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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

Corresponding Author: M.S. Okundamiya, Department of Electrical and Electronic Engineering, Ambrose Alli University,P.M.B. 14, Ekpoma, Nigeria

1384

Influence of Orientation on the Performance of a Photovoltaic Conversion

System in Nigeria1M.S. Okundamiya and2A.N. Nzeako

1Department of Electrical and Electronic Engineering, Ambrose Alli University,P.M.B. 14, Ekpoma-310006, Nigeria

2Department of Electronic Engineering, University of Nigeria, Nsukka-410001, Nigeria

Abstract: This study investigates the effects of orientation of photovoltaic surface and proposes the optimumtilt 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. Theinclination of the surface is assumed to be varying from 0 to 90 with an increment of 1, and the total globalsolar radiation on the tilted surface is estimated using the Hay-Davis-Klucher-Reindl (HDKR) Model. Analysisindicates 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 systemtowards 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 toelectricity.

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((), bothrelated 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 isthe knowledge of its optimum tilt angle that maximizes itscollected solar radiation (Kern and Harris, 1975). Thisdepends on latitude (L ), solar declination (*), and days ofthe year. Qiu and Riffat (2003) suggested that the tiltangle of the PV surface set within the optimum tilt angleof 10 as an acceptable practice. Yang and Lu (2007)recommend that the tilt angle exceeding 40 should beavoided. Other recommendations for optimum tilt angleare based only on the latitude (Gunerhan and Hepbasli,2007; Ulgen, 2006).

In previous studies, the authors (Okundamiya andNzeako, 2010; 2011a) developed correlations betweenmonthly mean daily global solar radiations on a horizontalsurface and monthly mean daily ambient temperatures(minimum and maximum), and between the monthlymean daily diffuse and global solar radiations on ahorizontal surface as a function of the clearness index forselected cities in Nigeria (Okundamiya and Nzeako,2011b). This study examines the influence of orientationof a south-facing photovoltaic surface and proposes theoptimum tilt angles for harvesting solar electricity in threecities in Nigeria (Abuja, Benin City and Katsina). The

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Res. J. Appl. Sci. Eng. Technol.,3(12): 1384-1390, 2011

1385

Fig. 1: Map of study locations in Nigeria

locations of these three cities in Nigeria are shown inFig. 1, where Abuja is located on latitude 9.08 andlongitude 7.53, Benin City on latitude 6.34 andlongitude 5.63, and Katsina on latitude 13.00 andlongitude 7.60.

MATERIALS AND METHODS

A ten-year (1996 - 2005) data set of monthly meandaily minimum and maximum ambient temperatures are

obtained from the archives of the National Aeronauticsand Space Administration (NASA, 2011) for the studylocations. These data sets are applied to the temperature-based (Okundamiya and Nzeako, 2010) and diffuse solarradiation (Okundamiya and Nzeako, 2011b) models. Thecomputation of the global solar irradiance on the tilted PVarray is based on the Hay-Davis-Klucher-Reindl (HDKR)model (Duffie and Beckman, 2006), with the groundreflectance (albedo) assumed to be 0.2 and the azimuthhas been fixed at 0 in this study. The detailed analysis ispresented in the Appendix.

In order to achieve maximum global solar radiationon the PV surface, three optimization methods: monthlybased, seasonal based and annual based, are implemented.

The monthly based optimization method uses a fixedmonthly average tilt angle, while the seasonal and annualmethods utilize a fixed seasonal average tilt and fixedannual tilt angles, respectively. This study was carried outin Benin City between January and July 2011.

SIMULATION AND RESULTS

The study made use of a computer program written inMATLAB programming language. The programcomputes the global solar irradiance on the tilted PV array

using the data discussed above. The angle of inclinationvaries from 0 to 90 with a step of 1. The relations usedfor simulating the global solar irradiance are presented inthe Appendix. Table 1 shows the results of the analysis ofglobal solar radiation for the different optimizationtechniques at optimum tilt angles for selected cities inNigeria. Figure 2 shows the influence of orientation onthe optimized global solar radiation using differenttechniques for the study locations, while Fig. 3 shows thevariation of optimum tilt angles with months of the year

for which global solar radiation is maximum. Figure 4illustrates the variation of monthly global solar irradiancewith tilt angles. Figure 5 shows a comparison of theoptimal annual irradiance at different optimum tilt anglesfor the study locations.

DISCUSSION

The results presented in Table 1 indicate that globalsolar irradiance varies with geographical locations, and itincreases with increasing latitudes. The monthly basedoptimization shows that during rainy season (April -August), the global solar radiation on the PV surface isoptimum if oriented due south in the horizontal direction

(with zero tilt), and decreases with increasing tilt ($)angles (Fig. 4). In March (the end of dry season/commencement of rainy season) and September (the endof rainy season/commencement of dry season), the globalsolar radiation on the PV surface increases withincreasing tilt angle until a maximum irradiance isattained at approximately L + 4 ($opt.L + 4) andL -3 ($opt.L - 3), respectively. The optimum tilt, however,exceeds 4 L during the climax of the dry season. Theannual based optimization method generates a maximumannual global solar radiation at optimum tilt angle ranging

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MonthlyGlobalsolariradiance

(kWh/m/month)

2

240

220

200

180

160

140

120

100

Jan.

Feb.

Mar

.

Apr.

May.

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

Monthly

Seasonal

Annual

240

220

200

180

160

140

120

100

Jan.

Feb.

Mar.

Apr.

May.

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.


(kWh/m/month)

2

240

220

200

180

160

140

120

100

Jan.

Feb.

Mar.

Apr.

May.

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.


(kWh/m/month)

2

Table 1: Results of the analysis of the influence of orientation atoptimum 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 44Feb. 193.2 168.4 211.7 31 27 35Mar. 198.4 167.8 222.4 13 10 17Apr. 181.4 151.2 216.0 0 0 0May 172.9 147.0 220.7 0 0 0Jun. 151.6 126.8 209.8 0 0 0Jul. 137.7 110.6 196.8 0 0 0Aug. 129.7 110.6 180.7 0 0 0Sep. 141.9 114.2 182.6 6 3 10Oct. 176.9 141.2 211.4 25 20 30

Nov. 221.2 171.3 225.4 39 34 42Dec. 237.1 198.5 223.3 43 39 47

Yearly 2170 1812 2526

Seasonal based optimization

--------------------------------------------------------------------------Global Irradiance(kWh/m2/month) Optimum Tilt ()------------------------------------- -----------------------------------

Months Abuja Benin city Katsina Abuja Benin city Katsina


Nov. 219.8 171.2 224.2 32 29 36Dec. 233.3 196.0 219.9 32 29 36

Yearly 2153 1799 2507Annual based optimization----------------------------------------------------------------------------Global Irradiance(kWh/m2/month) Optimum Tilt (o)------------------------------------- -----------------------------------

Months Abuja Benin city Katsina Abuja Benin city Katsina


Nov. 205.0 162.3 203.7 15 12 14Dec. 213.0 180.8 194.4 15 12 14

Yearly 2039 1724 2347

fromL+1 (in Katsina) to approximately L + 6 (in Abujaand Benin City). The seasonal based optimization method

generates a maximum annual global solar radiation if the

PV surface is positioned horizontally ($= 0) during rainyseason, and inclined at L +23 during dry season.

Implementation of the annual average tilt angleimproves the annual global solar radiation in Abuja,

(a)

(b)

(c)

Fig. 2 : Influence of orientation on the optimized global solarradiation using different techniques for the studylocations (a) Abuja (b) Benin City (c) Katsina

Benin City and Katsina, respectively, by over 2.6, 1.7 and2.4%, while the implementation of seasonal average tilt

angles (0 andL+23) 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

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1387

50

40

30

20

10

0

Jan.

Feb.

Mar.

Apr.

May.

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

Abuja

Benin city

Katsina

OpimumTltangle()

0

Jan.250

200

150

100

50

00 10 20 30 40 50 60 70 80 90

Apr.Jul.

Oct.

Inclination ()

Monthlyglobalsolarirad

iance

(kWh/m/month)

2

(a)

250

200

150

100

50

00 10 20 30 40 50 60 70 80 90

Monthlyglobalsolariradiance

(kWh/m

/month)

2

Inclination ()

(c)

250

200

150

100

50

00 10 20 30 40 50 60 70 80 90

Monthlyglobalsolariradiance

(kWh/m/m

onth)

2

(b)

Inclination ( )0

0100

200300

400

0

8

16

24-0

0.2

0.4

0.6

0.8

1.0

DayHour

IT(kWh/m2)

( a )

0100

200300

400

0

8

16

240

0.2

0.4

0.6

0.8

1.0

DayHour

IT(kWh/m2)

( b )

Fig. 3: Variation of optimum tilt angle with months of the yearfor monthly based optimization

Fig. 4: Variation of monthly global solar irradiance with tiltangles (a) Abuja (b) Benin City (c) Katsina.

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0100

200300

400

0

8

16

24-0

0.2

0.4

0.6

0.8

1.0

DayHour

IT(kWh/m

2)

(c)

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 themonthly 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 globalsolar 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

earths surface follows an oblique path length in the early

morning and in the late afternoon. The result of thisoblique 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.

CONCLUSION

In this study, the effects of orientation of a south-

facing 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 thePVCS can be optimized if the surface is positioned

horizontally ($ = 0) between April-August, and inclinedat 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-3)

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

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 15, respectively. The annual optimum tilt angle

is considerably greater than the local latitude in this study.

Appendix: For a tilted surface (surface with anyorientation) at time t, the cosine of the angle of incidenceis 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 solardeclination, L is the latitude, $ is the surface inclination(tilt) angle, ( is the surface orientation (azimuth) andT isthe hour angle. All the angles are in degrees. For a planesurface with due south orientation (( = 0), the cosine ofthe angle of incidence is:

cos2 = sin* (sinN cos$ - cosN sin$ ) +cos* cosT (cosN cos$ + sinN sin$) (A2a)

cos2 = sin* sin(N-$) + cos* cosT cos(N-$) (A2b)

For a horizontal surfaces, the angle of incidence is the zenith angle ofthe sun (that is, at 0 or 90 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 = 90, T = Ts and(A3) becomes:

cosTs = - sin*sinN/cos*cosNTs = cosG

1 (-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 radiationon the horizontal surface (Alam et al., 2005) given as:

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(A5)

RbZ

=

= +

+

cos

cos

sin sin( ) cos cos cos( )

sin sin cos cos cos

The hourly diffuse and global solar radiation is respectively computed(Liu and Jordan, 1962) as:

(A6)IdHd s

ss s

=

24

180

cos cos

sincos

(A7)IH s

ss s

=

24

180

cos cos

sincos

And hourly beam radiation is:

(A8)I I Ib d=

where I, Ib, and Id respectively is the hourly global, beam and diffusesolar radiation on a horizontal surface, while T andTs, respectively isthe hour angle and sunset hour angle. The anisotropy index, Ai is givenas:

(A9)AI

Ii

b=0

where I0 is the hourly extraterrestrial radiation on a horizontal surfacedefined as:

(A10)I Id

sc01 0 0 33

360

365= +

+

. cos

sin sin

cos cos cos

The horizon brightening is given as:

(A11)fI

I

b=

The global solar irradiance on the tilted PV array is (Duffie andBeckman, 2006):

(A12)

( )

I R I I A I

I A f

T b b d i d g

d i

= + +

+

+ +

( )cos

cos sin

1

2

1 12

12

3

where,$ is the inclination of the surface andDg is the ground reflectanceor albedo.

ACKNOWLEDGMENT

This study was partially funded by ETF 2009AST&D Intervention (Reference no. AAU/REG/ETF.560/475).

REFERENCES

Aboumahboub, T., K. Schaber, P. Tzscheutschler and

T. Hamacher, 2010a. Optimization of the Utilization

of Renewable Energy Sources in the ElectricitySector. Proceedings of the 5th IASME/WSEAS

International ConferenceonEnergy &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 andEngineering

Academy and Society, Stevens Point, Wisconsin,

USA, pp: 83-89.

Ahmad, M.J. and G.N. Tiwari, 2009. Optimization of tiltangle 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 solarcollector. 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).

7/29/2019 v3-1384-1390

7/7


1390

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.

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