Assessment of Total Harmonics Effects on Grid-Connected Powered
Inverter Using Sine-Referenced and Static-band Hysteresis of Current
Controllers
AbstractThis article presents an assessment of total harmonics effects on grid-connected powered inverter using sine-
referenced and static-band hysteresis of current controllers. To realize this art, current transducer, static-band and sine-referenced
hysteresis current controllers, solar energy source, maximum power point tracker, grid supply and voltage source DC-AC
converter are engaged. The system has these features are: (i) Light weight owing to none transformer-less system application (ii)
Efficient in injection of power
Under static-band hysteresis current controlled fed-back system, at upper and lower bands of 130Vand 50V, a total harmonic
distortion, THD of 1.815% and output voltage, vo of 220Vrms (320V peak) were realized whereas in sine-referenced band
hysteresis current controlled fed-back system at upper and lower bands of 430V and 340V, a THD of 1.019% and vo of 220Vrms
are released. The computer simulations and spectral analyses of the system were presented
Keywords : Assessment, DC-AC Converter, Static-band, Grid-connected, sine-referenced, Hysteresis.
Received: May 18, 2021. Revised: February 21, 2022. Accepted: March 20, 2022. Published: April 27, 2022.
1. Introduction
Harmonics is the increasing frequency waveform, overlaid
upon the fundamental frequency that is adequate to deface its
wave-shape. Harmonics rises in power electronic systems as a
result of introduction of power electronics drives for
alternating current-to-direct current motors, direct current fans,
pumps, etc [1].
The consequences of excessive presence of harmonics in
power electronics systems-based devices such as in grid-
connected inverter systems, are flopping of some load needs,
hotness in the system, superfluous voltage, blunder in metering
and control, faulty of relays operations, fading in
communication and control signals [2]. There are innumerable
means of mitigating total harmonics distortions (THD) in
power electronic systems. A few of them are: waveform
regulation by transformer connections, pulse-width modulation
schemes, waveform control by multiple commutations in each
cycle, waveform controlled by using delta-star transformer
output, utilization of filters, and high pulsed rectifier
cascading. In PWM, there are various sub-divisions such as
carrier-based modulation schemes, third harmonic-injection
method, space vector modulation, and random pulse width
modulation with their merits and demerits. Example, in
random pulse width modulation scheme, it relies majorly on
randomizing the frequency of the carrier waveform in order to
allocate the intense energy of the harmonic frequency of the
DC-AC converter output voltage in a constricted high
frequency range. The vital advantage of this scheme is to
mitigate the energy of the harmonics, which in turn will
minimize the THD of the DC-AC converter output voltage [3-
10]. But, this act definitely will also distress the energy of the
basic frequency component by reducing the size of the
amplitude that affects the value of waveform.
The main purpose of this paper is to investigate the
percentage level of total harmonics distortion on single phase
grid-connected powered inverter using sinusoidal and fixed-
band hysteresis of current controllers. A key and distinguishing
feature of the power circuit configuration in this research work
is that in case of any short-circuit condition between the power
MOSFETS on the same leg, the system can handle it without
any device blow due to the presence of inductors La and Lb as
shown in Fig.1 unlike in conventional H-bridge inverter
systems[11-17].
CANDIDUS.U EYA1, OMEJE CRESCENT.O2, NWOKOCHA NATHAN3, BENJAMIN N.UGWU4
1Electrical Engineering, University of Nigeria Nsukka, NIGERIA
1Africa Centre of Excellence, University of Nigeria, NIGERIA
2Electrical and Electronics, University of Port Harcourt, Rivers State, NIGERIA
3Federal College of Education (Tech), Omoku, Rivers State, NIGERIA
4Electrical/Electronics Engineering, Enugu State Polytechnic, Iwollo, NIGERIA
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DOI: 10.37394/23201.2022.21.7
Candidus U. Eya, Omeje Crescent O.,
Nwokocha Nathan, Benjamin N. Ugwu
E-ISSN: 2224-266X
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2. Methodology
The major component values used in this paper are listed in
Table 1.The circuit diagram is shown in Fig.1. The ,method
that is adopted in this research is all about analytical and
simulation methods.
Table1. Materials used in this work
Components
Values
PV module Voltage
72V
Grid Frequency
50Hz
Grid Voltage
220V
Duty ratio
0.850
L and Lo inductors
1.15mH and
9.5mH
Input Capacitor &
R6030ENXC7G MOSFET
1000uF & 600V
Carrier frequency
23kHz
.
3. Principle Operation of the Grid-
connected DC-AC Converter System
Once the peak power is sensed, the signal is communicated
to the analog-to-digital converter, (A/DC) in control section.
The A/DC digitizes signal and delivers it to the controller’s
signal processing section. The control section then triggers
DC-DC boost converter into operation. Under this condition,
the output voltage of the combined solar panels is raised
appreciably which is delivered to inverter input terminals after
matching the voltage per current of PV and the boost converter
voltage per current. The DC-AC converter remains in idle
mode as long as no firing signals are placed on the gate
terminals of the switches. However, once triggering pulses
(vg21 and vg22) strike the gate terminals of the MOSFETS
(MS1, MS2), it establishes a gate to source voltage more than
or equal to the edge voltage to open up the channel of the
MOSFET. Therefore, the previously developed voltage
between drain and the source, pumps the greater carriers from
the source to drain terminals through the inversion layers,
which transform the DC power TO AC power. The
complementary triggering pulses (vg23 and vg24) turn on
MOSFETS (MS3, MS4) during the negative half cycled
operation. The output waveform of the DC-AC converter is a
square form-based waveform. Then an inductor, Lo filters the
ripples and removes most of the harmonics to generate a
triangular-sinusoidal waveform as the inductor output
waveform. The controller section has a defined region, which
contains the referenced current, the top current band bound
and lesser band bound.
The output filter inductor in Fig.1 also acts as a harmonizing
point between the DC-AC converter and the grid supply. As
soon as the output of the inductor is made, the regulator
section forces it to trail the modulating current in-between the
top and low band bounds respectively in order to be injected to
the utility network at power factor of either the sine-referenced
band or static-band current controller applied
Fig.1. Proposed Power Circuit of the system drawn in proteus
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Candidus U. Eya, Omeje Crescent O.,
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The instantaneous voltage across the DC-AC converter
output can be written as follow:
vvv gridLinv
(1)
(2)
(3)
vinv
- Instantaneous DC/AC voltage, Lo- inductance of
output inductor, Vm-peak utility voltage,
-circular
frequency ,
L
i
-instantaneous current of the output inductor
and T-operating period.
4. Harmonization of Filtered DC-AC
Converter Current and Voltage of the
Grid
When the prime current is recognized in the proposed system,
the DC-AC converter delivers it to the power grid via the
action of switching ON and OFF of the power MOSFET
switches. The control side of the AC part comprises
comparator, the current band regulator, reference sine wave
storage part, signal storage entity, A/D converter and sensory
current device. The sensory current device detects the current
passing through the inductor and delivers the signal to the
comparator. This hysteresis comparator compares the inductor
current with the top(upper) and lower current band bounds due
to the operations of hysteresis current controller schemes that
could either be static-band current controller or sine-
referenced current controller to get the gratification of IEEE
Std 929-2000 for suitable delivering of DC power into grid.
Those two schemes were applied in this research work. And
their analyses are deduced as follow:
5. Synchronization of Inverter Current
and Grid Voltage by Static-band Current
Controller
The procedure of the static-band current regulator is
expressed in eq.4:
If the alternating current from the utility supply current at n=1
and is written as:
(4)
For the top current band , is expressed as
(5)
Then, the lower current limit, of the wave shape is expressed
as in eq.6
(6)
If ; switch OFF MS1 and MS2; turn ON S3 and S4;
but If ;Turn OFF S3 and S4 ;turn
ON MS1 and MS2; Imax= peak of the modulating current, iL -
output inductor current, H- band limit of the hysteresis ; -
top band current;
-lower band current; -reference current
If the inductor current flowing is sensed by the current
sensing device, it delivers the message to the comparator for
judgement. When the inductor current is more than upper
current band level, the comparator outputs the error current
signal to trigger the power switches by switching OFF MS1
and MS2; and holding ON MS3 and MS4 in order to decrease
the current gradient and to force the inductor to trail the
modulating current. In addition to that, the output voltage of
the DC/AC converter will be very close to the boosted peak
DC voltage with negative signal. However if the filtered
DC/AC converter current is smaller than the lower current
band bound, the comparator establishes current error signal
that switches OFF MS3 and MS4; and switches ON MS1 and
MS2 for raising the current gradient so that the inductor
current is limited within the hysteresis band bounds. Under this
prevailing situation the output voltage across the DC/AC
converter is at the peak. Therefore the continuously dwindling
and raising up of current gradient as the inductor current is
passing ensures suitable harmonization of the filtered DC/AC
converter current to bear the equal frequency and in phase with
the grid voltage. Henceforth, it brings the power factor of the
system at unity. Fig.2 illustrated simulated result of the static-
band hysteresis current based regulator used for regulating the
DC-AC current injection in to the grid network.
Furthermore, the harmonization of DC-AC current and utility
voltage at unity power factor wave shapes is displayed Fig.4.
But provided the output inductor current is contained within
the band, the regulator continues on its usual switching state.
And once it tracks it well, the current passing through inductor
and the grid voltage concurrently start from the similar origin,
rise at their peak points of various amplitudes at angles of 𝜋/2
and 𝜋, returns to origin at angles 𝜋 and 2𝜋 to complete one
cycle. Under this situation, they are described to be
harmonized and at power factor of 1 (unity).
The Fig.2 shows static-band current controller waveforms.
They are generated by the equations 4, 5 and 6 and are applied
in control unit in Simplorer software used in controlling utility-
connected DC-AC voltage system of Fig.1. The upper band
limit, lower limit and peak reference voltage are 130V, 50V
and 90V. The current tracker explore between these two bands
to ensure good synchronization (harmonization) between the
DC-AC converter output current and the utility voltage
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Candidus U. Eya, Omeje Crescent O.,
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Fig.2: Static-band current regulator wave shapes
.
The Fig.3 showed that the peak synchronized voltage is
320.00V and peak harmonized current of 98.00A was injected
into grid system. The current distortion was reduced, however
not wiped because of presence of asymmetrical frequencies
accompanied with the static-band hysteresis based-current
regulator on the course of controlling the passage of current to
the grid system. The harmonic spectral order of the output
inductor current was done with Fast Fourier Transform (FFT)
and is displayed in Fig.4. The spectral value of total harmonic
distortion (THD) is 1.8146%.
Fig.3: Synchronized waveforms of grid-connected DC-AC converter system under static-band hysteresis current regulator.
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Fig.4: Spectral harmonic content of filtered DC-AC converter output current under static band current controller.
6. Sine-referenced Current Controller for
Harmonization of DC-AC Converter
Current and Utility Voltage at Unity
Power Factor
The algorithm of the sine-referenced current controller is
deduced in eq.7-9 as follow:
(7)
The top band limit of the wave shape, is expressed as in eq. 8.
(8)
For the lower band of waveform is
(9)
So, in positive half cycle, i.e. when the reference current is
more than zero:
For;
If ; switch OFF MS1 and MS2; switch ON MS3 and
MS4;
If ; switch OFF MS3 and MS4 ; SWITCH ON MS1
and MS2;
For negative half part, i.e. when the is below zero.
If ;
If ; switch ON MS1 and MS2; switch OFF MS3 and
MS4;
If ; switch ON S3 and S4 ; switch OFF S1 and S2;
If sine-referenced current more than zero and the output
inductor current is more than top current band limit, the
comparing device sends error current signals to activate
turning OFF MS1 and MS2 ; on the other hand turn ON MS3
and MS4. The action ensured current gradient minimization
thus compelling the output inductor current to follow sine-
referenced current. In addition, the DC-AC converter output
voltage is dropped down to be equal Vmpp. During the
positive half cycle, once the output inductor current is lower
than the minor current band limit, the comparing device issues
out error current signal to switch OFF MS3 and MS4; and turn
ON MS1 and MS2. This instantly pulls up the voltage across
the DC-AC converter to be equivalent to +Vmpp and also
makes the filtered DC-AC converter current to trace and track
the sine-referenced current. On the negative half cycle, i.e.
when the sine-referenced current is smaller than zero, there
exists swapping of the minor current band limit with the top
current band bound. Once the output inductor current is
smaller than the top current band bound, the comparing device
matches the two signals and delivers the error signal that
instantly switches ON MS1 and MS2; and turns OFF MS3 and
MS4. Therefore, voltage across DC-AC converter equal to
+Vmpp as well as compelling the output inductor current to be
suitably tracing sine-referenced current whereas injecting the
output current of the inverter into the grid utility. However,
once the output inductor is more than the lower current band
bound, then the error current signal sets ON MS3 and MS4;
and turns OFF MS1 and MS2. The DC-AC converter voltage
becomes the equivalent as boosted voltage due to decrease in
current gradient. The uninterruptedly transition of voltage
caused by spontaneously switching ON and OFF of the power
switches as a results the error current signal from the
comparator section ensured seamless harmonization of the
filtered DC-AC converter current and grid voltage at unity
power factor. Hence, the DC-AC converter current harmonic
distortion is curtailed to the lowest level. The wave shapes of
the sine-referenced current controller and the resultant
harmonization of output inductor current and grid voltage were
displayed in Fig. 5 and 6.
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Candidus U. Eya, Omeje Crescent O.,
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Fig.5 the sine-referenced current controller waveforms
Fig.6 showed a seamless harmonization of filtered DC-AC
converter current and grid voltage on the course of power
injection into the grid utility under the influence of sine-
referenced current controller. This implies that they have the
identical frequency and are in the same phase. Furthermore, it
means that they began at the same zero angles, reach lowest
point at
2
nevertheless of various peaks, meet at zero axes at
for half cycle; and complete the cycle in the same trend at
2
.
Fig.6: Synchronized inverter current and grid voltage at under sine-referenced hysteresis current controller.
The spectral total harmonic distortion of the sine-reference
current controller is shown in Fig.7
Fig.7: Spectral Harmonic content of filtered DC-AC converter output current under sine-referenced current controller
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7. Discussion of Computer Simulated
Results
The simulated results of grid connected DC-AC converter
system operated at switching frequency of 23 kHz regulated by
sine-referenced and static-band hysteresis of current
controllers were carried out in Simplorer software. The sine-
referenced current controller illustrated a better performance
characteristic than the static-band current controller. It has
smaller percentage THD of 1.0195% in Fig 7. The toothed-
like waveform of coupling inductor current of static-band
current controller is larger than that of sine-referenced current
band. The cleaned DC-AC converter current injected into the
grid utility under static-band approach in Fig.4 is 99.10A while
the current going into the grid utility under the sine-
referenced-band approach of Fig.7 is 75.12A. The spectral
harmonic spectrum display of the static-band current controller
is displayed in Fig.4 of high amplitudes more than that of
Fig.7.
Table2. Comparative Results of the two methods
Grid Injecting current
controlled method
sine-referenced
band current
controller
Static -band current
controller
Magnitude of
injected current
99.10A
75.12A
Band limit range
50 - 130
340 - 430
Total Harmonic
Distortion,THD
1.815%
1.019%
Power factor
1.00
0.97
THD
1.815%
1.019%
8. Conclusion
An assessment of total harmonic effects on grid-connected
powered inverter using sine-referenced and static-band
hysteresis of current controllers has been presented, analyzed
and simulated in Simplorer software. From the Table 2, it is
observed that the sine-referenced current controlled method
offered lower total harmonics distortions, and higher power
factor than the static-band current controller. And because of
it, there are higher power losses in static-band current
controlled scheme than the second one. Moreover, the static-
band current method draws more current from the inverter than
the sine-referenced current controller. In other word, it stresses
inverter more than other method.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
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