FPGA-based fault analysis for 7-level switched ladder multi-level inverter using decision tree algorithm

International Journal of Reconfigurable and Embedded Systems (IJRES)
Vol. 12, No. 2, July 2023, pp. 157~164
ISSN: 2089-4864, DOI: 10.11591/ijres.v12.i2.pp157-164  157
Journal homepage: http://ijres.iaescore.com
FPGA-based fault analysis for 7-level switched ladder
multi-level inverter using decision tree algorithm
Nithya Ramalingam, Anitha Thiagarajan
Department of Electronics and Instrumentations, Faculty of Engineering, Annamalai University, Chidambaram, India
Article Info ABSTRACT
Article history:
Received Sep 12, 2022
Revised Dec 26, 2022
Accepted Jan 14, 2023
The proposed method involves the fault analysis of the inverter switches
present in the multi-level inverter (MLI) circuitry. The decision tree machine
learning algorithm is incorporated for the fault analysis of the inverter
switches. The multi-level inverter utilized in this work is a 7-level switched
ladder multi-level inverter. There is 4 number of switches in the design of a
7-level inverter driven by the non-carrier digital pulse width modulation
signals. The non-carried-based digital pulse-width modulator (DPWM)
generation is generated using the event angle for the 7-level of the switched
ladder inverter. The proposed method investigates the stuck-at-fault
occurrences of the 4 switches in the inverter by manipulating the decision
tree parameters such as entropy, information gain, and decision tree. Based
on the decision tree, the very high-speed integrated circuit hardware
description language (VHDL) code is developed by making use of the
behavioral modeling and validated for the power, area in the Xilinx Vivado
tool. The real-time feasibility is verified for the proposed method by
synthesizing the developed VHDL code in the field programmable gate
array (FPGA) device.
Keywords:
Decision tree algorithm
Fault analysis
Field programmable gate array
Switched ladder inverter
Switching angle method
This is an open access article under the CC BY-SA license.
Corresponding Author:
Nithya Ramalingam
Department of Electronics and Instrumentations, Faculty of Engineering, Annamalai University
Annamalai Nagar, Chidambaram, Tamil Nadu 608002, India
Email: nithyaramalingam1989@gmail.com
1. INTRODUCTION
The multi-level inverter is a power converter that converts DC to AC voltage and is used in many
industrial applications. Conventionally, the multi-level inverter (MLI) circuits were driven by the static DC
source with its performance based on the topology, driving sources, switch types, pulse width modulation
(PWM) generation, and control algorithm. In real-time, the advent of renewable resources provided the
opportunity to prominently use power inverters. Though the power inverters were used, the fault occurrence
in the circuitry is a major issue that affects the performance of the power applications. To overcome these
faulty circuits, several soft computing techniques and bio-inspired algorithms were utilized, but the accuracy
of the fault identification was low and demanded enhancement for real applications.
Artificial intelligence techniques such as deep learning and machine learning algorithms are used in
recent times to precisely detect faults in power systems. The fault analysis for photovoltaic (PV) systems can
be achieved by using the machine learning algorithm [1]. Machine learning algorithms are used to find the
faults of switching devices in the PV system with fewer computations [2], [3]. To fasten the error detection in
the PV system, deep learning can be considered that includes the equilibrium optimizer algorithm and long
short-term memory (LSTM) in real-time implementation [4]. The decision tree is suitable for the fault
analysis of the non-linear behavior of the PV modules [5].

 ISSN: 2089-4864
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Ensemble learning is utilized for the feature extraction and phase selection for grid-connected PV
systems [6]. The performance of the grid-connected PV systems is enhanced by developing the ensemble
learning-based fault identification algorithm considering the dynamic nature of the solar panel [7]. The full
processing system that consists of a photovoltaic power station can identify the fault occurrence on the run
using machine learning algorithms [8]. The output voltage timing waveforms of the closed-loop PV grid-
connected inverters are monitored for faults in working conditions using the insulated gate bipolar transistor
(IGBT) open-circuit fault diagnosis [9].
To optimize the open circuit faults in the inverter topology design, machine learning techniques are
tried rather than extracting the fault harmonic of the switch [10]. By utilizing the supervised machine
learning algorithm, the fault occurrence can be identified using the k-nearest neighbors (KNN) algorithm, and
prediction for the next step in the inverter input voltage can be achieved through the LSTM algorithm [11].
The power system parameters are forecasted by artificial intelligence to eradicate the sudden flow of current,
power failure, and current leakage in industrial drives [12]. The line location and variable impedance faults
happening in the transmission line connected inverter-generator can be diagnosed using the machine
learning-based technique [13]. The faulty phases are extracted by the Pearson correlation coefficient-based
technique for the micro-grid fed inverter based generator [14]. The classification and regression tree (CART)
method can be utilized for the fault location of a single-phase grounding in real-time power converters [15].
The DC faults can be analyzed using the teager-kaiser energy operator algorithm which has low computation
time and complexity [16].
The fault detection in power electronics systems is fused with short-time fourier transform to
examine the three-phase inverters [17]. The switching faults are tested for tolerance to affirm the durability of
the multi-level inverter [18]. The fault identification is performed with the cascaded H-bridge multilevel
inverter (CHMLI) circuit using the deep convolutional neural network through imaging [19]. The 7-level
multi-level inverter is diagnosed for faults using the cuckoo search algorithm with radial basis function is
advantageous for prediction [20]. The AC/DC interleaved boost converter is checked for output ripple faults
using the artificial neural network (ANN) model [21]. The open-circuit faults of IGBT can be located using
the accuracy-weighted random forest algorithm [22].
To implement the fault analysis method, several digital controllers are available, but the field
programmable gate array (FPGA) is used for the real-time control of the power inverters. The very high
speed integrated circuit hardware description language (VHDL) code is developed for the digital pulse-width
modulator (DPWM) generation and its control of the DC-DC voltage regulator and implemented in the
FPGA for real-time validation [23] The FPGA-based control for the PV-fed DC-DC-AC converter gives
accuracy and low total harmonic distortion (THD)% in the implementation of 81-level MLI [24]. The FPGA-
based neuro-genetic algorithm for backward propagation of neural networks can be used for fault detection in
induction motor drives [25]. This paper deals with the analysis of the fault that occurs in the switches of the
switched ladder type MLI circuit using the decision tree algorithm implemented in the FPGA device. The
next section discusses the working of the proposed algorithm in detail.
2. PROPOSED METHOD: DECISION TREE-BASED FAULT ANALYSIS FOR MLI
The proposed method identifies the fault in the level-7 switched ladder multi-level inverter using the
decision tree machine learning algorithm. Level 7 consists of 3 levels each in a positive and negative cycle
and a zero level in the AC output. The switched ladder inverter uses the trinary pattern for the inputs of the
DC voltages. For the level-7 starter lightning and ignition (SLI), the switching voltages are 1 V, 3 V, -1 V,
and -3 V which constitute the four switches namely SW1, SW3, SWb1, and SWb3 respectively. The switch
patterns are generated for the four switches based on the 12 switching angles that are generated by the half
height-switching angle method (HH-SAM) algorithm. The four switch patterns for the 7-level SLM are given
in Table 1. The topology of the 7-level switch ladder multilevel inverter (SLMLI) utilized for this work is
depicted in Figure 1. The voltage pattern is given in trinary form for each ladder stage of the inverter. The
proposed 7-level SLMLI utilizes only 8 switches to attain the required output of the MLI circuit. Also, there
is no need for carriers for the generation of PWM signals as compared to the cascaded based reversing
voltage inverter circuit [26]. Though the reverse voltage inverter uses 10 switches for the 15-levels, the
proposed Switched Ladder Trinary Multi-Level Inverter (SLTMLI) uses only 8 switches and is more precise
in the generation of the 15-levels [27].
The four switch patterns are represented by the decimal equivalent considering the SW1 as the most
significant bit (MSB) and SWb3 as the least significant bit (LSB). Thus the switches SW1, SW3, SWb1, and
SWb3 are manipulated for the used states namely 0, 1, 2, 4, 6, 8, and 9. The remaining equivalent values such
as 3, 5, 7, 10, 11, 12, 13, 14, and 15 are destinated as unused states. The data set for identifying the switching
table is developed as per the used and unused states. The used states are considered to be valid with the

Int J Reconfigurable & Embedded Syst ISSN: 2089-4864 
FPGA-based fault analysis for 7-level switched ladder multi-level inverter … (Nithya Ramalingam)
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decision of “YES” designated as ‘Y’ and the unused states are taken as invalid with the decision of “NO”
designated as ‘N’. The decision tree algorithm is utilized in this work to identify the switching faults of the 7-
level switched ladder multi-level inverter (SLM). The entropy is manipulated for the switches of the SLM
from SW1 to SWb3. The formulation for the entropy for the SW1 is given by (1).
𝑆𝑊1 = −
13
22
𝑙𝑜𝑔2 (
13
22
) −
9
22
𝑙𝑜𝑔2 (
9
22
) (1)
Similarly, the entropy for the number of “1s” and number of “0s” in the SW1 is depicted in (2) and (3)
respectively.
𝑆𝑊1(1) = −
4
10
𝑙𝑜𝑔2 (
4
10
) −
6
10
𝑙𝑜𝑔2 (
6
10
) (2)
𝑆𝑊1(0) = −
9
12
𝑙𝑜𝑔2 (
9
12
) −
3
12
𝑙𝑜𝑔2 (
3
12
) (3)
The gain of the SW1 is given by (4).
𝐺𝑎𝑖𝑛 = 𝐸𝑛𝑡𝑟𝑜𝑝𝑦 𝑜𝑓 𝑆𝑊1 −
10
22
(𝐸𝑛𝑡𝑟𝑜𝑝𝑦 𝑜𝑓 "1s" in SW1) −
10
22
(𝐸𝑛𝑡𝑟𝑜𝑝𝑦 𝑜𝑓 "0s" in SW1) (4)
The calculation of entropy and gain for the SW3 are evaluated as depicted in (5).
𝑆𝑊3 = −
13
22
𝑙𝑜𝑔2 (
13
22
) −
9
22
𝑙𝑜𝑔2 (
9
22
) (5)
Similarly, the entropy for the number of “1s” and number of “0s” in the SW3 is depicted in (6) and (7)
respectively.
𝑆𝑊3(1) = −
3
9
𝑙𝑜𝑔2 (
3
9
) −
6
9
𝑙𝑜𝑔2 (
6
9
) (6)
𝑆𝑊3(0) = −
10
13
𝑙𝑜𝑔2 (
10
13
) −
3
13
𝑙𝑜𝑔2 (
3
13
) (7)
The gain of the SW3 is given by (8).
𝐺𝑎𝑖𝑛 = 𝐸𝑛𝑡𝑟𝑜𝑝𝑦 𝑜𝑓 𝑆𝑊3 −
9
22
(𝐸𝑛𝑡𝑟𝑜𝑝𝑦 𝑜𝑓 "1s" in SW3) −
13
22
(𝐸𝑛𝑡𝑟𝑜𝑝𝑦 𝑜𝑓 "0s" in SW3) (8)
Table 1. Switching pattern for the fault identification in the 7-level SLM
Levels SW1 SW3 SWB1 SWB3 Decision Equivalent
0 0 0 0 0 Y 0
1 1 0 0 0 Y 8
2 0 1 1 0 Y 6
3 0 1 0 0 Y 4
2 0 1 1 0 Y 6
1 1 0 0 0 Y 8
0 0 0 0 0 Y 0
-1 0 0 1 0 Y 2
-2 1 0 0 1 Y 9
-3 0 0 0 1 Y 1
-2 1 0 0 1 Y 9
-1 0 0 1 0 Y 2
0 0 0 0 0 Y 0
Unused states 0 0 1 1 N 3
0 1 0 1 N 5
0 1 1 1 N 7
1 0 1 0 N 10
1 0 1 1 N 11
1 1 0 0 N 12
1 1 0 1 N 13
1 1 1 0 N 14
1 1 1 1 N 15

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Figure 1. Circuit topology for the proposed 7-level switched ladder multi-level inverter
Due to the symmetricity of the switch patterns, the number of 1’s and 0’s for the negative switches
are the same which leads to the same value of the entropy and gain as in positive switches. Thus the negative
switches are not considered for the evaluation in the decision tree algorithm. Table 2 consolidates the entropy
and gain for the two switches SW1 and SW3. The gain of SW3 is 0.13976 and higher than SW1 with
0.09217. Now comparing the two switches, the SW3 is the root node for the decision tree of the proposed
fault identification in 7-level SLM. The flowchart for the proposed method is depicted in Figure 2. The
VHDL code is used to develop the proposed decision tree algorithm for the identification of the faults in the
7-level SLM.
Table 2. Entropy and gain calculation for the switches using the decision tree algorithm
Sl.No Parameters SW1 SW3
1 Entropy total 0.97603 0.97603
2 The entropy of only 1’s 0.97095 0.91849
3 The entropy of only 0’s 0.81128 0.77934
4 Gain 0.09217 0.13976
Figure 2. Flowchart for the proposed decision tree algorithm based fault analysis of 7-level SLM
3. RESULTS AND DISCUSSION
The proposed fault analysis of switches in the ladder MLI is evaluated using the decision tree
algorithm using the VHDL code. The decision tree parameters namely entropy and gains are manipulated for

161
deriving the splitting tree. Initially, the positive side switches are considered for the decision tree and the gain
value is maximum for the SW3 as compared to the remaining switches, thus, the SW3 is considered the root
node for the tree. With the SW3 as the root node, there are 13 combinations for fault free decision and 9
combinations for faulty decision as depicted by (13,9). The decision tree (DT) checks for the value of SW3
and based on the value of either “0” or “1”, the next node SW1 is evaluated with 3 positive decisions and 6
negative decisions as given (3,6) for SW3=0. For SW3=1, the SW1 node is evaluated for (10,3). Similarly,
the next nodes of SWB3 are evaluated as (3,2) with SW3=1 and SW1=1. For SW3=0 and SW1=X, the nodes
of SWB3 and SWB1 are utilized for the decision of fault and fault free switches in the inverter. Figure 3
shows the complete decision tree for the proposed fault analysis for the switching combination of the
multilevel inverter.
The VHDL code is developed for the derived decision tree using the nested-if-else loop in
behavioral style. The simulation for the developed VHDL is verified using the ModelSim compiler as shown
in Figure 4. The Xilinx Vivado tool is used for the validation of the synthesizable code of the proposed
switching fault analysis. The register transfer level (RTL) schematic for the proposed method is given in
Figure 5. The proposed method is evaluated for power consumption using the Xilinx Vivado tool as given in
Figure 6. Figure 7 depicts the AC output for the 7-level switched ladder trinary multi-level inverter with the
THD% value. The dynamic power manipulated for the proposed switching fault analysis is 1.134 W and the
static power is 0.095 W. The device utilization chart for the proposed method using the Xilinx Vivado tool is
given in Table 3. Table 4 depicts the comparison of the proposed method with THD% and proves to be low
at 12.52% compared to multi-carrier sinusoidal pulse width modulation (MCSPWM) and multi-carrier space
vector pulse width modulation (MCSVPWM) in [28] and since no carrier is used, the modulation index (M)
is not assigned.
SW3
SW1
SW1
SWB3
SWB3
SWB3
SWB1
SWB1
SWB1
No
Fault
Fault
Fault
No
Fault
Fault
No
Fault
Fault Fault
No
Fault
No
Fault
(13,9)
'1'
'1'
'1'
(3,6)
(0,4)
(3,2)
'0'
'0'
(10,3)
'0'
(0,2) (3,0)
'1'
'1'
'1'
'1'
'1'
'1'
'0'
'0'
'0'
'0'
'0'
'0'
(4,2)
(6,1)
(1,1)
(5,0)
(0,1) (1,0)
(2,0) (0,1) (0,1) (1,0)
(2,1)
(1,1)
Figure 3. Decision tree for the proposed switching fault identification in SLM
Figure 4. Simulation output for the proposed decision tree based switching fault identification in SLM

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Figure 5. RTL schematic for the proposed decision tree based switching fault identification in SLM
Figure 6. Power dissipation for the proposed decision tree based switching fault identification in SLM
Figure 7. THD% evaluation for the proposed 7-level SLTLI using the MATLAB Simulink tool
Table 3. Device utilization for the proposed decision tree-based switching fault identification in SLM
Resource Utilization Available Utilization (%)
Look up table (LUT) 25 63,400 0.04
Flip-flops (FF) 8 126,800 0.01
Input/output (IO) 10 170 5.88
Clock buffer (BUFG) 1 32 3.13

163
Table 4. Comparison of THD% for the 7-level MLI AC OUTPUT
Methods THD% for the simulation AC output
MCSPWM [28] MCSVPWM [28] Proposed
7-level with M=0.8 24.33 21.84 12.52
7-level with M=0.7 25.31 24.27
4. CONCLUSION
The proposed switching fault analysis using the decision tree algorithm is validated using VHDL
code. The developed VHDL code identifies the stuck-at faults of the inverter switches using the decision tree
algorithm. The parametric evaluation for the proposed method seems to be satisfactory and feasible for the
real-time fault analysis of the multi-level inverter. The proposed algorithm can be utilized for identifying
faults in the switches of the higher resolution inverter level design and can direct towards the use of neural
network-based fault identification in multi-level inverter switches.
ACKNOWLEDGEMENTS
The authors would like to thank Annamalai University, Chidambaram for providing the simulation
laboratory in utilizing the EDA tools and in contributing to this research article.
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BIOGRAPHIES OF AUTHORS
Nithya Ramalingam was born in 1989 in Cuddalore, Tamil Nadu. She
obtained B.E. [Electronics and Communication] degree from Anna University in the year
2010 and M.Tech. [Embedded Systems] degree from Sathyabama University in the year
2012. She has put in 6 years of service in teaching. She is currently a research scholar in
the Department of Electronics and Instrumentation Engineering at Annamalai University,
Chidambaram, Tamil Nadu, India. Her research interest includes VLSI design,
development of digital control for converters, FPGA implementation of control algorithms,
renewable energy sources-based power converters for real applications. She can be
contacted at email: nithyaramalingam1989@gmail.com.
Anitha Thiagarajan received her B.E., M.E., and Ph.D. degrees in
Electronics and Instrumentation Engineering from the Annamalai University,
Chidambaram, India in 1998, 2005, and 2017 respectively. She is currently working as
Associate Professor at the Department of Electronics and Instrumentation Engineering,
Annamalai University, India since 1999. Her current research interests include power
electronic converters, renewable energy systems, process control, and embedded
systems. She published more than thirty papers in international journals and has more
than ten years of research experience in power electronics. She can be contacted at
email: rgm_anitha@rediffmail.com.

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