Comparison of methods for estimating daily and hourly diffuse solar radiation

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  • ELSEVIER

    Applied Energy 51 (1995) 119-123 1995 Elsevier Science Limited

    Printed in Great Britain. All rights reserved 0306-2619/95/$9.50

    0306-26 I 9 (94)00048-4

    Comparison of Methods for Estimating Daily and Hourly Diffuse Solar Radiation

    S. K. Srivastava, A. Gaur, O. P. Singh & R. N. Tiwari

    Department of Applied Sciences (Energy Lab.), Institute of Engineering and Technology, Sitapur Road, Lucknow 226020, Uttar Pradesh, Ind ia

    ABSTRACT

    Daily and hourly diffuse radiations measured using a pyranometer and shading ring have been compared with the values calculated using several correlations. For the daily diffuse radiation, the correlation of Duffle & Beckman (Solar Engineering of Thermal Processes, John Wiley, 1980), Liu & Jordan (Solar Energy, 4(3) (1960) 1-19), Erbs et al., (Solar Energy, 28 (1982) 293) and Bruno (Solar Energy, 20(1) (1978) 97-100) have been used while the hourly diffuse radiation was calculated using the correlations of Hottel, Orgill & Holland (Solar Energy, 19 (1977) 357) and Liu & Jordan. It has been uniformly observed that Liu & Jordan's method may be con- sidered a suitable method for the estimation of daily and hourly diffuse radiations in clear-sky conditions in the plain areas of northern lndia.

    INTRODUCTION

    The calculation of energy used in buildings and the performances of solar devices require a knowledge of direct and diffuse solar radiation. There are several stations where only global radiation is measured and so an estimate of diffuse radiation is desirable. The split of total solar radiation on a horizontal surface into its beam and diffuse components is of interest in two contexts. The first method, for calculating the total radiation on the surfaces of other orientations from data for a horizontal surface, requires separate treatments of beam and diffuse radiations. Secondly, the estimates of long-term performances of concentrating collectors must be based on estimates of availability of beam radiation. However, if data on both the global and diffuse radiations are available, it is often necessary

    119

  • 120 S. K. Srivastava, A. Gaur, O. P. Singh, R. N. Tiwari

    in compiling long unbroken sequences of data, to estimate the missing values of diffuse radiation. In this paper, the method for estimating the daily and hourly diffuse radiations on a horizontal surface is reviewed.

    EXPERIMENTAL DATA

    The measurement of diffuse radiation was made with a pyranometer, by shading, with a ring, the instrument from beam radiation. The ring was used to allow continuous recording of the diffuse radiation without the positioning of shading devices. An adjustment was made after a few days by changing the declination.

    For the measurement of global radiation, a separate pyranometer was used. The calibration factors of the pyranometers, manufactured by National Instrument Ltd, Calcutta, India, used for the measurement of global and diffuse solar radiation on a horizontal surface were 5.37 mV/ cal/cm2/min and 5.50 mV/cal/cm2/min respectively. The measurement was made at the Institute of Engineering & Technology, Lucknow (26 45' N, 80 53' E).

    MATHEMATICAL MODELS

    Experimental values of the daily diffuse radiation have been compared with the values obtained by the methods of Liu &Jordan, ~ Bruno, 2 Duffle and Beckman 3 and Erbs et aL 4 Except in the case of Bruno, the daily global radiation on the horizontal surface was taken to calculate the daily diffuse radiation. In the case of Bruno, extraterrestrial radiation values have been used.

    Hourly diffuse radiation was calculated using the correlations of Liu & Jordan, l Orgill & Holland 5 and Hottel; 6 the results were compared with the experimental values.

    RESULTS AND DISCUSSION

    Daily diffuse radiation (Hd) from global radiation on a horizontal surface

    The diffuse radiation on a horizontal surface was measured by blocking the beam radiation using a shading ring for several months. The daily total radiation (including the diffuse component), as well as the clearness index for some of the days in the month of March, have been listed in

  • Estimation of diffuse solar radiation 121

    TABLE 1 Daily diffuse radiation (Ha) on a horizontal surface with clearness index (Kr).

    Date Diffuse radiation ( W/m e) KT

    Measured Calculated

    Liu & Duffle & Erbs Bruno Jordan Beckman et al.

    05.3.94 1 141.20 1 455-66 1 765-14 1 830.56 1 440.08 0.652 06.3.94 887-60 1 149.23 1 445.39 1 077.52 1 610.97 0.725 07.3.94 1 103.12 1 898.19 2350-42 2477-63 1 356.85 0.607 08.3.94 1 077.80 1 179-46 1 472.35 1 187.13 1 621.24 0.721 09.3.94 1 179-24 1 212.14 1 498.83 1 265.99 1 617.21 0.715 11.3.94 1 242.64 1 529-18 1 859-95 1 938.08 1 480.44 0.647 15.3.94 1 623-04 1 759.93 2 183.45 2 300.28 1 411.08 0.603 16.3.94 2231.68 2139-20 2717-46 2740.68 1 171.76 0.498 19.3.94 1 229.96 1 420.99 1 716.25 1 678.87 1 624-34 0.643 21.3.94 1 420.16 1 637.32 1 993.32 2 084.99 1 550.83 0.642 22.3.94 1 014.40 1 283.48 1 596.78 1 311.55 1 745.63 0.719 23.3.94 1 103.16 1 396.62 1 695.08 1 564.21 1 698.23 0.696 24.3.94 1 115.84 1 454-64 1 757.63 l 709.05 1 679-64 0-685

    Table 1. The diffuse components have been compared with the values calculated using the correlations of Liu & Jordan, Duffle & Beckman, Erbs et al. and Bruno. The method of Liu & Jordan is the most suitable for the calculation of Ha. The values of Ha calculated using the Bruno 2 method have been found to be more accurate for some of the days (see Table 1). The method of Erbs et al. is also suitable, because for some of the dates, it predicts the diffuse radiation more accurately than the Liu & Jordan method. The method of Duffle & Beckman may not be used effectively for the calculation of H d. Only the data for March have been presented as very calm conditions and clear skies were observed for long periods during this month. Similar observations have also been made for other months (not shown).

    Hourly diffuse radiation (Id) on horizontal surface

    Values of the hourly diffuse radiation have been calculated using the correlations of Hottel, Orgill & Hollands, and Liu & Jordan. These have been compared with measured values (see Table 2). The measured hourly diffuse radiation for 15 March 1994 have been compared with the values calculated using different correlations, and similar observations have been made for other days also (not shown). It appears that the

  • 122 S. K. Srivastava, A. Gaur, O. P. Singh, R. N. Tiwari

    TABLE 2 Hourly diffuse radiation (Id) on a horizontal surface with hourly clearness index (Kr)

    (15 March 94).

    Time ( h ) Diffuse radiation (l'V/m 2) K r

    Measured Calculated

    Hottel Orgill & Liu & Holland Jordan

    07.00-08.00 76.08 71.92 131.18 79.71 0.329 08.00-09.00 139.48 89.84 231.36 130.06 0-459 09.0o-10.00 177.52 99.44 297.02 171.16 0.501 10.00-11.00 177.52 104.87 283.62 200.25 0.618 11.00-12.00 190-20 107.38 273-85 215.29 0.652 12.00-13.00 190.20 107-38 249.60 215-29 0-675 13.00-14.00 190.20 104.87 216.53 200.25 0-690 14.00-15.00 177.52 99.44 179.50 171.16 0.696 15.00-16.00 139.48 89.84 148.75 130.06 0.678 16.00-17.00 114.12 71.92 99.49 79.71 0.657 17.00-18.00 50.72 29.24 42.18 23-56 0-405

    correlation of Liu & Jordan predicts hourly diffuse radiation with the highest accuracy. Except during the morning hours, the Hottel method predicts too low values of the hourly diffuse radiation. In the morning hours, the method of Orgill and Hollands gave higher values while in the afternoon this prediction method is quite acceptable.

    CONCLUSIONS

    The Liu & Jordan method may be considered to be the most suitable for estimating the daily diffuse radiation. However, correlations of Erbs et al. and Bruno are also acceptable.

    For the estimation of hourly diffuse radiations, the correlation given by Liu & Jordan is quite acceptable. The Hottel method, for hourly diffuse radiations, may be used for the morning hours while the method of Orgill & Holland may be used in the afternoon.

    ACKNOWLEDGEMENT

    One of the authors (OPS) is thankful to the Council of Scientific & Industrial Research, New Delhi, for providing financial assistance.

  • Estimation of diffuse solar radiation 123

    REFERENCES

    1. Liu, B. Y. H. & Jordan, R. C., The interrelationship and characteristic distribu- tion of direct, diffuse and total solar radiation. Solar Energy, 4(3) (1960) 1-19.

    2. Bruno, R., A correlation procedure for separating direct and diffuse insolation on a horizontal surface. Solar Energy, 20(1) (1978) 97-100.

    3. Duffie, J. A. & Beckman, W. A., Solar Engineering of Thermal Processes. Wiley Inter-Science, New York, 1980.

    4. Erbs, D. G. et al., Estimation of the diffuse radiation fraction for hourly, daily and monthly average global radiation. Solar Energy, 28 (1982) 293.

    5. Orgill, J. F. & Holland, K. G. T., Correlation equation for hourly diffuse radiation on a horizontal surface. Solar Energy, 19 (1977) 357.

    6. Rayab, F. M. & Sam, A. K., Correlation between estimated and measured hourly and daily solar fluxes over Bahrain. Applied Energy, 40 (1991) 83-9.

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