World Applied Sciences Journal 22 (9): 1334-1343, 2013
ISSN 1818-4952
© IDOSI Publications, 2013
DOI: 10.5829/idosi.wasj.2013.22.09.316
Selection of Models for Calculation of Incident Solar Radiation on Tilted Surfaces
Abdul Qayoom Jakhrani, 2Saleem Raza Samo,
3
Andrew Ragai Henry Rigit and 4Shakeel Ahmed Kamboh
1
Faculty of Engineering, Universiti Malaysia Sarawak, 94300, Kota Samarahan, Sarawak, Malaysia
2
Department of Energy and Environment Engineering, Quaid-e-Awam University of Engineering,
Science and Technology (QUEST), Nawabshah, Sindh, Pakistan
3
Department of Mechanical and Manufacturing Engineering, Faculty of Engineering,
Universiti Malaysia Sarawak, 94300, Kota Samarahan, Sarawak, Malaysia
4
Department of Mathematics and Computational Science, Faculty of Computer Science and
Information Technology, Universiti Malaysia Sarawak, 94300, Kota Samarahan, Sarawak, Malaysia.
1
Abstract: The purpose of this study was to examine the performance of tilted surface solar radiation models
for selection of estimated amount of solar radiation. The model results were evaluated on the basis of
one-sample statistical test. The statistical test includes four measures namely the mean, standard deviation,
standard error mean and the range of 95% confidence interval of the difference. The analysis revealed that
yearly average solar radiation data recorded by local meteorological stations were 7% less than satellite-derived
data acquired from National Aeronautics and Space Administration. The estimated results of tilted surface
radiation models showed that Reindl et al., model executed maximum variation and Klucher model displayed
minimum error as per one-sample statistical test among the examined models. It was concluded from the study
that Klucher model could be preferred for the estimation of tilted surface radiations.
Key words: Mathematical models
One-sample statistical test
INTRODUCTION
Energy is an essential element for the economic
and social development of any country. It improves the
quality of life, whether it is in the form of oil, gasoline,
nuclear or from any renewable energy [1]. Among all
renewable energy resources, solar energy is one of the
most rapidly growing green energy technologies of the
world. These sources are environment and nature friendly,
does not produce emissions that contribute greenhouse
effect or destroy ecological balance [2, 3]. Solar systems
are practicable form of power supply where the grid
connections are not available and the extension of power
transmission lines is expensive [4-8]. However, their
proper design and sizing is necessary for uninterrupted
power supply. This ultimately requires long term recorded
data of solar radiation. Unfortunately, such data is not
readily available in most of the developing countries.
Corresponding Author:
Solar radiation
Tilted surface models
Thus, the systems could not consistently supply the
designed power due to malfunctioning of its components
[9-12].
Solar Radiation Data: In general, solar radiation data is
described in terms of total solar radiation, which is the
combination of beam plus diffuse and ground reflected
radiation. Most of the total radiation is measured on
horizontal surfaces by local meteorological stations.
However, it can also be observed through satellites [13].
The local meteorological measurements provide more
perfect estimates, because it holds the site specific
characteristics. Moreover, the solar conversion systems
are tilted towards the sun in order to maximize the amount
of solar radiation incident on photovoltaic module
surface. The availability of recorded data on tilted
surfaces is very rare. Therefore, the tilted surface radiation
in most cases is calculated from horizontal surface
Abdul Qayoom Jakhrani, Department of Energy and Environment Engineering, Quaid-e-Awam
University of Engineering, Science and Technology (QUEST), Nawabshah, Sindh, Pakistan.
Tel: +92-244-9370362, Fax: +92-244-9370362.
1334
World Appl. Sci. J., 22 (9): 1334-1343, 2013
radiation by means of empirical models [14]. Although, a
large number of empirical models exist but they are
validated using the data collected from the meteorological
stations of United States, Canada, Australia and Northern
European countries. Furthermore, the existing models
were formulated based on different procedures using
different elements [15]. It is prime need to evaluate the
models and verify their suitability according to the local
environmental conditions before application for the
design and development of solar systems. The purpose of
this study is to evaluate the performance of tilted surface
solar radiation models based on the one-sample statistical
test results. The models which perform well and provide
less variation could be recommended for the estimation of
available solar radiation of the area.
Solar Radiation on Tilted Surfaces: Tilted surface solar
radiation (HT ) is composed of three parts such as beam
radiation ( H T ,b ) , ground reflected radiation (H T ,r ) and
diffuse radiation ( H T , d ) . It is defined as:
H T = H T ,b + H T , r + H T , d
(1)
Beam radiation ( H b ) is that part of total solar
radiation, which is received from the sun without
atmospheric scattering [16]. It is often referred as direct
solar radiation. The amount of beam radiation on a tilted
surface ( ) from the horizontal surface and rotated
from north to south axis is computed by multiplying the
direct horizontal irradiation ( H b ) by the geometric factor
( Rb ) .
H T ,b = H b Rb
(2)
The value of H b can be obtained by subtraction of
diffused radiation ( H d ) from total radiation ( H ) , after
computing the value of H d through empirical models [17].
The geometric factor ( Rb ) is the ratio of beam radiation on
the tilted surface to that on horizontal surface
( R b = cos / cos z ) . The most favorable solar azimuth angle
( ) for collectors or PV modules is usually 0° in the
northern hemisphere or 180° in the southern hemisphere
[18]. Therefore, the value of R b is computed by:
Rb =
cos( − )cos cos + sin ( − )sin
cos cos cos + sin sin
(3)
The part of total solar radiation that is reflected by
the surface of the earth and by any other surface
intercepting object such as trees, terrain or buildings onto
a surface exposed to the sky is termed as ground reflected
radiation or albedo [19]. A tilted surface at slope from
the horizontal has a view factor (Fc–g) to the ground and
Fc–g = (1 – cos )/2. Assuming that the reflection of the
beam and diffuse radiation is falling on the ground is
isotropic and that the surroundings have a diffuse
for the total solar radiation.
reflectance of
g
Subsequently, the reflected radiation (H T ,r ) from the
surroundings on the surface will be:
HT ,r = H
 1 − cos 

2


g
(4)
If the measuring station is located on a rooftop with
a low reflectance, then the reflected part of solar radiation
is very much lower than the direct and diffuse
components. Because of that situation, an isotropic model
can be used for the calculation of reflected component on
the inclined planes.
The diffuse radiation ( H d ) is that fraction of total
solar radiation which is received from the sun when its
direction has been changed by atmospheric scattering
[20]. The direction of diffuse radiation is highly variable
and difficult to determine [21]. It is distributed over the
whole sky dome, which is a function of conditions of
cloudiness and atmospheric clearness, which are
extremely unpredictable. The diffuse radiation fraction is
also the combination of three components, namely
isotropic diffuse, circumsolar diffuse and horizon
brightening [17]. The isotropic diffuse radiation
component is received evenly from the entire sky dome.
The circumsolar diffuse part received from onward
dispersion of solar radiation and concentrated in the
section of the sky around the sun [22]. The horizon
brightening component is concentrated near the horizon
and it is most obvious in the clear skies [23]. If the diffuse
radiation is considered to be only isotropic, then it is the
ratio of diffuse on the tilted surface with a slope ( ) to that
on the horizontal surface, denoted by R d . Since,
R d= (1 + cos ) / 2 and H d is computed from the empirical
equations [17].
The mathematical models used to determine the
amount of tilted surface solar radiation ( H T ) can be
classified into two types of models namely isotropic and
anisotropic. Isotropic sky models assume that the
intensity of diffuse sky radiation is uniform over the sky
dome [24]. Hottel and Woertz [25] were the first who
assumed that the combination of diffuse and ground
reflected radiation is isotropic. That, the sum of diffuse
from the sky and ground reflected radiation on the tilted
surface is the same regardless of orientation. Thus, the
total radiation on the tilted surface is the sum of beam
1335
World Appl. Sci. J., 22 (9): 1334-1343, 2013
radiation and the diffuse radiation. The improvement of
Hottel and Woertz [25] model was given by Liu and
Jordan [26]. The radiation on tilted surface was
considered to be composed of three parts such as beam,
reflected from ground and diffuse. The circumsolar and
horizon brightening components of diffuse radiation were
taken as zero. Liu and Jordan [26] assumed that the
diffuse radiation is isotropic only. Jimenz and Castro [27]
proposed that the beam radiation on a horizontal surface
is 80% of the global solar radiation, whereas, the
remaining 20% is contributed by the diffuse radiation.
Koronakis [28] modified the assumption of isotropic
sky diffuse and suggested that the slope ( = 90°)
provides 66.7% of the total sky dome as a diffuse solar
radiation. Tian et al. [21] considered the diffuse
radiation received on tilted surface with view a factor of
Fc–s = (1 – /180). Badescu [29] presented a model for the
solar diffuse radiation on a tilted surface with a view
factor of Fc–s = (3 + cos 2 )/4.
The anisotropic sky models were developed by
various researchers to incorporate the contribution of
circumsolar and horizon brightening components in
isotropic sky models. Almost, all researchers took the
same value of the beam and reflected part of radiation as
recommended by Liu and Jordan [26] and ammended only
the part of diffuse radiation. Temps and Coulson [30]
presented a clear sky model and incorporated two factors
in Liu and Jordan [26] model. One factor 1 + sin3( /2)
includes for horizon brightening and other factor (1 + cos2
sin3 z) to account the effects of circumsolar radiation.
Klucher [31] modified and refined the Temps and Coulson
[30] model to stimulate the conditions present during
partly cloudy skies by incorporating a modulating
function (F ) to determine the magnitude of clear sky
effects. It reduces both Liu and Jordan [26] and
Temps and Coulson [30] model under extreme values of
F . If F = 0, it reduces to the isotropic sky model as given
by Liu and Jordan [26] and if F = 1, it reduces to the clear
sky model as given by Temps and Coulson [30]. Hay and
Davies [32] suggested that the diffuse radiation from the
sky is composed of an isotropic and circumsolar
component only, whereas, the horizon brightening
component was not taken into account. The anisotropy
index (Ai) was used to quantify the diffuse radiation.
Some part of diffuse radiation was treated as circumsolar
and the remaining part of the diffuse radiation was
assumed to be isotropic. Reindl et al. [33, 34] took into
account the horizon brightening factor in addition to
isotropic diffuse and circumsolar radiation. Reindl et al.
[33, 34] used same definition of Ai as given by Hay and
Davies [32]. However, a modulating function f = H b / H
was added to the Temps and Coulson [30] model as a
correction term of sin3 ( / 2). In contrary to other
anisotropic sky models, Duffie and Beckman [17]
proposed a combination of Hay and Davies [32], Klucher
[31] and Reindl et al. [33, 34] model, which is referred as
HDKR model. The description of selected tilted surface
models is shown in Table 1.
Previous Studies on Different Model Performance:
Several researchers examined the performance of isotropic
and anisotropic sky models and recommended the model
for estimation of tilted surface radiation based on their
own findings. Kudish and Ianetz [35] examined three
empirical models, one isotropic and two anisotropic for
computing total solar radiation on a tilted surface in Israel
and concluded that the results of all three models varied
with time, season and location. Muneer and Kambezidis
[36] evaluated various models to check their ability of
accurate predictions for the availability of incident
irradiation on tilted surfaces with measured values in
Athens, Greece. Bilbao et al. [37] investigated the
performance of five models for the estimation of hourly
diffuse solar radiation on tilted surface using horizontal
total radiation data from six meteorological stations in
Spain. Nijmeh and Mamlook [38] tested Liu and Jordan
[26] and Hay and Davies [32] model by using the data of
horizontal global and diffuse radiation to predict the
global radiation on tilted surface and concluded that the
performance of models depends on the seasons of the
year. Diez-Mediavilla et al. [39] compared the performance
of ten different empirical models to estimate the amount of
diffuse radiation incident on south facing surface tilted at
the angle of 40° on both hourly and daily basis near
Valladolid, Spain. Loutzenhiser et al. [40] discovered that
the most models underestimated the results in the
afternoon hours in the month of October. Majority of
models overestimated the results for most hours during
the day in the months of March and April. However, their
study was limited to a specific location and time period.
Barakat [41] observed that the Hay and Davies [32]
model performed well for calculation of tilted surface
radiations. Harrison and Coombes [42] presented his
findings on the basis of root mean square error that
isotropic sky models generally underestimate, while the
Klucher [31] model overestimates the diffuse irradiance
and the Hay and Davies [32] model gives the best overall
performance in all sky conditions. De Miguel et al. [43]
recommended Liu and Jordan [26] model for calculation of
hourly diffuse from daily diffuse values. Kamali et al. [44]
1336
World Appl. Sci. J., 22 (9): 1334-1343, 2013
Table 1: Description of selected models for estimation of incident solar radiation on tilted surface
Author (s)
Description of Models
Liu and Jordan (1963)
 1 − cos
HT =
H b Rb + H g 
2

Klucher (1979)
 1 − cos 
 1 + cos  
' 3  
H T =+
H b Rb H g 
 + Hd 
 × 1 + F sin    ×
2
2



 
 2 
'
2
3
1 + F cos sin z
(
 1 + cos

 +Hd 
2





)
2

F='  1 − H d H 


(
Reindl et al., (1990a and 1990b)
)
H T =( H b + H d Ai ) Rb + H
 1 − cos
2
g 

 1 + cos
 + H d (1 − Ai ) 
2



 1 +
 
Hb
 
sin 3   
H
 2  
Ai (=
H bn H on ) ( H b H o )
=
HDKR Model (2006)
(
)
H T =H b + H d Ai Rb + H
examined eight different models to estimate solar
irradiation on tilted surfaces using daily measured solar
irradiation data in Iran and recommended Reindl et al.
[33, 34] model for computing solar incident irradiation on
tilted surfaces.
Notton et al. [45] examined 94 different combinations
of models for calculation of hourly solar radiation on tilted
surface and recommended Klucher [31] model for the
estimation of diffuse solar irradiation followed by Iqbal
[46] and Hay and Davies [32] models. Noorian et al. [47]
evaluated twelve different models and concluded that
south facing tilted surfaces demonstrated good agreement
with measured and modeled data whereas, all model
produced large errors for west facing tilted surface.
Noorian et al. [47] discovered that Skartveit and Olseth
[48], Hay and Davies [32] and Reindl et al. [33, 34] models
displayed the most accurate predictions for south facing
tilted surface. Evseev and Kudish [49] assessed eleven
models to predict the global solar radiation incident on
tilted surface at Beer Sheva, Israel and concluded that the
models cannot be graded or ranked on the basis of
statistical and graphical analysis, since they exhibited
different trends. They found that Muneer and Kambezidis
[36] model demonstrated best results for cloudy sky
conditions. Pandey and Katiyar [50] reported that Klucher
[31] model shows comparatively good estimations as
compared with experimental values at low inclination
angles because it incorporates the effect of cloudy sky
conditions.
It is revealed from the review that various models and
combination of models are available for estimation of tilted
surface radiations. The abundant of such models
indicated the complexity of the task for converting diffuse
 1 − cos 
 +Hd
2

g 

 1 + cos
(1 − Ai ) 
2



3    
 1 + sin    

 2   
solar radiation measured on a horizontal surface to that on
a tilted surface [43]. The reported models were found to be
mutually consistent. However, the approach of
researchers was different due to incorporation of different
influential factors in their models. Researchers
recommended different models and combination of models
according to their findings. Therefore, the selection of a
single model or group of models needs to be examined
and validated as per local geographical and environmental
conditions before application for the design and
development of solar systems.
MATERIALS AND METHODS
A total of four tilted surface radiation model results
were investigated, one isotropic model proposed by
Liu and Jordan [26] and three anisotropic models given
by HDKR [17], Klucher [31] and Reindl et al. [33, 34]
as shown in Table 1. The predicted model results were
totally based on the input data of sources concerned.
Two input data sets were used for the examination of
model perofrmance. One set of data were obtained from
local meteorological office based at Kuching, Sarawak by
Malaysian Meteorological Services (MMS) and other set
was acquired from National Aeronautics and Space
Administration (NASA). These both data sets were used
for comparison purpose and appropriate selection of
required models. For this study, five years recorded data
from 2005 to 2009 of total solar radiation and ten years
data from 2000 to 2009 for other environmental parameters
were obtained from MMS. The long term recorded data of
solar radiation was not available at the respective
department (i.e. at MMS Regional Office Kuching,
1337
World Appl. Sci. J., 22 (9): 1334-1343, 2013
Sarawak). Therefore, twenty three years satellite-derived
data from July 1983 to June 2006 was also acquired from
NASA for comparison purpose. The amount of beam and
diffuse components of solar radiation on the horizontal
surface was computed from monthly mean total radiation
data using Erbs et al. [51] model. The monthly mean daily
extraterrestrial solar radiation on the horizontal surface
was computed by taking the values of a single day
(close to monthly mean values) for every month of the
year by using days suggested by Kalogirou [52] which
were representing the individual month. The proposed
days were; 17th of January and July, 16 th of February,
March and August, 15th of April, May, September and
October, 14th of November, 11th of June and 10th of
December. The monthly average daily extraterrestrial solar
radiation on the horizontal surface was determined using
empirical relationships. The detailed description of
fundamental equations can be found in Kalogirou [52]
and Duffie and Beckman [17].
Models can be selected either on the basis of data
availability of the desired location or applying intuitive
methods based on experience or by means of statistical
analysis of model performance. Since, the long term time
series data was not available in the area. The statistical
analysis was preferred as compared to intuitive methods.
Therefore, for this study, the models were selected on the
basis of one-sample statistical test, which includes four
measures namely mean, standard deviation, standard
error mean (SEM) and range of 95% confidence interval.
These measures provide the consistency and variation in
the model estimated results.
RESULTS AND DISCUSSIONS
Comparison of MMS and NASA Data: The available
amount of total solar radiation at Kuching, Sarawak with
MMS and NASA data sources are shown in Figure 1 [53].
It was observed that, both data sources reported lowest
average daily solar radiation availability in the month of
January with 12.80 MJ/m2 and 14.26 MJ/m2 and the second
worst month was observed as December with 13.42 MJ/m2
and 14.98 MJ/m2 respectively. The MMS data source
indicates the maximum radiation in the month of August
with 17.21 MJ/m2, whereas, the NASA sources reported
the month of April with 17.96 MJ/m2. The monthly average
daily total radiation on yearly basis by MMS data was
15.44 MJ/m2 and NASA was 16.63 MJ/m2.
It was found that MMS data sources showed 7% less
amount of total solar radiation with more variation on
monthly average yearly basis. The variation was due to
the short term radiation record. NASA data indicates more
amount of global solar radiation with less deviation in the
monthly average values. This was due to the fact that
satellites could not incorporate the local geographical and
environmental characteristics and merely gives overall
picture of radiation behavior in large scale. It can be
observed from the figure that MMS data showed less
availability of solar radiation in the month of June as
compared to NASA data. This could be due to one year
bad weather conditions confronts in the month of June
which make the average of MMS data much lower than
that of NASA. Since, the NASA data was not affected
due to its long term radiation record. It was discovered
from the analysis that both data sources could be equally
important but preference might be given to local data
source with long term record. However, such record does
not exist at present in Kuching.
Comparison of Results and Selection of Model: The
comparison of results revealed that Liu and Jordan [26]
and HDKR [17] models demonstrated almost same results
by the use of MMS data. However, HDKR [17] model
executes slightly more values in NASA data than Liu and
Jordan [26] model as shown in Figure 2. This was due to
addition of the circumsolar component in diffuse radiation
fraction in HDKR [17] model. Reindl et al. [33, 34] model
displayed highest estimated values among all models.
It may be consideration of all diffuse components
individually in their model and incorporation of
modulating factor, which was multiplied by the term used
for horizon brightening. Klucher [31] model demonstrated
lower estimated results than Reindl et al. [33, 34] model
and slightly higher than Liu and Jordan [26] and HDKR
[17] models. It was due to the incorporation of a
modulating factor (F ). Statistically, it was discovered that
Liu and Jordan [26] model executed the higher values than
anisotropic models in good weather conditions and lower
results in bad weather conditions. However, all examined
models established around 1.5% of mean difference in
predicted values among each other.
It was found from the analysis, that all tilted surface
models predicted more incident solar energy irradiation on
tilted surface (HT) than on horizontal surface radiation (H)
due to the optimization of slope. The slope was fixed at
10° due south to make the incidence angle close to the
beam radiation in worst months of year. It was observed
that Liu and Jordan [26] and Reindl et al. [33, 34] models
predicted less amount of solar radiation in good weather
conditions and overall Klucher [31] model performs well
on yearly average basis.
1338
World Appl. Sci. J., 22 (9): 1334-1343, 2013
Fig. 1: Measured values of total solar radiation on horizontal surface at Kuching
Fig. 2: Estimated values of incident solar radiation on tilted surface by different models
The results of one-sample statistical test of tilted
surface models are graphically illustrated in Figures 3 and
4. It was found that the higher mean, standard deviation
(SD), standard error mean (SEM) and range of 95%
confidence interval was given by Reindl et al. [33, 34]
model with the use of MMS data. The less error was
executed by Klucher [31] model. Liu and Jordan [26] and
HDKR [17] models demonstrated similar behavior with
less error than Reindl et al. [33, 34] model and more than
Klucher [31] model. However, the mean of Klucher [31]
model was found to be more than Liu and Jordan [26]
and HDKR [17] models but its error was less than
examined models. The evaluation of NASA data reveals
that higher SD, SEM and range was given by Liu and
Jordan [26] model than Reindl et al. [33, 34] model.
However, Reindl et al. [33, 34] model executed higher error
by the use of MMS data. Klucher [31] model again
executed lowest error among all models, whereas, HDKR
[17] model displayed slightly more error than Klucher [31]
model and less error than Reindl et al. [33, 34] model.
It was found that Reindl et al. [33, 34] model
predicted the highest estimated values of about
15.4MJ/m2 and Liu and Jordan [26] model demonstrated
the lowest values 15.2 MJ/m2. Moreover, Liu and Jordan
[26] model performs well in cloudy weather conditions due
to low estimation of solar radiation. The results of
one-sample statistical analysis revealed that Reindl et al.
[33, 34] and Liu and Jordan [26] model executed higher SD
of 1.40 and 1.38, SEM of 0.40 and 0.39 respectively. The
less SEM of 0.38 was executed by Klucher [31] model.
Therefore Klucher [31] model could be chosen for the
estimation of tilted surface radiation.
1339
World Appl. Sci. J., 22 (9): 1334-1343, 2013
Fig. 3: Mean and SD of incident solar radiation on tilted surface by different models
Fig. 4: SEM and Range of incident solar radiation on tilted surface by different models
CONCLUSIONS
In this study, the solar radiation data and the
estimated results of selected tilted surface models were
compared and recommended for selection of solar
radiation estimation using one-sample statistical test. It
was revealed that the recorded yearly average solar
radiation data of MMS sources were 7% less than NASA
data sources. The causes of more variation in MMS data
were due to its short term record. Since, the local
meteorological data took into account the effect of site
specific and geographical features of the location as
compared to NASA. Therefore, the local long term timeseries data could be preferred if available.
It was found that Reindl et al. [33, 34] model
predicted the highest estimated values and Liu and Jordan
[26] model demonstrated the lowest. The results of
statistical analysis revealed that Reindl et al. [33, 34]
and Liu and Jordan [26] model executed higher SD of 1.40
and 1.38, SEM of 0.40 and 0.39 respectively. The less SEM
1340
World Appl. Sci. J., 22 (9): 1334-1343, 2013
of 0.38 was executed by Klucher [31] model. Therefore,
Klucher [31] model could be preferred for the estimation
of tilted surface radiations.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit and
S.R. Samo, 2012. Assessment of Solar and Wind
Energy Resources at Five Typical Locations in
Sarawak. Journal of Energy and Environment,
4(1): 1-6.
Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit, S.R. Samo
and S.A. Kamboh, 2012. Estimation of Carbon
Footprints from Diesel Generator Emissions. 2012
IEEE International Conference in Green and
Ubiquitous Technology, 7-8 July, Bandung,
Indonesia.
Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit, S.R. Samo,
L.P. Ling and R. Baini, 2012. Cost Estimation of a
Standalone Photovoltaic Power System in Remote
Areas of Sarawak, Malaysia. NED University Journal
of Research, Thematic Issue on Energy, pp: 15-24.
Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit, S.R. Samo
and S.A. Kamboh, 2012. Life Cycle Cost Analysis of
a Standalone PV System. 2012 IEEE International
Conference in Green and Ubiquitous Technology, 7-8
July, Bandung, Indonesia.
Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit and
S.R. Samo, 2011. Model for Estimation of Global Solar
Radiation in Sarawak, Malaysia. World Applied
Sciences Journal (Special Issue of Food and
Environment), 14: 83-90.
Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit and
S.R. Samo, 2010. A Simple Method for the Estimation
of Global Solar Radiation from Sunshine Hours and
Other Meteorological Parameters. IEEE ICSET, 6-9
December, Kandy, Srilanka.
Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit, R. Baini,
S.R. Samo and L.P. Ling, 2012. Investigation of Solar
Photovoltaic Module Power Output by various
Models. NED University Journal of Research,
Thematic Issue on Energy, pp: 25-34.
Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit, S.R. Samo
and S.A. Kamboh, 2012. Estimation of Incident Solar
Radiation on Tilted Surface by Different Empirical
Models. International Journal of Scientific and
Research Publications, 2(12): 1-6.
Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit, S.R. Samo
and S.A. Kamboh, 2012. A Novel Analytical Model
for Optimal Sizing of Standalone Photovoltaic
Systems. Energy, 46(1): 675-682.
10. Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit, S.R. Samo
and S.A. Kamboh, 2013. Sensitivity Analysis of a
Standalone Photovoltaic System Model Parameters.
Journal of Applied Sciences, 13(2): 220-231.
11. Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit, L.P. Ling
and R. Baini, 2012. Prediction of Power output from
Different Photovoltaic Cell Models. In Proceedings of
2nd International Conference on Energy and
Environment: Role of Energy Resources in
Sustainability of Environment, 16-18 January,
Nawabshah, Sindh, Pakistan.
12. Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit and
S.R. Samo, 2011. Determination and Comparison of
Different Photovoltaic Module Temperature Models
for Kuching, Sarawak. IEEE First Conference on
Clean Energy and Technology, Legend Hotel, 27 -29
June, Kuala Lumpur, Malaysia.
13. Okundamiya, M.S. and A. Nzeako, 2011. Empirical
Model for Estimating Global Solar Radiation on
Horizontal Surfaces for Selected Cities in the Six
Geopolitical Zones in Nigeria. Journal of Control
Science and Engineering, pp: 1-7.
14. Jakhrani, A.Q., A.K. Othman, A.R.H. Rigit and
S.R. Samo, 2011. Comparison of Solar Photovoltaic
Module Temperature Models. World Applied
Sciences Journal (Special Issue of Food and
Environment), 14: 1-8.
15. Jakhrani, A.Q., A.K. Othman and A.R.H. Rigit, 2010.
Estimation of Global Solar Radiation from Sunshine
Hours by Empirical Relationships at Sarawak State.
In Proceedings of International Conference on
Environment 2010, Green Technologies for the
benefits of Bottom Billions, 13-15 December,
Parkroyal Hotel, Penang, Malaysia.
16. Liou, K.N., 2002. An Introduction to Atmospheric
Radiation. Vol. 84. 2nd ed. Academic Press, pp: 1-583.
17. Duffie, J.A. and W.A. Beckman, 2006. Solar
Engineering of Thermal Processes. 3rd ed. John Wiley
and Sons, Inc. New York, USA, pp: 1-928.
18. Kreith, F. and D.Y. Goswami, 2011. Principles of
Sustainable Energy. Vol. 46. CRC Press, Boca Raton,
FL, USA, pp: 373-420.
19. Perez, R., R. Stewart, C. Arbogast, R. Seals and
J. Scott, 1986. An Anisotropic Hourly Diffuse
Radiation Model for Sloping Surfaces: Description,
Performance Validation, Site Dependency Evaluation.
Solar Energy, 36(6): 481-497.
20. Kondratev, K.I.A., 1969. Radiation in the
Atmosphere. Academic Press, 12: 3-11.
1341
World Appl. Sci. J., 22 (9): 1334-1343, 2013
21. Tian, Y.Q., R.J. Davies-Colley, P. Gong and
B.W. Thorrold, 2001. Estimating Solar Radiation on
Slopes of Arbitrary Aspect. Agriculture for
Meteorology, 109: 67-74.
22. Widén, J., 2009. Distributed Photovoltaics in the
Swedish Energy System. Model Development and
Simulations. Licentiate Thesis, Uppsala Universitet,
Sweden, pp: 1-89.
23. Robinson, D. and A. Stone, 2004. Solar Radiation
Modelling in the Urban Context. Solar Energy,
77(3): 295-309.
24. Posadillo, R. and R. López Luque, 2009. Evaluation of
the Performance of Three Diffuse Hourly Irradiation
Models on Tilted Surfaces according to the
Utilizability Concept. Energy Conversion and
Management, 50(9): 2324-2330.
25. Hottel, H.C. and B.B. Woertz, 1942. Performance of
Flat-Plate Solar Heat Collectors. Transactions on
ASME, 64: 91.
26. Liu, B.Y.H. and R.C. Jordan, 1963. The Long-term
Average Performance of Flat-Plate Solar Energy
Collectors. Solar Energy, 7(2): 53-74.
27. Jimenz, J.I. and Y. Castro, 1982. Solar
Radiation on Sloping Surfaces with Different
Orientations in Granda, Spain. Solar Energy,
28: 257-262.
28. Koronakis, P.S., 1986. On the Choice of Angle of Tilt
for South Facing Solar Collectors in Athens Basin
Area. Solar Energy, 36: 217-225.
29. Badescu, V., 2002. 3D Isotropic Approximation for
Solar Diffuse Irradiance on Tilted Surfaces.
Renewable Energy, 26: 221-223.
30. Temps, R.C. and K.L. Coulson, 1977. Solar Radiation
Incident Upon Slopes of Different Orientations. Solar
Energy, 19: 179.
31. Klucher, T.M., 1979. Evaluation of Models to
Predict Insolation on Tilted Surfaces. Solar Energy,
23(2): 111-114.
32. Hay, J.E. and J.A. Davies, 1980. Calculation of Solar
Radiation Incident on an Incline Surface. First
Canadian Solar Radiation Data Workshop, April
17-19, 1978, Toronto, Ontario, Canada, Ministry of
Supply and Services, Canada.
33. Reindl, D.T., W.A. Beckman and J.A. Duffie, 1990.
Diffuse Fraction Correlations. Solar Energy, 45: 1.
34. Reindl, D.T., W.A. Beckman and J.A. Duffie, 1990.
Evaluation of Hourly Tilted Surface Radiation
Models. Solar Energy, 45: 9.
35. Kudish, A.I. and A. Ianetz, 1991. Evaluation of the
Relative ability of Three Models, the Isotropic,
Klucher and Hay, to Predict the Global Radiation on
a Tilted Surface in Beer Sheva, Israel. Energy
Conversion and Management, 32: 387-394.
36. Muneer, T. and H. Kambezidis, 1997. Solar Radiation
and Daylight Models for the Energy Efficient
Design of Buildings: Architectural Press Oxford, UK,
pp: 1-224.
37. Bilbao, J., D. Miguel, A. Ayuso and J.A. Franco,
2003. Iso-radiation Maps for Tilted Surfaces in the
Castile and Leon region, Spain. Energy Conversion
and Management, 44: 1575-1588.
38. Nijmeh, S. and R. Mamlook, 2000. Testing of Two
Models for Computing Global Solar Radiation on
Tilted Surfaces. Renewable Energy, 20(1): 75-81.
39. Diez-Mediavilla, M., A. De Miguel and J. Bilbao,
2005. Measurement and Comparison of Diffuse Solar
Irradiance Models on Inclined Surfaces in Valladolid,
Spain. Energy Conversion and Management,
46(13): 2075-2092.
40. Loutzenhiser, P., H. Manz, C. Felsmann, P. Strachan,
T. Frank and G. Maxwell, 2007. Empirical Validation of
Models to Compute Solar Irradiance on Inclined
Surfaces for Building Energy Simulation. Solar
Energy, 81(2): 254-267.
41. Barakat, S., 1983. Comparison of Models for
Calculating Solar Radiation on Tilted Surfaces.
National Research Council Canada, Division of
Building Research, Ottawa, Canada, pp: 317-322.
42. Harrison, A. and C. Coombes, 1988. Comparison of
Model and Indirectly Measured Diffuse Sky
Irradiances of Tilted Surfaces. Atmosphere Ocean, 26:
193-202.
43. De Miguel, A., J. Bilbao, R. Aguiar, H. Kambezidis
and E. Negro, 2001. Diffuse Solar Irradiation Model
Evaluation in the North Mediterranean Belt Area.
Solar Energy, 70(2): 143-153.
44. Kamali, G.A., I. Moradi and A. Khalili, 2006.
Estimating Solar Radiation on Tilted Surfaces with
various Orientations: A Study Case in Karaj, Iran.
Theory and Applications of Climatology, 84: 235-241.
45. Notton, G., P. Poggi and C. Cristofari, 2006.
Predicting Hourly Solar Irradiations on Inclined
Surfaces Based on the Horizontal Measurements:
Performances of the Association of well-known
Mathematical Models. Energy Conversion and
Management, 47(13): 1816-1829.
1342
World Appl. Sci. J., 22 (9): 1334-1343, 2013
46. Iqbal, M., 1980. Prediction of Hourly Diffuse Solar
Radiation from Measured Hourly Global Radiation on
a Horizontal Surface. Solar Energy, 24(5): 491-503.
47. Noorian, A.M., I. Moradi and G.A. Kamali, 2008.
Evaluation of 12 Models to Estimate Hourly Diffuse
Irradiation on Inclined Surfaces. Renewable Energy,
33(6): 1406-1412.
48. Skarstein, O. and K. Uhlen, 1989. Design
Considerations with Respect to Long-Term Diesel
Saving in Wind/Diesel Plants. Wind Engineering,
13(2): 72-87.
49. Evseev, E.G. and A.I. Kudish, 2009. The Assessment
of Different Models to Predict the Global Solar
Radiation on a Surface Tilted to the South. Solar
Energy, 83(3): 377-388.
50. Pandey, C.K. and A. Katiyar, 2009. A Note on
Diffuse Solar Radiation on a Tilted Surface. Energy,
34(11): 1764-1769.
51. Erbs, D.G., S.A. Klin and J.A. Duffie, 1982. Estimation
of Diffuse Radiation Fraction for Hourly, Daily and
Monthly- Average Global Radiation. Solar Energy,
28: 293.
52. Kalogirou, S.A., 2009. Solar Energy Engineering:
Processes and Systems. 1st ed. Academic Press,
pp: 1-760.
53. NASA, 2012. NASA Surface Meteorology and Solar
Energy. Retrieved 24-02-2012, from National
Aeronautics and Space Administration, USA.
http://eosweb.larc.nasa.gov/cgi-bin/sse/global.cgi:
1343