سمريةمعة الجا مجلة ا: اساسيةعلوم ا ل والتطبيقية( مجلد ال2 ( العدد) 2 ، ديسمبر) 2017 م88 Estimating global , direct , diffuse and reflected solar radiation on horizontal and tilted surfaces in Tripoli , Libya Ali. S. Al-Nuaimi* Tarig Elmabrouk Department of physics – Faculty of Science- Omar Al-Mukhtar university – Beida – Libya E mail ; [email protected], [email protected]Keywords: Global radiation ,direct , diffuse radiation , horizontal , tilted surfaces ,Renewable Energy, Tripoli , Libya Introduction: Solar energy occupies one of the most important types of renewable energy sources . It is the energy provide by the sun .Solar radiation data are fundamental inputs for solar energy applications , such as photovoltaic , and solar thermal systems . The design of a solar energy conversion system requires knowledge regarding the availability of global solar radiation and its component at the location of interest (1). An accurate knowledge of the solar radiation data for a particular location is a pre requisite , in estimating the thermal performance and economic efficiency of solar energy systems .The availability of these data may be of the form of types of total , direct , diffuse , and reflected radiation . These data may be needed on daily , monthly or yearly time scales . Each of these forms is important and has particular usage in specific applications. In a recent report(2) Libya is the 16 th largest country in the world in terms of land mass according to OPEC.org. Its economy depends primarily on revenues from the oil sector , which contribute about 95 percent of export earning .Libya has the potential to become a renewable energy giant according to Responding to Climate Change .Libya is located on the cancer orbit line and is exposed to the sun rays through the year with long hours during the day . It boasts a very high daily solar radiation rate – on a flat coastal plain it is about 7.1 kilowatt hours per square meter per day , and in the south region it is about 8.1 kWh/m 2 /day. If we compare this amount for instance with the Great Britain we see that Great Britain has half than this amount which is about 2.95 kWh/m 2 /day . Libya could generate approximately five times the amount of energy from solar power than it currently produces in crude oil . If this country which is estimated to be 88 per cent desert used only 0.1% of its landmass to harness solar power , it could produce the equivalent to almost seven million barrels of crude oil per day in energy . Renewable energy technology is still in its very early days in Libya and a clear strategy and timetable is needed to take it forward .In particular , work needs to be done to develop the skills and knowledge needed to install and maintain renewable energy systems .(3) Many models have been developed to estimate the amount of global solar radiation on horizontal surfaces using various climatic parameter, such as sunshine hours Many authors find it is
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والتطبيقيةلعلوم الأساسية ا :مجلة الجامعة الأسمرية
م2017(، ديسمبر 2( العدد )2المجلد )
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Estimating global , direct , diffuse and reflected solar radiation on horizontal
and tilted surfaces in Tripoli , Libya
Ali. S. Al-Nuaimi* Tarig Elmabrouk
Department of physics – Faculty of Science- Omar Al-Mukhtar university – Beida – Libya
rather important to determine the beam ( direct ) , and diffuse components of total radiation incident
on a horizontal surface . Once these components are determined , they can be transported over tilted
surface, and hence , the short as well as the long term performances of tilted flat plate solar collectors ,
photovoltaic , modules and other solar devices can be estimated (4) . Many authors have presented
empirical correlations to estimate the monthly average daily diffuse radiation on a horizontal surface (
5, 6) El-Sebaii and Trabea (7) proposed correlations for estimating horizontal diffuse radiation in Egypt.
Total radiation consists of three components ; beam ( direct ) radiation , diffuse radiation , and ground (
reflected ) radiation . el- Sebaii etal (8) calculated global, direct and diffuse radiation on horizontal and
tilted surfaces in Jeddah , Saudi Arabia . al- Ayed et al (9) proposed empirical correlations for calculating
the monthly average of daily global , direct and diffuse solar radiation on horizontal surfaces in Riyadh
using the data of 1 year .Al-Nuaimi (10) estimated global solar radiation in north Libya . Bannani et al
(11) estimated monthly average solar radiation using data for 11 stations at different locations in Libya.
Al- Dabbas(12) analyzed the characteristics of the solar radiation climate of the daily global radiation
and diffuse radiation in Amman , Jordan .Ueyama (13) estimated hourly and diffuse solar radiation for
the compilation of solar radiation distribution maps in Japan . Gana and Akpootu (14) used an Angstrom
type empirical correlation for estimating global solar radiation in north – eastern Nigeria .Falayi et al
(15) used correlations to estimate monthly mean of daily diffuse solar radiation in some selected cities
in Nigeria . Al-rawahi et al (16) predicted hourly solar radiation on horizontal and inclined surfaces
forMuscat / Oman .Abbasi and Qureshi (17) estimated global , and diffuse solar radiation for
Nawabshah , Sindh , Pakistan using measured data of bright sunshine hours for twenty two years .Bindi
et al (18) used different methods for separating diffuse and direct components of solar radiation and
their application in crop growth models in Italy .
The main objective of this paper is to estimate the various component of solar radiation in
some selected Libyan cities .
Materials and Method :
Data of the sunshine duration hours for Tripoli was e obtained from the national Meteorological
organization in Libya .These data were used to estimate the direct , diffuse and reflected solar radiation
. A model was used to calculate these parameters. A computer programme in Matlab was developed .
The deviation between the estimated and satellite values was determined using the statistical
parameters as given by Nguyen et al [18] as follows :
Mean Bias error (MBE):
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N
HHMBE Sm
N
i
)(
1
(7)
Root Mean square Error (RMSE):
N
HH
RMSESm
N
i
2
1
)(
(8)
The mean percentage error id calculated using the following formula
100]
)(
[
N
HHH
MPE mcalm
To calculate the various solar parameters.
The model :
In this study the estimation of the monthly average daily global solar radiation on a horizontal surface
is based on a modified version of the original Angstrom – type equation . This equation is a regression
equation that relates monthly average daily solar radiation to clear sky radiation at a location and
average fraction of possible sunshine hours [19], but Page [20] and Duffie and Beckman [21] have made
some modifications on the equation to base it on extraterrestrial radiation on horizontal surface rather
than on clear sky radiation as follows :
)(00 S
Sba
H
H (1)
Where H is the monthly average daily global radiation 0H is the monthly average daily
extraterrestrial radiation , S is the monthly average daily hours of bright sunshine (in hours), 0S is the
monthly average day length (in hours ) , and (a) and (b) are regression empirical coefficients obtained
from the relationship given by Tiwari and Suneja [22] as follows :
)(323.0cos235.0110.00S
Sa
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)(694.0cos553.0449.10S
Sb (2)
The monthly average daily extraterrestrial radiation on a horizontal surface ( 0H ) can be computed
from the equation given by Duffie and Beckman [21] as follows:
]sinsin180
sincos][cos365
360cos033.01[
240
sssc
nIH (3)
Where scI is the solar constant (= 1367 Wm-2), is the latitude of the city or location , is the solar
declination angle , s is the mean sunrise hour angle for the given month , and n is the number of day
of the year starting from the first of January . The solar declination angle ( ) , and the mean sunrise
hour angle ( s ) can be calculated respectively , as given by Duffie and Beckman [21] as follows:
365
)284(360sin[45.23
n (4)
)tantan(cos 1
s (5)
For a given month , the maximum possible sunshine duration (monthly average day length 0S ) cab be
computed by using the following equation as given by Duffie and Beckman[21] :
sS 15
2)tantan(cos
15
2 1
0 (6)
The monthly average of daily global solar radiation incident on a horizontal surface H is
calculated as follows
)]([0
0S
SbaHH (7)
The clearness index (KT) is defined as the ratio of the measured horizontal terrestrial solar
radiation to the calculated horizontal extraterrestrial solar radiation is calculated from the
following relation
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0H
HKT (8)
The monthly mean daily diffuse fraction of solar radiation is calculated by the following
equation
T
d KH
H13.100.1
The beam ( direct ) bH solar radiation is calculated from the following relation
db HHH (9)
To calculate the monthly average daily total solar radiation incident on a tilted surface with an
angle facing toward equator , the following steps were followed
1- To calculate the direct ( beam ) incident solar radiation on a tilted surface
bbtb RHH (10)
Where tbH is the total beam solar radiation incident on a tilted surface , and bH is the beam
solar radiation incident on a horizontal surface and bR is the tilt factor which is the ratio of
flux incident on a tilted surface and the flux incident on a horizontal surface and is given by the
following relation
h
bR
cos
cos (11)
Where is the angle of incidence of solar radiation on a tilted surface , and h is the angle of
incidence of solar radiation on a horizontal surface
s
s
h
bR
coscoscossinsin
)cos(coscos)sin(sin
cos
cos
(12)
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2- To calculate the diffuse solar radiation incident on a tilted surface tdH , the following
relation is used
(13)
Where dR is the tilt factor for diffuse radiation , and is given by
2
cos1 dR (14)
Where is the angle of inclination of the solar collector
3- To calculate the reflected solar radiation from the earth’s surface on the tilted surface of the
solar collector , the following relation is used
rdbtr RHHH )( (15)
Where rR is the tilt factor for reflected solar radiation from the earth , and is calculated from
the following relation
)2
cos1(
rR (16)
Where is the coefficient of reflectivity of the earth’s surface which varies 0.07 for water to
0.75 for ice , and is 0.22 for concrete , and in most cases an average of 0.2 is taken as in our
study
4- Finally the total solar radiation incident on a tilted surface can be calculated using the sum of
the above three steps as follows :
trtdtbt HHHH (17)
Results and Discussion:
Table 1 shows the location of the Tripoli and its elevation above mean sea level .
Table 1 the location of Tripoli
ddtd RHH
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City Latitude N Longitude E Elevation (m)
Tripoli 32.89 13.18 12.0
Figures 1 shows the comparison between the monthly average daily global radiation on a horizontal
surface as calculated by the model versus the averages as obtained from NASA for Tripoli .
Figure 1. Comparison between the monthly average daily global radiation on a horizontal surface as calculated by the model
versus the averages as obtained from NASA for Tripoli.
It can be seen from this figure that the model works very well during the summer months and there is
a rather little underestimation by the model during the winter season.
Figures 2, shows the scatter plot of the calculated data versus the data measured by NASA for Tripoli
.
0
1
2
3
4
5
6
7
8
9
JAN FEB MAR APR MAY JUNE JULY AUG SEP OCT NOV DEC
Sola
r ra
dia
tio
n (
kw/m
2 )
Month
Tripoli
H(Model)
H(NASA)
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Figure 2. Scatter plot between calculated and measured monthly average hourly solar radiation for the year 2005 for Tripoli
city
It can be seen from this figure that almost all the values congregate very close to the regression line.
This means the performance of this model seems to be very good in estimating average monthly daily
solar radiation .
Table (2) shows the various parameters as calculated by the model
Month 0H
0SS
H TK
January 5.85 0.65 3.74 0.64
February 7.17 0.69 4.70 0.66
March 8.79 0.65 5.61 0.64
April 10.24 0.65 6.57 0.64
May 11.12 0.75 7.49 0.67
June 11.44 0.75 7.69 0.67
July 11.26 0.88 7.82 0.69
August 10.56 0.87 7.32 0.69
September 9.26 0.74 6.21 0.67
October 7.64 0.70 5.03 0.66
November 6.16 0.80 4.21 0.68
December 5.48 0.87 3.80 0.69
y = 1.2499x - 2.2823
0
5
10
0 2 4 6 8 10
H(M
od
el)
H(NASA)
H(NASA) Vs H(Model)
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Table (3) shows the calculated global , beam , and diffuse solar radiation for the three cities under
study
Month Global radiation(H) beam radiation(Hb) Diffuse radiation(Hd)
January 3.74 2.70 1.04
February 4.70 3.48 1.22
March 5.61 4.05 1.56
April 6.57 4.77 1.80
May 7.49 5.69 1.79
June 7.69 5.85 1.85
July 7.82 6.13 1.69
August 7.32 5.73 1.59
September 6.21 4.70 1.51
October 5.03 3.74 1.29
November 4.21 3.26 0.96
December 3.80 2.97 0.82
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Figure 2. Comparison between the monthly Radiation on a horizontal surface as calculated by the model versus the calculated
global , beam , and diffuse solar radiation for Tripoli.
Tables (4, 5, 6 ) show the various solar radiation parameters incident on tilted surfaces for three
selected solar collectors angles ( 300 , 450, 600 )
Table (4) solar radiation parameters on tilted surface for solar collector angle 300
Month Rb Htb Rd Htd Rr Htr Ht
January 1.672 4.52 0.93 0.97 0.01 0.05 5.54
February 1.437 5.00 0.93 1.14 0.01 0.06 6.21
March 1.198 4.86 0.93 1.46 0.01 0.08 6.39
April 0.994 4.74 0.93 1.68 0.01 0.09 6.51
May 0.852 4.85 0.93 1.67 0.01 0.10 6.62
June 0.786 4.60 0.93 1.72 0.01 0.10 6.42
July 0.813 4.99 0.93 1.57 0.01 0.10 6.66
August 0.929 5.32 0.93 1.48 0.01 0.10 6.90
September 1.117 5.25 0.93 1.40 0.01 0.08 6.74
October 1.352 5.06 0.93 1.20 0.01 0.07 6.33
November 1.606 5.23 0.93 0.89 0.01 0.06 6.18
December 1.748 5.20 0.93 0.77 0.01 0.05 6.02
0
1
2
3
4
5
6
7
8
9Ja
n
Feb
Mar
Ap
r
May
Jun
e
July
Au
g
Sep
Oct
No
v
De
c
Sola
r ra
dia
tio
n (
kw/m
2)
Global Radiation(H)
Beam Radiation(Hb)
Diffuse Radiation(Hd)
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Figure 2. Comparison between the solar radiation parameters on tilted surface
for solar collector angle 300 for Tripoli.
Table (5) solar radiation parameters on tilted surface for solar collector angle 450
Month Rb Htb Rd Htd Rr Htr Ht
January 1.847 4.99 0.85 0.89 0.03 0.11 5.99
February 1.514 5.27 0.85 1.04 0.03 0.14 6.45
March 1.177 4.77 0.85 1.33 0.03 0.16 6.27
April 0.888 4.24 0.85 1.54 0.03 0.19 5.97
May 0.687 3.91 0.85 1.53 0.03 0.22 5.66
June 0.594 3.48 0.85 1.58 0.03 0.23 5.28
July 0.632 3.88 0.85 1.44 0.03 0.23 5.55
August 0.796 4.56 0.85 1.35 0.03 0.21 6.13
September 1.062 4.99 0.85 1.28 0.03 0.18 6.46
October 1.394 5.22 0.85 1.10 0.03 0.15 6.46
November 1.753 5.71 0.85 0.82 0.03 0.12 6.65
December 1.954 5.81 0.85 0.70 0.03 0.11 6.62
0
1
2
3
4
5
6
7
8
Jan Feb Mar Apr MayJune July Aug Sep Oct Nov Dec
Sola
r ra
dia
tio
n (
kw/m
2)
Chart Title
Htb
Htd
Htr
Ht
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Figure 3. Comparison between the solar radiation parameters on tilted surface
for solar collector angle 450 for Tripoli.
Table (6) solar radiation parameters on tilted surface for solar collector angle 600
Month Rb Htb Rd Htd Rr Htr Ht
January 1.896 5.12 0.75 0.78 0.05 0.19 6.09
February 1.488 5.18 0.75 0.91 0.05 0.24 6.33
March 1.075 4.36 0.75 1.17 0.05 0.28 5.81
April 0.721 3.44 0.75 1.35 0.05 0.33 5.12
May 0.475 2.71 0.75 1.34 0.05 0.37 4.42
June 0.362 2.12 0.75 1.38 0.05 0.38 3.89
July 0.409 2.51 0.75 1.26 0.05 0.39 4.16
August 0.608 3.49 0.75 1.19 0.05 0.37 5.04
September 0.934 4.39 0.75 1.13 0.05 0.31 5.83
October 1.342 5.02 0.75 0.97 0.05 0.25 6.24
November 1.781 5.80 0.75 0.72 0.05 0.21 6.73
December 2.027 6.03 0.75 0.62 0.05 0.19 6.84
0
1
2
3
4
5
6
7So
lar
rad
iati
on
(kw
/m2 )
Htb
Htd
Htr
Ht
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Figure 4. Comparison between the solar radiation parameters on tilted surface
for solar collector angle 600 for Tripoli.
0
1
2
3
4
5
6
7
8
Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec
Sola
r ra
dia
tio
n (
kw/m
2)
Chart Title
Htb
Htd
Htr
Ht
0
1
2
3
4
5
6
7
8
Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec
Sola
r ra
dia
tio
n (
kw/m
2 )
Chart Title
Ht30
Ht45
Ht60
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Month Ht30 Ht45 Ht60
Jan 5.54 5.99 6.09
Feb 6.21 6.45 6.33
Mar 6.39 6.27 5.81
Apr 6.51 5.97 5.12
May 6.62 5.66 4.42
June 6.42 5.28 3.89
July 6.66 5.55 4.16
Aug 6.9 6.13 5.04
Sep 6.74 6.46 5.83
Oct 6.33 6.46 6.24
Nov 6.18 6.65 6.73
Dec 6.02 6.62 6.84
Average 6.38 6.12 5.54
0
2
4
6
8
Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec
Axi
s Ti
tle
Chart Title
Ht30
Ht45
Ht60
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Table (7) gives the statistical test made on the results
Table 7 gives the statistical test made on the results
City MBE RMSE PE
Tripoli -0.53 0.71 10.69
Conclusion:
It can be concluded from this study that we can use this simple model to estimate the monthly
average daily global radiation on a horizontal surface for Tripoli city in Libya, as there is a rather good
agreement between the calculated values by the model and the measured values as obtained from
NASA. It also gives better estimate for summer months .
0
1
2
3
4
5
6
7
8
Ht30
Ht45
Ht60
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