Indian Journal of Science and Technology, Vol 9(46), DOI: 10.17485/ijst/2016/v9i46/101922, December 2016
ISSN (Print) : 0974-6846
ISSN (Online) : 0974-5645
Temperature based Radiation Models for the
Estimation of Global Solar Radiation
at Horizontal Surface in India
R. Meenal1*, P. Gaziz Boazina2 and A. Immanuel Selvakumar1
Department of Electrical Technology, Karunya University, Coimbatore - 641114, Tamil Nadu, India;
[email protected], [email protected]
2
Renewable Energy Technologies, Karunya University, Coimbatore - 641114, Tamil Nadu, India;
[email protected]
1
Abstract
Background/Objectives: The objective of this study is to compare five different temperature based empirical
models and to select the most accurate model to estimate the monthly average Global Solar Radiation (GSR) in India.
Methods/Analysis: Five empirical equations namely Hargreaves and Samani, Bristow and Campbell, Pandey and Katiyar
First, second and third order models have been employed to estimate monthly average GSR on horizontal surface using
minimum and maximum temperature. Using these equations GSR is estimated at New Delhi (Latitude 28.61° N, Longitude
77.20° E) and Chennai (Latitude 13.08° N, Longitude 80.27° E), India and the meteorological data for this work have been
obtained from India Meteorological Department (IMD), Pune from 2002-2012. Findings: Solar radiation data are not easily
available in all locations due to higher cost and difficulty in measurement. It can be estimated by empirical equations using
meteorological parameters like sunshine hour, temperature and relative humidity, out of which temperature is the most
commonly available meteorological data. Empirical coefficients appeared in correlation equations based on temperature
have been found using the latest computing MATLAB software. Estimated GSR values were compared with measured
values based on statistical measures such as Root Mean Square Error (RMSE) and correlation coefficient (R). Comparing
five equations, it is found that third order correlation provides good results with R = 0.9882 and RMSE = 0.840. From the
results, it is concluded that the temperature based models has good potential for estimating GSR for any locations where
measurement of sunshine duration data are not possible. Improvements: Further, in future, these empirical equations
and temperature based ANN models would be applied for different places having good solar potential such as Hyderabad,
Bhubaneswar and other states of India would be reported.
Keywords: Empirical Equations, Monthly Average Global Solar Radiation, Temperature
1. Introduction
Solar energy is the most important renewable energy
source to supply major part of world’s energy demand.
Accurate knowledge of solar radiation is necessary for
different solar energy applications. The solar radiation
components are generally measured using pyranometer,
solarimeter, pyroheliometer, etc. It is not possible to
install measuring instruments at every site due to high
costs and maintenance problems, resulting in nonavailability of measured solar radiation data for most
* Author for correspondence
sites worldwide. Due to the lack of measured GSR data,
the estimation of solar radiation at the earth’s surface is
essential. Therefore number of correlations and methods
have been developed to estimate GSR based on the
readily available meteorological parameters like sunshine
duration, temperature and relative humidity which are
used as the input for radiation models at any location.
In1 and 2proposed the theoretical model for estimating
the GSR based on the sunshine duration. The most
widely used parameter to estimate GSR is sunshine
duration3–6. But sunshine data and cloud observations are
Temperature based Radiation Models for the Estimation of Global Solar Radiation at Horizontal Surface in India
not easily available in all locations. There are number of
mathematical7 and Clear sky8 models are available which
are not suitable to estimate the GSR during monsoon
months or cloudy sky. In India around two to three months
in a year are cloudy. It is very difficult to estimate the
accurate results of solar radiation using a clear sky model.
Therfore it is necessary to develop some precise solar
radiation model which use commonly available measured
parameter such as air temperature9–11. The temperature
based models12,13 can be used to estimate monthly average
daily GSR for any location in India where measurements
of the sunshine hour are not available.
2. Materials and Methods
A total of five temperature based models are in the
literature. Explanatory variables used in the models
include maximum temperature, minimum temperature,
solar hour angle, extraterrestrial radiation, declination
angle, day of the year and latitude. An angstrom type
regression model based on minimum and maximum
temperatures was used in this study as follows:
(1)
Where H is the monthly average global solar radiation
on horizontal surface a and b are constants, Tmax is the
maximum temperature, Tmin is the minimum temperature
and H0 is the monthly average daily extraterrestrial
radiation (MJ/m2/day) which can be expressed as:
(2)
Where Isc is the solar constant. Dn is the day of year
starting from first January; L is the latitude of location
under consideration:
δ is declination angle as given below:
(3)
And ωs is sunset hour angle in degree as given below:
(4)
The temperature based models assume that the
difference in maximum and minimum temperature is
directly related to
ratio at ground level.
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Hargreaves and samani9 recommended a simple
equation to estimate GSR which requires only temperature
and latitude as follows:
(5)
where ΔT = Tmax – Tmin
Bristow and Campbell10 developed the following
equation for estimating GSR with a different
structure in which H is an exponential function of
.
(6)
Where a, b, c are the emprirical coefficients.
In11 proposed the folllowing Equations :
(7)
(8)
Global solar radiation for New Delhi and Chennai
station is estimated by using the above mentined
five radiation models with maximum and minimum
temperature data as its input. Pandey and Katiyar model
with their third order equation gives more accurate
estimates than first order and second order correlations.
2.1 Data for the Analysis
The database considered in this study contains monthly
average maximum temperature, monthly average
minimum temperature and monthly average daily global
solar radiation in MJ/m2/day on a horizontal surface of
the periods between 2002 and 2012 for the locations New
Delhi and Chennai. The data were collected from India
Meteorology Department (IMD) Pune. The computer
codes for the temperature based empirical models were
developed using latest computing MATLAB software.
2.1.1 Statistical Indicators of Estimation Models
The following statistical tests were used to evaluate the
performance of the models: MBE, MPE, RMSE and R.
Mean Bias Error is given by:
(9)
Indian Journal of Science and Technology
R. Meenal, P. Gaziz Boazina and A. Immanuel Selvakumar
Where
are the ith measured values,
ith calculated values and the number of observations. This
test gives information on long-term performance. A low
MBE ideally zero value is preferred. It is an indicator for
the average deviation of the calculated values from the
measured data.
Mean Percentage Error is given by:
(10)
A percentage error between -10% and +10% is
considered acceptable.
Root Mean Square Error is given by:
Figure 1. Bristow and Campbell model (New Delhi).
(11)
Correlation Coefficient (R) measures the degree of
linear relationship between the calculated value and the
measured value. For better data modeling, the R value
should approach to 1 as closely as possible.
3. Results and Discussion
The monthly average of daily values of the meteorological
data for the locations New Delhi and Chennai collected
from IMD, Pune have been analyzed and calculated. The
complete data are then divided into two sets. The subdata set 1 (2002–2008) are employed to develop empirical
correlations between the monthly average of daily solar
radiation fraction (H/H0) and meteorological parameters
maximum temperature (Tmax) and minimum ambient
temperatures (Tmin). The regression equations obtained
are given in Table 1 and Table 3. Furthermore, the five
empirical correlations are evaluated using the sub-data
set 2 (2009-2012). It can be seen from Table 2 and Table 4
that correlation coefficient ranges from 0.90 to 0.98 which
is closer to 1. This means that the equations obtained
represent the measured data satisfactorily. It can also be
found that the RMSE values vary between 0.84 and 1.85.
The monthly mean values of the daily global-radiation
calculated from the five models were compared with the
corresponding measured values. The results are illustrated
in Figure 1 to Figure 12. It is clear from the Figures 1 to 12
that the deviation between the measured and calculated
value is very small.
Vol 9 (46) | December 2016 | www.indjst.org
Figure 2. Bristow and Campbell model (Chennai).
Figure 3. Hargreaves and Samani model (New Delhi).
Figure 4. Hargreaves and Samani model (Chennai).
Indian Journal of Science and Technology
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Temperature based Radiation Models for the Estimation of Global Solar Radiation at Horizontal Surface in India
Figure 5. First order model (New Delhi).
Figure 6. First order model (Chennai).
Figure 7. Second order model (New Delhi).
Figure 8. Second order model (Chennai).
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Figure 9. Third order model (New Delhi).
Figure 10. Third order model (Chennai).
Figure 11. Measured and estimated GSR MJ/m2
(New Delhi).
Figure 12. Measured and estimated GSR MJ/m2
(Chennai).
Indian Journal of Science and Technology
R. Meenal, P. Gaziz Boazina and A. Immanuel Selvakumar
Table 1. Regression Equations developed for the location – New Delhi (Latitude 28.61° N,
Longitude77.20° E)
S.No
1
Models
Hargreaves and
Samani
2
Bristow and
Campbell
3
Linear
4
Second order
5
Third order
Regression Equations
Table 2. Results of temperature based models for the location - New Delhi (Latitude 28.61° N,
Longitude 77.20° E)
Model
R
RMSE (MJ/ m2/day)
MPE (%)
MBE (MJ/ m2/day)
Hargreaves
and Samani
0.9667
1.1945
-2.8346
-0.3411
Bristow and
Campbell
0.9689
1.1946
-2.0815
-0.1625
First order
0.9084
1.8596
-2.6696
-0.1629
Panday and Katiyar
Second order
Third order
0.9674
0.9882
1.2289
0.8400
-2.3936
-1.5997
-0.2139
-0.1209
Table 3. Regression Equations developed for the location – Chennai (Latitude 13.08° N,
Longitude 80.27° E)
S.No
1
Models
Hargreaves and
Samani
2
Bristow and
Campbell
3
Linear
4
Second order
5
Third order
Regression Equations
Table 4. Results of temperature based models for the location - Chennai (Latitude 13.08° N,
Longitude 80.27° E)
Model
R
RMSE (MJ/ m2/day)
MPE (%)
MBE (MJ/ m2/day)
Vol 9 (46) | December 2016 | www.indjst.org
Hargreaves
and Samani
0.9427
1.5549
4.8529
1.0324
Bristow and
Campbell
0.9199
1.8253
3.3561
0.8591
First order
0.9522
1.6470
5.1432
1.1335
Panday and Katiyar
Second order
Third order
0.9530
0.9259
1.6363
1.7611
5.0633
3.5455
1.1196
0.8976
Indian Journal of Science and Technology
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Temperature based Radiation Models for the Estimation of Global Solar Radiation at Horizontal Surface in India
4. Conclusion
Five temperature based empirical equations have been
employed for estimating global solar radiation on the
horizontal surface. The differences between the results
of the different models are negligible. The third order
equation with the highest value of R and least value of
RMSE (R = 0.9882 and RMSE = 0.840) which is reported
to be recommended is given as:
From Table 2 and Table 4, it is observed that the third
order equation provides more accurate results than first
order and second order equations for the estimation of
GSR on the horizontal surface for New Delhi and Chennai,
India. From the results, it is concluded that the solar
radiation model with temperature as its input has good
potential for estimating GSR on horizontal surface for any
locations where the measurement of sunshine hour data
are not available and among the five correlations third
order equation provides best result.
5. Acknowledgement
India Meteorological Department, Pune is acknowledged
for providing meteorological data.
6. References
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