96 Journal of Science & Technology Vol. (19) No. (1) 2014 Effect of Altitude and Tilt Angle on Solar Radiation in Tropical Regions Effect of Altitude and Tilt Angle on Solar Radiation in Tropical Regions Abdul-Aziz Mohamed Saeed Aldobhani (1) ABSTRACT Solar radiation is the main factor that affects the PV system design. Because of high shortage in solar radiation data in many regions, the mathematical models are necessary to use in solar radiation data estimation. In this study Hotel method is modeled and applied to extend the knowledge about the solar radiation on horizontal surface, fixed tilt surface and optimal tilt angle surface in tropical climate regions. In addition, the study inspects in the effect of altitude on solar radiation, and analyzes the variation in solar radiation data in areas that have high diversity in altitude regions. The data provides the PV system designer the exact percentages increase in solar radiation in important times in the year caused by rising in altitude and shifting the tilt angle from horizontal to optimum fixed annually tilt angle and optimum daily tilt angle. The study concludes to the main recommendations that can help the PV system designers to improve the output of PV system. In addition, the study analyzes the combination effect of solar radiation in different altitudes and tilt angles to recommend the designers the procedures of improving the peak sun hours of design month for PV systems. Keywords: PV system, Solar radiation, Altitude, Tilt angle, Zenith angle. 1. INTRODUCTION Solar radiation is the main factor that affects on PV system design. The amount of solar energy collected by a solar panel is a function of local solar radiation. There is a significant potential for utilizing the photovoltaic solar energy in Yemen which receives more than 5.5 KW/m2/day on a horizontal surface for the most regions around the year [1]. There is a shortage in solar radiation data in most regions in Yemen. The amount of solar radiation incident on tilted surface at any time is a complex function that depends on several parameters like the global radiation on a horizontal surface, the ground reflectance, and the day of the year [2]. The tilt angle of PV system, region altitude and climate 1- Deportment of Electronic engineering, Faculty of engineering, University of Science and Technology, Sana'a, Yemen
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Effect of Altitude and Tilt Angle on Solar Radiation in Tropical Regions
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96 Journal of Science & Technology
Vol. (19) No. (1) 2014
Effect of Altitude and Tilt Angle on Solar Radiation in Tropical Regions
Effect of Altitude and Tilt Angle on Solar Radiation in
Tropical Regions
Abdul-Aziz Mohamed Saeed Aldobhani(1)
ABSTRACT
Solar radiation is the main factor that affects the PV system design. Because of high shortage in solar radiation data in many regions, the mathematical models are necessary to use in solar radiation data estimation. In this study Hotel method is modeled and applied to extend the knowledge about the solar radiation on horizontal surface, fixed tilt surface and optimal tilt angle surface in tropical climate regions. In addition, the study inspects in the effect of altitude on solar radiation, and analyzes the variation in solar radiation data in areas that have high diversity in altitude regions. The data provides the PV system designer the exact percentages increase in solar radiation in important times in the year caused by rising in altitude and shifting the tilt angle from horizontal to optimum fixed annually tilt angle and optimum daily tilt angle. The study concludes to the main recommendations that can help the PV system designers to improve the output of PV system. In addition, the study analyzes the combination effect of solar radiation in different altitudes and tilt angles to recommend the designers the procedures of improving the peak sun hours of design month for PV systems. Keywords: PV system, Solar radiation, Altitude, Tilt angle, Zenith angle.
1. INTRODUCTION
Solar radiation is the main factor that affects on PV system design. The amount of solar energy collected by a solar panel is a function of local solar radiation. There is a significant potential for utilizing the photovoltaic solar energy in Yemen which receives more than 5.5 KW/m2/day on a horizontal surface for the most regions around the year [1]. There is a shortage in solar radiation data in most regions in Yemen. The amount of solar radiation incident on tilted surface at any time is a complex function that depends on several parameters like the global radiation on a horizontal surface, the ground reflectance, and the day of the year [2]. The tilt angle of PV system, region altitude and climate
1- Deportment of Electronic engineering, Faculty of engineering, University of Science and
Technology, Sana'a, Yemen
97 Journal of Science & Technology
Vol. (19) No. (1) 2014
Effect of Altitude and Tilt Angle on Solar Radiation in Tropical Regions
influences are the main factors that affect on amount of daily and average monthly solar radiation that is received by the square meter of PV array. The total yearly solar energy that is received by tilted PV panels could be better than the incident energy on horizontal one. This amount will be increased for optimum fixed tilt angle of PV solar system in different latitude. Thus, the amount of solar radiation is increasing and the output of PV array is increasing. The knowledge about the solar radiation on horizontal surface or fixed tilt surface is not sufficient to optimize the design of PV system. In addition, the solar radiation data in most regions is not covered the effect of altitude in solar radiation. The effect of altitude on solar radiation as a result the PV system design could be observed in areas that have high diversity in altitude. Many regions in Yemen, as a case study have large variations in elevation in few square kilometers. Hence the effect altitude on solar radiation has to be studied carefully to find out the required factors in PV system design. Many papers are published in different countries to study the effect of either the altitude or tilt angle of PV panels on the solar radiation as a result on the output energy of PV system. For example: Guglielmos. Aglietti and others in [3] examined the possibility to harvest solar energy in the high atmosphere, as an intermediate solution between round-based PV devices and satellite solar power in UK.Stefano Redland and others in [4] harnesses the solar power at high altitude and transmits it to the ground via the mooring cable. The model of a tethered lighter than air spherical balloon is used to simulate the behavior of the system in working conditions. TamerKhatib, A. Mohamed, K. Sopian in [5] use Liu and Jordan model to optimize the monthly tilt angle for solar panels for five main sites in Malaysia. Anu George, Robins Anto in [6] estimated theoretically the values of optimal tilt angle over each month for a PV panel installed in Kerala, India (9.55°N, 76.81ºE) using geographic factor method, clearness index method and declination angle method. DrissLahjouji, HassaneDarhmaoui in [7] developed A mathematical model to calculate solar radiation on an inclined surface as a function of the tilt angle. The study shows that the monthly optimal tilt angle allows maximum solar radiation collection. This study will investigate in the effect of altitude on solar radiation in tropical region. Also the study will figure out and analyze the effect of tilt angle on solar radiation in different altitude levels. The main purpose of this study is to find out the required progressions that will improve the Peak sun hours for design month the PV array in different altitude regions. This paper is organized as follows: introduction and a literature reviews in this field have been introduced in this section. Section two explains the effect of the main influences on solar radiation in, Section three analyzes and investigates the effect of altitude and tilt angle on solar radiation as well on PV panels output. The last section gives the final conclusion and recommendations that can improve the peak sun hours of different types of PV system.
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Effect of Altitude and Tilt Angle on Solar Radiation in Tropical Regions
2. Factors that effect on solar radiation
The main factor that can affect the PV system design is the amount of solar
radiation in different months within the year. The minimum solar radiation is
the mainly value that is used to design the standalone PV systems for different
loads. In addition, the maximum cloudy days per year is another important
factor in the design of standalone PV system for critical loads. A big diversity
in amount of solar radiation in different months dissipates a big available power
from PV array if the system is designed concerning the minimum monthly
radiation system design. As well the long cloudy days have the main effect on
the total storage capacity, as a result the cost of standalone PV system. The
solar radiation per square meter can be increased by the following two
methods:
By change the tilt angle of PV panels in different times per year
By increase the altitude of system location.
These two influences will be investigated in section 3.As well as to recognize
these two influences the air mass and main parameters that verify the optimal
tilt angle will be discussed.
2.1 Effect of Air mass on solar radiation The atmosphere scatters and absorbs some of the Sun’s energy that
is incident on the Earth’s surface. The amount of energy reflected,
scattered and absorbed depends on the amount of atmosphere that
the incident radiation travels through as well as the levels of dust
particles and water vapor present in the atmosphere.
The distance travelled through the atmosphere by the Sun’s rays incident on the Earth is accounted for by a quantity called air mass (AM) which can be calculated from Equation (1) or equation (2) [8][2].
(1)
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Effect of Altitude and Tilt Angle on Solar Radiation in Tropical Regions
Where: θ is the Zenith angle.
Air mass affects the amount of spectral content of solar radiation reaches to
earth's surface, and varies with sun position and altitude. Accordingly outside
the Earth's atmosphere AM = 0, when the sun is directly overhead and the
average extraterrestrial insolation at the edge of the atmosphere (solar constant)
is 1367 w/m2 [8][9].
Higher altitudes complicate things somewhat because the higher you go above
sea level, the fewer atmospheres there is and the more the composition of that
atmosphere differs from the atmosphere at sea level. The effect of air mass is
most felt when the sun is lower in the sky and so it has a bigger impact on the
insolation of high latitude places.
2.2 Effect of array tilt on solar radiation [9] The power of solar radiation that incident on a PV module depends not only on
the power contained in the sunlight, but also on the angle between the module
and the sun. The tilt angle has a major impact on the solar radiation incident on
a surface. When the absorbing surface and the sunlight are perpendicular to
each other, the power density will always be at its maximum when the surface
is perpendicular to the sun. Typically the amount of solar radiation incident on
a tilted module surface is the component of the incident solar radiation which is
perpendicular to the module surface. However, as the angle between the sun
and a fixed surface is continually changing, the power density on a fixed PV
module is less than the available incident sunlight [10].
For a fixed tilt angle, the maximum power over the course of a year is obtained
when the tilt angle is equal to the latitude of the location [2]. However, steeper
tilt angles are optimized for large winter loads, while lower tilt angles use a
greater fraction of light in the summer. The simulation below calculates the
maximum number of solar insolation as a function of latitude and module
angle. The optimal tilt angle is the angle that can eliminate the effect of
declination angle (δ) during different time per year on different latitude
locations. The declination of the sun is the angle between the equator and a line
drawn from the center of the Earth to the center of the sun. The declination is a
function of number of day per year[2].
(2)
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Effect of Altitude and Tilt Angle on Solar Radiation in Tropical Regions
The declination angle varies seasonally due to the tilt of the Earth on its axis of rotation and the rotation of the Earth around the sun. If the Earth were not tilted on its axis of rotation, the declination would always be 0°. However, the Earth is tilted by 23.45° and the declination angle varies between 23.25º in summer solstice and -23.25º in winter solstice. Only at the spring and fall equinoxes is the declination angle equal to 0° [10].The optimal tilt angle for a given moment is the one that keeps the sunlight perpendicular to the tilted surface at that moment and is equal to 90°[2][10].
3. Improving the solar radiation.
To improve the output power of PV panels the factors that affect solar radiation
should be studied carefully before PV system is installed. The incidence solar
radiation per square meter can be improved by change the elevation of installed
PV system in regions that have a variety of altitudes.
As mentioned previously the altitude is one of the main factors that are effect
on air mass as a result the total solar radiation per meter square. In addition, the
tilt angle of PV array has a complicated effect on total solar radiation in
different times per year and in different altitude locations.
To track a significant solar radiation, the effect of altitude and tilt angle has to be studied indifferent times per year. Hotel method in tropical climate regions is modeled in this paper to study the effect of these two influences on different times per year and different altitude levels and different tilt angles of meter square of surfaces.
3.1 Estimation of clear sky radiation Hotel has presented a method for estimating the beam radiation transmitted through clear atmosphere in four climate types [2]. The method takes into account zenith angle on horizontal surface (θZ)and altitude (A).The atmosphere transmission of the beam radiation could be calculated by:
)cos/exp(10 Zb kaa
Where constants 0a , 1a and k are for the slandered atmosphere with 23km
visibility and are founded from 0a *, 1a * and k*, which are given for altitude
less than 2.5 km by: 2*
0 )6(00821.04237.0 Aa
2*1 )5.6(00595.05055.0 Aa
2* )5.2(01858.02711.0 Ak
(3)
(4)
(5)
(6)
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Effect of Altitude and Tilt Angle on Solar Radiation in Tropical Regions
Where: A is the altitude of the observer in kilometers.
Hence, 0a , 1a and k are calculated as following:
0*00 raa
1*11 raa
krkk *
The changes in the Hotel correction factor r0, r1 and rk depend on climate types and given in Table (1). Also, the variation in zenith angle on horizontal surface (θZ) in equation (3)is a function of latitude (φ) , declination (δ) and hour angle (ω) and is given by :
sinsincoscoscoscos Z
The declination is a function of the day in year n (n=1 on 1 January and can be calculated by using equation (11)
)365
284360sin(45.23
n
Hence the total beam radiation (Ib) on horizontal surface can be calculated by using Equation (12)
bb GI 0
Where GO is the solar radiation incident on horizontal plane outside the atmosphere and given by:
ZSCO
nGG cos)]
365
360cos(033.01[
Where the maximum solar radiation outside atmosphere 1367SCG Wh/m2,
n is the day in the year (n=1 on January,1) The relationship between the transmission coefficient for beam radiation (τb) and diffuse radiation (τd) for a clear day is given by equation (14):
b
O
dd
G
I 294.0271.0
Where: Id is the incident diffuse radiation on horizontal plane. The total solar radiation on the tilted surface in south north direction and oriented in vertical axis (IT) can be calculated by:
)2
cos1()
2
cos1(
gdbbT IIRII
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
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Effect of Altitude and Tilt Angle on Solar Radiation in Tropical Regions
Where β is the tilt angle of surface, g is the reflectance of the ground, I is the
total incident solar radiation on horizontal surface and Rb is ratio between beam radiation on the tilted surface to that on horizontal and can be calculated by:
The zenith angle (θ) is given by:
cossinsincos cossincossin
coscoscoscos coscossinsincos
sinsinsincos (17)
Where: is the surface azimuth angle. Table (1) shows the correction factors