Harmonic Reduction in Two-level Power Inverter using Enhanced-
Direct Current (DC) Based-Modulation Technique
CANDIDUS U. EYA1,2,3, UGWUIJEM CHIKADIBIA DANIEL3,
UZOMA STEPHEN EGESIMBA4, EZIKE MORRIS OBIORA5, LUKUMBA PHIRI6
1Africa Centre of Excellence for Sustainable Power and Energy Development,
University of Nigeria,
NIGERIA
2Laboratory of Industrial Electronics, Power Devices, and New Energy Systems,
University of Nigeria,
Nsukka,
NIGERIA
3Department of Electrical Engineering,
University of Nigeria,
Nsukka,
NIGERIA
4Department of Electrical/Electronic Education School of Secondary Education (Tech.)
Federal College of Education (Tech.), P.M.B 11, Omoku, Rivers State,
NIGERIA
5Electrical/Electronic Engineering, Federal Polytechnic,
Ohodo, Enugu, State,
NIGERIA
6Information and Communications University,
P.O. Box 30226, Lusaka,
ZAMBIA
Abstract: - Harmonic reduction in a two-level power inverter using an enhanced-direct current (dc) based
modulation technique is presented in this paper. A buck-boost power inverter is the test system used in this
study with an enhanced-DC-based based-modulation technique. In this research, an enhanced-based modulation
technique is made up of negative bias-rectified sinewave signals and triangular wave signals. The negative
rectified-bias sinewave and carrier wave modulation techniques are compared to produce firing signals for
triggering the DC-DC buck-boost power switch. The anticipated system is exceptional because the triggering
signals for switching the DC-DC power section generated positive trains of signals with two exclusive sections
that handle both the higher and lower harmonics distortions concurrently unlike conventional techniques. The
overall AC voltage output of the system produces 323.5V 50Hz pure sine wave with THD of 0.1072% and AC
of 5.97A with THD of 0.0521% as well as efficiency of 96.68%. The proposed system experimental work was
carried out.
Key-Words: - Enhanced, Harmonics, Modulation, Inverter, Two-level, Triangular.
Received: April 23, 2024. Revised: August 26, 2024. Accepted: September 19, 2024. Published: November 22, 2024.
1 Introduction
Power electronics as a discipline, has revolutionized
the power sector since its inception. This is obvious
in the power DC-AC converters. Power DC-AC
converters invert DC power to AC power for
energizing AC loads, [1]. Uninterruptible power
supply (UPS), Adjustable speed drives (ASDs),
static var compensators, active filters,), flexible AC
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Candidus U. Eya, Ugwuijem Chikadibia Daniel,
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transmission systems (FACTSs), and voltage
compensators, to name a few applications, are
driven as the result of power electronics, [2], [3].
There are numerous power inverters such as single-
phase two-level inverters, single-stage-multilevel
inverters, three-phase two-level inverters, three-
phase multilevel inverters, current source inverters,
voltage source inverters, hybrid, bidirectional power
inverters, multiphase inverter etc., [4], [5].
However, the target of this research is the two-level
waveform of a DC-AC power converter.
The key benefit of this research system is
tailored towards mitigating the high percentage of
harmonic contents prevalent in conventional two-
level DC-AC power converters. Once the harmonics
are lessened, other harmonics' reduced-link merits
like a decrease in system heating effects, pure sine
voltage output waveforms, reduced power losses,
increase in efficiency, high voltage ratio and cost
effectiveness of the product cannot be isolated from
the operating system.
2 Problem Formulation
One of the key problems of two-level power
inverters is the presence of excessive harmonic
distortion (THD) rates. The existence of high
harmonics distortions defaces and reduces the
quality and efficiency of output voltage and current
waveforms. Apart from disfiguring the shape of the
waveforms, the market value of the system is not
left out. Additionally, the high presence of harmonic
distortions results in greater thermal effects. This
paves the way for the malfunctioning of the system.
Filters and different modulation techniques have
been proposed by many researchers with both merits
and demerits.
3 Problem Solution
The author in [5] used a sinewave modulation
technique and single-pulse generated by a DC-based
modulation scheme. They equally used adaptive
techniques to tackle the low-order harmonics.
However, they obtained a THD of 11.15% at AC
voltage and frequency of 44.93V and 50Hz which is
higher than the IEEE standard. The sinusoidal pulse
width modulation, SPWM, and large LC filter were
used by authors in [5] and [6]. Two demerits of this
technique are, that the system becomes large and
expensive as a result of the utilization of a large size
of filter and there would be losses of triggering
action of the power switches of both the DC-DC
power converter and DC-AC converter. The DC and
harmonics elimination techniques were utilized in
reducing the total harmonics distortion, [7]. They
realized a THD of 3.87% at an AC voltage of 43V
and the fundamental frequency of 50Hz of their
research system. This implies that by the moment
there is every chance of an increase in system output
voltage attaining 311V(220Vrms). Two staged
conversion buck-boost multilevel DC-AC power
converters for solar power generation method were
presented in [8] utilizing high triggering frequency
based on SPWM. A THD of 64.62% was
accomplished at 50V by the authors. This led to the
system having low power factor operation and high
losses.
A traditional staircase modulation technique
utilized in [9] was applied in regulating a hybrid
multilevel DC-AC power converter configuration
with a lower number of switching components. In
[10], a zero-crossing digital modulator was used to
exploit the basic component and reduce certain low
ripples in the power inverter. Apart from this
modulating scheme acting on low harmonics, it has
difficult computational analysis.
The efficiency improvement of DC-DC power
converters by parallel switch arrangement was
studied by the authors in [11]. The solitary switch
utilized in their work was switched by uniform
triggering pulses at 25 kHz. The 25 kHz triggering
pulses were realized with the help of an Arduino
UNO microcontroller that accomplished a
conversion efficiency of 70%. However, the
uniform pulses produced mitigated low harmonics.
A lot of DC-DC converter configurations were
reviewed by authors in [12] based on their various
degrees of efficiency performances. However, only
circuit configuration modulation techniques that
also contribute significantly to the efficiency of DC-
DC converters were not taken into consideration by
the authors in their work.
Reference [13] worked on the Harmonic
reduction method for a single-phase DC-AC
converter without an output filter using half-wave
rectified AC signals compared with DC voltage for
producing switching pulses for triggering the DC
power switch. The percentage THD of the output
voltage of 227V of the inverter realized was 4.97%
within the IEEE standard. However, the half-wave
rectified AC signals used were operating in a
discontinuous current mode which would lead to a
decrease in the system efficiency.
The common things on the already work
reviewed are handling the harmonics generated by
the DC-DC input converters with uniform switching
pulses. This shows that they either take care of the
high-order harmonics or low-order harmonics
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differently. So, this paper aimed to close the gap
between handling low-order harmonics and high-
order harmonics by comparing the negative DC
bias-rectified sinewave with negative carrier wave
signals in every cycle. The DC bias-rectified
sinewave with negative carrier wave signals
operates in continuous current mode. The outcome
of the comparison will produce two distinctive
regions in a cycle. One region with large space takes
care of mitigating low-order harmonics while the
compressed region reduces the high-order
harmonics and this is a unique feature other ones do
not possess. This implies that for every cycle, both
low-order harmonics are minimized at the same
time, unlike the conventional schemes that handle
either differently. So as soon as both high and low
order are reduced simultaneously per cycle, the
power losses will be minimized, low output filter or
negligible filter will be utilized, improved output
waveforms will be obtained, negligible heating
effects and good efficiency.
3.1 Materials and Methodology
The materials used in this work are active switches
(IGBTs) and passive elements (inductor, La, diode,
Dm, filters, Ca, La, Cb) This paper adopts analytical,
simulation and implementation methods. The
functional circuit for the proposed system is shown
in Figure 1. The first stage used a conventional
boost DC-DC power converter and operation duty
cycle above 50% to produce the boosted voltage as
shown in the input supply of Figure 1. The second
stage utilizes the boosted voltage to generate AC
power by sequential switching actions of Power
switches SQ1-SQ4.
Sw G
E
G
E
R-L-C
Load
Vs
Ca
Cb
La
Dm
Lb
SQ1G
E
G
E
G
E
SQ3
SQ4SQ2
Fig. 1: Two level Buck-boost DC-AC power
converter, [14], [15]
Equations for the duty cycle, inductance, and
capacitance of the system of the DC-DC buck-boost
converter are given in (1), (2), and (3), [1]. These
are used for the design of the boost converter as
referred to in [1].
(1)
(2)
(3)
3.2 Enhanced-Direct Current (DC) Based-
Modulation Technique
Enhanced-direct current (DC) based-modulation
technique (EDBMT) is accomplished by comparing
the triangular wave with negative rectified AC
biased-voltage signals. The negative rectified AC
biased-voltage signals are operating in continuous
current mode. The negative voltage of the triangular
waveform is expressed as in equation 4. The (4) is
an expression model for representing triangular
waveforms of repeating sequence blocks in
MATLAB/Simulink environment. It is deduced
from Figure 2. The EDBMT in (6) is realized by
comparing (4) and (5f)
Fig. 2: Graphical representation of one cycle of
negative carrier wave
(4)
The voltage waveform of the negative rectified
AC biased-voltage signal is deduced in equation
5(a-e) using the Figure 3.
Fig 3: Graphical representation of one cycle of
negative rectified AC voltage
(5a)
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(5b)
(5c)
(5d)
(5e)
Where and n
represent the negative carrier wave, carrier wave
switching frequency, the amplitude of the triangular
wave, negative reference signal voltage, negative
silent DC-biased voltage, the amplitude of reference
rectified voltage and integer respectively. The dc-
biased reference signal has the range of
in a positive direction. This implies
that is less than zero but greater than .
This generates the following pulsating voltage
expression, .
(6)
The (6) produces two distinct regions for
reducing both low and high-order harmonics
simultaneously unlike the conventional methods.
3.3 Modulation Technique for single-phase
Inverter
The single-phase power switches’ firing pulses are
realized by comparing (7) and (8) to generate (10)
as well as comparing (7) and (9) to produce (12).
The (11) and (13) are the complementary signals of
(10) and (12) respectively.
The expression of carrier wave is written in (7),
[16] while the modulating signal and its 180o phase-
shifted are represented in (7) and (8), [17], [18].
(7)
(8)
(9)
(10)
(11)
(12)
(13)
Where , , and
are the triangular wave for H-bridge, the
amplitude of the triangular wave, the voltage of
modulating sine wave, the voltage of phase-shifted
sine wave and its amplitude and power switches of
the H-bridge respectively.
4 Simulated Results’ Discussion
MATLAB/ Simulink model of the proposed system
of Figure 1 is presented in Figure 4. It is observed
that the modelled system has total harmonic
distortions voltage and current of 0.1072% and
0.0521%. Figure 4 also presented Simulink built-up
blocks of the negative DC-bias rectified sine
waveform in comparison with the negative carrier
wave.
The results obtained during the simulation of the
system in MATLAB/Simulink environment are
discussed as follows. Figure 5a graphically
illustrates where the voltages of the proposed
modulation scheme are plotted again time. It is
noticed that the negative DC-biased rectified
sinewave has a peak voltage of -0.96V and a
frequency of 100Hz. The carrier wave signal has -
1.1V and a switching frequency of 7.8 kHz. Figure
5b presented the improved switching signals. It is
observed that the switching pulses have two unique
regions for every cycle. One region with
compressed pulses and the second region with
spaced pulses. It also showed that for every cycle,
the compressed region has 40 small pulses while the
spaced region has two pulses.
The 40 small pulses tackled the high-order
harmonics while the two pulses handled the low-
order harmonics simultaneously unlike the
conventional PWM. And by so doing the total
harmonics distortion is highly mitigated.
Figure 6(a) shows the power output of the test
system at a steady state after undergoing a transient
time response of 0.015 seconds. Figure 6(b)
represents the output voltage and current waveforms
of the inverter. It can be observed that the voltage
and current waveforms have 323.5 V and 5.5A at
steady state.
Figure 7 displayed a plot of voltage and current
versus normalized frequency. The plot shows the
presence of appearances of ripples on both output
voltage and current against normalized frequency. It
indicated that the ripples in the voltage output
waveform spread from 0.01 to 0.42 rads and
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disappeared while the ripples in the voltage output
waveform spread from 0.01 to 0.2 rads.
Harmonics voltage output against frequency is
plotted in Figure 8. It is noticed that at an output
voltage of 323.5V and
operating frequency of 50Hz, the system has a
THD of 0.1072%. And it corresponded with the
value shown in Figure 4.
Fig. 4: The MATLAB/Simulink model for the proposed system
Fig. 5: (a) Comparison of negative triangular wave and DC-biased rectified sine wave. (b)Enhanced switching
pulses
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Fig. 6: (a) power output (b) Output Voltage and Voltage
Fig. 7: Output voltage and current versus frequency
Fig. 8: Harmonics display of Output Filtered Voltage of the Proposed System under RLC Loads
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Table 1. Comparison analysis of the proposed system with other already published two-level inverters
Modulation
techniques
Harmonic
Mitigation
Method for
the DC-AC
Converter
in a Single
Phase
System[5]
Modeling of the
single-phase
inverter in isolated
photovoltaic
systems to
investigate the
effect of low-
frequency ripple
on the capacitive
input filter with a
uniform
modulation
scheme[7]
Two-Stage
Buck-Boost
Multilevel
Inverter for
PV Power
Generation.
Faculty of
Energy Eng,
PWM[8]
Saw-tooth
based-
unipolar
modulation
with DC-
compared
with a
triangular
wave.[10]
Triangular
wave-
based
bipolar
modulation
DC-
compared
with
triangular
wave.[10]
Harmonic
reduction
method for
a single-
phase DC-
AC
converter
without
output
filter.[13]
Proposed
system
DC-AC
Power
converter
Output
voltage
44.930V
43.00V
50.00V
294.10V
297.40V
227V
323.5V
Percentage
level of
THD of
voltage
output
11.150%
3.87%
64.62%
0.2865%
0.1471%
4.97%
0.1072%
Table 1 compares the proposed system with
other already published work on two-level power
inverters. According to the authors in [5] the AC
output voltage of their inverter and its percentage
total harmonic distortions are 44.930V and
11.150%. [7] has 43V and 3.87% as its inverter and
percentage total harmonic distortions respectively.
The inverter output voltage and percentage total
distortion of [8] is 50V and 64.62%. Moreover,
297.40V and 0.1471% are the output voltage of the
DC-AC converter and THD [10]. [13], also
presented 227V and THD of 4.97%. However, in
the proposed system, the output voltage and THD
are 323.5V and 0.1072% So, it is observed that the
proposed modulation scheme used in the DC-DC
power switch in switching and delivering power to
the test system shows that the inverter output
voltage has the lowest percentage harmonics
distortions and highest voltage output value among
the other ones in the Table 1 for comparison
analysis.
Table 2 shows simulation parameters and
results. It observed that the test system has power
out of 1931.295W and the efficiency of 96.68%.
5 Discussion of Laboratory Results
The results obtained from the laboratory
implementation of the proposed system are
displayed in Figure 9, Figure 10, Figure 11 and
Figure 12. Figure 9 presented a digital oscilloscopic
display -13V negative carrier wave that was
compared with a -10.V DC-biased rectified
modulating signal.
Table 2. Simulation parameters and results
Items
Ratings
Input Voltage Vs
48.00V
Input Inductance, La, and
Capacitance C1
0.20mH and 47.5μF-98
μF
Duty Cycle, D
0.49-0.95
Input current
41.55A
Power input
1994.40W
Power output
1931.295W
Voltage Ripple
1.01%
Inverter Peak Voltage and
Current
323.5V and 5.5A
Frequency of the negative
rectified voltage
100Hz
Fundamental and Switching
Frequencies
50Hz and 7.8kHz
Total Harmonic Distortion
0.1072%
Negative DC-biased Voltage
-0.101V
Efficiency
96.68%
Filter Capacitance Cf and
Inductance Lf
50μF and 4.12mH
Amplitude of modulating
Waveform and negative
carrier wave
-0.96V and -1.1V
The -13V negative carrier wave shown in Figure
9 is the laboratory-implemented triangular wave.
This triangular wave is operating at a frequency of
7.8kHz. On the other hand, the DC-biased rectified
modulating signal operated at 100Hz. Figure 9 has
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already been shown in Figure 3 and Figure 4 and
represented in (4) and (5e).
The improved switching pulses are displayed in
Figure 10 they showed two distinctive regions as
already shown in computer simulated waveform of
Figure 4. Figure 10 showed that the spaced regions
have two pulses while the compressed section has
32 pulses at a switching frequency of 7.160kHz.
These two regions led to the mitigation of the THD
in the system.
Figure 11 depicts the voltage waveform
obtained across the RLC load. It is observed that it
has a maximum value of 256V at the operating
frequency of 50Hz. It represented the practical
output voltage of the inverter.
Figure 12 shows the energized laboratory
hardware prototype of the proposed system with
buck-boost inverter and oscilloscopic display of
voltage waveform. It consists of an implemented
DC-DC power converter section, control units, a
DC-AC power converter, and a digital oscilloscope.
The control units are made of a DC control unit and
an AC control unit. The DC control unit is
responsible for producing enhanced switching
pulses for triggering the DC-DC power converter's
switch.
6 Conclusion
Presented in this paper is harmonic reduction in a
two-level power inverter using an enhanced-direct
current (DC) based- modulation technique. The
simulation of the proposed system was done in
MATLAB/Simulink 2018a and prototype validation
was carried out in the Industrial Electronics Lab.
Under the simulation part, the following results
were obtained: DC-offset of rectified sinewave
signal at amplitude of -0.96V and frequency of
100Hz, triangular wave of -1.1V and 7800Hz,
enhanced switching pulses with two unique regions
and frequency of 7.8kHz for boost switch, Sw, input
power of 1994.40W, output current of 5.5A, and
output voltage of 323.5V with THD of 0.1072%.
50Hz and pure sine waveform.
Fig. 9: Lab. Implementation of Comparison of negative triangular wave and DC-biased rectified sine wave
Fig. 10: An enhanced switching pulses
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Fig. 11: Output Voltage of Two-level buck-boost DC-AC Converter
Fig. 12: Prototype of the test system with the proposed modulation scheme
Experimentally, the results realized are as
follows: negative DC-biased rectified sinewave
signal at an amplitude of -10V and frequency of
101.56Hz, triangular wave of -13.0V and 7.16kHz
improved switching pulses with two distinct regions
and frequency of 7.16kHz for buck-boost switch,
Sw, output current of 4.50A, and output voltage of
256V, 50Hz and pure sine waveform.
It is observed that there are good similarities
between the simulated results of the proposed
system and the experimented system. This validates
the research work carried out in this paper. This
means that there are close relationships or
similarities between the waveforms of simulated
work in the MATLAB/Simulink environment and
the oscilloscopic waveforms of the laboratory
implementation of the same work. The enhanced
modulation scheme used is desired to be extended to
be applied in other stages of power conversion
systems, and hybrid multilevel inverters in future
research in distributed generations. For instance,
complementing the switching pulses will enable
producing complementary switching for switching
two power switches in bidirectional DC-DC power
converters.
Acknowledgment:
The authors acknowledge the support received from
the Africa Centre of Excellence for Sustainable
Power and Energy Development (ACE-SPED),
University of Nigeria, Nsukka that enabled the
timely completion of this research work. They also
appreciate and acknowledge the Laboratory of
Industrial Electronics, Power Devices, and New
Energy Systems, University of Nigeria, Nsukka that
assisted us in using their Computer systems to carry
out the MatLab/Simulink simulation work
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WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2024.19.35
Candidus U. Eya, Ugwuijem Chikadibia Daniel,
Uzoma Stephen Egesimba,
Ezike Morris Obiora, Lukumba Phiri
E-ISSN: 2224-2856
343
Volume 19, 2024
43881-4. https://doi.org/10.1007/978-3-030-
43881-4A.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- Candidus .U Eya, carried out the
conceptualization and laboratory experimental
coupling of different sections of the work. He also
typed the work.
- Ugwuijem Chikadibia Daniel worked on
designing of the system parameters and simulating
the system using MATLAB/Simulink software.
- Uzoma Stephen Egesimba is responsible for the
statistical analysis of the research system.
- Ezike Morris Obiora participated in harmonic
analysis of the system and in checking any
typographical errors in the work.
- Lukumba Phiri played the role of online gathering
of materials and review research of the related
work and critical analysis of the implemented
work.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
There is no source of funding.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on SYSTEMS and CONTROL
DOI: 10.37394/23203.2024.19.35
Candidus U. Eya, Ugwuijem Chikadibia Daniel,
Uzoma Stephen Egesimba,
Ezike Morris Obiora, Lukumba Phiri
E-ISSN: 2224-2856
344
Volume 19, 2024
