eest part a 2015 33(6) 3129-3150 asst. prof. kumari namrata (1)

Energy Education Science and Technology Part A: Energy Science and Research

2015 Volume (issue) 33(6): 3129-3150

Comparative analysis of solar

energy potential for some cities of

Jharkhand, India: A case study

K. Namrata1,*

, S. P. Sharma2, S. B. L. Seksena

1

1Department of Electrical Engineering, NIT Jamshedpur, Jharkhand, India

2Department of Mechanical/Energy Engineering, NIT Jamshedpur, Jharkhand, India

Received: 22 August 2015; accepted: 24 September 2015

Abstract

In the proposed research work, a linear regression model is developed for estimating the global solar

radiation most accurately for the region of Jharkhand, a state in India. The proposed model uses sunshine

hours as the principal input parameter for the cities like Jamshedpur ( N'4822, E'1186

), Ranchi (

N'2123, E'2085

), Dhanbad ( N'4823, E'2786

), Hazaribagh ( N'5923, E'2185

) and Bokaro (

N'4023, E'0986

). The values of the regression constants for each of the cities are obtained from the

curve fitting between the ratio of monthly average global to extraterrestrial radiation and ratio of monthly

average sunshine hours to the maximum day length. The effectiveness of the proposed linear regression

model is evaluated by estimating the global solar radiation for the cities in the Jharkhand region. The

results of the city Ranchi by the proposed approach are compared with the measured data and the values

obtained from other empirical models in terms of statistical indicators like mean absolute percentage error

(MAPE), coefficient of correlation (R2), mean bias error (MBE), mean percentage error (MPE), root

means square error (RMSE), Nash – Sutcliffe equation (NSE) and t – statistical test (t – stat). Further, the

average values of the regression constants are utilized in developing the suitable regression model for the

entire Jharkhand region where there is no estimation of global solar radiation by the previous approaches.

Keywords: Global solar radiation; Jharkhand; Regression constant; Statistical test

©Sila Science. All Rights Reserved.

_____________________

*Corresponding author: Tel./fax: +91-620-275-8144.

E-mail address: [email protected] (K. Namrata).

3130 K. Namrata, S. P. Sharma / EEST Part A: Energy Science and Research 33 (2015) 3129-3150

Nomenclature:

G Monthly average daily global solar radiation (kJ/m2-day)

ETR Monthly average daily extraterrestrial solar radiation (kJ/m2-day)

0I Solar constant (1367 W/m2)

ba, Regression constants

n Day of the year (starting from 1st January)

n Monthly average daily hours of bright sunshine hours

N Monthly average of the maximum possible daily hours (day length of bright sunshine)

n

N Clearness-index

f Eccentricity correction factor

Latitude of the location

Solar declination

s Sunrise hour angle

MAPE Mean absolute percentage error

MBE Mean bias error

MPE Mean percentage error

RSME Root mean square error

NSE Nash-Sutcliffe equation 2R The coefficient of correlation

statt t – statistical test

h Elevation of location above mean sea level (km)

1. Introduction

Global solar radiation is considered as the most important parameters in the performance

prediction and designed of any solar energy system. Solar energy occupies [1] one of the most

important places among the various possible alternative energy sources. An accurate knowledge

of solar radiation distribution at a particular geographical location is not only important for the

development of many solar energy devices and for estimates of their performances, but also for

the wider world community [2]. Obviously, measured data is the best form of this knowledge

unfortunately, there are very few meteorological station that measure global solar radiation,

where no measured data are available a common application has been to determine this parameter

by appropriate correlation which are empirically established models [3-8], which have been used

to calculate solar radiation, utilizing available meteorological, geographical and climatologically

parameters such as sunshine hours, air temperature, latitude, precipitation, relative humidity and

cloudiness. The most commonly used parameter for estimating global solar radiation is sunshine

duration. Among various correlations the modified version of Angstrom equation [9] who

proposed a linear relationship between the ratio of average daily global radiation to the

corresponding value on a completely clear day and the ratio of average daily sunshine duration

and its derivation has been widely used. There is an obvious relationship between sunshine

duration and the amount of solar energy received at the earth’s surface. Extraterrestrial radiation

K. Namrata, S. P. Sharma / EEST Part A: Energy Science and Research 33 (2015) 3129-3150 3131

can be precisely evaluated for any place and for any day of the month [10] from the solar

constant and relevant astronomical variables. Under overcast conditions, clearness index ( Nn / )

becomes zero and regression constant ‘ a ’ thus represents the global radiation received at the

ground through an overcast sky as a function of extraterrestrial radiation. The regression constant

‘b ’ expresses the rate of increase of global radiation with increase in clearness index. So, many

investigations have been reported [11-17] which is based on monthly mean values of number of

days ‘ n ’ and global solar radiation. Typical values of regression constants ‘a and b’ published in

literature [18] are from 0.14 to 0.54 and 0.18 to 0.73 respectively. Lower values of ‘ a ’ are

invariably associated with higher values of ‘b’ and vice-versa.

The main objectives of this paper are:

To develop a linear regression model for estimating monthly average global solar

radiation in some selected cities in Jharkhand.

To estimate the monthly average daily global solar radiation on a horizontal surface at

Ranchi using the proposed model, including different empirical relations.

Compare each model with measured data of Ranchi using a statistical test which includes

MAPE, R2, MBE, RMSE, NSE and t-stat.

Estimation of monthly average global solar radiation with the proposed models for all the

selected cities of Jharkhand.

2. Material and methods

2. 1. Study location

2. 1. 1. General climate of Jharkhand

Jharkhand is located in the eastern part of India and is enclosed by Bihar to the northern

side, Chhattisgarh and Uttar Pradesh to the western side, Orissa to the southern part and West

Bengal to the eastern part. Jharkhand envelops a geographical area of 79.70 lakh hectares. A lot

many areas of Jharkhand lie on the Chhota Nagpur Plateau. Many rivers pass through the Chhota

Nagpur plateau. They are: Damodar, Brahmani, Koel, Subarnarekha and Kharkai rivers. The

higher watersheds of these rivers stretch out within the Jharkhand state. Much of the Jharkhand

state is still enclosed by forest.

There are three well-defined seasons in Jharkhand. The cold-weather season, from November

to February, is the most pleasant part of the year. In these months the temperature in Jharkhand

ranges from C7 to C27 . The hot-weather season lasts from March to mid-June. In the month of

May the minimum temperature is about C25 and the maximum temperature is C45 . The season

of the southwest monsoon from mid June to October, brings nearly all of the state’s annual

rainfall, which ranges from about 1,000 mm in the west-central part of the state to more than

1,500 mm in the southwest. Rainfall on the plateau is generally heavier than on the plains. Nearly

half of the annual precipitation falls in July and August.


2. 1. 2. Climatological data of Jharkhand

In order to utilize solar energy for useful and efficient applications, knowledge of weather

parameters of that location is essential. The empirical formula suggested by various authors

employs these parameters to estimate the incident global solar radiation for a particular location

in the absence of measured data. These empirical formulas include the number of sunshine hours,

relative humidity, maximum and minimum temperatures, mean sea level pressure, wind speed,

number of rainy days, etc. In order to get an idea of the seasonal and annual variation of these

parameters each individual parameter has to be analyzed and discuss separately. A critical

assessment and study of it will enable us to utilize these parameters for developing and improving

the efficiency of thermal devices based on thermal energy conversion.

In brief about Jharkhand state:

1. On average the temperatures are always high.

2. Most rainfall is seen in the month of June and July.

3. The warmest month is April and May.

4. The coolest month is January.

2. 2. Solar radiation on horizontal surface

Various climate models have been developed for use in predicting the monthly average global

solar radiation, the popular one being the Angstrom-type regression equation developed by

Angstrom. This relates monthly average daily global radiation to the average daily sunshine

hours, and is given by the following expression:

1

N

nba

ETR

G

ETR (extraterrestrial radiation on a horizontal surface) can be precisely evaluated for any

place and for any day for a month from the solar constants and relevant astronomical variables. The daily value of the extraterrestrial radiation on a horizontal surface (ETR) was

computed according to the following equations:

2sinsin180

sincoscos0

360024

ssfIETR

The eccentricity correction factor f , solar declination and the sunrise hour angle

s can be respectively calculated as:

3365

360cos033.01

nf


4

365

284360sin45.23

n

5tantanarccos s

615

2sN

2. 3. Evaluation of regression constants for selected cities of Jharkhand employing Angstrom

method

In this section a linear regression model has been developed for estimating monthly average

of daily global solar radiation on a horizontal surface for five selected cities of Jharkhand namely

Jamshedpur ( N'4822 , E'1186 ), Ranchi ( N'2123 , E'2085 ), Dhanbad ( N'4823 , E'2786 ),

Hazaribagh ( N'5923 , E'2185 ) and Bokaro ( N'4023 , E'0986 ).

For this value of global solar radiation G and hour of bright sunshine ( n ) were measured at

the city Jamshedpur,Dhanbad,Hazaribagh and Bokaro for the period (2010-14,) using

Pyranometer and in city Ranchi these values were collected from the Solar Radiation Handbook

(Solar Energy Centre, MNRE, India Meteorological Department.The standard methodology is

followed (Equations 2 to 6) to calculate the extraterrestrial and global radiation for the above

places. Extraterrestrial radiation can be precisely evaluated for any place and for any day of the

month from the solar constant and relevant astronomical variables. The values of global to

extraterrestrial ( )G

ETRand clearness index ( )n N are plotted in Figs. 1-5 for the selected cities of

Jharkhand. The slope of the plot and its intercept on the ordinate will represent, respectively the

values of regression constants ‘ a ’ and ‘b ’. These values are shown in Table 1.

Fig. 1. Relationship between G

ETR and

N

n for the city Jamshedpur.



ETR and

N

n for the city Ranchi.


ETR and

N

n for the city Dhanbad.



ETR and

N

n for the city Hazaribagh.


ETR and

N

n for the city Bokaro.


Table 1. Regression constant for selected locations

Location Regression constants

a b ba

Jamshedpur 0.2026 0.514 0.7166

Ranchi 0.2111 0.489 0.7001

Dhanbad 0.1978 0.529 0.7268

Hazaribagh 0.2056 0.5101 0.7157

Bokaro 0.2039 0.5104 0.7143

3. Description of models for estimating global solar radiation

To evaluate the monthly average global solar radiations on a horizontal surface, the following

models are considered:

a. Rietveld Model

Rietveld [21] examined several published values of ‘a’ and ‘b’ and noted that ‘a’ is related

linearly and ‘b’ hyperbolically to the mean value of S such that this equation is believed to be

applicable anywhere in the world and yields superior results for cloudy conditions, for S < 0.4.

0.18 0.62 7G

SETR

where, N

nS .

b. Ogleman Model

Ogleman et al. [22] proposed the use of a correlation which relates the global solar radiation to

S in a quadratic form as:

20.195 0.675 0.142 8G

S SETR

c. Akinoglu Model

Akinoglu and Ecevit [23] suggested a quadratic correlation between the ratio of G

ETRand S to

estimate the values of global solar radiation for 58 locations displaced in several countries. This

equation, whose coefficients have the same values, respectively, for all tested locations is

20.145 0.845 0.280 9G

S SETR


d. Glover Model

Glover and McCulloch [24] attempted to introduce latitude dependency to one of the

Angstrom-Prescott coefficients and presented the following

0.29cos 0.52 10SG

ETR

e. Gopinathan Model

Gopinathan [20] proposed ‘a’ and ‘b’ are related to three parameters, the latitude, the

elevation and the sunshine hours.

Sha 290.00639.0cos539.0309.0

Shb 359.00926.0cos027.1527.1

0.32 0.42 11G

SETR

f. Present Model

0.2111 0.489 12G

SETR

4. Comparison and validation of models with statistical errors

There are many parameters which deal with the assessment and comparison of monthly mean

daily solar radiation estimation models. Here the statistical parameters like the mean bias error

(MBE) and the root mean square error (RMSE) helps to calculate the error or the deviation of the

calculated value of the measured value. Mean percentage error (MPE) and coefficient of

correlation (R2) tests the linear relationship between predicted and measured values. The best

result is when these statistics are closer to zero, but the coefficient of correlation should approach

to 1 as closely as possible for better modeling. To improve the results and better comparison the

Nash–Sutcliffe equation (NSE) is also selected as an evaluation criterion. A model is more

efficient when NSE is closer to 1. The errors that have been estimated help to compare the

models, but they do not make the model statistically significant. The t-statistic allows models to

be compared and at the same time it is carried out to determine statistical significance of the

predicted values by the models.


a. The mean bias error

1

13, ,

1

nMBE H H

i calc i measn

This test provides information on long-term performance. A low MBE value is desired. A

negative value gives the average amount of underestimation in the calculated value. So, one

drawback of these two mentioned test is that overestimation of an individual observation will

cancel underestimation in a separate observation.

b. Mean percentage error

14100*

1 ,

,,1%

n

measiH

measiH

calciH

nMPE

c. Root mean square error

12

2

, ,

1

115

n

i calc i measRMSE H Hn

The value of RMSE is always positive, representing zero in the ideal case. The normalized

root mean square error gives information on the short term performance of the correlations by

allowing a term by term comparison of the actual deviation between the predicted and measured

values. The smaller the value, the better is the model’s performance.

d. Nash–Sutcliffe equation

2

, ,

1

2

,

1

1 16

n

i calc i meas

n

meas i meas

H H

NSE

H H


where measH is the mean measured global radiation. A model is more efficient when NSE is closer

to 1.

e. MAPE

, ,

1 ,

117

ni meas i calc

i meas

H HMAPE

n H

f. Coefficient of correlation

The coefficient of correlation, R2 can be used to determine the linear relationship between the

measured and estimated values.

g. t-statistical test

It is one of the tests for mean values, the random variable t with n−1 degrees of freedom may

be written here as follows:

12 2

2 2

118

n MBEt

RMSE MBE

The smaller the value of t the better is the performance. To determine whether a model’s

estimate is statistically significant, one simply has to determine, from standard statistical tables,

the critical t value. For the model’s estimates to be judged statistically significant at the

calculated t value must be less than the critical value.

5. Results and discussion

5. 1. Regression analysis

From the results highlighted in Table 1 the following first order Angstrom correlation models

have been developed for use in estimating values of global solar radiation at each of the

respective five cities as given below:

a. For Jamshedpur

0.2026 0.514 19G n

ETR N


b. For Ranchi

0.2111 0.489 20G n

ETR N

c. For Dhanbad

0.1978 0.529 21G n

ETR N

d. For Hazaribagh

0.2056 0.5101 22G n

ETR N

e. For Bokaro

0.2039 0.5104 23G n

ETR N

It is apparent from Eqs.19-23 that neither ‘ a ’ nor ‘ b ’ vary with latitude or altitude in any

systematic manner. However, the values of the sum of the regression constants ba ; which

represent the maximum Clearness Index ( 1Nn ), averaged over the period of analysis, are

found to be almost equal for the five cities. The values of ba obtaining for Jamshedpur,

Ranchi Danbad, Hazaribagh and Bokaro are 0.717, 0.700, 0.726, 0.715 and 0.714 respectively.

The averaged values of ‘ a ’ and ‘ b ’for the five selected cities were used in then developing a

linear regression model for estimating solar radiation in Jharkhand.

0.204 0.5105 24G n

ETR N

Eq. (24) is to be used in estimating global solar radiation for any city of Jharkhand (India).


5. 2. Validation of estimated solar radiation on horizontal surface using different models and

statistical analysis of models

The estimated values of the monthly average global solar radiation using various models and

proposed models (Eqs. 7-12) along with the measured data for city Ranchi is shown in Table 2

and plotted in Fig. 6. The resuits obtained from statistical test (Eqs. 13-18) are summarized in

Table 3 as well as plotted in Figs. (7-13). It is evident from this table, that present model (Eqs.

12) has the best correlation coefficient with R2=0.975, while the Akinoglu model has a

correlation factor of R2

= 0.972 followed by Oglemann, Glover and Rietveld models having the

correlation coefficients 0.97, 0.96 and 0.955 respectively. The lowest correlation coefficients

R2=0.889 is from Gopinathan model. The accuracy of each model used in the estimation of

global solar radiation was tested by calculating the mean bias error (MBE %) and the root mean

square error (RMSE) from Eqs. (13) and (15) respectively. It was observed that the lower the

RMSE the more accurate the equation used. Positive MBE shows over-estimation and a negative

MBE show under estimation. In comparison with all the models, present model estimates the

lowest RMSE having 7.82% and the highest one with Gopinathan model (24.9%) followed by

Glover (20.11%), Rietveld (12.5%), Oglemann (9.23%) and Akinoglu (8.47%). The MBE values

obtained from the models are positive in some cases and negative in others. Values of MBE from

all the models except present model indicate an over-estimation. Present model has very little

under-estimation, i.e. 6.28%. Also, the highest values of NSE (0.91) as shown in Fig. 11 and

lowest values of t-test results (Table 3) indicate the superiority of the proposed model with

respect to others. The RMSE% value, which is a measure of the accuracy of estimation, has been

found to be the lowest for the present model (7.83%). The transmissivity of the atmosphere of

global solar radiation under perfectly clear sky conditions is given as the sum of the regression

coefficients, a+b. Also, the transmissivity of an overcast atmosphere is interpreted as the

intercept ‘a’. Hence, the need to compare present regression relation with others in terms of the

atmospheric transmissivity values. From present regression constants (a=0.211 and b=0.489) i.e.

0.7001. The clear-sky transmissivity of most tropical regions in general seems to lie between 0.68

and 0.75 [18].

From the statistical results a new linear model based on the

Angstrom model is extremely recommended to estimate monthly average daily global solar

radiation for Ranchi (Jharkhand) and in elsewhere with similar climate conditions areas where

radiation data are unavailable. Further, the other individual new proposed models are also being

recommended for estimating the average daily global solar radiation for Jamshedpur, Bokaro,

Dhanbad and Hazaribagh.


Table 2. Comparison between measured and estimated monthly average daily global

radiation (MJ/m2-day) for the city Ranchi

Month Rietveld

Model

Oglemann

Model

Akinoglu

Model

Glover

Model

Gopinathan

Model

Proposed

Model Measured

Jan 17.079 16.230 16.157 17.204 16.687 14.966 15.630

Feb 19.279 18.427 18.380 19.499 18.917 17.072 17.690

March 21.293 20.623 20.647 21.756 21.198 19.130 20.820

April 24.096 23.258 23.265 24.552 23.798 21.323 22.210

May 23.431 23.001 23.083 24.225 23.688 20.930 21.190

June 16.324 16.973 16.718 18.322 18.945 15.505 16.750

July 14.959 15.683 15.282 17.132 17.952 14.257 14.500

Aug 14.304 15.004 14.610 16.405 17.240 14.074 13.890

Sept 15.408 15.860 15.761 16.946 17.387 14.569 14.900

Oct 16.293 16.272 16.337 17.151 17.128 15.071 15.760

Nov 16.710 16.072 16.061 16.979 16.569 14.721 15.340

Dec 16.211 15.397 15.323 16.324 15.845 14.201 14.680

Fig. 6. The measured and predicted monthly average daily global solar radiation ( G ) for

the city Ranchi in the generation of different models.

0

5

10

15

20

25

30

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Glo

bal

Sola

r R

adia

tion

(M

J/m

2-d

ay)

Month

Rietveld Ogleman Akinoglu Glover Proposed Model Gopinathan Measured data

Table 3. Validation of the models under different statistical test for the city Ranchi Statistical

Parameters Present Rietveld Oglemann Akinoglu Glover Gopinathan

R2 0.975 0.955 0.97 0.972 0.96 0.889

MBE

kJ/m2-day -628.56 1002.25 786.667 688.667 1927.917 182.833

MPE -0.035608 0.057789 0.047651 0.040859 0.116453 0.114

RMSE

kJ/m2-day 783.47218 1250.13 923.9352 847.4825 2011.553 2049.563

NSE 0.9196574 0.795446 0.888267 0.905993 0.470383 0.450179

MAPE 0.0378174 0.062028 0.049228 0.042562 0.116453 0.114

t-stat 4.4473602 4.448678 5.384275 4.426255 11.3959 6.6268


Fig. 7. Coefficient of Correlation (R2) of six models.

Fig. 8. MBE of the six models.

0,84

0,86

0,88

0,9

0,92

0,94

0,96

0,98

1

Present Rietveld Oglemann Akinoglu Glover Gopinathan

R2

Model

R2

-1000

-500

0

500

1000

1500

2000

2500


MB

E (

kJ/

m2-d

ay)

Model

MBE

Fig. 9. MPE of the six models.


Fig. 10. RMSE of the six models.

-0,06

-0,04

-0,02

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14


MP

E (

%)

Model

MPE

0

500

1000

1500

2000

2500


RM

SE

(k

J/m

2-d

ay)

Model

RMSE

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1


NS

E

Model

NSE

Fig. 11. NSE of the six models.

Fig. 12. MAPE of the six models.


Fig. 13. t-Stat of the six model.

5. 3. Prediction of monthly average global solar radiation for cities Jamshedpur, Ranchi,

Dhanbad, Hazaribagh and Bokaro

The characteristic distribution of global solar radiation at Jamshedpur, Ranchi, Dhanbad,

Hazaribag and Bokaro shows an interesting and encouraging results from the availability and

application point of view, Fig. 14 shows a plot of the values of monthly average daily global solar

radiation along with the extraterrestrial radiation for these cities. The results are also tabulated in

Table 4. It is to be noted that the variation of cloudiness is primarily responsible for the day to

day variation of the daily global radiation. The variation of average global to extraterrestrial

radiation ( ) over the year for these cities are also shown in Table 4. The index is

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14


MA

PE

(%

)

Model

MAPE

0

2

4

6

8

10

12


t-S

tat

Model

t

minimum during the months of July- August, indicating the presence of thick clouds and a

transmission of only 35.6 and 36.7 % for these months respectively of the extraterrestrial

insolation on horizontal surface. In the peak summer month April the sky is fairly clear

( ) and allows on the average nearly 57.62% of the extraterrestrial radiation to

reach the earth’s surface. In winter months the clear sky conditions are obvious from the high

values of global to extraterrestrial radiation

( for the months of Jan., Feb., March,

Oct., Nov. and Dec. respectively.

From Table 4 it is observed that maximum average daily global solar radiation is received in

the months of April and May in all cities of Jharkhand, while it is minimum in the monsoon

session (July-August) and slightly moderate in winter (November–January) in all parts of

Jharkhand. Table 5 shows the comparison of annual average global solar radiation for different

cities of Jharkhand and it is evident that annual global solar radiation received at Ranchi is lowest

as compared to all areas of Jharkhand. The annual average global solar radiation for Bokaro is 3146 K. Namrata, S. P. Sharma / EEST Part A: Energy Science and Research 33 (2015) 3129-3150

maximum followed by Jamshedpur, Hazaribagh and Dhanbad. It is further noted that the annual

global solar radiation received at Bokaro is 14.03% higher than that of Ranchi, while it is 13.63,

13.20 and 12.09 % respectively for Jamshedpur, Dhanbad and Hazaribagh.

The values of global solar radiation calculated from single newly proposed model for

Jharkhand is also compared with individual model of various cities and it is found that deviation

in values of global solar radiation is in the range of -11.35 % to 0.108 % for selected cities of

Jharkhand. Hence, a newly proposed model to predict the monthly average global solar radiation

is recommended for any location of Jharkhand.

Table 4. Monthly average daily global solar radiation (MJ/m2-day) for various cities of

Jharkhand

Month

Jamshedpur Ranchi Dhanbad Hazaribag Bokaro

ETR

G

G

ETR

ETR

G

G

ETR

ETR

G

G

ETR

ETR

G

G

ETR

ETR

G

G

ETR

Jan 25.294 15.646 0.619 24.992 14.966 0.599 24.733 15.296 0.618 24.846 15.174 0.611 24.807 15.471 0.624

Feb 29.143 17.653 0.606 28.890 17.072 0.591 28.673 17.340 0.605 28.768 17.458 0.607 28.735 17.665 0.615

March 33.979 19.549 0.575 33.818 19.130 0.566 33.679 19.284 0.573 33.740 19.564 0.580 33.718 19.499 0.578

April 37.724 22.034 0.584 37.676 21.323 0.566 37.632 21.869 0.581 37.652 21.511 0.571 37.645 22.220 0.590

May 39.631 21.547 0.544 39.683 20.930 0.527 39.725 21.426 0.539 39.707 21.714 0.547 39.714 21.806 0.549

June 40.084 15.660 0.391 40.182 15.505 0.386 40.264 16.036 0.398 40.229 15.445 0.384 40.241 15.687 0.390

July 39.717 14.517 0.366 39.793 14.257 0.358 39.855 14.690 0.369 39.828 14.296 0.359 39.838 14.691 0.369

Aug 38.255 13.914 0.364 38.247 14.074 0.368 38.237 14.201 0.371 38.242 13.810 0.361 38.240 14.206 0.372

Sep 35.029 14.692 0.419 34.906 14.569 0.417 34.800 14.340 0.412 34.846 14.512 0.416 34.830 14.301 0.411

Oct 30.471 15.217 0.499 30.248 15.071 0.498 30.056 15.152 0.504 30.139 14.960 0.496 30.110 15.171 0.504

Nov 26.012 15.365 0.591 25.722 14.721 0.572 25.473 15.393 0.604 25.581 15.276 0.597 25.544 15.098 0.591

Dec 23.980 14.858 0.620 23.666 14.201 0.600 23.397 14.620 0.625 23.514 14.391 0.612 23.473 14.675 0.625


Fig. 14. Monthly average solar radiation on a horizontal surface for various cities of Jharkhand.

Table 5. Comparison of average daily global solar radiation (MJ/m2-day) for various cities

of Jharkhand

Month

Jamshedpur Ranchi Dhanbad Hazaribagh Bokaro Jharkhand

G

(MJ/m2)

G

(MJ/m2)

G

(MJ/m2)

G

(MJ/m2)

G

(MJ/m2)

G

(MJ/m2)

Jan 15.647 14.966 15.296 15.175 15.471 15.311

Feb 17.653 17.073 17.340 17.458 17.666 17.439

March 19.549 19.131 19.284 19.565 19.500 19.408

April 22.035 21.323 21.870 21.512 22.221 21.792

May 21.548 20.930 21.426 21.715 21.806 21.485

June 15.661 15.506 16.036 15.446 15.688 15.664

July 14.518 14.257 14.691 14.297 14.692 14.487

Aug 13.914 14.074 14.201 13.810 14.207 14.041

Sep 14.692 14.569 14.340 14.512 14.301 14.485

Oct 15.218 15.071 15.152 14.961 15.172 15.116

Nov 15.366 14.721 15.394 15.277 15.098 15.169

Dec 14.859 14.201 14.620 14.391 14.675 14.549

Sum Σ 200.66 195.82 199.65 198.12 200.50 198.94


6. Conclusions

From the study of global solar radiation on horizontal surfaces at Jharkhand the prospect of

application and efficient utilization of solar energy seems to be very bright. The sun shines for

about 2700 hour per year and this abundance of sunshine is an indication of clear sky condition

at Jharkhand. This is also confirmed from the high clearness index throughout the year, with the

exception of monsoon months.

The objective of this study was to evaluate various model for the estimation of monthly

average daily global solar radiation on a horizontal surface from bright sun shine hours for some

selected cities of Jharkhand and to select the most appropriate model for Jharkhand state. The

values of monthly average global solar radiation are calculated using the models suggested by

Rietveld ,Ogleman, Akinoglu, Glover, Gopinathan and Present model. The selected model were

compared with the present model for estimating monthly average global solar radiation for

Ranchi, on the basis of statistical error tests such as mean bias error (MBE), the mean percentage

error (MPE), Root mean square error (RMSE), Nash- Sutcliffe equation (NSE), correlation

coefficient and the t-test.

From the statistical results a new

empirical linear model

0.204 0.5105n

G ETRN

based on Angstrom model is extremely recommended to estimate monthly average daily global

solar radiation for any city of Jharkhand and in elsewhere with similar climate conditions areas

where radiation data is unavailable. Furthermore, the other individual new proposed models are

also being recommended for estimating the average daily global solar radiation for Ranchi,

Jamshedpur, Bokaro, Dhanbad and Hazaribagh.

From the analysis of the solar radiation data for Jharkhand, it is observed that on the annual

average basis, it is fairly consistent, with an annual average total of nearly 6100 MJ/m2. The

maximum average daily global solar radiation is received in the month of April and May in all

cities of Jharkhand, while it is minimum in the monsoon session (July- August) and slightly

moderate in winter (November-January) in all parts of Jharkhand. The comparative study of

annual average global solar radiation for different cities of Jharkhand showed that annual global

solar radiation received at Ranchi is lowest as compared to all areas of Jharkhand. The annual

average global solar radiation is maximum at Bokaro followed by Jamshedpur, Hazaribagh and

Dhanbad. It is further noted that global solar radiation received at Bokaro is 14.03% higher than

that of Ranchi, while it is 13.6%, 13.20% and 12.09% respectively for Jamshedpur, Dhanbad and K. Namrata, S. P. Sharma / EEST Part A: Energy Science and Research 33 (2015) 3129-3150 3149

Hazaribagh. The values of global solar radiation calculated from single newly proposed model for

Jharkhand is also compared with individual model of various cities and it is found that deviation

in values of Hg is in the range of -11.3% to 0.18% for selected cities of Jharkhand. Hence, a newly

proposed model to estimate the monthly average global solar radiation is recommended for any

location of Jharkhand.

References

[1] Massaquoi JGM. Global solar radiation in Sierra Leone (West Africa). Solar Wind Technol

1998;5:281-283.

[2] Ibrahim SMA. Predicted and measured global solar radiation in Egypt. Solar Energ 1985;35:185-188.

[3] Okundamiya MS, Emagbetere JO, Ogujor EA. Evaluation of various global solar radiation models for

Nigeria. Int J Green Energ 2015;12.

[4] Aras H, Balli O, Hepbasli A. Global solar radiation potential: Part 1. Model development. Energ

Source 2006;27:7-11.

[5] Ahmad MJ, Tiwari GN. Solar radiation models-A review. Int J Energ Res 2011;35:271-290.

[6] Muneer T, Younes S, Munawwar S. Discourses on solar radiation modeling. Renew Sustain Energ

Rev 2007;11:551-602.

[7] Donatelli B, Fontana MGF. Software to estimate daily radiation data from commonly available

meteorological variables. European J Agronomy 2003;18:363-367.

[8] Younes S, Muneer T. Improvements in solar radiation models based on cloud data. Build Service

Engineer Res Technol 2006;27:41-54.

[9] Angstrom A. Solar and terrestrial radiation. Q J Roy Met Soc 1924;50:121.

[10] Elagib NA. Day length and extraterrestrial radiation for Sudan-A comparative study. Int J Sustain

Energ 1999;20:93-109.

[11] Abdalla Yousef AG. New correlations of global solar radiation with meteorological parameters for

Bahrain. Int J Solar Energ 1994;16:111-120.

[12] Salima G, Geoffrey MSC Determining Angstrom constants for estimating solar radiation in Malawi.

http://www.tandfonline.com/author/Emagbetere%2C+J+O

http://www.tandfonline.com/author/Ogujor%2C+E+A

Int J Geosci 2012;3:391-397.

[13] Al-Madani HMN, Abdalla YAG, Olwi IA. An empirical correlation for monthly global solar

radiation with bright sunshine hours for Saudi Arabia. Int J Solar Energ 1994;15:103-108.

[14] Duffie JA, Beckman WA. Solar engineering of thermal process. Second edition, John Wiley, New

York, 1994.

[15] Reddy SJ. An empirical method for the estimation of total solar radiation. Solar Energ

1979;13:289-290.

[16] Abdalla Yousef AG. Solar radiation over Doha (Qatar). Int J Sustain Energ 1987;5:1-9.

[17] Namrata K, Sharma SP, Seksena SBL. Comparison of different models for estimation of global solar

radiation in Jharkhand (India) Region. Smart Grid Renew Energ 2013;4:348-352.

[18] Sukhatme SP. Solar energy principles of thermal collection and storage. Second edition, Tata

McGraw-Hill, 1997.

[19] Solar Radiation Handbook, Solar Energy Centre, MNRE.

[20] Gopinathan KK, Solar A. A sunshine dependent global insolation model for latitudes between 60N

and 70N. Renew Energ 1992;2:401- 404.

[21] Rietveld MR. A new method for estimating the regression coefficients in the formula relating solar

radiation to sunshine. Agricul Meteorolog 1978;19:243-252. 3150 K. Namrata, S. P. Sharma / EEST Part A: Energy Science and Research 33 (2015) 3129-3150

[22] Ogelman H, Ecevit A, Tasdemiroglu E. A new method for estimating solar radiation from bright sun-

shine data. Solar Energ 1984;33:619- 625.

[23] Akinoglu BG, Ecevit A. A further comparison and discussion of sunshine based models to estimate

global solar radiation. Solar Energ 1990;15 :865-872.

[24] Glover J, Mc Gulloch JDG. The empirical relation between solar radiation and hours of sunshine.

Quarterly J Royal Meteorologic Soci 1958;84:172-175.

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