Research Journal of Applied Sciences, Engineering and Technology 3(12): 1384-1390, 2011
ISSN: 2040-7467
© Maxwell Scientific Organization, 2011
Submitted: July 11, 2011
Accepted: September 25, 2011
Published: December 26, 2011
Influence of Orientation on the Performance of a Photovoltaic Conversion
System in Nigeria
1
M.S. Okundamiya and 2A.N. Nzeako
Department of Electrical and Electronic Engineering, Ambrose Alli University,
P.M.B. 14, Ekpoma-310006, Nigeria
2
Department of Electronic Engineering, University of Nigeria, Nsukka-410001, Nigeria
1
Abstract: This study investigates the effects of orientation of photovoltaic surface and proposes the optimum
tilt angle for a photovoltaic array oriented due south in three cities in Nigeria (Abuja, Benin City and Katsina).
Three optimization methods (monthly based, seasonal based and annual based) are implemented. The
inclination of the surface is assumed to be varying from 0º to 90º with an increment of 1º, and the total global
solar radiation on the tilted surface is estimated using the Hay-Davis-Klucher-Reindl (HDKR) Model. Analysis
indicates that the photovoltaic (PV) surface positioned at monthly optimized tilt angles will generate an increase
exceeding 10% of its annual total irradiance.
Key words: Global solar irradiance, HDKR model, Nigeria, optimum tilt angle, orientation, photovoltaic
INTRODUCTION
The present day climate change problems have led to
the search for renewable energy sources in order to
maintain a green environment (Cetin et al., 2009). The
problems are caused by emissions of carbon dioxide
(CO2) in the atmosphere, which are generated by intensive
burning of fossil fuels in order to satisfy the growing
energy needs of humanity. Global emission reduction
targets and the growing anxiety on the impeding scarcity
of fossil resources make a transition of the energy system
towards a carbon free electricity supply necessary
(Aboumahboub et al., 2010a, b; Borghesi, 2010).
Renewable energy technology is capable of
alleviating the already over stretched ecosystem. It is
capable of supplying the energy needed for rapid
developments, especially in rural areas. One of the
applications of the renewable energy technology is the
installation of photovoltaic (PV) systems that generate
power without emitting pollutants and requiring no fuel.
This application is well-known in both developed and
developing countries (Kurokawa and Ikki, 2001). It
involves Building Integrated PV (BIPV) or stand-alone
PV systems that absorbs solar radiation and converts it to
electricity.
Global solar radiation varies with geographical
latitude, season, and time of the day due to the various sun
positions in the sky. This creates the problem of designing
the orientation and optimum tilt (inclination) angle of a
PV module in order to optimize the global solar radiation
collection at fixed latitudes. The performance of the PV
Conversion System (PVCS) is highly dependent on its
orientation, optical and geometric properties, macro- and
micro-climatic conditions, geographical position, and
period of use (Yang and Lu, 2007; Gunerhan and
Hepbasli, 2007). The orientation of the PV surface is
described by its tilt angle ($) and the azimuth ((), both
related to the horizontal. The orientation is considered to
be optimal when facing south (in the northern
hemisphere) or when facing north (in the southern
hemisphere), as suggested in previous works (Calabro,
2009; Ahmad and Tiwari, 2009).
A prior requirement for the design of fixed PVCS is
the knowledge of its optimum tilt angle that maximizes its
collected solar radiation (Kern and Harris, 1975). This
depends on latitude (L ), solar declination (*), and days of
the year. Qiu and Riffat (2003) suggested that the tilt
angle of the PV surface set within the optimum tilt angle
of ±10º as an acceptable practice. Yang and Lu (2007)
recommend that the tilt angle exceeding 40º should be
avoided. Other recommendations for optimum tilt angle
are based only on the latitude (Gunerhan and Hepbasli,
2007; Ulgen, 2006).
In previous studies, the authors (Okundamiya and
Nzeako, 2010; 2011a) developed correlations between
monthly mean daily global solar radiations on a horizontal
surface and monthly mean daily ambient temperatures
(minimum and maximum), and between the monthly
mean daily diffuse and global solar radiations on a
horizontal surface as a function of the clearness index for
selected cities in Nigeria (Okundamiya and Nzeako,
2011b). This study examines the influence of orientation
of a south-facing photovoltaic surface and proposes the
optimum tilt angles for harvesting solar electricity in three
cities in Nigeria (Abuja, Benin City and Katsina). The
Corresponding Author: M.S. Okundamiya, Department of Electrical and Electronic Engineering, Ambrose Alli University,
P.M.B. 14, Ekpoma, Nigeria
1384
Res. J. Appl. Sci. Eng. Technol., 3(12): 1384-1390, 2011
Fig. 1: Map of study locations in Nigeria
locations of these three cities in Nigeria are shown in
Fig. 1, where Abuja is located on latitude 9.08º and
longitude 7.53º, Benin City on latitude 6.34º and
longitude 5.63º, and Katsina on latitude 13.00º and
longitude 7.60º.
MATERIALS AND METHODS
A ten-year (1996 - 2005) data set of monthly mean
daily minimum and maximum ambient temperatures are
obtained from the archives of the National Aeronautics
and Space Administration (NASA, 2011) for the study
locations. These data sets are applied to the temperaturebased (Okundamiya and Nzeako, 2010) and diffuse solar
radiation (Okundamiya and Nzeako, 2011b) models. The
computation of the global solar irradiance on the tilted PV
array is based on the Hay-Davis-Klucher-Reindl (HDKR)
model (Duffie and Beckman, 2006), with the ground
reflectance (albedo) assumed to be 0.2 and the azimuth
has been fixed at 0º in this study. The detailed analysis is
presented in the Appendix.
In order to achieve maximum global solar radiation
on the PV surface, three optimization methods: monthly
based, seasonal based and annual based, are implemented.
The monthly based optimization method uses a fixed
monthly average tilt angle, while the seasonal and annual
methods utilize a fixed seasonal average tilt and fixed
annual tilt angles, respectively. This study was carried out
in Benin City between January and July 2011.
SIMULATION AND RESULTS
The study made use of a computer program written in
MATLAB programming language. The program
computes the global solar irradiance on the tilted PV array
using the data discussed above. The angle of inclination
varies from 0º to 90º with a step of 1º. The relations used
for simulating the global solar irradiance are presented in
the Appendix. Table 1 shows the results of the analysis of
global solar radiation for the different optimization
techniques at optimum tilt angles for selected cities in
Nigeria. Figure 2 shows the influence of orientation on
the optimized global solar radiation using different
techniques for the study locations, while Fig. 3 shows the
variation of optimum tilt angles with months of the year
for which global solar radiation is maximum. Figure 4
illustrates the variation of monthly global solar irradiance
with tilt angles. Figure 5 shows a comparison of the
optimal annual irradiance at different optimum tilt angles
for the study locations.
DISCUSSION
The results presented in Table 1 indicate that global
solar irradiance varies with geographical locations, and it
increases with increasing latitudes. The monthly based
optimization shows that during rainy season (April August), the global solar radiation on the PV surface is
optimum if oriented due south in the horizontal direction
(with zero tilt), and decreases with increasing tilt ($)
angles (Fig. 4). In March (the end of dry season/
commencement of rainy season) and September (the end
of rainy season/commencement of dry season), the global
solar radiation on the PV surface increases with
increasing tilt angle until a maximum irradiance is
attained at approximately L + 4º ($opt . L + 4) and L 3º ($opt . L - 3), respectively. The optimum tilt, however,
exceeds 4 L during the climax of the dry season. The
annual based optimization method generates a maximum
annual global solar radiation at optimum tilt angle ranging
1385
Res. J. Appl. Sci. Eng. Technol., 3(12): 1384-1390, 2011
from L+1º (in Katsina) to approximately L + 6º (in Abuja
and Benin City). The seasonal based optimization method
generates a maximum annual global solar radiation if the
PV surface is positioned horizontally ($ = 0º) during rainy
season, and inclined at L +23º during dry season.
Implementation of the annual average tilt angle
improves the annual global solar radiation in Abuja,
Monthly
Monthly Global solar iradiance
(kWh/m2/month)
Seasonal
240
Annual
220
200
180
160
140
120
Dec.
Oct.
Oct.
Nov.
Sep.
Sep.
Sep.
Aug.
Aug.
Aug.
Jul.
Jul.
Jun.
Jul.
Apr.
May.
Feb.
Mar.
Jan.
100
Monthly Global solar iradiance
(kWh/m2/month)
(a)
240
220
200
180
160
140
120
Dec.
Nov.
Jun.
Apr.
May.
Feb.
Mar.
Jan.
100
(b)
Monthly Global solar iradiance
(kWh/m2/month)
240
220
200
180
160
140
120
Dec.
Oct.
Nov.
Jun.
Apr.
May.
Feb.
Mar.
100
Jan.
Table 1: Results of the analysis of the influence of orientation at
optimum tilt angles for selected cities in Nigeria
Monthly based optimization
-------------------------------------------------------------------------Global Irradiance
(kWh/m2/month)
Optimum Tilt (o)
------------------------------------- ----------------------------------Months Abuja Benin city Katsina Abuja Benin city Katsina
Jan.
228.4
204.0
224.9
40
38
44
Feb.
193.2
168.4
211.7
31
27
35
Mar.
198.4
167.8
222.4
13
10
17
Apr.
181.4
151.2
216.0
0
0
0
May
172.9
147.0
220.7
0
0
0
Jun.
151.6
126.8
209.8
0
0
0
Jul.
137.7
110.6
196.8
0
0
0
Aug.
129.7
110.6
180.7
0
0
0
Sep.
141.9
114.2
182.6
6
3
10
Oct.
176.9
141.2
211.4
25
20
30
Nov.
221.2
171.3
225.4
39
34
42
Dec.
237.1
198.5
223.3
43
39
47
Yearly 2170
1812
2526
Seasonal based optimization
-------------------------------------------------------------------------Global Irradiance
(kWh/m2/month)
Optimum Tilt (º)
------------------------------------- ----------------------------------Months Abuja Benin city Katsina Abuja Benin city Katsina
Jan.
226.4
201.8
223.0
32
29
36
Feb.
193.2
168.3
211.6
32
29
36
Mar.
190.2
161.1
213.4
32
29
36
Apr.
181.3
151.2
216.0
0
0
0
May
172.9
147.0
220.7
0
0
0
Jun.
151.6
126.8
209.8
0
0
0
Jul.
137.7
110.6
196.9
0
0
0
Aug.
129.7
110.6
180.7
0
0
0
Sep.
141.5
114.1
180.5
0
0
0
Oct.
175.8
140.1
210.5
32
29
36
Nov.
219.8
171.2
224.2
32
29
36
Dec.
233.3
196.0
219.9
32
29
36
Yearly 2153
1799
2507
Annual based optimization
---------------------------------------------------------------------------Global Irradiance
(kWh/m2/month)
Optimum Tilt (o)
------------------------------------- ----------------------------------Months Abuja Benin city Katsina Abuja Benin city Katsina
Jan.
209.8
186.9
200.6
15
12
14
Feb.
187.1
163.9
200.7
15
12
14
Mar.
198.3
167.7
222.1
15
12
14
Apr.
172.5
145.7
207.3
15
12
14
May
156.2
136.4
198.9
15
12
14
Jun.
134.4
116.5
183.7
15
12
14
Jul.
125.1
103.8
176.0
15
12
14
Aug.
122.8
106.4
170.4
15
12
14
Sep.
140.5
113.2
182.1
15
12
14
Oct.
175.0
140.3
205.6
15
12
14
Nov.
205.0
162.3
203.7
15
12
14
Dec.
213.0
180.8
194.4
15
12
14
Yearly 2039
1724
2347
(c)
Fig. 2 : Influence of orientation on the optimized global solar
radiation using different techniques for the study
locations (a) Abuja (b) Benin City (c) Katsina
Benin City and Katsina, respectively, by over 2.6, 1.7 and
2.4%, while the implementation of seasonal average tilt
angles (0º and L+23º) improves the annual global solar
radiation for Abuja, Benin City and Katsina, respectively,
by over 8.4, 6.1 and 9.4%. The implementation of the
monthly average tilt angle gives the highest increase of
1386
Res. J. Appl. Sci. Eng. Technol., 3(12): 1384-1390, 2011
250
Katsina
Abuja
Benin city
40
solar iradiance
Monthly global
2
(kWh/m /month)
Opimum Tlt angle ( 0 )
50
150
30
100
20
10
50
0
0
Jul.
Oct.
(a)
200
150
100
0
20
30
40 50
60
Inclination (°)
70
80
100
50
0
10
20
30
40 50
60
Inclination (°)
1.0
0.6
0.4
T
I (k Wh /m2)
0.8
0.2
-0
24
4 00
16
3 00
20 0
8
1 00
0
0
H our
D ay
(b)
1.0
0.8
2
IT (kWh/m )
90
70
80
90
Fig. 4: Variation of monthly global solar irradiance with tilt
angles (a) Abuja (b) Benin City (c) Katsina.
90
0.6
0.4
0.2
0
24
400
16
300
8
0
80
150
(a )
Hou r
70
(c)
0
10
40 50
60
Inclination (0)
200
50
0
30
250
Monthly global solar iradiance
(kWh/m2/month)
Jan.
Apr.
250
20
10
Dec.
Nov.
Oct.
Sep.
Aug.
Jul.
Jun.
May.
Apr.
Mar.
Feb.
Jan.
0
Fig. 3: Variation of optimum tilt angle with months of the year
for monthly based optimization
Monthly global solar iradiance
(kWh/m2/month)
(b)
200
200
100
0
Day
1387
Res. J. Appl. Sci. Eng. Technol., 3(12): 1384-1390, 2011
(c)
1.0
IT (kWh/m 2)
0.8
0.6
0.4
0.2
-0
24
16
300
400
200
8
0
100
0
Hour
Day
Fig. 5: Comparison of optimal annual global irradiance at different optimum tilt angles (a) Abuja (b) Benin City (c) Katsina
over 9.2, 6.8 and 10.2% respectively. Although the
monthly based approach yields the maximum annual
global solar radiation, the loss of energy when using the
seasonal approach is less than 0.8% (which is negligible)
as shown in Fig. 2. Figure 3 clearly indicates the unique
$opt for each month of the year for which maximum global
solar radiation is obtained.
The variation of the monthly global solar irradiance
for the study locations (Fig. 4) is almost uniform. The
time variation of irradiance (Fig. 5) shows that global
solar radiation is symmetrical about the solar noon. It is
pertinent to note that the solar radiation reaching the
earth’s surface follows an oblique path length in the early
morning and in the late afternoon. The result of this
oblique incidence through the atmosphere is a greater
atmospheric attenuation and lesser intensity of solar
radiation. At optimum tilt angles, global solar irradiance
of 0.9348, 0.8139 and 1.0075 kW/m2 occurs in November
30, January 1 and February 1, in Abuja, Benin City and
Katsina, respectively.
than 0.8% can be neglected. For stand-alone PV systems,
the annual optimum tilt angle for a south facing azimuth
in Abuja, Benin City and Katsina are found to be 15,
12 and 15º, respectively. The annual optimum tilt angle
is considerably greater than the local latitude in this study.
Appendix: For a tilted surface (surface with any
orientation) at time t, the cosine of the angle of incidence
is deduced (Liu and Jordan, 1962) as:
cos2 = sin* sinN cos$ - sin* cosN sin$ cos( +
cos* sinN sin$ cos( cosT + cos* cosN cos$ cosT
+cos* sin$ sin( sinT
(A1)
where, 2 is the angle of incidence, * is the solar
declination, L is the latitude, $ is the surface inclination
(tilt) angle, ( is the surface orientation (azimuth) and T is
the hour angle. All the angles are in degrees. For a plane
surface with due south orientation (( = 0), the cosine of
the angle of incidence is:
cos2 = sin* (sinN cos$ - cosN sin$ ) +
cos* cosT (cosN cos$ + sinN sin$)
CONCLUSION
In this study, the effects of orientation of a southfacing photovoltaic surface and the optimum tilt angles
for harvesting solar electricity in three cities in Nigeria is
presented. The results indicate that the performance of the
PVCS can be optimized if the surface is positioned
horizontally ($ = 0º) between April-August, and inclined
at optimum tilt angle (between September and March).
The monthly optimum tilt angles increase with increasing
latitudes. During this period (between September and
March), the minimum tilt angle of approximately (L-3º)
is obtained in September.
In order to minimize the design and installation
costs of the PVCS, the seasonal average fixed optimum
tilt angles can be utilized since its total energy loss of less
(A2a)
cos2 = sin* sin(N-$) + cos* cosT cos(N-$) (A2b)
For a horizontal surfaces, the angle of incidence is the zenith angle of
the sun (that is, at 0º or 90º when the sun is above the horizon), hence,
$ = 0 and (A2) becomes:
cos2z = sin* sin(N) + cos* cos N cos(T)
(A3)
where, 2Z is the zenith angle of incidence. When 2Z = 90º, T = Ts and
(A3) becomes:
cosTs = - sin*sinN/cos*cosN
Ts = cosG1 (-tan* tanN)
(A4)
where, Ts is the sunset hour angle in degrees. The geometric ratio
(factor) is ratio of beam radiation on the tilted surface to beam radiation
on the horizontal surface (Alam et al., 2005) given as:
1388
Res. J. Appl. Sci. Eng. Technol., 3(12): 1384-1390, 2011
Rb =
=
cosθ
cosθZ
sin δ sin( Φ − β ) + cosδ cosω cos(Φ − β )
sin δ sin Φ + cosδ cosω cos Φ
REFERENCES
(A5)
The hourly diffuse and global solar radiation is respectively computed
(Liu and Jordan, 1962) as:
Id =
I=
cosω − cosω s
πω s cosω s ⎞
⎛
⎜ sin ω s −
⎟
⎝
180 ⎠
(A6)
cosω − cosω s
πω s cosω s ⎞
24 ⎛
⎜ sin ω s −
⎟
⎝
180 ⎠
(A7)
π Hd
24
πH
And hourly beam radiation is:
Ib = I − I d
(A8)
where I, Ib, and Id respectively is the hourly global, beam and diffuse
solar radiation on a horizontal surface, while T and Ts, respectively is
the hour angle and sunset hour angle. The anisotropy index, Ai is given
as:
Ai =
Ib
I0
(A9)
where I0 is the hourly extraterrestrial radiation on a horizontal surface
defined as:
⎤
360d ⎞ ⎡ sin δ sin Φ
⎛
I 0 = I sc ⎜ 1 + 0.033 cos
⎟⎢
⎥
⎝
365 ⎠ ⎣ + cosδ cos Φ cosω ⎦
(A10)
The horizon brightening ƒ is given as:
f =
Ib
I
(A11)
The global solar irradiance on the tilted PV array is (Duffie and
Beckman, 2006):
⎛ 1 − cos β ⎞
I T = Rb ( Ib + I d Ai ) + I d ρ g ⎜
⎟+
⎝
⎠
2
⎡ 1 + cos β ⎛
⎤
3⎛ β ⎞ ⎞
I d (1 − Ai ) ⎢
⎜ 1 + f sin ⎜ ⎟ ⎟ ⎥
⎝
⎠
2
2
⎝
⎠
⎢⎣
⎥⎦
(A12)
where, $ is the inclination of the surface and Dg is the ground reflectance
or albedo.
ACKNOWLEDGMENT
This study was partially funded by ETF 2009
AST&D Intervention (Reference no. AAU/REG/
ETF.560/475).
Aboumahboub, T., K. Schaber, P. Tzscheutschler and
T. Hamacher, 2010a. Optimization of the Utilization
of Renewable Energy Sources in the Electricity
Sector. Proceedings of the 5th IASME/WSEAS
International Conference on Energy & Environment,
World Scientific and Engineering Academy and
Society, Stevens Point, Wisconsin, USA, pp:
196-204.
Aboumahboub, T., K. Schaber, P. Tzscheutschler and
T. Hamacher, 2010b. Investigating optimal
configuration of a prospective renewable-based
electricity supply sector. Proceedings of the 5th
IASME/WSEAS International Conference on Energy
and Environment, World Scientific and Engineering
Academy and Society, Stevens Point, Wisconsin,
USA, pp: 83-89.
Ahmad, M.J. and G.N. Tiwari, 2009. Optimization of tilt
angle for solar collector to receive maximum
radiation. Open Renewable Energy J., 2: 19-24.
Alam, M.S., S.K. Saha, M.A.K. Chowdhury,
M. Saifuzzaman and M. Rahman, 2005. Simulation
of solar radiation system. Am. J. Appl. Sci., 2(4):
751-758.
Borghesi, S., 2010. The European Emission Trading
Scheme and Renewable Energy Policies: Credible
Targets for Incredible Results? The Berkeley
Electronic Press University of Siena, Retrieved from:
http://www.bepress.com/feem/paper529, pp: 1-29.
Calabro, E., 2009. Determining optimum tilt angles of
photovoltaic panels at typical north-tropical latitudes.
J. Renew. Sustain. Energ., 1(033104): 6,
Doi:10.1063/1.3148272.
Cetin, E., A. Yilanci, Y. Oner, M. Colak, I. Kasikci and
H.K. Ozturk, 2009. Electrical analysis of a hybrid
photovoltaic/hydrogen/fuel cell energy system in
Denizli, Turkey. Int. J. Energ. Build., 41: 975-9981.
Duffie, J.A. and W.A. Beckman, 2006. Solar Engineering
of Thermal Processes, 3rd Edn., John Wiley and
Sons, New York.
Gunerhan, H. and A. Hepbasli, 2007. Determination of
the optimum tilt angle of solar collectors for building
applications. Building Environ., 42(2): 779-783.
Kern and Harris, 1975. On the optimum tilt of a solar
collector. Solar Energy, 17(2): 97-102.
Kurokawa, K. and O. Ikki, 2001. The Japanese
experiences with national PV-System programmes.
Solar Energy, 70(6): 457-466.
Liu, B.Y.H. and R.C. Jordan, 1962. Daily insolation on
surfaces tilted towards equator. Trans. ASHRAE, 67:
526-541.
NASA, 2011. Surface Meteorology and Solar Energy
Data and Information. Retrieved from: http://eosweb.
larc.nasa.gov/sse, (Accessed on: March, 2011).
1389
Res. J. Appl. Sci. Eng. Technol., 3(12): 1384-1390, 2011
Okundamiya, M.S. and A.N. Nzeako, 2010. Empirical
model for estimating global solar radiation on
horizontal surfaces for selected cities in the six
geopolitical zones in Nigeria. Res. J. Appl. Sci. Eng.
Technol., 2(8): 805-812.
Okundamiya, M.S. and A.N. Nzeako, 2011a. A linear
regression model for global solar radiation on
horizontal surfaces in warri, Nigeria. ISRN Renew.
Energ., (In Press).
Okundamiya, M.S. and A.N. Nzeako, 2011b. Estimation
of diffuse solar radiation for selected cities in
Nigeria. ISRN Renew. Energ., Article ID 439410.
Qiu, G. and S.B. Riffat, 2003. Optimum tilt angle of solar
collectors and its impact on performance. Inter. J.
Ambient Energy, 24(1): 13-20.
Ulgen, K., 2006. Optimum tilt angle for solar collectors.
Energy Sources, Part A, 28(13): 1171-1180.
Yang, H.X. and L. Lu, 2007. The optimum tilt angles and
orientations of PV claddings for Building Integrated
PV applications. J. Solar Energy Engineering, 129:
253-255.
1390