The Behaviours of Various DC Choppers during Shading Occurrence in
PV Systems
SAMEER KHADER, ABDEL-KARIM DAUD
Department of Electrical Engineering,
Palestine Polytechnic University (PPU),
P.O. Box 198, Hebron,
PALESTINE
Abstract: - This paper investigates how the DC choppers behave during the shading occurrence at different time
intervals of the year. Three types of DC choppers are implemented during the same shading conditions and
intervals of time. The studied parameters are the duty cycle, output power, current, and switch losses. The
mathematical model is built and implemented using the MATLAB/Simulink platform. The obtained results
show that the SEPIC converter has the highest rate of duty cycle, which means more switching losses are
generated. Concerning the average output power, the Modified Single Ended Primary Converter (MSEPIC) has
the highest rate, while the Boost Converter has the lowest rate. The MPP power, duty cycle, and switching
losses are studied under various shading rates. The duty cycle has the highest rate on the SEPIC converter,
while MSEPIC has the lowest rate. Despite that, the switching losses are tremendously high at MSEPIC
compared to SEPIC converters. Furthermore, simulation studies show that Boost and SEPIC converters have
better performance in frequent cloudy weather conditions.
Key-Words: - Modified SEPIC Converter, PID Controller, Photovoltaic Source, PWM, MPPT,
Modelling, Partial Shading.
Received: August 23, 2023. Revised: February 16, 2024. Accepted: March 14, 2024. Published: April 22, 2024.
1 Introduction
As well-known renewable energy (RE) resources
found widespread utilization throughout the whole
world, aiming at reducing the dependency on fossil
oil sources, and reducing the negative impact of
conventional energy sources on the environment,
[1], [2]. One of the most important RE resources is
the photovoltaic (PV) solar energy source, which
has a sustainable status and is friendly to the
environment, [3], [4]. The mentioned PV source
depends on the sun location during the year and has
a variable irradiation rate with an average value of
about 5.3 kWh/m2 per day for Palestine, which is
located at a latitude of 31.58°N and a longitude
angle of 35.14°E. Usually, the PV system consists
of several power generation, conversion, and control
units that are the core of the system. Shadowing is
one of the most important factors that causes a
significant reduction in generated energy, [5], [6].
Taking into account the approach of [7], direct
detection of the maximum power at any value of
solar irradiation and temperature during the daytime
is realized. Various DC-DC converters are applied,
such as the single and modified single-ended
primary-inductance converters SEPIC and MSEPIC,
respectively, in addition to the well-known boost
converter, [8], [9]. Figure 1(a) illustrates the
principal electrical circuit for MSEPIC, while
Figure 1(b) presents the control circuit with a partial
shading condition. The proposed model is analyzed
and simulated in MATLAB/ Simulink, and m-file
code, [10]. Closed-loop feedback control with a PID
controller based on a triggering system is developed
for the MSEPIC converter to maintain a constant
output voltage, as shown in Figure 1(b).
a) Principle electrical circuit
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b) Control circuit
Fig. 1: Modified SEPIC Converter, [11]
Fig. 2: Plot of solar altitude versus azimuth for
different months of the year at a latitude of 31.58 N,
[12]
2 Mathematical Modelling
2.1 The Sun Path for Palestine
Depending on the sun’s position, the position of the
PV panel, and surrounding objects, partial or
complete shading can occur. The sun position is
defined as a function of the daytime, latitude, and
longitude in order to determine the shaded area of
the PV panel. According to [13], [14], the solar
equations are implemented in the Excel platform,
[15], for Palestinian city of Hebron, which is located
at a latitude of 31.58°N and a longitude angle of
35.14°E. The plots of altitude versus azimuth angles
are displayed in Figure 2, where it is clearly shown
that the existence of hard shadow such as trees or
solid obstacles severely affects the winter months
rather than the summer months.
2.2 The Effect of Shading on Circuit
Parameters
When solar irradiation intensity varies during the
day, it causes a significant change in the extracted
power in terms of voltage and current at a given
temperature. This variation can occur due to soft
and hard shading factors, such as cloudy weather
that causes soft shading and trees or buildings that
cause hard shading. The significant variation occurs
in the generated current while there is a light change
in the voltage. To estimate the effect of shading on
the PV system parameters, the PV voltage and
current are derived as follows, [11], [12] and shown
in Figure 3.
Fig. 3: Equivalent circuit for PV cell
The cell voltage at standard test conditions is:
ln
(1)
where A is the diode idealistic factor, Id is the diode
saturation current, Iph is the cell photo current, IPV is
the photovoltaic current, K is the Boltzmann
constant, q is the electric charge, and Rs is the PV
series resistance. While the photocurrent in terms of
irradiation and temperature is:
(2)
where Gr is the reference solar irradiation and ISC is
the short circuit current.
The output cell current is:
exp
1 (3)
The diode current can be stated as:
(4)
where B is the diode idealistic factor, Eg is the band
gap energy of the semiconductor, Tc and Tr are the
cell and reference temperature, respectively, and Ior
is a constant given at standard conditions. The
idealistic diode factors A and B have values that
vary between 1 and 2 depending on I-V
performance shaping and approximations.
2.3 Photovoltaic System in a SIMULINK
Environment
A photovoltaic model is built on the
MATLAB/Simulink platform without the shading
effect, as shown in Figure 4 for the solar panel type
SUNPOWER, SPR-315E, with a 315-watts peak
and a conversion efficiency of 20.5% , [16]. To
show the effect of shading on PV performances,
three PV panels are connected in series with 0%,
33%, and 66% shading rates, as shown in Figure 5.
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The obtained results are graphically presented in
Figure 6, where it’s clearly shown that the effect of
shading causes a dramatic reduction in total PV
power up to 53% of the total value, and concerning
current, the reduction exceeds 22%. Furthermore,
the overall performance deformation occurs when
the MPPT algorithm detects less power with a
reduced voltage that corresponds to the maximum
power point. Figure 7 illustrates the time domain of
solar variation, Vmpp and Vout for December 21st with
a 15% shading rate, while Figure 8 and Figure 9
illustrate the 3D variation of solar irradiation, power
and voltage at MPP during the previous mentioned
day using a boost converter.
Fig. 4: Simulink model for a single PV array with
no shading effect
Fig. 5: PV panels with various shading rate
Fig. 6: PV performances for SPR-315E at STC
Fig. 7: Solar and voltage variation during
December 21st with 15% shading
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Fig. 8: Power at MPP for SPR-315E at various
shading rate
Fig. 9: Voltage at MPP for SPR-315E at various
shading rates
3 Shading and Converters
As previously mentioned, three converter types are
simulated under the same shading conditions and
rated temperature of 25°C with data given in Table
1. The following simulation results can be discussed
as follows:
3.1 The Average Irradiation
To estimate the effect of shadow rate on the main
PV and load parameters, it is necessary to determine
the average value of solar irradiation. Referring to
Figure 7, where the shadow region is illustrated, the
average daily irradiation can be presented according
to eq. (5):
sin
sin
;
with
%
.100 (5)
where Td is the day duration, [17], Tsr and Tss are the
sunrise and sunset respectively, Gmax is the
maximum irradiation at full sun, Tshs and Tshe are the
start and end times of the shadow, respectively, and
Ksh is the shadow rate that varies in the range of 0%
to 90%, [17], [18], [19], [20].
Solving eq. (5) for certain days of the year and
at fixed start and end shadow times (Tshs=9:30,
Tshe=13:30) AM and varying the shadow rate yields
Figure 10(a) where the average value drops from
65% to 43%. While Figure 10(b), shows the average
values of voltage at MPP as the shadow rate
increases.
a) Average irradiation
b) Average voltage at MPP
Fig. 10: Solar irradiation, voltage and power at
December 21st
0
10
20
30
40
50
60
70
0 20406080100
Gavg,%
Shadingrate,%
53
53,2
53,4
53,6
53,8
54
54,2
0 20406080100
Vmpp,V
Shadingrate%
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3.2 The Variation of Duty Cycle and Output
Voltage
The duty cycle depends on the chopper type, input,
and output voltage at a given solar irradiation. The
duty cycle can be expressed according to eq. (6):
(6)
where VLoad is the load voltage and Vmpp is the
voltage at MPP and given irradiation.
Figure 11 illustrates the change of duty cycle for
various converter types, and the shading rate varies
from 0% to 90%. It can be shown that the variation
of Vmpp is negligible among the entire shading rates,
as shown in Figure 10(b), where the voltage varies
in the range of 54.2V to about 52V as the shadow
rate changes from 0% to 90%.
Fig. 11: Duty cycle at variable shading rate
The percentage load voltage variation with
respect to the reference voltage and various shading
rates can be estimated according to eq. (7).
∆%
∗100 (7)
where Vref=80V is the stated reference load voltage
and VLoad is the actual load voltage obtained at
various chopper types.
Figure 12 shows that the SEPIC converter has
the largest voltage change with respect to the
reference, while the MSEPIC converter has the least
voltage
change, which is around 0.9%, converted to
a physical value of Vref=80V and VLoad=79.28V.
Fig. 12: Percentage change of load voltage
3.3 The Variation of Load Power and
Efficiency
As the shading rate increases, the load power
decreases as well, while the chopper losses slightly
increase due to the observed change in the duty
cycle. According to [4], the daily lost power due to
continuous transistor switching aimed at operating
at MPP can be presented as follows:
(8)
where Tday is the day duration; n1 is the day number
(n1=1..365); Am = Gmax/250, Bm = 2.4, and Kq=1.12
is the correction factor; ag2 = -0.066, ag1 = 0.062,
and ag0 = 0.78.
PQD is the dissipated power of the transistor switch
that can be expressed according to eq. (9) in terms
of solar irradiation.
(9)
where
ag6 = -0.0083, ag5= 0.01, ag4 = 0.04, ag3=-0.043,
ag2= -0.066, ag0 = 0.78,
and
sin
600
250
0,15
0,25
0,35
0,45
0,55
0,65
0 20406080100
Dutycycle
Shadingrate%
BOOST MSEPIC SEPIC
0
0,5
1
1,5
2
2,5
0 20406080100
Voltagechange%
Shadingrate%
BOOST MSEPIC SEPIC
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The observed transistor energy loss in terms of
heat for both described chopper types is illustrated
in Figure 13. It can be noticed that due to the large
value of the duty cycle of the SEPIC converter, the
transistor losses have larger values compared to the
BOOST converter. The output average power can be
presented according to eq. (10):
__
and
%
_∗100 (10)
a) Boost converter
b) SEPIC converter
Fig. 13: IGBT transistor loss at various shading
The obtained simulation results according to eq.
(10) are displayed in Figure 14 for three converter
types. As well as shown in Figure 14(a), increasing
the shading rate heavily affects the load power;
furthermore, BOOST and SEPIC converters have
identical changes, while MSEPIC is affected due to
shading. Figure 14(b) confirmed that the efficiency
of the MSEPIC converter reduces as the shadow rate
increases, while other converters have, to some
extent, unaffected efficiency. Which means
MSEPIC converter presents an inefficient solution
in areas with frequent shading status.
a) Average output power
b) Average efficiency
Fig. 14: Output power and efficiency on December
21st
3.4 The Most Affected Month of Shadowing
To see which months are most affected by shading,
the average irradiation rate is calculated at the same
shading conditions of 60% and the same shading
start and end duration for all twelve months at the
21st of the month. The result is illustrated in Figure
15 according to eq. (11).
_%
100 (11)
where GUSH= 636.67 Wh/m2-day is the average
irradiation in June 21st which is the longest day of
the year, and GSH is the average irradiation under
shading conditions for a given month.
It can be shown that the winter months are the
most affected by the shadow, with irradiation
reduction up to 20% at a 60% shading rate.
0,12
0,122
0,124
0,126
0,128
0,13
0,132
0,134
0 20406080100
Pq,Watt
Shadingrate%
0,635
0,64
0,645
0,65
0,655
0,66
0,665
0,67
0 20406080100
Pq,Watt
Shadingrate%
110
130
150
170
190
210
0 50 100
Pout,Watt
Shadingrate%
BOOST MSEPIC SEPIC
90
92
94
96
98
100
102
0 20406080100
Efficiency,%
Shadingrate%
BOOST MSEPIC SEPIC
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Table 1. Data specification for SPR-315E-WHT-D
q K Iph Id RS RP
1.602e-19 C 1.38e-
23J/K 6.14A 0.059A 0.15 1090
NS NP Vcell VOC ISC VMPP
32 3 0.6V 64.6V 6.14A 54.7V
IMPP PMPP Eg NPm Vpv Rload
5.76A 312 W 1.1 1 54.7V
9.6
Vin, V Vo, V D L1, mH L2, mH C1,
F
Variable Variable 0.1 –
0.9 1.98 0.99 660
C2, F Co, F Ro, Ω TC
660 10 9.5 25C
a) Average irradiation at 60% shading rate
b) The percentage changes
Fig. 15: Average irradiation at 21st of the month
4 Conclusion
Taking into account the obtained simulation data at
various chopper configurations, shading levels, and
shading time intervals, the following conclusions
can be drawn:
- The shading effect linearly affects the MPP
current, while this effect has a nonlinear effect
on the MPP voltage.
- Concerning the output or load power, MSEPIC
converts less power compared to other chopper
configurations. Furthermore, the chopper losses
are tremendously high in MSEPIC compared to
other converters.
- The winter months are the most affected by the
shading condition, where the average irradiation
falls by 20% when shading has a 60% effect?
- Therefore, it’s recommended that Boost and
SEPIC be most effective during shading
conditions. This means installing MSEPIC
converters must be avoided in frequent shading
conditions. The same recommendation is valid
for regions with a long winter season.
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Contribution of Individual Authors to the Creation
of a Scientific Article (Ghostwriting Policy)
- Sameer Khader implemented the SIMULINK model
and presented building performances, conclusions,
and paper preparation.
- Abdel-Karim Daud has performed the literature
review, carried out the mathematical model,
analyzed the numerical results, discussed the results,
drawn a conclusion, and finalized the paper.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
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_
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