Computers and Electrical Engineering 96 (2021) 107481

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Computers and Electrical Engineering

journal homepage: www.elsevier.com/locate/compeleceng

OC fault diagnosis of multilevel inverter using SVM technique and

detection algorithm✩
Kumari Sarita, Sachin Kumar, R.K. Saket ∗
Department of Electrical Engineering, Indian Institute of Technology (BHU), Varanasi (UP), India

ARTICLE INFO ABSTRACT

Keywords: The Open Circuit (OC) faults occurring in switches of Multilevel Converters (MLC) may lead
Fault detection to undesirable operation of the converter. Therefore, fault detection and its localization in
Fault classification minimum time are necessary. This paper focuses on the fast fault detection algorithm based on
Support vector machine
the two samples technique and the fault localization algorithm using the Entropy of Wavelet
Entropy of wavelet packet
Packets (EWP) as a feature. The EWP feature is used to classify and localize the OC faults in
Open circuit fault
IGBTs
Insulated Gate Bipolar Transistors (IGBTs) of three-phase, three-level inverter using Support
Multilevel converter Vector Machine (SVM) based fault classification algorithm. The proposed technique can detect
Two-sample algorithm the fault in single IGBT and multiple IGBTs in a lesser time range of microseconds to 0.33 ms.
It gives better performance and accuracy (99.70%) than previously proposed SVM algorithms,
as the EWP-based feature extraction process used in this paper is simple and accurate with a
less computational burden.

1. Introduction

The reliability assessment of power electronics converters is essential for the secure operation of the converters. The overall
performance and reliability of power system depend on the reliability and performance of its components. The converters and
inverters are crucial components of the electrical power system. The quality of power is improved by implementing various
power electronics-based Flexible AC Transmission System (FACTS) devices that involve power electronic switches [1], and different
optimization techniques are also implemented to improve the power. The quality of power is disturbed with RE penetration due
to the variable outputs and interfacing converters [2]. The fault in the converter’s switches leads to the distorted output current
waveforms [3] and hence results in reduced power quality. The distorted waveforms lead to heating losses in the converters or
may change the response of the system [4]. So, to avoid these distorted waveforms, it requires an adequate operation of converter
switches. The OC faults must be detected and isolated to achieve the switches’ adequate operation in the minimum possible time.
Therefore, fault detection and diagnosis must be reliable and fast. The authors in [5] have discussed the structure of the multilevel
converter for getting fault-tolerant operation of the converter with improved performance.
Neural network-based Multilayer Perceptron (MLP) technique, SVM, Self-Organizing map (SOM), and K-means machine learning
techniques are discussed by the authors [6] to detect and classify the faults. The authors observed that supervised learning-based
algorithms (MLP and SVM) give accurate results during fault detection. The research papers related to fault detection of switches
based on the analysis of voltage characteristics and current signals are discussed in [7–9]. The faults are detected after one or more
than one cycle of the signals with these techniques. The authors [10,11] have used the residual-based detection technique to detect

✩ This paper is for special section VSI-aisg. Reviews processed and recommended for publication by Guest Editor Dr. S. Padmanaban.
∗ Corresponding author.
E-mail addresses: kumarisarita.rs.eee19@itbhu.ac.in (K. Sarita), sachinkumar.rs.eee18@itbhu.ac.in (S. Kumar), rksaket.eee@iitbhu.ac.in (R.K. Saket).

https://doi.org/10.1016/j.compeleceng.2021.107481
Received 18 May 2020; Received in revised form 15 November 2020; Accepted 22 September 2021
Available online 14 October 2021
0045-7906/© 2021 Elsevier Ltd. All rights reserved.
K. Sarita et al. Computers and Electrical Engineering 96 (2021) 107481

the converter’s fault. The fault detection technique, including observer-based residual generation and transient energy derived from
the superimposed components of voltage and current signals, are discussed in [12,13], respectively. These techniques can detect the
fault in less than one cycle of the current signal with a low computational burden, but these techniques cannot provide the faulty
switch location in less time.
The observer-based condition monitoring of converter is discussed in [3,14]. The data information of generated voltage, flux
linkage, and stator resistance of electrical machines are obtained. The electrical machine is connected to the converter, and all
the data information is implemented for the analysis of an observer-based condition monitoring algorithm [3]. The fault detection
technique, with more than two parameters, makes the detection system complex. The authors in [14] have also used a residual
observer-based fault detection algorithm for detecting the converter OC faults. The fault detection time is observed to be in the
range of 15 ms to 20 ms. The time can be decreased by reducing the computational burden involved in the residual calculation for
tripping the faulty switch in the minimum possible time. Also, the detection time should be as minimum as possible.
The authors [6] have discussed the advantages and concepts of the SVM technique, which does not require information on one
complete cycle of current signal when compared with other fault detection techniques, including the current signature method
and Artificial Intelligence (AI) methods. The SVM technique is faster than other proposed techniques because it gives results in
less than half cycle. The fastness and accuracy of fault detection and classification techniques depend on selecting features and its
computational time. A fast feature extraction technique is discussed by the authors [15]. This technique includes Wavelet Packet
Decomposition (WPD), the entropy of wavelet packets in different forms such as Shannon and log wavelet entropy. The feature
extraction technique using the wavelet packet entropy has not been implemented in the previous literature for the fault detection
and classification of the converter’s switches. Therefore, it is required to investigate this technique with its capability of feature
extraction in the fault detection and classification of IGBTs based converters.
An observer-based algorithm based on a single parameter for fault detection is proposed. The parameter is the current signal.
The proposed algorithm takes only current coming out to the inverter. It detects the fault in IGBTs using two samples of the current
signal. The EWP-SVM technique is used for fault classification and localization of faulty IGBTs of the three-phase three-level inverter.
The proposed algorithm can detect the fault in a single IGBT and the fault in multiple IGBTs. The current signals of all three phases
are estimated based on the two-samples algorithm using the load impedance and the output voltage. These estimated signals are
compared with the actual inverter output currents for fault detection. This makes the detection technique faster and accurate than the
other fault detection techniques available in the literature. The comparison of detection time of different supervised and unsupervised
machine learning-based algorithms for fault detection of IGBTs is also discussed. The flow chart of the proposed technique is shown
in Fig. 1. The figure can be divided into three parts: (i) inverter model and current measurement, (ii) OC fault detection, and (iii)
classification and localization of faulty IGBTs. In the first part, the three-phase, three-level inverter model is Simulated, and currents
are measured for fault diagnosis. The second part deals with the detection of OC faults in the IGBTs using a two-samples based fault
detection algorithm. The third part is representing the steps involved in the fault classifications and localization of faulty IGBTs.
The EWP and mean values of the currents are extracted and used as features for training the SVM based fault classifier, and then,
it is validated with the new dataset under different OC faults in IGBTs of the inverter. The SVM algorithm results are the condition
of the IGBTs of the inverter, whether they are working normally. If OC fault has occurred in any of the IGBTs, the SVM algorithm
outputs the location of the faulty IGBTs.
The paper is organized as follows. The problem statement formulated, and the proposed fault diagnosis system is discussed in
Section 2. The methodologies and features extraction techniques, including a two-sample based algorithm, WPD, EWP, and SVM,
are implemented, which is discussed in Section 3. The simulation of the three-phase, three-level inverter, and fault diagnosis system
is explained in Section 4. The results obtained from the simulated fault diagnosis system using the proposed methodology and the
comparison of the proposed technique with the existing literature techniques are discussed in Section 5. Finally, the work done is
concluded with scopes for the future works in Section 6.

2. Problem formulation

The faults in three-phase output lines of converters are easy to identify but detection of OC faults in IGBT switches is complicated
work. The localization of the faulty switches is a more difficult task. The fault in a single switch may lead to undesirable operation
of power electronics-based drives and control systems. Therefore, detection and localization of faults of IGBTs are too essential.

2.1. Problem statement

The fastest OC fault detection techniques observed in literature are observer-based techniques. For minimizing the detection
time in the order of micro-seconds, the algorithm should involve less computational burden. The detection algorithm becomes slow
while considering more processing parameters of the system. Moreover, the selection of features and their extraction is essential
for fault diagnosis. The most commonly used features proposed in the literature include entropy [16], WT [17], mean value, phase
angle [16], and dq0 transformation of the time series current or voltage waveform [16]. These features sometimes do not accurately
detect faults and may result in the wrong classification of faults due to approximately equal values of features under different fault
conditions. This paper proposes a different approach for feature extraction using EWP. It gives accurate results for OC fault detection
of IGBTs of three-phase, three-level inverter. Furthermore, the classification of faults is significant to distinguish between similar
faults. The classification is done using the SVM learning technique. The problem of minimization of fault detection time has also
been resolved. The proposed fault detection technique detects the fault within a few microseconds to 0.33 ms time range.

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K. Sarita et al. Computers and Electrical Engineering 96 (2021) 107481

Fig. 1. Flow chart of the proposed system.

2.2. Proposed fault diagnosis system

The proposed method is simulated and implemented. The significant contributions of this paper and the steps involved in the
proposed algorithm are given as follows.
(i) Simulation of three-phase, three-level IGBTs based inverter model,
(ii) simulation of Sinusoidal Pulse Width Modulation (SPWM) for pulse triggering in the IGBTs,
(iii) fault detection using two samples-based algorithms,
(iv) measurement of three-phase currents of the inverter for features extraction,
(v) extraction of features including EWP and mean of the three-phase currents under different fault conditions generated in the
Simulink model,
(vi) training of SVM model-based fault classification and localization technique,
(vii) validation and testing of the SVM classifier-based trained model for fault classification and localization of the faulty IGBTs,
and
(viii) comparative analysis of proposed algorithm with the available algorithms in the literature used for features extraction and
fault diagnosis.
Fig. 1 shows the schematic diagram of the proposed fault diagnosis system consisting of three phases three-level inverter, current
measurements, fault detection, features extraction, and training of SVM model using the features including EWP and mean of three-
phase currents. The inverter model is simulated with six IGBTs, and pulses for these IGBTs are generated using the SPWM technique.
The three-phase currents are measured at the inverter’s output and sent to two samples-based fault detection algorithm block, which
detects the OC fault. The current signals are also sent to the features extraction block, which computes EWP and means the three-
phase currents’ value. The extracted features of three-phase currents are then used for the training of the SVM algorithm. Afterward,
the trained SVM model is validated for fault classification and localization by generating different IGBTs OC faults in the Simulink
model. The SVM algorithm provides the condition of IGBTs of the inverter and locates the faulty IGBTs if OC faults have occurred.
Fig. 2 shows the schematic diagram for two-samples based fault detection algorithm. The load impedance and the voltage are used
to estimate the current signals using a two-samples based algorithm. Then the actual current signals of three-phases are compared
with the estimated current signals. In Fig. 2, 𝑒𝑎 , 𝑒𝑏 , and 𝑒𝑐 are representing the estimated currents of phases a, b, and c, respectively.
The comparison of estimated and actual signals is made, and the detector represents the difference between the two outputs 𝑑𝑎 ,
𝑑𝑏 , and 𝑑𝑐 , respectively. If the magnitude of any of the detector output is higher than the threshold value of current, it indicates
OC fault or noise spike. The OC fault can be distinguished from the noise spike, as discussed in Section 3.1. The fault diagnosis is
necessary after the fault is detected. The SVM-based fault classification method is used for the fault classification, and localization of
faulty IGBT using EWP and mean of current signals as features. The methodologies including two-samples based OC fault detection
technique, EWP, SVM techniques are discussed in detail in Section 3.

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K. Sarita et al. Computers and Electrical Engineering 96 (2021) 107481

Fig. 2. Schematic diagram for two-samples based fault detection algorithm.

Fig. 3. WPD of a signal into Approximate (A) and detail (D) coefficients up to 3 levels.

3. Proposed methodologies

The detection of OC faults in IGBTs of the converter is done with three-phase output currents of the inverter. The proposed
algorithm is based on processing the two consequent samples of the current signal. In this section, the proposed two samples-based
OC fault detection algorithm is explained mathematically. The methodology of feature extraction from the current signal is also
discussed in Section 3.2. The entropy of wavelet packet is used as the feature for fault diagnosis algorithm using SVM technique.

3.1. Two-samples based fault detection technique

The output current and voltage of the converter give the information of OC faults in the switches. The two-samples based OC
fault detection technique is shown in Fig. 4. The samples of the inverter’s output current are taken for detecting the OC fault in the
inverter’s IGBTs. The peak and RMS values of the signal are estimated using a two-samples algorithm. For this, a window of two
samples is used. When the next sample appears, the old sample of current is shifted out. If the estimated value of RMS current of
the inverter is observed greater than the threshold value, this indicates the inverter’s problem. This is because of either OC fault or
noise. The current threshold value is decided based on the value of load connected and the output voltage. The current is determined
as the ratio of voltage to the load; the current is calculated each time the load changes, and the current threshold value also changes
accordingly. The problem is to distinguish between noise and OC fault. Due to noise, the signal’s RMS value may increase and may
result in the false operation of the OC fault detector. A fault counter is set to overcome this problem, which is incremented when
the RMS value is larger than the current threshold value and decremented when the RMS current value is lesser than the current

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K. Sarita et al. Computers and Electrical Engineering 96 (2021) 107481

Fig. 4. Flow chart of two-samples based OC fault detection algorithm.

threshold value. If the counter crosses a particular set limit of counts, it indicates that OC fault in the inverter switches. This way,
the OC fault is detected. The threshold count value is chosen as per the severity of noise at the inverter output current. Therefore,
the effect of transient and noise can be distinguished from OC faults using the proposed algorithm.
Mathematical model of two samples-based algorithm is as follows. The three-phase currents of the inverter are 𝑖𝑎 , 𝑖𝑏 , and 𝑖𝑐 ,
respectively. The current of phase-a is taken for the development of mathematical model of the two-samples based algorithm. The
expression of current of phase-a for 𝑘𝑡ℎ time instant is given in Eq. (1). The expression of same current for (𝑘 + 1)𝑡ℎ time instant is
given in Eq. (2).

𝑖𝑎 (𝑘) = 𝐼𝑎𝑚 𝑠𝑖𝑛(𝜔𝑡𝑘 ) (1)

𝑖𝑎 (𝑘 + 1) = 𝐼𝑎𝑚 𝑠𝑖𝑛(𝜔(𝑡𝑘 + 𝛥𝑡)) (2)

On simplifying Eq. (2), the simplified expression is given in Eq. (3).

𝑖𝑎 (𝑘 + 1) − 𝑖𝑎 (𝑘)𝑐𝑜𝑠(𝜔𝛥𝑡)
= 𝐼𝑎𝑚 𝑐𝑜𝑠(𝜔𝑡𝑘 ) (3)
𝑠𝑖𝑛(𝜔𝛥𝑡)
On adding the squares of Eqs. (1) and (3), and simplifying the expression, the simplified expression of the resulting equation is
given in Eq. (4). The estimated peak value of current of phase-a is given in Eq. (5).

2 (𝑖𝑎 (𝑘))2 + (𝑖𝑎 (𝑘 + 1))2 − 2𝑖𝑎 (𝑘)𝑖𝑎 (𝑘 + 1)𝑐𝑜𝑠(𝜔𝛥𝑡)

𝐼𝑎𝑚 = (4)
𝑠𝑖𝑛2 (𝜔𝛥𝑡)
√
(𝑖𝑎 (𝑘))2 + (𝑖𝑎 (𝑘 + 1))2 − 2𝑖𝑎 (𝑘)𝑖𝑎 (𝑘 + 1)𝑐𝑜𝑠(𝜔𝛥𝑡)
𝐼𝑎𝑚 = (5)
𝑠𝑖𝑛2 (𝜔𝛥𝑡)
The frequency (f) of the current signal is 50 Hz, and the Oversampling Factor (OF) is taken as 200 such that the sampling
frequency of the signal becomes 2 ∗ 𝑂𝐹 ∗ 𝑓 Hz. The OC fault detector signal is constructed using the proposed two samples-based
algorithm for all three-phase currents for monitoring the IGBTs of the inverter. The difference between the estimated detection
current signal and the inverter’s original current signal indicates OC fault in the IGBTs. The constructed signal using the values

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K. Sarita et al. Computers and Electrical Engineering 96 (2021) 107481

Fig. 5. (a) Estimated current of phase-a of the inverter, (b) Original current of phase-a of the inverter under multi-IGBTs OC faults at S1 and S5.

Fig. 6. (a) OC fault detection by comparing estimated and original current signals, (b) The difference of actual and estimated current signal, fault occurring
and alarm generation.

of loads, voltage, frequency, and estimated peaks is shown in Fig. 5(a). The original phase-a current of the inverter is shown in
Fig. 5(b). The OC fault has occurred in the IGBTs S1 and S5 in the time interval of 0.4011 to 0.5011 s. The difference between
peak values and rms values of the estimated signal and the original signal indicates OC faults. The setting of the threshold limit is
dependent on various factors, including the type of loads, noise spike range, and application range. This paper selects a threshold
value after investigating the difference coming in the current amplitude during OC faults in the IGBTs. When the estimated current’s
peak value differs with a magnitude more significant than the threshold value of 20 A [18], the OC fault is detected, and a fault
detection alarm is generated, as shown in Fig. 6(a). The threshold value may differ as per the factors mentioned earlier. After the
fault is removed, the alarm is automatically turned off if the difference between the inverter current signal and the estimated current
signal does not cross the threshold limit for one complete cycle. The difference between the estimated signal and the actual signal,
along with alarm generation, is shown clearly in Fig. 6(b).

3.2. Features extraction technique

There are various feature extraction techniques available in the previous literature. These techniques still have some compu-
tational complexity, and some are even not fast and accurate. Some of these are always in need of research and development for
improving accuracy. In this era, the entropy-based feature extraction technique gives accurate results when it is used for fault
detection and classification problem. Entropy’s performance as a feature of the signal is better than other statistical techniques,
including maximum–minimum values, mean values, WT coefficients, Principal Component Analysis (PCA), etc. The entropy-based
features extraction technique involves calculating the uncertainty and complexity occurring in the signal during a fault condition.
In this section, the decomposition of wavelet packets (WP) and entropy feature extraction are discussed as follows.

3.2.1. Wavelet Packet Decomposition (WPD)

WPD is used to extract any signal feature by calculating energy at each node of the WP decomposed. The WPD technique helps
to improve the time–frequency resolution, which is not possible by DWT. In WPD, the features are selected by calculating the
energy of coefficients of the decomposed wavelet packets at each node. The approximate and detailed coefficients of wavelets are

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K. Sarita et al. Computers and Electrical Engineering 96 (2021) 107481

decomposed in a sequence up to a level specified. Fig. 3 shows the decomposition of a signal up to three levels. In this way, if the
level of decomposition is N, then the signal is decomposed into 2𝑁 parts of different frequencies [15].
The decomposed wavelet packets are represented in the form of coefficients sequence functions of approximate and detailed
parts of the signal. If p(k) and q(k) are the coefficients of approximate and detailed parts of the signal s(t) and length of both, the
coefficients are 2N. Then, the WP of the signal can be represented as sequence functions of p(k) and q(k) as given by (6) and (7).
√ 2𝑁−1
∑
𝑠2𝑛 (𝑡) = 2 𝑝(𝑘)𝑠𝑛 (2𝑡 − 𝑘) (6)
𝑘=0
√ 2𝑁−1
∑
𝑠2𝑛+1 (𝑡) = 2 𝑞(𝑘)𝑠𝑛 (2𝑡 − 𝑘) (7)
𝑘=0

where, n is the integer number (0, 1, 2,..). For n=0, the signal function is called as scaling function and when the value of n is 1,
the sequence gives first wavelet function. The WP sequence function can be represented as given in (8).

𝑊 𝑃𝑖,𝑛,𝑘 (𝑡) = 2−𝑗∕2 𝑠𝑛 (2−𝑗 𝑡 − 𝑘) (8)

In (8), n is equal to 0, 1, 2, . . . , (2𝑗

− 1) and this equation satisfies the scaling and WP functions. The terms k, j, and n are used to
represent the localizing, scaling, and modulating parameters, respectively. The function represented in (8) is modeled mathematically
using these parameters for analyzing the fluctuations occurring in the signal. This analysis is done for checking the condition of
the signal under different operating conditions at position 2𝑗 .𝑘, where j is the scaling term at different frequencies of approximate
and detailed packets corresponding to a particular value of n. When the signal s(t) is decomposed into WP, its WP coefficients are
calculated as the inner product of the signal s(t) and corresponding WP function of the signal as given in (9).
𝐶𝑗,𝑛,𝑘 = 𝑖𝑛𝑛𝑒𝑟𝑝𝑟𝑜𝑑𝑢𝑐𝑡(𝑠(𝑡), 𝑊 𝑃𝑗,𝑛,𝑘 (𝑡))
(9)
𝐶𝑗,𝑛,𝑘 = 𝑠(𝑡)𝑊 𝑃𝑗,𝑛,𝑘 (𝑡)𝑑𝑡
∫
The WP coefficients in (9) gives a measure of frequency in the signal s(t). These coefficients are represented as WP nodes with a
particular frequency band and used as features of the signal s(t). When phase current of the inverter is passed through WP function
to find the coefficients 𝐶𝑗,𝑛,𝑘 , many coefficients are obtained, which are features at each node of the signal. The features are collected
and combined in a single function so that single information can be formed with these coefficients without any loss of information
of any coefficient. An entropy function is used to combine these coefficients for getting single information from a large number of
coefficients.

3.2.2. Entropy of Wavelet Packet (EWP)

Entropy is found to be a very good tool for feature extraction of the faulty signal. The EWP gives information about the stored
energy of the signal. If s is the signal and 𝑠𝑖 is signal coefficient on an orthogonal basis. Then, the entropy (S) must be additive
∑
function i.e. S(0)=0 and S(s)= 𝑁 𝑖=1 𝑆(𝑠𝑖 ). There are different forms of entropy available in the literature involving Shannon, log
energy, threshold, etc. [15,19–21]. The normalized form of Shannon entropy is expressed as given in (10). Shannon entropy is
helpful in the analysis of uncertainty and also the complexity of the probability distribution.

∑
𝑁
𝑆(𝑠) = − 𝑠2𝑖 𝑙𝑜𝑔(𝑠2𝑖 ) (10)
𝑖=1
∑
where, 𝑠2𝑖 (𝑖 = 1, 2, … ., 𝑛) denotes the probability density with 𝑠2𝑖 >= 0 and 𝑠2𝑖 = 1. The EWP of the signal s can be expressed as
given in (11).
∑
𝑛
𝑊𝑠 = − 𝑠2𝑖 (𝑖)𝑙𝑜𝑔𝑠2𝑖 (𝑖) (11)
𝑖=1

where, 𝑠2𝑖 represents the wavelet packet energy distribution. Another type of entropy that is used commonly is log energy-based
entropy as given in (12).
∑
𝑛
𝑊𝑙𝑜𝑔 = − 𝑙𝑜𝑔(𝑠2𝑖 ) (12)
𝑖=1

For the decomposed wavelet packets, the entropy is computed using (11) and (12). These equations’ entropy values are used as
features for training the SVM algorithm to detect and classify the converter switch faults. The use of entropy values gives an
advantage of a reduced number of features and less computation.
It is observed that entropy can compute and detect the uncertain changes in the signal easily. Out of the three types of entropy
mentioned above, Shannon’s entropy is used for calculating the EWP of each node of the signal WP. It is done by creating a MATLAB
function. The function computes EWP using the WP coefficients as calculated in (9). The (13) represents the function to calculate
EWP using the calculated coefficients in (9). In this equation, j is the length of decomposition or the level of decomposition, and L is

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Table 1
Features extracted from three-phase currents under different conditions.
𝐸𝑎 𝐸𝑏 𝐸𝑐 𝑚𝑎 𝑚𝑏 𝑚𝑐 Condition
212824.1 232767.1 230627 0.024232 0.099569 −0.1266 Normal
−528036 226000.2 223641.4 −2.41677 0.022212 −0.09882 S1Fault
206616.5 228515.1 −512955 0.108387 0.038223 2.320638 S2Fault
208682.5 −503301 227831.4 0.107576 −2.38199 −0.20357 S3Fault
−489986 229893.9 227801.7 2.487486 0.065952 −0.15011 S4Fault
203742.8 226072.3 −490194 −0.02133 0.071495 −2.42589 S5Fault
203918.3 −505414 225215.3 0.012456 2.424408 −0.03163 S6Fault
−541682 228799.7 −516510 −2.39018 0.029873 2.320632 S1S2Fault
−499737 −511318 229168.4 2.463128 −2.3676 −0.17466 S3S4Fault
203585.4 −511364 −506902 −0.02416 2.421913 −2.39152 S5S6Fault
209336.5 −506869 −526074 0.111277 −2.37858 2.292185 S2S3Fault
206375 −512002 −487274 −0.02193 −2.3476 −2.47528 S3S5Fault
−504716 −501638 227688 2.415644 2.459758 −0.04989 S4S6Fault
−495512 231168.1 −516056 2.461062 0.091045 2.326121 S2S4Fault
−527081 227833.8 −493525 −2.44417 0.031784 −2.42567 S1S5Fault
−535658 228281.2 −1351997 −2.4254 0.037347 0.000436 S1S2S5Fault
−514149 −507588 −511426 2.396325 2.455514 −2.39738 S4S5S6Fault
−547141 −505682 −527545 −2.38914 −2.37902 2.2975 S1S2S3Fault
204093.7 −1352887 −506057 70.091661 0.00027 2.347946 S2S3S6Fault
−410077 −392293 −399118 −2.41984 −2.37021 −2.48568 VsUpperFault
−381581 −373640 −390125 2.44328 2.481177 2.337141 VsLowerFault

the number of WP coefficients in each node for j level WPD with n = 0, 1, 2, . . . ., (2𝑗 − 1). The calculated EWP values of three-phase
currents of the inverter are tabulated in Table 1 for different fault conditions.
∑
𝐿
2
𝐸𝑊 𝑃𝑗,𝑛 = − 𝑙𝑜𝑔(𝐶𝑗,𝑛,𝑘 ) (13)
𝑘=1

The present work’s main objective is to propose a fast and more accurate fault detection and classification technique. The
accuracy, along with fastness, is possible with a less computational process in features selection and fewer features, indicating
the faults effectively and accurately. For this, the paper proposes a technique including the concept of fault detection using two
samples of the monitoring signal, EWP, and SVM to detect and locate the faults in switches of IGBTs based converter in very less
time.
The features extracted from the three-phase currents of the IGBTs based converter under different fault conditions are tabulated
in Table 1. The EWP of three-phase currents are calculated using the formula given in (13) and tabulated in Table 1 as Ea, Eb,
and Ec for phases a, b and c, respectively. Along with entropy, the mean is also calculated to improve the SVM fault detection
algorithm’s performance. The mean of the three-phase currents is calculated by using the formula as given in (14). In this equation,
𝑚𝑎 , 𝑚𝑏 , and 𝑚𝑐 are the mean values of currents of phases a, b and c, respectively, and N is the number of samples taken.
∑
𝑚𝑎 = 𝑖𝑎 ∕𝑁
∑
𝑚𝑏 = 𝑖𝑏 ∕𝑁 (14)
∑
𝑚𝑐 = 𝑖𝑐 ∕𝑁

4. Simulation studies

The simulation model of a three-phase, three-level inverter consisting of six IGBTs switches are used to implement the proposed
OC fault diagnosis technique. The inverter switches are triggered using the SPWM model, which is also simulated in the same
Simulink. The Simulink model of the fault diagnosis system is shown in Fig. 7 consisting of inverter block, features extraction
block, SVM based-algorithm block, and fault diagnosis outputs. Various combinations of open circuit faults are simulated, as given
in Table 1. When the simulation is run under normal and different fault conditions, the fault detection output blocks indicate the
condition of each of the fault combinations made in the simulation during the training process. The features are extracted from
the three-phase currents using the equations discussed in Section 3. These features are then passed through the SVM-based fault
classifier, which is already trained with the training data shown in Table 1. The fault detection block shows the output of the fault
diagnosis algorithm. The particular fault condition is indicated by ‘1’, and others are shown as ‘0’. For example, if the Simulink is
run under normal condition, the fault detection system outputs ‘Normal’ block as ‘1’ and others as ‘0’.
Three-phase output currents of the proposed three-phase, three-level inverter are illustrated in Fig. 8. The current and voltage
waveforms are smooth under the normal operating conditions of the inverter. The EWP values and mean values of all three-phase
currents are computed. The MATLAB functions are formed, which consist of the mathematical formulas of EWP and mean values
of three-phase currents given in Section 3. The outputs of these functions are used as features for the SVM algorithm. One more
function is created, which consists of the SVM algorithm requiring features data as input and giving converter operation condition
and switch condition as output. To get the proposed simulation model’s desirable performance, firstly, the model is trained for

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Fig. 7. Simulink model of the fault diagnosis system.

Fig. 8. Three-phase output currents of the 3-phase, 3-level inverter under normal condition.

different fault conditions. The simulation model is run under different possible faults, including a single IGBT fault, multiple IGBTs
faults, and supply line fault. The current measurement data is used to extract the features to train the SVM model for fault diagnosis.
After training the SVM algorithm, it is validated for different faults in the converter. During validation and testing of the proposed
algorithm, it is observed that it is giving correct fault detection results. The fault detection outputs under normal and different fault
conditions of IGBTs are discussed in Section 6.

5. Results and discussion

The current waveforms change when OC faults occur in the IGBTs of the inverter. The EWP is also different for current waveforms
under normal and fault conditions. The fault detection system outputs and three-phase currents under OC fault in single IGBT (S1)
and under OC faults in multiple IGBTs (S1, S2, and S5) are shown in Fig. 9 and Fig. 10, respectively. These figures are showing that
the fault in a particular switch is detected in less time (microseconds range) when the switch comes into action. All three-phase

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K. Sarita et al. Computers and Electrical Engineering 96 (2021) 107481

Fig. 9. (a) Three-phase currents and (b) OC fault detection for single IGBT (S1) fault.

Fig. 10. (a) Three-phase currents and (b) OC fault detection for multiple IGBTs (S1, S2, S5) faults.

currents are monitored individually so that whenever OC fault occurs in IGBTs, it can be detected in minimum possible time. For
example, if OC fault occurs in S3, the phase-a current will reflect it after a few seconds, but it will be reflected in the phase-b
current earlier. Therefore, all phase currents are monitored using a two-samples based fault detection algorithm. The OC fault
detection output using the currents of phase-b and phase-c are shown in Fig. 11 and Fig. 12, respectively. It is clear from Fig. 11,
that the magnitude of currents of phase-b and phase-c decrease under OC fault in the S1 switch. The differences in the magnitude
of currents of phase-b and phase-c with the estimated signals of phase-b and phase-c using the two-samples technique reflect the
OC fault in the IGBT of the inverter. However, the effect of S1 OC fault in phase-a current is dominant, and a large difference is
visible in phase-a current as compared to the currents of phase-b and phase-c. Similarly, for OC faults in other IGBTs, the effect is
detectable in a better way in phase-b and phase-c currents. Therefore, a two-samples-based OC fault detection technique is applied
to the currents of all three-phases to detect the fault in the minimum possible time.

5.1. Fault diagnosis using EWP-SVM technique

The SVM model is showing accurate result during training time when EWP is used as a feature for fault classification. Also, while
validating the model, it is giving accurate fault diagnosis and classification results as shown in Fig. 13.
The types of OC faults considered for validating the proposed algorithm include six single IGBT OC faults, twelve multiple IGBTs
OC faults, and two source terminal OC faults. During validation of the proposed technique of fault diagnosis, the particular class of
OC fault is detected correctly, and the faulty IGBTs are localized accurately with an overall accuracy of 99.70%. Further, the model
is validated with the training dataset of the features; the accuracy is obtained 100% as shown in Fig. 13.

5.2. Comparison between Proposed Technique and existing techniques

In this section, various OC fault detection techniques available in the literature are compared with the proposed two-samples
based detection technique. A comparison is also made among the simple entropy and EWP methods of feature extraction. Comparing
the proposed technique for detection and localization of OC faults in IGBTs of the converter with the other techniques is described.

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K. Sarita et al. Computers and Electrical Engineering 96 (2021) 107481

Fig. 11. OC fault detection output with current of phase-b under (a) OC fault in S1 and (b) OC faults in S1, S2, and S5.

Fig. 12. OC fault detection output with current of phase-c under (a) OC fault in S1 and (b) OC faults in S1, S2, and S5.

Fig. 13. Classification results using proposed EWP-SVM technique.

5.2.1. Fault detection techniques

The important factor in fault diagnosis is the minimization of fault detection time. The literature shows that the fault detection
time is less than or equal to the half cycle of the fault waveform using the DWT-SVM technique. The fault detection time in a
decreasing manner is as follows: The PCA-MRVM technique gives fault detection result in more than one cycle of samples data;

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K. Sarita et al. Computers and Electrical Engineering 96 (2021) 107481

Fig. 14. Classification results using simple entropy as feature extraction.

the ESO technique takes 150 ms, Kalman filter, and sliding mode observer techniques takes 100 ms and 50 ms, respectively. In the
previous literature, the fastest fault detection technique proposed is the ESO technique, which compares the measured and theoretical
values of full-arm voltage for fault detection in less than 15 ms. The technique was applied for the detection of the faulty sub-module
in the modular multilevel converter. The technique was not implemented for switch fault detection of the multilevel converter. The
other observer-based fault detector is also studied in the literature survey, which involves complex calculations and computational
burden. With the proposed EWP-SVM technique, the fault is detected before a one-quarter cycle of the fault current waveform. In
fact, the OC fault is detected in the smallest time span by using the two consequent samples of the current signal, which is less
time than the time of detection using other techniques proposed in the literature as tabulated in Table 2. The proposed algorithm
can detect the fault in a single IGBT, faults in multiple IGBTs, and fault in supply. The fault detection system is reliable and faster
with the proposed technique. It is also observed that EWP is giving accurate OC fault diagnosis results as compared to other feature
extraction method including PCA, WT, SMO, and ESO.

5.2.2. Fault diagnosis techniques

In many papers in previous literature, simple entropy and mean have been implemented for fault diagnosis algorithm. Fig. 14
shows the fault diagnosis result when these features are used in a three-phase three-level inverter simulation model. From Fig. 14, it
is observed that there is a wrong classification issue in this case because the entropy values of signals under different fault conditions
and normal conditions are approximately equal. The model is getting confused in classifying the fault from normal condition or one
class’s fault from another. The entropy values of three-phase currents under single IGBT (S1) OC fault conditions are found to
be approximately equal to that of the entropy values under S1S2S5 fault. Therefore, the fault diagnosis output under S1 fault is
showing faults in S1, S2, and S5 switches together. Similarly, the entropy of three-phase currents under S2 faults is approximately
equal to that of currents’ entropy under S2S3S6 faults. Therefore, the S2 switch’s fault is detected as S2, S3, and S6 faults together
as tabulated in Table 3. Due to these types of wrong classification issues, the fault detection algorithm’s accuracy using simple
entropy is approximately 66 percent when validated for 21 different conditions of the IGBTs, as mentioned in Table 1. Therefore,
an alternative approach based on the EWP feature is proposed for accurate fault localization as shown in Fig. 13.
Hence, from the comparative analysis, the EWP method gives better results than simple entropy. The EWP is enough for fault
detection, but the mean value is also considered for the mean value technique’s performance analysis in fault detection. It is observed
that mean and EWP together are giving better and accurate results as compared to mean and simple entropy together. While
implementing the EWP technique in any diagnosis system can be used alone for accurate fault detection to reduce the computational
burden.

6. Conclusions and scopes for the future work

The proposed two-samples based OC fault detection technique is found to be fast and accurate. The OC faults are detected
in less than 0.33 ms. The paper has discussed the EWP-SVM technique, which can diagnose the fault in a single IGBT, multiple
IGBTs, and OC fault in the supply terminals. For feature extraction, the EWP technique is more accurate and simple with a less
computational burden as compared with the other observer and PCA based features extraction techniques. SVM algorithm gives
accurate fault diagnosis results using the three-phase currents using the EWP feature because only one feature of currents is used,

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K. Sarita et al. Computers and Electrical Engineering 96 (2021) 107481

Table 2
Fault diagnosis results using Simple Entropy-SVM technique.
Actual fault Fault detected
S1 S1S2S5
S1S2 S1S2S5
S1S2S3 S1S2S3
S1S2S5 S1S2S5
S1S5 S1S5
S2 S2S3S6
S2S3 S2S3S6
S2S4 S2S4
S3 S3S5
S3S4 S3S4
S3S5 S3S5
S4 S4
. .
. .
. .
. .
S3S6 S3S5

Table 3
Comparison of fault detection time of different techniques.
Technique Detection time (ms) Reference
Extended State Observer (ESO) 150 [22]
Kalman Filter 100 [23]
Sliding Mode Observer (SMO) 50 [24]
Wavelet-RBFNN less than half cycle of current waveform [15]
PCA-mRVM more than one cycle [25]
Residual-based observer 15–20 [14]
2 sample-EWP-SVM Technique less than 0.33 ms Proposed Technique

which is entropy. The proposed EWP-SVM technique is fit for implementing a fault diagnosis system to get reliable and faster
fault detection schemes. The results show that SVM with simple entropy and energy resulted in the wrong classification in fault
diagnosis, which has been avoided by implementing the EWP-SVM technique. The mean value of the signal under a fault condition
is also different from its value under normal conditions. Thus mean value alone cannot be used as a feature in fault classification
algorithm because of the similarity of signals under different fault conditions. Therefore, it is used along with the EWP feature for
better performance of the proposed algorithm. The detection time of the OC fault of IGBTs-based converter can be further decreased,
and accuracy can be improved with other supervised based machine learning techniques or by combining the SVM technique with
other feature extraction techniques. The level of signal to noise ratio and other transient effects that can be avoided by the proposed
detection technique with different types of loads can be analyzed for checking the reach of the proposed technique.

Declaration of competing interest

No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending
conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.compeleceng.2021.107481.

Acknowledgment

The authors thank the Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi,
India, for providing the support and facilities of the laboratory for the accomplishment of this research work.

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Kumari Sarita is currently pursuing a Ph.D. in Electrical Machines and Drives from Electrical Engineering, Indian Institute of Technology (BHU), Varanasi, Uttar
Pradesh, India. Her current research interest includes renewable energy resources, predictive maintenance of electrical equipment, and power system reliability.

Sachin Kumar is an Assistant Professor in the Department of Electrical Engineering, Govind Ballabh Pant Institute of Engineering & Technology, Ghurdauri,
Pauri Garhwal (UK) India. He is currently a doctoral research scholar in the Department of Electrical Engineering, IIT (BHU), Varanasi (UP) India. His interest
includes reliability engineering, power system reliability, renewable energy systems, and green energy conversion systems.

R.K. Saket is currently a Professor with the Department of Electrical Engineering, IIT (BHU) Varanasi, Varanasi, India. He is a Fellow of the Institution of
Engineers, India, SMIEEE, USA, MIET, U.K., and a Life Member of the Indian Society for Technical Education, New Delhi, India. He is an Editorial Board Member
of the Engineering, Technology and Applied Science Research, Greece.

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