figure 2, where s1∼s6 are the on/off signals of the 6 IGBTs of the inverter, si(i = 1, 2, .., 6) = 1 shows that IGBT is on, and si(i = 1,2, .., 6) = 0 shows that IGBT is off. (δa, δb, δc) are the current flow direction of the three-phase winding of the motor, δi(i = a, b, c) = 1 shows that current flows into the i-phase, and δi(i = a, b, c) = 0 shows that current does not flow into the i-phase.Figure 2
The current flow path of thec-phase IGBT when working normally.
(a)(b)(c)(d)(e)(f)Figure2 shows the operation state of uco. The results are shown in Table 1. The logical operation of the state of uco is performed in Table 1 making uco ≠ 0 by logical OR operation.Table 1
The truth table ofuco when IGBTs are working normally.
s5s6δcuco00100110101Udc000Udc0100100UdcSo, the formula ofuco is shown as follows:(6)uco=Udcs5s¯6δc+s5s¯6δ¯c+s¯5s¯6δ¯c=Udcs¯6s5+s¯5δ¯c.When the inverter works normally, the formulas ofuao, ubo, and uco are shown as(7)uao=Udcs2¯s1+s1¯δ¯a,ubo=Udcs4¯s3+s3¯δ¯b,uco=Udcs6¯s5+s5¯δ¯c.Based on (5) and (7), the three-phase voltage is shown as follows:(8)uanubnucn=Udc32−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4s3+s¯3δ¯bs¯6s5+s¯5δ¯c.Substituting (8) into (1), the hybrid logic dynamic model of the inverter is established as(9)i˙ai˙bi˙c=−RL000−RL000−RL+Udc3L2−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4s3+s¯3δ¯bs¯6s5+s¯5δ¯c+−1L000−1L000−1Leaebec.Equation (9) can be written in matrix form as(10)i˙=Ai+B1σ+B2e,where i=iaibic, δ=s¯2s1+s¯1δ¯as¯4s3+s¯3δ¯bs¯6s5+s¯5δ¯c, e=eaebec, A=−R/L000−R/L000−R/L, B1=Udc/3L2−1−1−12−1−1−12, and B2=−1/L000−1/L000−1/L.


## 3. The Diagnosis Method of Open-Circuit Fault in the Inverter

### 3.1. The Voltage Expansion Observer

In reality, there are a lot of disturbances in the inverter system, so the voltage extended observer is designed to estimate the output three-phase voltage in real time, thus eliminating the influence of some other unknown disturbances and uncertainties in the system and improving the accuracy of fault diagnosis.(11)xnt=fx,x1,…,xn−1,t+ωt+bu,y=xt,where xt is the system state variable, yt is the system output variable, fx,x1,…,xn−1,t is an unknown function, ωt is an unknown disturbance, and b is the gain of the input variable u.Treatingfx,x1,…,xn−1,t and ωt as additional state variables, the expansion observer of the system can be shown as(12)z1·=z2−g1z1−xt,⋯,zn·=zn+1−gnz1−xt+bu,zn+1·=−gn+1z1−xt.In (12), the system uses xt as input to track the expanded state variables xt, x(1) (t), ..., x(n−1) (t), x(n) (t). So z1 ⟶ x(t), …, zn ⟶ x(n−1)(t), zn+1 ⟶ a(t), a(t) = f(x, x(1),, x(n−1), t) + ω(t). gi(.) is a nonlinear function and it is generally taken as(13)falε,α,δ=εαsatε,ε>δ,signε,ε≤δ,(14)satε=ες,ε≤ς,signε,ε>ς.Rewrite the hybrid logic dynamic model (10) of the inverter as(15)i˙=Ai+B1σ+B2e=Ai+BB1σ+B2e=Ai+Bu+B2e,where B = diag (3) and u = B1σ = [uan, ubn, ucn]T.When the extended observer is designed according to equation (3.8), its expression is(16)z1·=z2−β1falε,α1,δ1+f0z1+bu1,z2·=−β2falε,α2,δ2,where z1 estimates the three-phase current i, z2 estimates three-phase voltage disturbance of motor drive system, β1 and β2 are observer coefficients, α1 and α2 are nonlinear factors, δ1 and δ2 are filter factors, ε = z1-i, f0(z1) = Az1, b = B2, and u1 = e.


### 3.2. Diagram of Open-Circuit Fault Diagnosis

#### 3.2.1. The Open-Circuit Fault of Single IGBT

Takec-phase IGBT single-phase open-circuit fault as an example. When only open-circuit faults occur in T5, the flow channel of the current is shown in Figure 3. The dotted line is the current direction under different switching modes.Figure 3
The flow path of the current when IGBT open-circuit fault only occurs inT5.
(a)(b)(c)(d)(e)(f)If the open-circuit fault occurs inT5, uco is different from (7), uco′ denotes the open-circuit fault voltage, and its truth table is shown in Table 2.Table 2
The truth table ofuco′ when the open-circuit fault only occurs in T5.
s5s6δcuco′001001101010000Udc0100100UdcBased on Table2, uco′ can be calculated by logical operation as (17)uco′=Udcs¯5s¯6δ¯c+s5s¯6δ¯c=Udcs¯6δ¯c.When the open-circuit fault occurs inT5, the formulas of uan, ubn, and ucn′ are shown as(18)uanubnucn′=Udc32−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4s3+s¯3δ¯bs¯6δ¯c.Based on (10) and (18), when the open-circuit fault occurs in T5, the formulas of voltage residual are shown as(19)Δuan=−Udc3s5s6¯δc,Δubn=−Udc3s5s6¯δc,Δucn=2Udc3s5s6¯δc.Equation (19) shows that when the open-circuit fault occurs in T5, we can obtain △uan = △ubn ≤ 0, △ucn ≥ 0, and △ucn = 2△uan = 2△ubn.


#### 3.2.2. Two IGBTs Occur in an Open-Circuit Fault

Two IGBTs in a phaseWhen the open-circuit fault occurs inT5 and T6 at the same time, the current flow path is as shown in Figure 4. The results of uco′ are shown in Table 3.Figure 4
The current flow path when the open-circuit fault occurs inT5 and T6 at the same time.
(a)(b)(c)(d)(e)(f)Table 3
The truth table ofuco″ when the open-circuit fault occurs in T5 and T6 at the same time.
s5s6δcuco″001001101010000Udc010Udc100UdcThe logical operation ofuco″ is shown in Table 3, making uco″ ≠ 0 by logical OR operation. So uco″ is shown as (20)uco″=Udcs¯5s¯6δ¯c+s¯5s6δ¯c+s5s¯6δ¯c=Udcδ¯c.When the open-circuit fault occurs inT5 and T6 at the same time, uan, ubn, and u′cn are shown as (21)uanubnucn′′′=Udc32−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4s3+s¯3δ¯bδ¯c.Based on (10) and (21), when the open-circuit fault occurs in T5 and T6 at the same time, the voltage residual is shown as (22)Δuan=−Udc3s5s6¯+δc¯s5¯s6¯−1,Δubn=−Udc3s5s6¯+δc¯s5¯s6¯−1,Δucn=2Udc3s5s6¯+δc¯s5¯s6¯−1.From (22), the relationship of Δucn, Δuan, and Δubn satisfied Δucn = −2Δuan = −2Δubn.Two IGBTs in two phases(1)
Two IGBTs at the same position in two phasesTake the open-circuit fault ofT3 and T5 as an example, and use the calculation method of the open-circuit fault of two switches in the same phase; the specific expressions of ubo′′′ and uco′′′ can be obtained as (23)ubo′′′=Udcs4¯δb¯,uco′′′=Udcs6¯δc¯.When the open-circuit fault occurs inT3 and T5, the phase voltage of each phase is(24)uanubn′′′ucn′′′=Udc32−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4δ¯bs¯6δ¯c.According to (10) and (24), the residual voltage of T3 and T5 is(25)Δuan=Udc3−s3s¯4δb−s5s¯6δc,Δubn=Udc32s3s¯4δb−s5s¯6δc,Δucn=Udc3−s3s¯4δb+2s5s¯6δc.According to (25), there is not a certain numerical relationship between the voltage residuals of the fault phases and those of the normal phase in a cycle, so it is impossible to locate the fault phases and the fault IGBTs by using the numerical relationship of voltage residuals.However, the voltage residual value of the fault phase is still twice as the normal two-phase voltage in a certain cycle. For example, when the IGBTsT3 and T6 are normally on, the expression of the three-phase voltage residual is(26)Δuan=−Udc3s3s¯4δb,Δubn=2Udc3s3s¯4δb,Δucn=−Udc3s3s¯4δb.When the IGBTsT4 and T5 are normally on, the three-phase voltage residual is(27)Δuan=−Udc3s5s¯6δc,Δubn=−Udc3s5s¯6δc,Δucn=2Udc3s5s¯6δc.When T4 and T5 are normal, the relationship between the IGBTsT3 and T5 is the same as that in the case of the open-circuit fault of the IGBT T5.(2)
Two IGBTs at different position in two phasesTake the open-circuit fault ofT4 and T5 of phase b and c as an example, and use the calculation method of the open-circuit fault of two switches in the same phase; uco′′′′ and uco′′′′ can be obtained as follows:(28)ubo′′′′=Udcs3+s¯3δ¯b,uco′′′′=Udcs¯6δ¯,cand when the open-circuit fault occurs inT4 and T5, the phase voltage of each phase is(29)uanubn′′′′ubn′′′′=Udc32−1−1−12−1−12−1s¯2s1+s¯1δ¯as3+s¯3δ¯bs¯6δ¯c.According to (10) and (29), the residual voltage of T4 and T5 is(30)Δuan=Udc3s4s3+s¯3δ¯b−s5s¯6δc,Δubn=Udc3−2s4s3+s¯3δ¯b−s5s¯6δc,Δucn=Udc3s4s3+s¯3δ¯b+2s5s¯6δc.From (30), when the IGBTs T4 and T6 are normally on, the three-phase voltage residual is as follows:(31)Δuan=Udc3s4s3+s¯3δ¯b,Δubn=−2Udc3s4s3+s¯3δ¯b,Δucn=Udc3s4s3+s¯3δ¯b.In conclusion, the fault diagnosis method of single switch open-circuit fault and two switches in the same phase are the foundation of the fault diagnosis in the different phase, and the fault location of two switches in the different phase is a special case of single switch open-circuit fault. Therefore, this paper only simulates the open-circuit fault of a single switch and the open-circuit fault of two switches in the same phase.


### 3.3. Establishment of Voltage Residual Information Table

The above methods are used to deal with the open-circuit fault of phasea and phase b, respectively. The residual voltage of phase a and phase b under different fault conditions can be obtained through calculation, and the results are shown in Table 4; and the open-circuit fault of a single switch and two switches in the same phase can be accurately located by looking up Table 4.Table 4
The voltage residual information table.
Bridge armFault switchRelationship between residualsNormallyΔuan=Δubn=ΔucnaT1Δuan=−2Δubn=−2Δucn≥0T2Δuan=−2Δubn=−2Δucn≤0T1 and T2Δuan=−2Δubn=−2ΔucnbT3Δubn=−2Δuan=−2Δucn≥0T4Δubn=−2Δuan=−2Δucn≤0T3 and T4Δubn=−2Δuan=−2ΔucncT5Δucn=−2Δuan=−2Δubn≥0T6Δucn=−2Δuan=−2Δubn≤0T5 and T6Δucn=−2Δuan=−2Δubn


### 3.4. The Diagnosis Strategy of Open-Circuit Fault in the Inverter

The flowchart of the inverter open-circuit fault diagnosis is shown in Figure5. In this paper, it is judged whether the open-circuit fault occurs by comparing the voltage residual with the threshold. In an ideal case, the voltage residual of each phase of the inverter tends to zero. When the open-circuit fault of inverter occurs, the maximum absolute values of the voltage residuals of each phase are assumed to be UT1, UT2, UT3, UT4, UT5, and UT6. So, the threshold range is(32)Uth=12maxUT1,UT2,UT3,UT4,UT5,UT6+Δ,where Uth is the threshold and Δ is the safety margin, which is used to reduce the influence of measurement error, noise, and disturbance in the actual system.Figure 5
The flowchart of inverter open-circuit fault diagnosis.


## 3.1. The Voltage Expansion Observer

In reality, there are a lot of disturbances in the inverter system, so the voltage extended observer is designed to estimate the output three-phase voltage in real time, thus eliminating the influence of some other unknown disturbances and uncertainties in the system and improving the accuracy of fault diagnosis.(11)xnt=fx,x1,…,xn−1,t+ωt+bu,y=xt,where xt is the system state variable, yt is the system output variable, fx,x1,…,xn−1,t is an unknown function, ωt is an unknown disturbance, and b is the gain of the input variable u.Treatingfx,x1,…,xn−1,t and ωt as additional state variables, the expansion observer of the system can be shown as(12)z1·=z2−g1z1−xt,⋯,zn·=zn+1−gnz1−xt+bu,zn+1·=−gn+1z1−xt.In (12), the system uses xt as input to track the expanded state variables xt, x(1) (t), ..., x(n−1) (t), x(n) (t). So z1 ⟶ x(t), …, zn ⟶ x(n−1)(t), zn+1 ⟶ a(t), a(t) = f(x, x(1),, x(n−1), t) + ω(t). gi(.) is a nonlinear function and it is generally taken as(13)falε,α,δ=εαsatε,ε>δ,signε,ε≤δ,(14)satε=ες,ε≤ς,signε,ε>ς.Rewrite the hybrid logic dynamic model (10) of the inverter as(15)i˙=Ai+B1σ+B2e=Ai+BB1σ+B2e=Ai+Bu+B2e,where B = diag (3) and u = B1σ = [uan, ubn, ucn]T.When the extended observer is designed according to equation (3.8), its expression is(16)z1·=z2−β1falε,α1,δ1+f0z1+bu1,z2·=−β2falε,α2,δ2,where z1 estimates the three-phase current i, z2 estimates three-phase voltage disturbance of motor drive system, β1 and β2 are observer coefficients, α1 and α2 are nonlinear factors, δ1 and δ2 are filter factors, ε = z1-i, f0(z1) = Az1, b = B2, and u1 = e.


## 3.2. Diagram of Open-Circuit Fault Diagnosis

### 3.2.1. The Open-Circuit Fault of Single IGBT

Takec-phase IGBT single-phase open-circuit fault as an example. When only open-circuit faults occur in T5, the flow channel of the current is shown in Figure 3. The dotted line is the current direction under different switching modes.Figure 3
The flow path of the current when IGBT open-circuit fault only occurs inT5.
(a)(b)(c)(d)(e)(f)If the open-circuit fault occurs inT5, uco is different from (7), uco′ denotes the open-circuit fault voltage, and its truth table is shown in Table 2.Table 2
The truth table ofuco′ when the open-circuit fault only occurs in T5.
s5s6δcuco′001001101010000Udc0100100UdcBased on Table2, uco′ can be calculated by logical operation as (17)uco′=Udcs¯5s¯6δ¯c+s5s¯6δ¯c=Udcs¯6δ¯c.When the open-circuit fault occurs inT5, the formulas of uan, ubn, and ucn′ are shown as(18)uanubnucn′=Udc32−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4s3+s¯3δ¯bs¯6δ¯c.Based on (10) and (18), when the open-circuit fault occurs in T5, the formulas of voltage residual are shown as(19)Δuan=−Udc3s5s6¯δc,Δubn=−Udc3s5s6¯δc,Δucn=2Udc3s5s6¯δc.Equation (19) shows that when the open-circuit fault occurs in T5, we can obtain △uan = △ubn ≤ 0, △ucn ≥ 0, and △ucn = 2△uan = 2△ubn.


### 3.2.2. Two IGBTs Occur in an Open-Circuit Fault

Two IGBTs in a phaseWhen the open-circuit fault occurs inT5 and T6 at the same time, the current flow path is as shown in Figure 4. The results of uco′ are shown in Table 3.Figure 4
The current flow path when the open-circuit fault occurs inT5 and T6 at the same time.
(a)(b)(c)(d)(e)(f)Table 3
The truth table ofuco″ when the open-circuit fault occurs in T5 and T6 at the same time.
s5s6δcuco″001001101010000Udc010Udc100UdcThe logical operation ofuco″ is shown in Table 3, making uco″ ≠ 0 by logical OR operation. So uco″ is shown as (20)uco″=Udcs¯5s¯6δ¯c+s¯5s6δ¯c+s5s¯6δ¯c=Udcδ¯c.When the open-circuit fault occurs inT5 and T6 at the same time, uan, ubn, and u′cn are shown as (21)uanubnucn′′′=Udc32−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4s3+s¯3δ¯bδ¯c.Based on (10) and (21), when the open-circuit fault occurs in T5 and T6 at the same time, the voltage residual is shown as (22)Δuan=−Udc3s5s6¯+δc¯s5¯s6¯−1,Δubn=−Udc3s5s6¯+δc¯s5¯s6¯−1,Δucn=2Udc3s5s6¯+δc¯s5¯s6¯−1.From (22), the relationship of Δucn, Δuan, and Δubn satisfied Δucn = −2Δuan = −2Δubn.Two IGBTs in two phases(1)
Two IGBTs at the same position in two phasesTake the open-circuit fault ofT3 and T5 as an example, and use the calculation method of the open-circuit fault of two switches in the same phase; the specific expressions of ubo′′′ and uco′′′ can be obtained as (23)ubo′′′=Udcs4¯δb¯,uco′′′=Udcs6¯δc¯.When the open-circuit fault occurs inT3 and T5, the phase voltage of each phase is(24)uanubn′′′ucn′′′=Udc32−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4δ¯bs¯6δ¯c.According to (10) and (24), the residual voltage of T3 and T5 is(25)Δuan=Udc3−s3s¯4δb−s5s¯6δc,Δubn=Udc32s3s¯4δb−s5s¯6δc,Δucn=Udc3−s3s¯4δb+2s5s¯6δc.According to (25), there is not a certain numerical relationship between the voltage residuals of the fault phases and those of the normal phase in a cycle, so it is impossible to locate the fault phases and the fault IGBTs by using the numerical relationship of voltage residuals.However, the voltage residual value of the fault phase is still twice as the normal two-phase voltage in a certain cycle. For example, when the IGBTsT3 and T6 are normally on, the expression of the three-phase voltage residual is(26)Δuan=−Udc3s3s¯4δb,Δubn=2Udc3s3s¯4δb,Δucn=−Udc3s3s¯4δb.When the IGBTsT4 and T5 are normally on, the three-phase voltage residual is(27)Δuan=−Udc3s5s¯6δc,Δubn=−Udc3s5s¯6δc,Δucn=2Udc3s5s¯6δc.When T4 and T5 are normal, the relationship between the IGBTsT3 and T5 is the same as that in the case of the open-circuit fault of the IGBT T5.(2)
Two IGBTs at different position in two phasesTake the open-circuit fault ofT4 and T5 of phase b and c as an example, and use the calculation method of the open-circuit fault of two switches in the same phase; uco′′′′ and uco′′′′ can be obtained as follows:(28)ubo′′′′=Udcs3+s¯3δ¯b,uco′′′′=Udcs¯6δ¯,cand when the open-circuit fault occurs inT4 and T5, the phase voltage of each phase is(29)uanubn′′′′ubn′′′′=Udc32−1−1−12−1−12−1s¯2s1+s¯1δ¯as3+s¯3δ¯bs¯6δ¯c.According to (10) and (29), the residual voltage of T4 and T5 is(30)Δuan=Udc3s4s3+s¯3δ¯b−s5s¯6δc,Δubn=Udc3−2s4s3+s¯3δ¯b−s5s¯6δc,Δucn=Udc3s4s3+s¯3δ¯b+2s5s¯6δc.From (30), when the IGBTs T4 and T6 are normally on, the three-phase voltage residual is as follows:(31)Δuan=Udc3s4s3+s¯3δ¯b,Δubn=−2Udc3s4s3+s¯3δ¯b,Δucn=Udc3s4s3+s¯3δ¯b.In conclusion, the fault diagnosis method of single switch open-circuit fault and two switches in the same phase are the foundation of the fault diagnosis in the different phase, and the fault location of two switches in the different phase is a special case of single switch open-circuit fault. Therefore, this paper only simulates the open-circuit fault of a single switch and the open-circuit fault of two switches in the same phase.


## 3.2.1. The Open-Circuit Fault of Single IGBT

Takec-phase IGBT single-phase open-circuit fault as an example. When only open-circuit faults occur in T5, the flow channel of the current is shown in Figure 3. The dotted line is the current direction under different switching modes.Figure 3
The flow path of the current when IGBT open-circuit fault only occurs inT5.
(a)(b)(c)(d)(e)(f)If the open-circuit fault occurs inT5, uco is different from (7), uco′ denotes the open-circuit fault voltage, and its truth table is shown in Table 2.Table 2
The truth table ofuco′ when the open-circuit fault only occurs in T5.
s5s6δcuco′001001101010000Udc0100100UdcBased on Table2, uco′ can be calculated by logical operation as (17)uco′=Udcs¯5s¯6δ¯c+s5s¯6δ¯c=Udcs¯6δ¯c.When the open-circuit fault occurs inT5, the formulas of uan, ubn, and ucn′ are shown as(18)uanubnucn′=Udc32−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4s3+s¯3δ¯bs¯6δ¯c.Based on (10) and (18), when the open-circuit fault occurs in T5, the formulas of voltage residual are shown as(19)Δuan=−Udc3s5s6¯δc,Δubn=−Udc3s5s6¯δc,Δucn=2Udc3s5s6¯δc.Equation (19) shows that when the open-circuit fault occurs in T5, we can obtain △uan = △ubn ≤ 0, △ucn ≥ 0, and △ucn = 2△uan = 2△ubn.


## 3.2.2. Two IGBTs Occur in an Open-Circuit Fault

Two IGBTs in a phaseWhen the open-circuit fault occurs inT5 and T6 at the same time, the current flow path is as shown in Figure 4. The results of uco′ are shown in Table 3.Figure 4
The current flow path when the open-circuit fault occurs inT5 and T6 at the same time.
(a)(b)(c)(d)(e)(f)Table 3
The truth table ofuco″ when the open-circuit fault occurs in T5 and T6 at the same time.
s5s6δcuco″001001101010000Udc010Udc100UdcThe logical operation ofuco″ is shown in Table 3, making uco″ ≠ 0 by logical OR operation. So uco″ is shown as (20)uco″=Udcs¯5s¯6δ¯c+s¯5s6δ¯c+s5s¯6δ¯c=Udcδ¯c.When the open-circuit fault occurs inT5 and T6 at the same time, uan, ubn, and u′cn are shown as (21)uanubnucn′′′=Udc32−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4s3+s¯3δ¯bδ¯c.Based on (10) and (21), when the open-circuit fault occurs in T5 and T6 at the same time, the voltage residual is shown as (22)Δuan=−Udc3s5s6¯+δc¯s5¯s6¯−1,Δubn=−Udc3s5s6¯+δc¯s5¯s6¯−1,Δucn=2Udc3s5s6¯+δc¯s5¯s6¯−1.From (22), the relationship of Δucn, Δuan, and Δubn satisfied Δucn = −2Δuan = −2Δubn.Two IGBTs in two phases(1)
Two IGBTs at the same position in two phasesTake the open-circuit fault ofT3 and T5 as an example, and use the calculation method of the open-circuit fault of two switches in the same phase; the specific expressions of ubo′′′ and uco′′′ can be obtained as (23)ubo′′′=Udcs4¯δb¯,uco′′′=Udcs6¯δc¯.When the open-circuit fault occurs inT3 and T5, the phase voltage of each phase is(24)uanubn′′′ucn′′′=Udc32−1−1−12−1−1−12s¯2s1+s¯1δ¯as¯4δ¯bs¯6δ¯c.According to (10) and (24), the residual voltage of T3 and T5 is(25)Δuan=Udc3−s3s¯4δb−s5s¯6δc,Δubn=Udc32s3s¯4δb−s5s¯6δc,Δucn=Udc3−s3s¯4δb+2s5s¯6δc.According to (25), there is not a certain numerical relationship between the voltage residuals of the fault phases and those of the normal phase in a cycle, so it is impossible to locate the fault phases and the fault IGBTs by using the numerical relationship of voltage residuals.However, the voltage residual value of the fault phase is still twice as the normal two-phase voltage in a certain cycle. For example, when the IGBTsT3 and T6 are normally on, the expression of the three-phase voltage residual is(26)Δuan=−Udc3s3s¯4δb,Δubn=2Udc3s3s¯4δb,Δucn=−Udc3s3s¯4δb.When the IGBTsT4 and T5 are normally on, the three-phase voltage residual is(27)Δuan=−Udc3s5s¯6δc,Δubn=−Udc3s5s¯6δc,Δucn=2Udc3s5s¯6δc.When T4 and T5 are normal, the relationship between the IGBTsT3 and T5 is the same as that in the case of the open-circuit fault of the IGBT T5.(2)
Two IGBTs at different position in two phasesTake the open-circuit fault ofT4 and T5 of phase b and c as an example, and use the calculation method of the open-circuit fault of two switches in the same phase; uco′′′′ and uco′′′′ can be obtained as follows:(28)ubo′′′′=Udcs3+s¯3δ¯b,uco′′′′=Udcs¯6δ¯,cand when the open-circuit fault occurs inT4 and T5, the phase voltage of each phase is(29)uanubn′′′′ubn′′′′=Udc32−1−1−12−1−12−1s¯2s1+s¯1δ¯as3+s¯3δ¯bs¯6δ¯c.According to (10) and (29), the residual voltage of T4 and T5 is(30)Δuan=Udc3s4s3+s¯3δ¯b−s5s¯6δc,Δubn=Udc3−2s4s3+s¯3δ¯b−s5s¯6δc,Δucn=Udc3s4s3+s¯3δ¯b+2s5s¯6δc.From (30), when the IGBTs T4 and T6 are normally on, the three-phase voltage residual is as follows:(31)Δuan=Udc3s4s3+s¯3δ¯b,Δubn=−2Udc3s4s3+s¯3δ¯b,Δucn=Udc3s4s3+s¯3δ¯b.In conclusion, the fault diagnosis method of single switch open-circuit fault and two switches in the same phase are the foundation of the fault diagnosis in the different phase, and the fault location of two switches in the different phase is a special case of single switch open-circuit fault. Therefore, this paper only simulates the open-circuit fault of a single switch and the open-circuit fault of two switches in the same phase.


## 3.3. Establishment of Voltage Residual Information Table

The above methods are used to deal with the open-circuit fault of phasea and phase b, respectively. The residual voltage of phase a and phase b under different fault conditions can be obtained through calculation, and the results are shown in Table 4; and the open-circuit fault of a single switch and two switches in the same phase can be accurately located by looking up Table 4.Table 4
The voltage residual information table.
Bridge armFault switchRelationship between residualsNormallyΔuan=Δubn=ΔucnaT1Δuan=−2Δubn=−2Δucn≥0T2Δuan=−2Δubn=−2Δucn≤0T1 and T2Δuan=−2Δubn=−2ΔucnbT3Δubn=−2Δuan=−2Δucn≥0T4Δubn=−2Δuan=−2Δucn≤0T3 and T4Δubn=−2Δuan=−2ΔucncT5Δucn=−2Δuan=−2Δubn≥0T6Δucn=−2Δuan=−2Δubn≤0T5 and T6Δucn=−2Δuan=−2Δubn


## 3.4. The Diagnosis Strategy of Open-Circuit Fault in the Inverter

The flowchart of the inverter open-circuit fault diagnosis is shown in Figure5. In this paper, it is judged whether the open-circuit fault occurs by comparing the voltage residual with the threshold. In an ideal case, the voltage residual of each phase of the inverter tends to zero. When the open-circuit fault of inverter occurs, the maximum absolute values of the voltage residuals of each phase are assumed to be UT1, UT2, UT3, UT4, UT5, and UT6. So, the threshold range is(32)Uth=12maxUT1,UT2,UT3,UT4,UT5,UT6+Δ,where Uth is the threshold and Δ is the safety margin, which is used to reduce the influence of measurement error, noise, and disturbance in the actual system.Figure 5
The flowchart of inverter open-circuit fault diagnosis.


## 4. Simulation

The simulation parameters of motor are given in Table5. When the inverter works normally, it suddenly changes the load value at t = 0.37 s, the three-phase voltage output by the actual system, and the voltage extension observer, and the residuals between the actual voltage and the observed voltage are shown in Figures 6 and 7 .Table 5
The inverter system parameters.
DescriptionValueFrequencyf50 HzDC side voltageUdc360VStator resistanceRs0.435 ΩRotor resistanceRr0.816 ΩStator leakage inductanceLls4 mHRotor leakage inductanceLrs2 mHMutual inductanceLm69.31 mHPole pairp2Moment of inertiaJ0.089 kg·m2Figure 6
The normal three-phase voltage of the actual system and the voltage extension observer.Figure 7
The residuals between the actual voltage and the observed voltage.From Figure7, the voltage expansion observer is consistent with the actual system, and it is shown that that the observer has a good tracking effect.During the simulation, the driving signal ofT5 is removed at t = 0.3 s, and t = 0.37 s suddenly changes the load value. The three-phase voltage and voltage residual are shown in Figure 8 when the open-circuit fault occurs in T5.Figure 8
The three-phase voltage and voltage residual when the open-circuit fault occurs inT5. (a) The three-phase voltage when the open-circuit fault occurs in T5. (b) The voltage residual when the open-circuit fault occurs in T5.
(a)(b)From Figure8, the c-phase voltage is distorted, and the voltage residual rapidly increases in the positive direction after 0.3 s. The voltage residuals in phase a and phase b negatively increase and the increasing trends of the two are approximately the same. The numerical relationship satisfies(33)Δucn=−2Δubn=−2Δuan≥0.By looking up the voltage residual information table in Table4, the voltage residual exhibits the characteristics of the open-circuit fault in T5. If Δucn > Uth is satisfied, the open-circuit fault occurs in T5. After 0.37 s, the system suddenly changes the load, and each phase amplitude of the voltage and voltage residual increase, but it can also detect that T5 has an open-circuit fault. It shows that the method proposed in this paper has certain antinoise interference.If the driving signals ofT5 and T6 are removed at t = 0.3 s and t = 0.37 s, the load suddenly changes. The three-phase voltage and voltage residual in which the open-circuit fault occurs in T5 and T6 are shown in Figure 9.Figure 9
The three-phase voltage and voltage residual when the open-circuit fault occurs inT5 and T6 at the same time. (a) The three-phase voltage when the open-circuit fault occurs in T5 and T6 at the same time. (b) The voltage residual when the open-circuit fault occurs in T5 and T6 at the same time.
(a)(b)The proposed fault diagnosis method is compared with other fault diagnosis methods; and the objector (for open-loop system, closed-loop system, or both), diagnosis time, robustness, cost, and fault type are the comparison index, and they are shown in Table6. From Table 6, the proposed fault diagnosis method has good performance compared with other fault methods.Table 6
Comparison of the proposed fault diagnosis method and other fault methods.
Fault diagnosis methodObjectorDiagnosis timeRobustnessCostFault typeThe neural network methodBothMore than one cycleLowLowSingleThe fuzzy logic methodBothMore than one cycleMediumHighMultiplePark’s vector approachOpen-loopMore than one cycleLowLowSingleSpectrum analysis methodBothMore than one cycleMediumHighSingleThe proposed methodBothAbout 1/3 cycleHighLowMultiple


## 5. Conclusion

In this paper, the mixed logic dynamic model of the inverter is established by the flow path of current when the inverter works normally and abnormally; and considering the dead time of the switching signal in the modeling process avoids the misdiagnosis of the fault. At the same time, a voltage expansion observer is designed to avoid the problem of increasing the fault rate by introducing other hardware circuits. The simulation results show that the method can be accurately located and has a short diagnosis time. In the future, it is possible to study the diagnostic method of the inverter of two IGBTs in different phases, where the open-circuit fault occurs at the same time, and add a certain fault-tolerant strategy to ensure that the inverter can work normally.



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*Source: 5526173-2021-04-26.xml*