Diagnosis of multiple open switch faults in three phase voltage source inverter

Abstract

Three phase Voltage Source Inverter (VSI) plays an important role in power electronic applications. Many types of faults occur in it which degrades the performance of the VSI. One possible fault in inverter is open circuit transistor fault. Knowledge of fault mode is extremely important to improve performance of VSI. This paper presents a method of open circuit transistor fault diagnosis which is based on combination of diagnostic variable and Fuzzy Logic. This method can detect single as well as multiple open circuit faults. Diagnostic variables are used to identify faulty phase and an average current is used to identify faulty switches. Fuzzy logic is used to improve performance of system under variable load conditions during faulty conditions.

Keywords

Fault diagnosis fuzzy logic diagnostic variable variable load

1 Introduction

The inverter, which is also known as DC-AC converter, converts DC power to AC power. The inverter is an adjustable frequency voltage source. It is classified into two types, voltage source inverter and current source inverter. It controls the fundamental output voltage and the frequency of the AC output voltage. Single phase inverters are used for low range power applications, while three phase inverters are used for medium to high power applications. The inverters are used in industrial applications such as electric motor drives, Uninterrupted Power Supply (UPS), active power filters, etc. Every machine in power electronics is affected by faults. Different types of faults can occur in VSI, which may affect the operation of whole system. These unexpected faults, degrades the performance of inverter. The maintenance cost of these steps is very high. It is necessary to avoid these unexpected inverter faults to improve performance. Therefore in three phase inverter, fault detection is required.

The Insulated Gate Bipolar Transistors (IGBTs) are used as a switch in many inverters. IGBT has the features like high voltage and current ratings. They can tolerate short circuit current up to 10μs [1]. Due to excess electric and thermal stress, IGBT causes failures. Various types of faults occur in switching devices, like open circuit fault, short circuit fault and intermittent gate-misfiring fault. These faults can cause problems for other parts in the system. Therefore monitoring of switching devices is important. It is required to identify the faulty switch to improve the stability and reliability of the system. Various methods have been developed for fault detection and diagnosis of Induction Motor Drive, Process Industry Equipments, Marine Engine Cooling System, Power Transformer, Nuclear Power Plant and Pneumatic Valve in Cooler Water Spray System [2 –7]. In Rule-based fault diagnosis system [8], knowledge of skilled person is implemented by using hundreds or thousands of IF_THEN rules. This method adds more informative data into faulty information. Difficulty of Rule-based system is in collecting information, to built rule base. In Model based approach [8], approximate representation of healthy model is implemented for diagnosis. Model based systems are used for finding faults in digital circuits like stuck at one and stuck at zero faults. Integrated circuits are diagnosed by using Casual Models, which requires expert knowledge based on the concrete knowledge of probability. Other approaches are based on Fuzzy Logic (FL), Artificial Neural Network (ANN) and combinations of Fuzzy Neuro System.

In [3], combination of Discrete Wavelet Transform (DWT) and Fuzzy Logic (FL) is used for diagnosis of open switch fault and intermittent gate misfiring fault in IGBT. FL deals with approximation. Traditional set has two values either zero or one. Fuzzy sets are used to handle the concept of partial one or partial zero. The fault identifier process by Fuzzy Interface System (FIS) leads to determine particular fault, which was occurred in the system. The structure of Fuzzy Classifier is based on the obtained rules, which are fuzzyfied in order to avoid the classification surface discontinuity. Sliding data window of 3 ms is used to capture segment of 30 ms [8]. A faulty transistor and corresponding fault is detected by using FL. Time required for fault diagnosis is 150 ms i.e. 5 cycles [1]. Advantages of this system are that detection variables are not depending on threshold values and low implementation efforts are required. Resistivity of this system is good against noise.

F. Charfi, F. Sellami, and K. Al-Haddad proposed a new method of open circuit fault diagnosis of IGBT [9]. Only three conditions are considered for study, two conditions are multiple faulty switches in same leg and a condition with faulty switches in different legs. Combination of Discrete Wavelet Transform (DWT) and Artificial Neural Network (ANN) is used. DB4 wavelet at level six is implemented to analyze transients of faulty transistors. Back propagation artificial neural network is used for fault classification. High implementation efforts are required to train the ANN; less than 5% error is reported. Resistivity of the system is depends on training of neural network. This system requires high implementation efforts to train ANN.

The Park’s vector approach developed in 1990 is the oldest technique in fault diagnosis of inverter. Single switch open and short circuit faults are detected by using normalization of three phase currents and average absolute values of normalized currents which are calculated using Park’s Vector Method. Park’s vector modulus of three phase motor current and phase difference are calculated for different faulty conditions. By observing above values faults are classified. This method is not suitable for variable load AC drive systems [13].

The Park’s vector method is more robust and carries more information for multiple open circuit fault diagnosis. Diagnostic variables are calculated and compared with threshold value K_d and K_f. Here K_f plays an important role for detecting single and multiple IGBT faults in same leg. K_d is used to differentiate double switch fault in different leg. K_d and K_f are decided by observing the diagnostic variable behavior [19].

The Modified Normalized DC Current Method is used to improve performance of diagnostic system. Largest value among all calculated diagnostic variables is taken as threshold and open circuit fault in single IGBT is detected. Normalized DC current is compared with threshold values. Threshold values are decided by experience. Effectiveness of such system under small current is very poor. Detection time required for fault identification is 18.4 ms [16].

Clustering Adaptive Neural Fuzzy Interface System (C-ANFIS) is proposed to detect open circuit IGBT fault under variable mechanical or electrical conditions. Better results are obtained with worst case error 2.26% . Single IGBT fault is detected by using this method [15].

In literature, different methods are presented on diagnosis of single switch open circuit fault. In this paper, combination of diagnostic variable method and Fuzzy Logic is proposed, which is able to detect single, multiple switch faults in same leg as well as in different legs. Problem of fault diagnosis under variable load conditions in the paper has been studied by others in the past [13 –15] which is restricted to single switch open circuit fault. The contribution of this work is to improve accuracy of multiple open switch fault diagnosis system. The problem of misidentifying faults during load variation in faulty condition is considered for discussion. The diagnostic variables are calculated by using average absolute values of current. Fuzzy fault diagnosis is suitable tool for diagnosis of fault in VSI. To detect faulty IGBTs under variable load condition during faulty condition, threshold values are calculated using Fuzzy Logic. Results of fuzzy fault diagnosis are presented to evaluate the performance of diagnostic system. The unique features and the main advantages of the results over others are discussed.

2 Three phase VSI

Structure of three phase VSI using IGBTs and experimental setup are shown in Figs. 1 and 2 respectively. Switches S1 to S6 are used to introduce open circuit fault in T1 to T6 respectively as shown in Fig. 1. The specifications of inverter are mentioned in Table 1. The Data Acquisition System (DAS) consist of a VSI, induction motor and real time interface. A protection circuit is provided to avoid the damage of the IGBTs, caused due to various faulty conditions. The variable load condition is implemented in the test bench for its application during the proposed methodology assessment as shown in Fig. 2. The current signals are acquired using Hall Effect sensor (CR 5420). All current signals are passed through filter. The current signals from the sensors are collected using TDS1000C-EDU. The 158 samples are collected for each cycle of current signal. The data packets are collected under healthy and all faulty conditions.

3 DQ transformation

The DQ transformation or Park’s vector approach is mathematical transformation. Three phase circuit such as voltage source inverter is simplified by this transformation. In this method, three phase current of inverter (I_a, I_b and I_c is converted into two phase current (i_d and i_q. DQ transformation is given by Equations (1) and (2) [13], $i_{d} = \sqrt{\frac{2}{3}} i_{a} - \frac{1}{\sqrt{6}} i_{b} - \frac{1}{\sqrt{6}} i_{c}$ (1) $i_{q} = \frac{1}{\sqrt{2}} (i_{b} - i_{c})$ (2)

Typical current patterns are obtained by using DQ transformation for healthy and faulty conditions are shown in Fig. 3. For normal operation of IGBTs, pattern is a circle. In case of an open circuit IGBT fault; there are some typical patterns for particular IGBT. The results show that DQ transformation offers potential for single switch open circuit fault classification. But these patterns are not useful for multiple open circuit fault diagnosis. Therefore diagnostic variable and mean value of current are calculated.

4 Multiple open switch fault diagnosis method

This method requires only three phase current as input. For normal condition, three phase VSI gives perfectly balanced three phase sinusoidal current as given in Equation (3). $i_{n} = {\begin{matrix} i_{a} = I_{m} sin (ω_{s} t + φ) \\ i_{b} = I_{m} sin (ω_{s} t - \frac{2 Π}{3} + φ) \\ i_{c} = I_{m} sin (ω_{s} t - \frac{2 Π}{3} + φ) \end{matrix}$ (3)

Where n = a, b, c and I_m is the maximum amplitude of current, ω_s is current frequency and Φ is the initial phase angle. Equation (3) cannot present a normal condition of the current of a VSI. There are harmonics of ω_s; which are filtered using MATLAB code as shown below. The three phase currents with and without harmonics are shown in Fig. 4.

MATLAB code for filter:

windowSize = 10;

ir = filter(ones(1,windowSize)/windowSize,1, i_a);

ib = filter(ones(1,windowSize)/windowSize,1, i_b);

iy = filter(ones(1,windowSize)/windowSize,1, i_c);

4.1 Normalization of three phase currents

The normalization of three phase current is required to avoid the problem of mechanical machine operating condition dependency. This process uses the output of DQ transformation i.e. i_d and i_q. Park’s vector modulus ( $| {\bar{i}}_{s} |$ ) is obtained by using Equation (4) [14], $| {\bar{i}}_{s} | = \sqrt{i_{d}^{2} + i_{q}^{2}}$ (4) When three phase current of inverter is divided by Park’s vector modulus, normalized three phase currents (I_nN) are obtained. It is given by Equations (5) and (6), $I_{nN} = \frac{i_{n}}{| is |}$ (5)

The range of normalized phase currents of three phase inverter is of ±0.8164. $i_{nN} = {\begin{matrix} i_{aN} = \sqrt{\frac{2}{3}} sin (ω_{s} t + Φ) \\ i_{bN} = \sqrt{\frac{2}{3}} sin (ω_{s} t - \frac{2 Π}{3} + Φ) \\ i_{cN} = \sqrt{\frac{2}{3}} sin (ω_{s} t - \frac{2 Π}{3} + Φ) \end{matrix}$ (6)

Where n = a, b, c.

4.2 Average absolute values of normalized current

Three phase normalized current are used to calculate average absolute values by using Equation (7) [14], $\frac{ω_{s}}{2 Π} \int_{0}^{\frac{2 Π}{w_{s}}} {| i}_{nN} | dt = \frac{1}{Π} \sqrt{\frac{8}{3}}$ (7)

4.3 Diagnostic variables

Average absolute values of normalized three phase current are used to calculate diagnostic variable. For each phase, one diagnostic variable needs to be calculated. The errors are calculated by using average absolute values of normalized current. These errors are used to calculate three diagnostic variables e_n (where n = a, b, c), given by Equation (8) [14]. The e_n is calculated to generate fault diagnostic signatures using Equations (12) to (14). $e_{n} = ξ - | i_{nN} |$ (8)

Where ξ is a constant value. The value of ξ is equal to the average absolute value of the normalized phase currents of inverter under normal operating condition which is given by (7). Therefore for three phase, three constants are obtained as given in Equations (9–11). $ξ_{a} = 0.5144$ (9) $ξ_{b} = 0.5173$ (10) $ξ_{c} = 0.5287$ (11)

Diagnostic variables have specific characteristics which are extremely important. All three diagnostic variables take approximately zero value for healthy condition. In faulty condition, at least one of the diagnostic variables becomes positive. If fault is introduced in switch, then diagnostic variable of phase, which contains that switch, takes positive value.

When fault is introduced in switch T1, the normalized current average value and the diagnostic variables of three phase output current are shown in Fig. 5.The diagnostic variable of corresponding phase i.e. e_b increases towards positive value 0.20048. At that time, other two diagnostic variables i.e. e_a and e_c become negative. Results shown in Fig. 5a are experimental results and details of background connected system are given in section 2.

For switches T3 and T6 fault condition, the waveforms of normalized average value of current and the diagnostic variables of three phase are shown in Fig. 6. Diagnostic variable of phase B increases to 0.51 when fault is introduced in switch T3 and T6 which is more than double of value obtained in single switch fault condition. In this condition diagnostic variables of other two phases become negative.

4.4 Average values of current

Diagnostic variables give information about the faulty phase. Diagnostic variables do not carry any information about the faulty switches. Therefore average current of three phases are used with diagnostic variables. Diagnostic variables detect faulty phase and average current identifies faulty switch from that faulty phase. $E_{n} = {\begin{matrix} N if e_{n} < k_{f} \\ P if k_{f} \leq e_{n} < k_{d} \\ P if k_{d} \leq e_{n} \end{matrix}$ (12) $M_{n} = {\begin{matrix} L if 〈 i_{nN} 〉 < 0 \\ H if 〈 i_{nN} 〉 < 0 \end{matrix}$ (13)

Where E_n and M_n are diagnostic variable and average current respectively.

Equations (12) and (13), E_n and M_n are used for fault diagnosis. K_d is used to identify two faulty switches in same phase, whereas K_f is used to detect two faulty switches in different phases. They are established by simply observing the behavior of E_n for various faulty conditions. Equations (12) and (13) create fault signatures as shown below;

IF (E₁==‘P’ && E₂==‘N’ && E₃==‘N’ && Ma==‘L’)

THEN (‘T1 is faulty’)

IF (E₁==‘P’ && E₂==‘N’ && E₃==‘N’ && Ma==‘H’)

THEN (‘T4 is faulty’)

IF (E1==‘P’ && E2==‘P’ && E3==‘N’ && Mc==‘H’)

THEN (T1 & T3 are faulty’)

4.5 Problem statement

Value of K_d is decided by observing maximum value from e_a, e_b or e_c when single switch is faulty. Similarly, K_f is minimum positive value from e_a, e_b or e_c, when two switches are faulty in different phases. The values of K_d and K_f are 0.20210 and 0.00553 respectively for 10 kW active power as shown in Table 2. Due to these logical values, thirteen different faults are detected at 10 kW load power. But the constant values of K_d and K_f are having a problem of misidentifying the faults when load is increased or decreased during faulty conditions, which is summarized in Table 3.

It is trouble-free to detect fault at 10 kW but this system misidentifies the fault at different load conditions. This problem can be solved by changing the values of threshold K_d and K_f with respect to load condition. For different load conditions, threshold values are calculated as shown in Tables 4–6.

The approach to achieve more accuracy in diagnosis method Fuzzy Interference System (FIS) is implemented with three phase current (I_a, I_b and I_c) as inputs and threshold values as output. Further FIS can solve the problem of nonlinear relationship between input current and K_d or K_f. The threshold values, K_d and K_f are decided by two different FISs. FISs are constructed by assembling knowledge of faulty conditions. Fuzzy rules or membership functions are modified by observing response of the diagnosis system. Triangular membership function is used for input and output variables. An algorithm is developed based on IF-THEN rules which tune K_d and K_f with respect to variable load.

4.6 Fuzzy logic block design

4.6.1 Membership function selection

Fuzzification is the process of converting crisp values into fuzzy values. Fuzzy values i.e. fuzzy set is represented by membership function. Fuzzy sets are classified into different types based on the membership function used viz. Normal fuzzy set, Subnormal fuzzy set, Convex fuzzy set and Non-convex fuzzy set. In this work, normalized three phase input current is monotonically increasing hence convex fuzzy set is used. Intuition method is used for assigning membership values. The range of normalized input current and output threshold values are splitted into Very Low, Low, Medium, High and Very High.

4.6.2 Formation of rule base

For any linguistic variable, there are three general forms in which rules can be formed. They are Assignment statement, Conditional statement and Unconditional statement. Assignment statements are used for rule base formation. The assigned values are combined by the assignment operator “=”. The assignment statement has advantages to restrict the values to a specific equality. The example of this type is shown below:

IF (I_amax = LOW && I_bmax = LOW && I_cmax =LOW)

THEN (K_d = Low)

IF (I_amax = HIGH && I_bmax = HIGH && I_cmax =HIGH)

THEN (K_d = HIGH)

4.6.3 Defuzzification

The results obtained by fuzzy system cannot be used as it is in the application, therefore output values are converted in crisp set. This method of conversion is called “Defuzzification” or “Rounding off”. Crisp outputs of threshold values are obtained by centriod of area defuzzification. Equation (14) is used for implementation. $Defuzzification = \frac{\sum P (i) XW (i)}{\sum W (i)}$ (14)

Where i is the number of element, P_(i) is ith element in output membership function and W_(i) is the weight of ith output.

5 Results and discussion

For the variable load condition K_d and K_f should be modified. This is achieved from FIS. FIS is capable to modify threshold values and detect accurate faults under variable load conditions. The calculated values of K_d and K_f by using FIS and manually selected threshold values are shown in Figs. 7 and 8. The graph in the Figs. 7 and 8 shows that, desired threshold values and threshold values calculated by using fuzzy logic are matching very closely. Improved performance of FIS system for higher load condition (more than 15 kW) will be obtained by changing range of input and output variables and by carefully designing fuzzy rules. In the given experiment, classification results are obtained under variable load conditions which have potential in fault diagnosis of single and multiple switches. It is seen that the fault diagnostic accuracy increasenoticeably.

Performance of proposed diagnostic method is evaluated and summarized based on the parameters like accuracy, fault detection time, implementation efforts, packet size and fault detection parameter. System is tested by varying active load power from 5 kW to 15 kW. Results of artificial intelligent based systems are compared with that of proposed diagnostic method. Three methods are implemented for comparison; these methods are Wavelet-Neural Network, Wavelet-Fuzzy and Wavelet-Fuzzy-Neural. The same method of feature extraction is used in above three methods. Three phase output current is sensed and analysis is done by taking each packet of 4 ms. The sampling rate of 2μs is used; hence total 2000 samples are tested at time. 30 statistical features are extracted from detailed coefficients of DWT. DB4 at level 2 is used for feature extraction. The extracted features are converted into cluster and each cluster is assigned to healthy and faulty conditions. Combination of Discrete Wavelet Transform (DWT) and Artificial Neural Network (ANN) is implemented. Clusters are used for training and testing of ANN. In second method, Fuzzy IF-THEN rules are implemented by observing features of detailed coefficients. Triangular membership function is assigned for input and output variables. The centriod of area method is used for defuzzification. In order to improve accuracy of Wavelet-Fuzzy and Wavelet-ANN; output of fuzzy logic is used to train ANN. This method is useful to reduce input data size of neural network.

Accuracy and fault detection time of different methods are shown in Tables 7 and 8 respectively. Accuracy of fault diagnostic system is tested over 87 samples. Out of these 38 samples are collected for healthy condition and 39 samples for a faulty condition. The Wavelet-ANN shows good results for 10 kW load, as it is trained for such condition. It is very difficult to collect training data set at variable load conditions. Some features of detailed coefficients at different faulty conditions are matching with each other or are slight different in coefficients. The accuracy of Wavelet-ANN depends on the training data and network parameters. It is difficult to train ANN for high and light load conditions. Computational complexity is increased due to DWT and huge data size required to train ANN, which increases fault detection time.

In case of Wavelet- Fuzzy, by observing polarities of detailed coefficients, significant accuracy is achieved for classification of single switch open circuit fault. Multiple open circuit fault diagnostics system requires additional number of fuzzy rules. In some faulty cases as mentioned in Wavelet-ANN, features are matching with each other at different conditions. Hence in Wavelet-Fuzzy fault diagnostic system false alarms are increased. The fault detection time required is less as compared to Wavelet-ANN. The computational complexity in case of ANN is more as compared to Fuzzy Logic.

The combination of Wavelet-Fuzzy-Neural is implemented to improve accuracy and reduce fault detection time. The output of Fuzzy Logic is used to train ANN; results of the fault diagnostic system are improved because 30% data is required to train ANN as compared to DWT-ANN method. The considerable accuracy is achieved. But in some cases performance of Fuzzy Logic is very poor and hence Fuzzy-ANN system is used. Detection time of Fuzzy-ANN lies in between Wavelet-Fuzzy and Wavelet-ANN.

In proposed Diagnostic Variable -Fuzzy Logic fault diagnostic system, accuracy at variable load conditions depends on threshold values. Threshold values are carefully selected by using Fuzzy Logic. They are closely matching with manually selected values as shown in Fig. 7. Remarkable accuracy of fault diagnostic system is achieved. The fault detection time of Diagnostic Variable - Fuzzy Logic method is low and it is very close to Wavelet- Fuzzy; as the computational complexity in both systems is same. Thus remarkable accuracy is achieved by reducing detection time.

False alarms against noise can be reduced by selecting higher threshold values but it leads to decreased resistivity of system against noise under light load condition. In this method threshold values are modified at light and heavy load a condition which improves resistivity of the system. During initial transient conditions, resistivity of system is improved by adding dead time of 20 ms. Hence this system has good resistivity against noise.

The comparison based on implementation efforts and packet size is given in Table 9. Diagnostic Variable -Fuzzy Logic fault diagnosis system requires high implementation efforts. Packet of 20 ms is used for analysis as frequency of VSI output current is 50 Hz.

The packet sizes of three methods are 4 ms, which is smaller than the packet size of the proposed method (20 ms). The DWT is able to capture the significant irregular data pattern such as sharp jump in current waveforms, which is important to determine the exact instant of a fault occurrence. Therefore one cycle of 360° can be divided into subcycles of 72° for analysis. The diagnostic methods based on wavelet transform do not require analysis of a complete cycle of 360°. But in case of proposed method, the pattern of DQ transform for healthy condition is circle as shown in Fig. 2a. A complete cycle of current is required to generate such patterns under healthy and faulty conditions. Similarly, diagnostic variables and average current values are calculated using Equations (12) to (13) require a complete cycle otherwise the system will misidentify the faults.

6 Conclusion

This method of fault diagnosis in three phase VSI is based on combination of Diagnostic Variable and Fuzzy Logic. The method is able to detect single and multiple open circuit fault in IGBT. This method is cost effective; it requires only three phase output current of inverter. The average absolute values of current and average values of current are used. Diagnostic variables are calculated for detection of faults and average current is used for diagnosis. This system is more effective under variable load conditions. Fault diagnosis methods based on DWT and artificial intelligence require huge training and testing data, which is very difficult to collect. Fuzzy logic provides precise values of thresholds for variable load conditions. For this reason diagnosis variable and Fuzzy Logic system shows potential in the detection and diagnosis of single and multiple open circuit fault in IGBTs. Classification accuracy can be improved further for heavy load condition by appropriate selection of input and output variables in fuzzy system.

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