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~ ) Pergamon Renewable Energy, Vot. 12, No. 3, pp. 303 313, 1997
© 1997 Elsevier Science Ltd All rights reserved. Printed in Great Britain
PII: S0960-1481(97)00039-6 0961~1481/97 $17.00+0.00
D A T A B A N K
Estimation of hourly solar radiation for India
G. V. PARISHWAD, R. K. BHARDWAJ and V. K. N E M A
Department of Mechanical Engineering, Motilal Nehru Regional Engineering College, Allahabad-211 004, India
(Received 10 March 1997; accepted 10 April 1997)
Abstract--The ASHRAE constants predict high values of the hourly beam radiation and very low values of the hourly diffuse radiation when used to predict radiation at Indian locations. Hence a procedure has been developed for the estimation of direct, diffuse and global hourly solar radiation on a horizontal surface for any location in India. To calculate hourly solar radiation, an exponential curve, similar to the one used by ASHRAE, was fitted to the measured solar radiation data of six cities from different regions of India. The statistical analysis was carried out for the data com- puted using ASHRAE constants and the set of constants obtained for India using the measured data of four different Indian cities selected randomly. Three statistical indicators were used to compare the accuracy of the developed procedure. The results show that ASHRAE constants are not suitable to estimate hourly solar radiation in India. Hourly solar radiation estimated by constants obtained for India are fairly comparable with measured data. The mean percentage error with Indian constants for these four Indian cities was found as low as 2.27, -6 .29 and -6 .09% for hourly beam, diffuse and global radiation, respectively. © 1997 Elsevier Science Ltd.
1. INTRODUCTION
Solar radiation reaching the Earth's surface depends on the local climatic conditions. Information on the availability of solar radiation is needed in many applications dealing with the harnessing of solar energy. A knowledge of monthly-mean values of the daily global and diffuse radiation on a horizontal surface is essential to design any solar energy system. However, the mean daily radiation is not always the most appropriate figure to characterize the potential utility of solar energy. While designing a solar energy system, one also needs to know insolation values at hourly intervals for inclined and horizontal surfaces. Hourly values of radiation enable us to derive very precise infor- mation about the performance of solar energy systems [1]. Such data is useful to engineers, architects and designers of solar systems as they endeavour to make effective use of solar energy.
Most locations in India receive abundant solar radiation, and solar energy utilization technology can be profitably applied to these regions. The best solar radiation information of a place is obtained from experimental measurements of the global and diffuse solar radiation at that place. In India, the Meteorological Department measures sunshine duration, global radiation, and diffuse radiation at some selected places. The measured data of 21 years have been compiled and is available in the form of tables giving the monthly average values of hourly global and hourly diffuse values in Ref. [2].
For locations where no measurements exist, hourly radiation can be estimated by using empirical correlation developed from the measured data of nearby locations having similar climatological conditions. Various climatic parameters such as humidity, temperature, rainfall, total amount of coverage and in particular, number of sunshine hours, etc., have been used in developing empirical
303
304 Data Bank
Table 1. Values of constants, A, B and C obtained for pre- dicting hourly solar radiation in India
Day A (W/m 2) B C
Jan. 21 610.00 0.000 0.242 Feb. 21 652.20 0.010 0.249 Mar. 21 667.86 0.036 0.299 Apr. 21 613.35 0.121 0.395 May 21 558.39 0.200 0.495 Jun. 21 340.71 0.428 1.058 Jul. 21 232.87 0.171 1.611 Aug. 21 240.80 0.148 1.624 Sep. 21 426.21 0.074 0.688 Oct. 21 584.73 0.020 0.366 Nov. 21 616.60 0.008 0.253 Dec. 21 622.52 0.000 0.243
relations as a substitute for the measurement of solar radiation. The first attempt to analyse the hourly global radiation data was made by Whiller [3] and Hottel and Whiller [4], who used data of widely separated locations to obtain the curves of hourly to daily radiation ratio against the sunset hour angle. Liu and Jordan [5] extended the day length of these curves. By using the corrected data of five U.S. locations, Collares-Pereira and Rabl [6] developed an analytical expression for hourly to daily global radiation ratio in terms of the sunset hour angle. The hourly correlation between daily diffuse transmission coefficient and daily clearness index obtained by Orgill and Hollands [7], Bruno [8], and Bugler [9] can be used to estimate the ratio of hourly diffuse to hourly global radiation. Liu and Jordan [5] determined the hourly distribution of diffuse radiation from daily radiation, whereas Gopinathan [1] obtained the same from sunshine duration. No general formula is available yet for prediction of the solar radiation reaching the Earth's surface over a given period of time at any location [10].
Hourly solar radiation calculated for Indian locations using constants given by ASHRAE (Table 1) predict higher beam radiation and lower diffuse radiation [11]. Since the hourly solar radiation data is measured by the Meteorological Department only at a few selected cities of India, the purpose of the present study is to develop a procedure for estimating hourly global (/) and diffuse (Id) radiation on a horizontal surface at any location in India where measured data is not available.
2. CALCULATION PROCEDURE
As recommended by ASHRAE [12], hourly global radiation (/), hourly beam radiation in the direction of rays (Ibn) and hourly diffuse radiation (Id) on the horizontal surface on a clear day are calculated using the following equations :
I = Ib, COSZ+Id (1)
lb, = A exp [-- B/cos z] (2)
Id = Clbn (3)
where A, B and C are constants whose values are to be determined from analysis of the solar radiation data and z is the zenith angle, which depends upon latitude of the location (L), hour angle (eB) and solar declination (6), and is calculated from the following equation :
cos z = sin L" sin 6 + cos L" cos 6" cos 09 (4)
Solar declination (6) is calculated by
fi = 23.45 sin [360" (284+N)/365] (5)
Data Bank 305
where N is the day of the year. The hour angle (w) is an angular measure of time and is equivalent to 15 ° per hour. It is measured from noon-based local apparent time (LAT) from the equation given by
(~0) = 15.0" (12.0-LAT) (6)
where the LAT value is obtained from the standard time by using the following equation [1 l]
LAT = ST + ET _+ 4. ( S T L - I) (7)
The equation of time correction (ET) is to consider small perturbations in the Earth's orbit and rate of rotation. It was taken from the graph given by Sukhatme [11]. The second correction arises because of the difference between the longitude of location (l) and standard time longitude (STL). As the mainland of India extends between longitude 67.5E and 97.5E, standard time in India is based on 82.5E (STL). The negative sign in this correction is applicable for the eastern hemisphere, while the positive is for the western hemisphere. For India, the negative sign is applicable as it lies in the eastern hemisphere.
2.1. Statistical methods used There are numerous statistical methods available in solar energy literature which deal with the
assessment and comparison of solar radiation estimation models [13, 14]. In the present study statistical indicators, namely correlation coefficient (R), normalized root mean square error (NRMSE) and mean percentage error (MPE) are calculated. They are defined as :
,N , ( ) f . , i - , i=1 i = l
NRMSE = , (9) 1 N
M P E = ~ i Mi x lO0 (10)
where Ci and Mi are the calculated and measured values of solar radiation, respectively, and N is the total number of observations.
The NRMSE provides information on the short-term performance of a model by allowing a term by term comparison of the actual difference between the estimated value and the measured value. The MPE provides information on the size of the discrepancy in the measurements. It quantifies the systematic component of the normalized difference for individual observations. The sign of the error indicates whether the calculated value is higher or lower than the measured value.
3. RESULTS A N D D I S C U S S I O N
When the exponential curve as described by eq. (2) is fitted to the measured solar radiation data [2] of six cities, namely, New Delhi, Mumbai ( formerly named Bombay), Calcutta, Chennai ( formerly
306 Data Bank
named Madras), Jodhpur and Nagpur from different regions (Fig. 1) of India, a set of the constants is obtained (Table 1). Geographical data of these cities is given in Table 2. The values have been determined for each month since they change during the year because of seasonal changes in the dust and water vapour content of the atmosphere, and also because of the changing Earth-Sun distance.
Thereupon, the monthly-mean of the hourly values of each of the beam-, diffuse-, and global- radiation were calculated for January to December separately using eqs (1) (3) for four randomly selected Indian cities from different regions--Pune, Thiruanatpuram ( formerly named Trivendrum), Shilong and Vishakhapatnam (Fig. l). These values were compared with the corresponding measured [2] values of the concerned cities. Comparative sample calculations of monthly-mean-hourly solar radiation values using ASHRAE constants and constants obtained for India in Vishakhapatnam for the month of September with measured values are shown in Table 3 for better understanding. It is clearly seen that eqs (1)-(3) with ASHRAE constants predict very high hourly beam radiation, very low hourly diffuse radiation and comparable hourly global radiation when compared with the measured data. All the three radiations, that is, beam, diffuse and global hourly solar radiation
72°E ' '80.*~[ 8~°E ' ,, 961~" ' [
/~::;~":"..-.-~k l INDIA [ /t 4 I /
32°NI . I "x., , rv. h I :.32~
L, . P / I )
, f j ' " ./".-'/ N e w Delhi ~ "".... I "i ":""~'~
l ",---.~ •. I 'J ~"), • l " ', ....... , / ...... ::.,,,
Mumbai
~ P u n e tnam: Z6oN,--~ k------------~ 6~
i Tldrua
7~ E
Chennal B A Y ' ~ OF " B E N G A L
, It
~ / J 0 200 400 luu
I N D I A N O C E A N I 86°E 88°E '
i I
"i
Fig. 1. Locations of the Indian stations selected for the study.
Data Bank
Table 2. Geographical data of the l0 Indian locations of the study
307
No.
Height above Latitude Longitude mean sea level
City (degrees) (degrees) (metres)
1. Calcutta 22.65N 88.45E 6 2. Chennai 13.00N 80.18E 16 3. Jodhpur 26.30N 73.02E 224 4. Mumbai 19.12N 72.85E 14 5. Nagpur 21.10N 79.50E 310 6. New Delhi 28.58N 77.20E 216 7. Pune 18.53N 73.85E 559 8. Shilong 25.57N 91.88E 1600 9. Thiruanantpuram 08.48N 76.95E 64
10. Vishakhapatnam 17.72N 83.23E 3
estimated by constants obtained for India are comparable with the measured data. The locations were selected for evaluation of constants and prediction in such a way that they were fairly distributed over the whole of India and for which measured data was available.
When the calculated values of hourly solar radiation using constants obtained for India are compared with the corresponding measured values, the resulting average correlation coefficients [eq. (8)] for Pune, Thiruanatpuram, Shilong and Vishakhapatnam are
R(beam) = 0.9268,
R(diffuse) = 0.9397,
R(global) = 0.9751,
which may be considered satisfactory. During this study the whole data of monthly-mean-hourly insolation values calculated by both
ASHRAE and Indian constants and that of measured values for direct, diffuse and global radiation for the 10 cities from January to December was processed. The yearly average of the NRMSE [eq.
Table 3. Comparative sample calculations of monthly mean hourly solar radiation in Vishakhapatnam for the month of September
Beam radiation Diffuse radiation Global radiation (kWh/m 2) (kWh/m 2) (kWh/m 2)
LAT 0* l* 2* 0* 1" 2* 0* 1" 2*
09.0 0.180 0.191 0.478 0.210 0.278 0.080 0.390 0.469 0.557 10.0 0.265 0.256 0.666 0.268 0.288 0.085 0.533 0.544 0.751 11.0 0.338 0.303 0.800 0.303 0.293 0.088 0.641 0.595 0.888 12.0 0.373 0.327 0.869 0.332 0.295 0.090 0.705 0.621 0.959 13.0 0.393 0.327 0.869 0.327 0.295 0.090 0.720 0.621 0.959 14.0 0.369 0.303 0.800 0.300 0.293 0.088 0.669 0.595 0.888 15.0 0.295 0.256 0.666 0.264 0.288 0.085 0.559 0.544 0.751 16.0 0.187 0.191 0.478 0.209 0.278 0.080 0.396 0.469 0.557
Note : Value given for a particular time corresponds to the surface during the one hour preceding the time.
* 0~Measured values; 1--Calculated by using constants using ASHRAE constants.
radiation flux incident on a horizontal
obtained for India; 2 Calculated by
308 Data Bank
Table 4. Yearly average normalised root mean square error for Pune, Thiruanantpuram, Shilong and Vishakhapatnam
LAT
Beam radiation Diffuse radiation Global radiation (%) (%) (%)
1" 2* 1" 2* 1" 2*
09.0 15.29 89.66 22.22 61.11 09.48 25.59 10.0 20.00 86.47 19.30 66.67 12.32 25.18 11.0 23.40 83.69 24.14 70.50 16.81 25.29 12.0 24.68 81.91 28.09 74.53 19.13 25.51 13.0 25.76 82.68 25.82 71.27 19.65 25.61 14.0 24.94 86.68 21.92 69.62 17.98 27.64 15.0 23.60 99.69 16.23 66.23 14.55 31.45 16.0 28.64 124.76 19.89 60.22 18.09 38.76 Average 23.29 91.94 22.20 67.52 16.00 28.13
* 1--Calculated by using constants obtained for India; 2--Calculated by using ASHRAE constants.
(9)] and the MPE [eq. (1)] obtained for radiation calculated for Pune, Thiruanatpuram, Shilong and Vishakhapatnam using ASHRAE constants and those constants obtained for India are given in Tables 4 and 5, respectively. These results show (Table 4) that the yearly average NRMSE values for beam, diffuse and global hourly solar radiation with ASHRAE constants are 91.94, 67.52 and 28.13 %, respectively, whereas the corresponding values are 23.29, 22.2 and 16% with Indian constants. It is, therefore, obvious that the Indian constants result in less NRMSE. Similarly, Table 5 shows that in general ASHRAE constants predict higher hourly beam radiation with an average MPE of 140.14% and lower hourly diffuse radiation of -64 .81% MPE and higher hourly global radiation by 29.41% MPE for these four cities, whereas Indian constants predict values as low as 2.27, - 6.29 and - 6.09% MPE, respectively.
To make a better comparison variation of the NRMSE and the MPE of (a) beam, (b) diffuse and (c) global hourly solar radiation for the four cities over the year are shown Figs 2 and 3, respectively. The results show that the developed procedure gives better performance when the sky is clear and for a large period of the year the sky is clear at most of the places in India. After summer from May-end
Table 5. Yearly average mean percentage error for Pune, Thiruanantpuram, Shilong and Vishakhapatnam
LAT
Beam radiation Diffuse radiation Global radiation (%) (%) (%)
1" 2* 1" 2* 1" 2*
09.0 0.74 132.88 18.43 --57.68 3.41 26.22 10.0 --4.77 126.67 --3.88 --63.78 --9.05 25.71 11.0 --4.23 130.61 -- 14.73 --67.28 -- 13.65 26.65 12.0 --4.32 131.80 19.92 --68.83 - 15.71 26.70 13.0 --2.99 135.62 --20.11 --68.91 --15.16 27.55 14.0 0.19 136.48 --16.74 --67.94 --11.34 29.54 15.0 8.01 150.04 --7.13 --64.95 -2 .68 33.59 16.0 25.53 177.04 13.77 --59.11 15.46 39.30 Average 2.27 140.14 --6.29 --64.81 -6 .09 29.41
* 1--Calculated by using constants obtained for India; 2--Calculated by using ASHRAE constants.
Data Bank 309
400
800
r.~ 200
1 O0
0 0
80
70
60;
5 o
3 0
20
10
C 0
(a) • ASHRAE ------ Indian
! I I I I I
2 4 O 8 10 12
Month of the Year
( b ) x ASHRAE Indian
-
I ! I I I I
2 4 8 8 10 12
Month of the Year
14
14
7 0
Data Bank
E
6 0
60 '
ioo 2O
10
310
0 I I ! I I I
0 2 4 6 8 10 12 14
Month of the Year Fig. 2. Variation of normalised root mean square error for (a) beam, (b) diffuse and (c) global solar
radiation for Pune, Thiruanantpuram, Shilong, and Vishakhapatnam over the year.
to September. Bay of Bengal Monsoons and Arabian Sea Monsoons cause rainfall in most parts of India, hence a slight rise in NRMSE and MPE in the calculated values by Indian constants was observed during this period. During November-January due to winter Monsoons Himachal Pradesh in the north and Arunachal Pradesh, Meghalaya, Assam, and Nagaland in the north-east get some rains. Hence the error level in the estimated values of hourly solar radiation for these parts of the country during this period is likely to be slightly high. In these figures, the contribution of Winter Monsoon effect is due to Shilong only which is damped out due to the remaining three cities.
4. CONCLUSIONS
ASHRAE constants are not suitable to estimate hourly solar radiation in India. The hourly solar radiation at any location in India may be estimated with fair accuracy using Indian constants. The input parameters are the longitude and latitude of the location, the day of the year and the time at which the information is required. The mean percentage error with Indian constants for four randomly selected Indian cities was found as low as 2.27, -6 .29 and -6 .09% for hourly beam, diffuse and global radiation, respectively. Since the method is very simple it will be useful, in general, for engineers, architects and solar system designers.
The results of this study can be used to estimate solar radiation for any location in India as the places selected for evaluation of constants and prediction thereof are fairly distributed over the whole of India.
Acknowledgments--One of the authors, Mr G. V. Parishwad, is grateful to the Department of Education, Ministry of Human Resource Development, and Mechanical Engineering Department, Motilal Nehru Regional Engineering College, Allahabad, for providing facilities for conducting research towards a doctoral degree under the Quality Improvement Programme.
Data Bank 311
600
400
800
r,~ 200
100
0
-100 0
20
~ -20,
~ - 4 0
-60
-80
0
( a ) o ASHRAE • Indian
I I t I I l I .
2 4 0 8 10 12 14 Month of the Y e a r
X A S H R A E ( b ) I Indian
! I I I I . I
2 4 6 8 10 12
Month of the Year
14
312 Data Bank
8 0 0 ASHRAE
(C) ~ indian
60
4 0 -
2 o
- 2 0 0 2 4 6 8 10 12 14
M e n t h e f the Year Fig. 3. Variation of mean percentage error for (a) beam, (b) diffuse and (c) global solar radiation for
Pune, Thiruanantpuram, Shilong, and Vishakhapatnam over the year.
REFERENCES
1. Gopinathan, K. K., Estimation of hourly global and diffuse solar radiation from hourly sunshine duration, Solar Energy, 1992, 48(1), 3.
2. Mani, A., Handbook of Solar Radiation Data for India. Allied Publishers, New Delhi, India, 1980. 3. Whiller, A., The determination of hourly values of total solar radiation from daily summation,
Arch. Meteorol. Geophys. Bioklimatol. Set. B, 1956, 7(2), 197. 4. Hottel, H. C. and Whiller, A., Evaluation of fiat plate solar collector performance, Trans. of the
Conf. on Use of Solar Energy, The Scientific Basis, Vol. II(I), Section A, p. 74. University of Arizona Press, 1958.
5. Liu, B. Y. H. and Jordan, R. C., The interrelationship and characteristic distribution of direct, diffuse and total solar radiation, Solar Energy, 1960, 4, 1.
6. Collares-Pereira, M. and Rabl, A., The average distribution of solar radiation--correlation between diffuse and hemispherical and between daily and hourly insolation values, Solar Energy, 1979, 22, 155.
7. Orgill, J. F. and Hollands, K. G. T., Correlation equation for hourly diffuse radiation on a horizontal surface, Solar Energy, 1977, 19, 357.
8. Bruno, R., A correlation procedure for separating direct and diffuse insolation on horizontal surface, Solar Energy, 1978, 20, 97.
9. Bugler, J. W., The determination of hourly insolation on an inclined plane using a diffuse radiation model based on hourly measured global horizontal insolation, Solar Energy, 1977, 19, 477.
10. Singh, G. M. and Bhatti, S. S., Statistical comparison of global and diffuse radiation correlation, Energy Convers. Mgmt, 1990, 30(2), 155.
11. Sukhatme, S. P., Solar Energy--Principles of Thermal Collection and Storage. Tata McGraw- Hill, New Delhi, India, 1990.
Data Bank 313
12. American Society of Heating, Refrigeration and Air-conditioning Engineers, ASHRAE Hand- book of Fundamentals, Atlanta, 1985.
13. Ma, C. C. Y. and Iqbal, M., Statistical comparison of solar radiation correlat ion--monthly average global and diffuse radiation on horizontal surfaces, Solar Energy, 1984, 33, 143.
14. Zeroual, A., Ankrim, M. and Wilkinson, A. J., The diffuse-global correlation : its application to estimating solar radiation on tilted surfaces in Marrakesh, Morocco, Renewable Energy, 1996, 7(1), 1.
