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Estimation of global solar radiation in Uttar Pradesh (India) and comparison of some existing correlations
Solar Ene~efyVol. 51, No. 1, pp. 27-29, 1993
00384)92X/93 $6.00 + .00 Copyright © 1993 Pergamon Press Ltd.
Printed in the U.S.A.
ESTIMATION OF GLOBAL SOLAR RADIATION IN UTTAR PRADESH (INDIA) AND COMPARISON OF SOME EXISTING CORRELATIONS S. K. SRIVASTAVA,O. P. S1NGH,and G. N. PANDEY Department of Applied Sciences (Energy Lab), Institute of Engineering and Technology, Sitapur Road, Lucknow-226 020 (U.P.) India Abstract--The global radiation in Uttar Pradesh (India) can be calculated using regression constants with a maximum deviation of 7.5%. The mean monthly values of global radiation calculated is compared to the experimental observation. A comparison with other correlations is also made.
e.m.f, which was measured on a recording millivoltmeter. The potentiometric recorder used to record the output of the pyranometer had a range of 0 - 1 0 mv, a chart width of 160 mm, and a normal chart speed of 20 m m per hour.
I. I N T R O D U C I ' I O N
Solar radiation data may be considered as an essential requirement to conduct feasibility studies for solar energy systems. In developing countries such as India, the facility for global radiation measurement is available only at a few places while bright sunshine hours are measured at many locations. Several m o d e l s [ I 5 ] for the calculation of global radiation at a particular site exist, but these models require local meteorological parameters. It is also well established that a constant derived for a particular location based on several assumptions may not be valid for other locations where the actual installation of solar energy system is to be made. In this article, mean monthly values of global radiation measured for April 1989 to March 1990 at Lucknow (26 °45'N, 80 ° 5 Y E) are presented. Lucknow is centrally located and climatic conditions of many big neighboring cities do not differ appreciably. Using a regression technique, the coefficients of an Angstrom-type linear relation, relating monthly daily average radiation values and the number of bright sunshine hours, were calculated. These coefficients are generally valid for almost all parts of Uttar Pradesh, which covers a large part of northern India.
3. M A T H E M A T I C A L M O D E L S
The method of estimating monthly mean daily global radiation on a horizontal surface was performed from sunshine records. The linear regression of Angstrom's equation as developed by Page is:
/~o - a +
bt
where monthly average daily extraterrestrial radiation on a horizontal surface. monthly average daily global radiation on a horizontal surface. ti = monthly average daily hours of sunshine monthly average m a x i m u m possible daily hours of sunshine (day length).
1-]O =
D
is called the monthly average clearness index (Kr). The regression constants a and b were calculated using standard regression technique. These constants
qo
2. E X P E R I M E N T A L DATA
Global radiation was measured using NI precision pyranometer (No. 0266) manufactured by National Instruments Ltd., Calcutta, India. The calibration factor of NI precision pyranometer, used for the measurement of global solar radiation from sun and sky on a horizontal surface, was 5.87 m v / c a l / c m 2 / m i n ( 8.41 ~tv/ w / m E). It consisted of a thin blackened surface supported inside a relatively massive well-polished case. When exposed to solar radiation, the blackened surface rose in temperature until its rate of loss of heat by all causes was equal to the rate of gain of heat by radiation. This rise in temperature set up a thermal
Table 1. Regression constants a and b used in different models Regression values
27
Correlations
a
b
a+ b
Present result Alnaser Rietveld Bahel et aL
0.2006 0.2843 0.1800 0.1750
0.5313 0.4509 0.6200 0.5520
0.7319 0.7352 0.8000 0.7270
28
S. K. SRIVASTAVA,O. P. SINGH,and G. N. PANDEY Table 2. Measured and calculated values of (////to) using different methods Present work
Month
(ti/.~)
Measured
Calculated
Rietveld
Bahel et al.
Alnaser
April
0.8022
0.6360
May
0.7933
0.6314
June
0.5255
0.5189
July
0.4685
0.4728
August
0.4574
0.4755
September
0.6132
0.5427
October
0.8143
0.6701
November
0.8414
0.6925
December
0.8135
0.6518
January
0.8146
0.6209
February
0.8638
0.6463
March
0.9598
0.6142
0.6268 (1.44) 0.6220 (1.48) 0.4798 (7.53) 0.4495 (4.93) 0.4436 (4.70) 0.5264 (3.00) 0.6333 (5.49) 0.6477 (6.47) 0.6329 (2.90) 0.6335 (2.06) 0.6596 (2.06) 0.6043 (1.61)
0.6774 (6.51) 0.6718 (6.40) 0.5058 (2.52) 0.4705 (0.51) 0.4636 (0.40) 0.5562 (2.49) 0.6849 (2.20) 0.7017 (1.33) 0.6844 (5.00) 0.6851 ( I0.00) 0.7156 (10.72) 0.6511 (6.01)
0.6178 (2.86) 0.6129 (2.93) 0.4651 (10.37) 0.4336 (8.29) 0.4275 (8.16) 0.5135 (5.38) 0.6245 (6.80) 0.6395 (7.65) 0.6241 (4.25) 0.6247 (0.64) 0.6518 (0.85) 0.5944 (3.22)
0.6460 (1.57) 0.6420 (1.68) 0.5212 (0.44) 0.4955 (4.80) 0.4905 (5.37) 0.5608 (3.34) 0.651 ! (1.90) 0.6638 (4.14) 0.6512 (0.09) 0.6516 (4.98) 0.6738 (4.25) 0.6269 (2.07)
were also calculated in terms of the latitude L as follows:
a=fL+g b=pL+q where the values off, g, p, and q were taken from the work of Alnaser [ 6]. The physical significance of the parameters 'a' and 'b' is that 'a' is a measure of the overall atmospheric transmission for totally cloudy conditions (ti/57 = 0 ) and is a function of the type and thickness of cloud cover, while 'b' expresses the rate of increase H / H o with ~i/57. The sum (a + b) denotes the overall atmospheric transmission under clear sky conditions. The calculation o f ( H / / t o ) was carried out by using monthly mean daily values H measured by a NI precision pyranometer and monthly mean daily values /to which were calculated using 11o for each specific day of the month[7]. The correlations of Rietveld[8 ]and Bahel et a/.[9] have been used to compare calculated global solar radiation.
4. RESULTS AND DISCUSSION Regression constants a and b have been calculated using recent experimental observation of mean monthly daily global radiation on horizontal surface. The same constants have been calculated using latitude of the place (L = 26°45'N) as proposed by Alnaser.
The constants of Rietveld [ 8 ] and Bahel et aL [ 9 ] have been listed in Table 1. The value o f ( a + b) in all the cases lies between 0.73-0.80. Monthly mean daily values of (ri/N) and (H/Ho) for April 1989 to March 1990 have been listed in Table 2. The bracketed quantities are the percentage deviations from the actual observations. It is well observed that the present constant predicts mean monthly values of global radiation accurately for almost all months (April 1989 to March 1990). Babel et al.[9]model predicts global radiation more accurately for January and February while the prediction of Alnaser for the month of December is well matched. The Rietveld model more accurately predicts during rainy season (July-September) with a maximum deviation of 2.5%. The constants of this work predict the global radiation of almost all major cities of Uttar Pradesh with a deviation of only 2-3% (not shown) during winter (December-February).
5. CONCLUSION The monthly mean daily global radiations can be calculated very accurately in Uttar Pradesh (India) with the regression constants a = 0.2006, b = 0.5313. The global radiation can be calculated for almost all places in Uttar Pradesh with a maximum variation of 7.5% for the whole year while it can be calculated with a variation of 2-3% during winter (DecemberFebruary).
Global solar radiation in Uttar Pradesh
29
REFERENCES
1. K. K. Gopinathan, A new model for estimating total solar radiation, Solar and Wind Technology 5, 107-109 (1988). 2. H. P. Garg and S. N. Garg, Improved correlation of daily and hourly diffuse radiation with global radiation for Indian stations, Solar and Wind Technology4, 113-126 (1987). 3. J. A. Sabbag, A. A. M. Sayigh, and E. M. A. EI-Salam, Technical note: Estimation of the total solar radiation from meterological data, Solar Energy 19, 307 ( 1977 ). 4. K. K. Gopinathan, The distribution of global and sky radiation throughout Lesotho, Solar and Wind Technology 5, 103-106 (1987).
5. Y. A. G. Abdalla and G. M. Feregh, Contribution to the study of solar radiation in Abu Dhabi, Energy Convers. Mgmt. 28, 63-67 (1988). 6. W. E. Alnaser, Empirical correlation for total and diffuse radiation in Baharain, Energy 14, 409-414 (1989). 7. S. A. Klein, Calculation of monthly average insolation on tilted surfaces, Solar Energy 9, 325-329 (1977). 8. M. R. Rietveld, A new method for estimating the regression coeificients in the formula relating solar radiation to sunshine, Agric. Met. 19, 243-252 (1978). 9. V. Babel, R. Srinivasan, and H. Baksh, Solar radiation for Dhahran, Saudi Arabia, Energy 11,985-989 (1986).
00384)92X/93 $6.00 + .00 Copyright © 1993 Pergamon Press Ltd.
Printed in the U.S.A.
ESTIMATION OF GLOBAL SOLAR RADIATION IN UTTAR PRADESH (INDIA) AND COMPARISON OF SOME EXISTING CORRELATIONS S. K. SRIVASTAVA,O. P. S1NGH,and G. N. PANDEY Department of Applied Sciences (Energy Lab), Institute of Engineering and Technology, Sitapur Road, Lucknow-226 020 (U.P.) India Abstract--The global radiation in Uttar Pradesh (India) can be calculated using regression constants with a maximum deviation of 7.5%. The mean monthly values of global radiation calculated is compared to the experimental observation. A comparison with other correlations is also made.
e.m.f, which was measured on a recording millivoltmeter. The potentiometric recorder used to record the output of the pyranometer had a range of 0 - 1 0 mv, a chart width of 160 mm, and a normal chart speed of 20 m m per hour.
I. I N T R O D U C I ' I O N
Solar radiation data may be considered as an essential requirement to conduct feasibility studies for solar energy systems. In developing countries such as India, the facility for global radiation measurement is available only at a few places while bright sunshine hours are measured at many locations. Several m o d e l s [ I 5 ] for the calculation of global radiation at a particular site exist, but these models require local meteorological parameters. It is also well established that a constant derived for a particular location based on several assumptions may not be valid for other locations where the actual installation of solar energy system is to be made. In this article, mean monthly values of global radiation measured for April 1989 to March 1990 at Lucknow (26 °45'N, 80 ° 5 Y E) are presented. Lucknow is centrally located and climatic conditions of many big neighboring cities do not differ appreciably. Using a regression technique, the coefficients of an Angstrom-type linear relation, relating monthly daily average radiation values and the number of bright sunshine hours, were calculated. These coefficients are generally valid for almost all parts of Uttar Pradesh, which covers a large part of northern India.
3. M A T H E M A T I C A L M O D E L S
The method of estimating monthly mean daily global radiation on a horizontal surface was performed from sunshine records. The linear regression of Angstrom's equation as developed by Page is:
/~o - a +
bt
where monthly average daily extraterrestrial radiation on a horizontal surface. monthly average daily global radiation on a horizontal surface. ti = monthly average daily hours of sunshine monthly average m a x i m u m possible daily hours of sunshine (day length).
1-]O =
D
is called the monthly average clearness index (Kr). The regression constants a and b were calculated using standard regression technique. These constants
qo
2. E X P E R I M E N T A L DATA
Global radiation was measured using NI precision pyranometer (No. 0266) manufactured by National Instruments Ltd., Calcutta, India. The calibration factor of NI precision pyranometer, used for the measurement of global solar radiation from sun and sky on a horizontal surface, was 5.87 m v / c a l / c m 2 / m i n ( 8.41 ~tv/ w / m E). It consisted of a thin blackened surface supported inside a relatively massive well-polished case. When exposed to solar radiation, the blackened surface rose in temperature until its rate of loss of heat by all causes was equal to the rate of gain of heat by radiation. This rise in temperature set up a thermal
Table 1. Regression constants a and b used in different models Regression values
27
Correlations
a
b
a+ b
Present result Alnaser Rietveld Bahel et aL
0.2006 0.2843 0.1800 0.1750
0.5313 0.4509 0.6200 0.5520
0.7319 0.7352 0.8000 0.7270
28
S. K. SRIVASTAVA,O. P. SINGH,and G. N. PANDEY Table 2. Measured and calculated values of (////to) using different methods Present work
Month
(ti/.~)
Measured
Calculated
Rietveld
Bahel et al.
Alnaser
April
0.8022
0.6360
May
0.7933
0.6314
June
0.5255
0.5189
July
0.4685
0.4728
August
0.4574
0.4755
September
0.6132
0.5427
October
0.8143
0.6701
November
0.8414
0.6925
December
0.8135
0.6518
January
0.8146
0.6209
February
0.8638
0.6463
March
0.9598
0.6142
0.6268 (1.44) 0.6220 (1.48) 0.4798 (7.53) 0.4495 (4.93) 0.4436 (4.70) 0.5264 (3.00) 0.6333 (5.49) 0.6477 (6.47) 0.6329 (2.90) 0.6335 (2.06) 0.6596 (2.06) 0.6043 (1.61)
0.6774 (6.51) 0.6718 (6.40) 0.5058 (2.52) 0.4705 (0.51) 0.4636 (0.40) 0.5562 (2.49) 0.6849 (2.20) 0.7017 (1.33) 0.6844 (5.00) 0.6851 ( I0.00) 0.7156 (10.72) 0.6511 (6.01)
0.6178 (2.86) 0.6129 (2.93) 0.4651 (10.37) 0.4336 (8.29) 0.4275 (8.16) 0.5135 (5.38) 0.6245 (6.80) 0.6395 (7.65) 0.6241 (4.25) 0.6247 (0.64) 0.6518 (0.85) 0.5944 (3.22)
0.6460 (1.57) 0.6420 (1.68) 0.5212 (0.44) 0.4955 (4.80) 0.4905 (5.37) 0.5608 (3.34) 0.651 ! (1.90) 0.6638 (4.14) 0.6512 (0.09) 0.6516 (4.98) 0.6738 (4.25) 0.6269 (2.07)
were also calculated in terms of the latitude L as follows:
a=fL+g b=pL+q where the values off, g, p, and q were taken from the work of Alnaser [ 6]. The physical significance of the parameters 'a' and 'b' is that 'a' is a measure of the overall atmospheric transmission for totally cloudy conditions (ti/57 = 0 ) and is a function of the type and thickness of cloud cover, while 'b' expresses the rate of increase H / H o with ~i/57. The sum (a + b) denotes the overall atmospheric transmission under clear sky conditions. The calculation o f ( H / / t o ) was carried out by using monthly mean daily values H measured by a NI precision pyranometer and monthly mean daily values /to which were calculated using 11o for each specific day of the month[7]. The correlations of Rietveld[8 ]and Bahel et a/.[9] have been used to compare calculated global solar radiation.
4. RESULTS AND DISCUSSION Regression constants a and b have been calculated using recent experimental observation of mean monthly daily global radiation on horizontal surface. The same constants have been calculated using latitude of the place (L = 26°45'N) as proposed by Alnaser.
The constants of Rietveld [ 8 ] and Bahel et aL [ 9 ] have been listed in Table 1. The value o f ( a + b) in all the cases lies between 0.73-0.80. Monthly mean daily values of (ri/N) and (H/Ho) for April 1989 to March 1990 have been listed in Table 2. The bracketed quantities are the percentage deviations from the actual observations. It is well observed that the present constant predicts mean monthly values of global radiation accurately for almost all months (April 1989 to March 1990). Babel et al.[9]model predicts global radiation more accurately for January and February while the prediction of Alnaser for the month of December is well matched. The Rietveld model more accurately predicts during rainy season (July-September) with a maximum deviation of 2.5%. The constants of this work predict the global radiation of almost all major cities of Uttar Pradesh with a deviation of only 2-3% (not shown) during winter (December-February).
5. CONCLUSION The monthly mean daily global radiations can be calculated very accurately in Uttar Pradesh (India) with the regression constants a = 0.2006, b = 0.5313. The global radiation can be calculated for almost all places in Uttar Pradesh with a maximum variation of 7.5% for the whole year while it can be calculated with a variation of 2-3% during winter (DecemberFebruary).
Global solar radiation in Uttar Pradesh
29
REFERENCES
1. K. K. Gopinathan, A new model for estimating total solar radiation, Solar and Wind Technology 5, 107-109 (1988). 2. H. P. Garg and S. N. Garg, Improved correlation of daily and hourly diffuse radiation with global radiation for Indian stations, Solar and Wind Technology4, 113-126 (1987). 3. J. A. Sabbag, A. A. M. Sayigh, and E. M. A. EI-Salam, Technical note: Estimation of the total solar radiation from meterological data, Solar Energy 19, 307 ( 1977 ). 4. K. K. Gopinathan, The distribution of global and sky radiation throughout Lesotho, Solar and Wind Technology 5, 103-106 (1987).
5. Y. A. G. Abdalla and G. M. Feregh, Contribution to the study of solar radiation in Abu Dhabi, Energy Convers. Mgmt. 28, 63-67 (1988). 6. W. E. Alnaser, Empirical correlation for total and diffuse radiation in Baharain, Energy 14, 409-414 (1989). 7. S. A. Klein, Calculation of monthly average insolation on tilted surfaces, Solar Energy 9, 325-329 (1977). 8. M. R. Rietveld, A new method for estimating the regression coeificients in the formula relating solar radiation to sunshine, Agric. Met. 19, 243-252 (1978). 9. V. Babel, R. Srinivasan, and H. Baksh, Solar radiation for Dhahran, Saudi Arabia, Energy 11,985-989 (1986).