CET Volume 86
DOI: 10.3303/CET2186124
Paper Received: 25 October 2020; Revised: 9 March 2021; Accepted: 10 April 2021
Please cite this article as: Velasquez P., Herrera C., Santis A., 2021, Simulation of the Effect of the Angle of Incidence on the Solar Panel for
Three Solar Photovoltaic (pv) Systems in the Bogotá Savanna– Subparamo, Chemical Engineering Transactions, 86, 739-744
DOI:10.3303/CET2186124
CHEMICAL ENGINEERING TRANSACTIONS
VOL. 86, 2021
A publication of
The Italian Association
of Chemical Engineering
Online at www.cetjournal.it
Guest Editors: Sauro Pierucci, Jiří Jaromír Klemeš
Copyright © 2021, AIDIC Servizi S.r.l.
ISBN 978-88-95608-84-6; ISSN 2283-9216
Simulation of the Effect of the Angle of Incidence on the Solar
Panel for Three Solar Photovoltaic (Pv) Systems in the
Bogotá Savanna– Subparamo
Pablo Velasqueza,*, Claudia Herrerab, Angelica Santisa
a
Universidad Cooperativa de Colombia, Avenida Caracas 37-63, Bogota
b
Colegio Pablo Neruda I.E.D, Cl. 16f Bis #102-70, Bogotá
pablo.velasquez@campusucc.edu.co
The planet's pollution from greenhouse gases resulting from fossil energy sources' inefficient use, has made
the scientific community reflect and has led it to search for new alternative and renewable energy sources to
supply increasing energy needs. One of the sources that have had significant growth worldwide in the last
decade is photovoltaic solar energy. However, one of the drawbacks with the use of photovoltaic technology is
conversion efficiency. For this, alternatives are sought, such as the study of new materials with structures that
facilitate the quantum photodetection of a given compound; minimize losses due to transient and harmonic in
the regulation devices and inverters, and losses in the storage and transport of the energy generated. One
proposal to increase the collection efficiency is solar tracking systems, making the panels remain
approximately perpendicular to the direct light beam (direct radiation), from dawn to sunset. In this research
work, three photovoltaic solar energy capture systems are compared using a simulation. The first case
corresponds a fixed system in a horizontal position; the second case is a system fixed with an inclination of 10
degrees south latitude, and the third, a two-axis tracker. The information collected is taken in the municipality
of Sibaté, the coordinates 4 ° 30 ' 09.5 " N, 74 ° 15 ' 20.2 " W in the Savanna of Bogotá. The purpose of this
study is to use clean electrical energy to obtain bio-hydrogen using electrolysis. In the simulation, two periods,
cloudy and clear, are determined based on a threshold taken experimentally in the panels and thus comparing
the three systems. The results show that in clear periods the solar tracker has an energy conversion gain of 5
%. On the other hand, in cloudy periods, the three systems' panels showed similarity in the energy
measurements captured.
1. Introduction
The pollution of the planet from gases that cause the greenhouse effect, a product of the inefficient use of
fossil energy sources, has made the scientific community reflect and has led it in the search for new
alternative and renewable energy sources to meet growing energy needs (Cediel et al. 2003). One of the
sources that have had significant development and growth worldwide in the last decade is photovoltaic solar
energy (PV) (REN21, 2020).
Several photovoltaic solar systems have been developed, which vary by their configurations depending on the
use. However, there is a coincidence for all it is necessary to work in search of improving the conversion
efficiency (Zoe, 2018; Shockley, 1961). Direct radiation on a sunny day can be up to 90 % of total solar
energy, and the remaining 10 % corresponds to diffuse radiation (Gueymard, 2002). This research addresses
the problem of radiation incidence received by solar panels. Since if the panels remain oriented so that direct
solar irradiation falls on them at an angle of 90 °, it is possible to increase the intensity of energy absorbed by
the solar panel, despite the relative movement of the earth to the sun for a day.
Numerous investigations are reported that are directed towards improving the conversion efficiency of
photovoltaic systems. A study carried out by the General Motors R&D Center, and the Chemical &
Environmental Sciences Laboratory in Detroit (USA) shows that the highest energy conversion from
photovoltaic systems with two-axis tracking occurs on clear days. If compared to modules installed with a fixed
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inclination (without movement to track the light beam), where the energy transformation is calculated to have
increased between 30 and 50 %, this is achieved because the energy received by the panels with tracker
corresponds largely to direct radiation (Nelson & Kelly, 2009).
General Motors (GM) published another work carried out in the test field by the same group of researchers, in
which the performance of four fixed systems with the same characteristics located in four positions, inclined 0
°, 27 °, 42 °, and 57 ° south latitude, in order to study the incidence of the inclination on the captured energy
and it was compared with a two-axis tracking system. This test was carried out for eight months in the city of
Milford (MI, USA). They found that, on sunny days, the energy captured by the monitoring system was twice
that of the one located horizontally (0 °). The analysis shows that solar tracker reduces solar energy
harvesting compared to the horizontally located system on cloudy days. A gain of 37 % was obtained in the
horizontal position system, and it is estimated that a gain of 50 % would be obtained (Nelson & Kelly, 2011).
On the other hand, the Observatory Road, Bouzareah and the Universities Amar Teldji University, University
A. Mira and National Polytechnic School, Algiers, Algeria, published a review of the main methods used for the
capture of photovoltaic energy under different environmental conditions. They reach conclusions very similar
to those already mentioned, that is, for clear or sunny periods, the advantage is given for two-axis trackers,
and cloudy periods, the highest gains were obtained from systems arranged horizontally (Koussa et al. 2011).
Recently, at Deemed University in the city of Bengaluru (India), an investigation was carried out where the
performance of a solar tracker PV energy harvesting system is compared with another previously used fixed
system, an increase of between 15 and 20 % depending on weather conditions (Rameez et al. 2020).
In this research work, three photovoltaic solar energy capture systems are compared using a simulation. The
first case corresponds to a fixed system in a horizontal position; the second case is a fixed system with an
inclination of 10 degrees south latitude, and the third, a two-axis tracker. The research will be carried out in the
municipality of Sibaté located at coordinates 4 ° 30 ' 09.5 " N, 74 ° 15 ' 20.2 " W, on the Bogotá Savanna.
Sibaté is located at an altitude of 2630 meters above sea level (masl) and an average temperature of 14 ° C,
spread over a sub-paramo thermal floor (Codazzi, 2002), with an unstable climate, as well as cold, cloudy,
and rainy, although there are hours of intense sun (Hofstede, 2003). These conditions generate uncertainty
regarding the amount of radiation that a PV system can capture, despite being located in the tropics, this
reason to simulate the three systems in order to evaluate which one can be used to obtain biohydrogen
through the electrolysis process.
2. Material and methods
2.1 Incident radiation
The incident irradiation on the earth's surface is affected by three factors: solar constant, distance from the
sun, and attenuation due to atmospheric transparency..
Solar constant (I0) is the amount of energy from the sun perpendicularly incident on a surface of unit area per
unit time placed outside the earth's atmospheres or terrestrial sphere at an average distance of 150 x 106 Km
of the sun. The current value is estimated at 1370 W / m2 and ranges approximately 1.2 W / m2 (NASA
SCIENCE, 2003).
Distance to the sun: The earth's translational movement in the earth's orbit changes the earth-sun distance
during the year, causing a variation in the solar radiation outside the earth's atmosphere. Analytically, the
incident extraterrestrial radiation can be found through the expression of Eq(1):
In = I0 (R0/R) (1)
Where I0 is the solar constant, R0 is the mean radius of the constant Earth orbit and R is the radius that varies
with the translational motion
Attenuation by atmospheric transparency: caused by gases such as atomic oxygen, nitrogen in the upper
layers of the atmosphere, selective absorption by water vapor, and other gases in lower layers. (UPME, 2005).
2.2 Direct radiation
It is the flow of radiation that reaches the earth's surface without having been affected in its direction. The
solar panel position to the sun relative defined by the elevation angle (h) and angle azimuthal (a). The
relationship that joins the elevation angle and azimuthal with the time of day and direct solar radiation (Ib) is
given by Eq(2):
Ib = Ibh*Cos(b) (2)
Where Ibh is the horizontal direct irradiation
In Eq(3), it sees the value of cosine:
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Cos(b) = n.k (3)
n is the unit normal to the surface of the solar panel. The value of the vector is shown in Eq(4)
n[sin(γ)sin(i)cos(γ), sin(i)cos(γ), cos(i)] (4)
γ angle to south
i angle of inclination to the horizon
k is the unit vector that indicates the direct sunlight beam's direction. The value of the vector is shown in
Eq(5).
K[ cos(h)sin(a), cos(h*sin(a), sin(h)] (5)
Now, these expressions are substituted into equation 2 for being as shown in Eq(6)
Ib = Ibh*[sin(i)cos(h) cos(a - γ), cos(i)sin(h)] (6)
2.3 Diffuse radiation
The dispersion of solar irradiation can be seen in Figure 1. We start from the extraterrestrial solar irradiation
(Ic), which is a constant value. This value reaches the atmosphere with a small variation, a product of the
earth's elliptical path, known as extraterrestrial radiation (Iext). Upon reaching the earth's atmosphere, it
fragments, 30 % is reflected, 23 % is absorbed (ultraviolet component due to ozone and an infrared
component due to water vapor), dispersed by molecules of gases, water, and particles existing in the air, a
part is reflected in the clouds. Finally, 47 % reaches the earth in the form of direct radiation (Ibh). Of the
reflected and scattered components, a part reaches the planet in diffuse radiation (Idh). (Iqbal, 1983), (UPME,
2005).
Figure 1: Scheme of the effect of the atmosphere on solar irradiation
Eq(7). is shown that the global horizontal irradiation (Gh) is the sum of the direct irradiation (Ibh) plus the
diffuse irradiation (Idh).
Gh = Ibh + Idh (7)
When the panels are in a horizontal position, when inclined with an angle (i) compared to the horizontal, a part
of the diffuse radiation comes from the ground. In this case, the fraction of the diffuse radiation resulting from
the sky is expressed in Eq(8):
= 1 + cos ( )2 ∗ ℎ (8)
The diffuse irradiation resulting from the ground received, Eq(9), by the solar panels is:
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= 1 + cos ( )2 ∗ ℎ ∗ (9)
Where: a is the albedo, which corresponds to the percentage of radiation that any surface reflects, and its
mean value is 0.3.
Indirect solar radiation is the sum of two diffuse fluxes and can be expressed, as shown in Eq(10):
= 1 + cos ( )2 ∗ ℎ ∗ + 1 + cos ( )2 ∗ ℎ (10)
With Idh expressed in Eq(11):
Idh = Gh – Ibh*sin(h) (11)
2.4 Total radiation
The total radiation (Gt) received by solar panels corresponds to the superposition of direct radiation and
diffuse radiation. The sum of direct and diffuse light leads to the following relationship expressed in Eq(12): = + (12)
2.5 Mathematical model of Photovoltaic cells
The mathematical model of a solar cell has been studied for more than three decades; its equivalent circuit
consists of a current source generated by solar irradiation, in parallel with a diode, and a resistance, RSH and a
resistance in series, Rs that represents the internal resistance of the material to the flow of the generated
current. The mathematical model is obtained from the electrical representation and is a function of solar
irradiation and cell temperature. The characteristic equation (Eq(13)) corresponding to the model is:
= − exp ( + ) − 1 − + (13)
Where I PH is a photocurrent, I S is the inverse saturation current of the cell, q represents the charge of the
electron (1.6 x 10 -19 C), k is the Boltzmann constant (1.38 x 10 -23 J / K), TC is the cell operating temperature
in Kelvin, (K), A is an ideality factor, RSH is the shunt resistance or leakage current, and RS is the internal
series resistance of the circuit. The photovoltaic current or photocurrent depends mainly on the intensity of
insolation and operating temperature, as seen in Eq(14): = + ( − ) λ (14)
Where I SC is the short-circuit current of the cell under standard conditions, that is, at 25 ° C and 1 KW / m
2 of
solar irradiance. KI is the temperature coefficient of the cell short-circuits current in A / ° C, Tc is the cell's
operating temperature. TRef is the cell's reference temperature, and λ is the ratio of solar irradiation in the field
to the standard. The saturation current of the cell varies with temperature, and is described as expresses in
Eq(15):
= ( 1 − 1 ) (15)
Being IRS the inverse saturation current of the cell for the reference temperature and solar radiation. EG is the
bang-gap (forbidden energy gap) of semiconductor energy or energy difference between the upper part of the
valence band and the lower part of the cell's conduction band. The ideal factor A depends on the photovoltaic
technology. For the simulation of the Math model, the Matlab tool was used.
3. Results and discussions
Various simulations are obtained from the mathematical models exposed, in which geographic location and
date must be determined to have greater precision in the simulation. The information collected is taken in the
municipality of Sibaté, at coordinates 4 ° 30 ' 09.5 " N, 74 ° 15 ' 20.2 "W, altitude 2630m above sea level, in
Colombia.
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Initially, a comparison is made for sunny days between the system with a solar tracker and two fixed positions
inclined 20 ° and 30 ° with a south direction. The comparison evaluates the incidence of the inclination angle.
It is observed in Figure 2 that the solar tracker has a maximum intensity of 930 W / m 2. In the fixed panel
inclined 30 °, the transformed power decreases drastically to a value of 790 W / m 2. In contrast, for the 20 °
inclination, it is 870 W / m 2. The difference between the solar tracking system and fixed panel at 30 ° from the
horizontal is approximately 15 % in this simulation.
Figure 2: Comparison of the solar tracker with two fixed positions
Next, simulate a solar tracker, a horizontal solar panel, and a 10 ° inclined solar panel on a clear day,
obtaining higher gains in the solar tracker, between 5 % and 7 % compared to fixed panels. The solar panel
placed horizontally, and the solar panel tilted 10 ° have very similar values as seen in Figure 3a. The 10 ° tilt
because the position is used optimally to prevent water accumulation in times of rain.
In Figure 3b simulation for panels is presented, solar tracker, fixed horizontal and fixed inclined 10°, in this
graphic no differences were observed between them it can be caused by that day dark as radiation received
by the panels it is the diffuse one, and due to the position in which the three systems are found they
accumulate equal intensity.
Figure 3: Comparison of the solar tracker, horizontal panel, and inclined 10 °: a) clear day b) dark day
The previous contrasts with reports of gain in two-axis tracking systems on sunny days, reaching up to 50 %
like that obtained in Detroit (Nelson & Kelly, 2011). That is a city located at latitude 42 º to the North or with
those reported in Jordan and Iran, in the order of 30 to 35%, whose location to the equator is approximately
32º north latitude (Abu-Khader et at. 2008) (MohsenMirzaei & ZamaniMohiabadi, 2018).
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There seems to be a direct relationship between latitude and gain in tracking systems, as reported in Detroit at
latitude 42 ° North, the gain is approximately 50 %, while in Jordan and Iran, in the order of 30 to 35 %, whose
location to the equator is approximately 32 º north latitude. It is essential to highlight that the Bogotá savanna
is in a sub-paramo climate; this condition causes prolonged periods of cloudiness, causing diffuse radiation to
predominate throughout the day (Codazzi, 2002), making the ideal system either a fixed system located
horizontally or with an inclination less than 10 ° south.
4. Conclusions
The theoretical results of the simulation of the three photovoltaic solar energy capture systems, solar tracker,
fixed inclined 10 ° and fixed horizontal, show that for sunny days the solar tracker converts between 5% and
7% more energy than any other system evaluated. The comparison on dark days the energy captured by the
three systems is similar between them, it does not present significant differences, this contrasts with reports of
gain in two-axis tracking systems on sunny days, which can reach up to 50% as the one obtained. in Detroit
(Abu-Khader, 2008). city that is located at latitude 42º north, or with those reported in Jordan and Iran, in the
order of 30 to 35%, whose location with respect to the equator is approximately 32º north latitude (Nelson &
Kelly, 2011).
It is important to bear in mind that the Savanna of Bogotá is located in a sub-paramo climate; this condition
causes prolonged periods of cloudiness, causing diffuse radiation to predominate throughout the day. It is
proposed to design an energy capture system that, on sunny days, tracks the solar disk to capture direct
radiation and, on cloudy days, moves to a horizontal position to capture diffuse radiation caused by clouds.
References
Abu-Khader, M. M., Badran, O. O., & Abdallah, S., 2008, Evaluating multi-axes sun-tracking system at
different modes of operation in Jordan. Renewable and Sustainable Energy Reviews, 12, 864–873.
Cediel, E., Hernandez, J., Cano, & Gordillo., 2003, Caracterizacion de módulos fotovoltáicos. Revista
Colombiana de Física, 42 161-165.
Codazzi, I. G., 2002, Atlas de Colombia. Bogota: Imprenta Nacional de Colombia.
Gueymard, C. M., 2002, Proposed reference irradiance spectra for solar energy systems testing. Solar
Energy, 73, 443-467.
Hofstede, R. S.,2003, Los Paramos del Mundo. Quito: Global Peatland Initiative NC-IUCN/ Eco Ciencia.
Iqbal, M., 1983, An introduction to solar radiation, Chapter 11: Solas Radiation Incidented on Tilted planes on
the earrth’s surface, Academic Press Canada, Toronto.
Koussa, M., Cheknane, A., & Hadji, S. M., 2011, Measured and modelled improvement in solar energy yield
from flat plate photovoltaic systems utilizing different tracking systems and under a range of environmental
conditions. Applied Energy, 88, 1756-1771.
MohsenMirzaei, & ZamaniMohiabadi, M., 2018, Comparative analysis of energy yield of different tracking
modes of PV systems in semiarid climate conditions: The case of Iran. Renewable Energy, Vol 119, 400-
409
NASA SCIENCE, 2003, SCIENCE NEW. accessed 24.09.2020
Nelson A. Kelly *, T. L., 2009, Improved photovoltaic energy output for cloudy conditions with a solar tracking
system. Solar Energy, 83, 2092-2102.
Nelson A. Kelly, T. L., 2011, Increasing the solar photovoltaic energy capture on sunny and cloudy days. Solar
Energy, 85 111-125.
Rameez Shaik, N., Beemkumar, H., Adharsha, K., Venkadeshwaran, A., & Dhass. (2020). Efficiency
enhancement in a PV operated solar pump by effective design of VFD and tracking system. Materials
Today: Proceedings, 33, 454-462 accessed 10.11.2020
REN21,2020, Renewables Global Status Report. accessed 21.11.2020
Shockley, W. Q., 1961, Detailed balance limit of efficiency of p-n junction solar cells. Journal of Applied
Physics, 32 510-519.
UPME, 2005, Atlas de Radiación Solar de Colombia.
accessed
12.09.2020.
Zoe,B. 2018, Simulation analysis and experiment on energy transfer characteristics of photovoltaic energy-
driven ice storage air conditioning system, Chemical Engineering Transactions, 66, 595-600
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