IMPROVED ASHRAE MODEL TO PREDICT HOURLY AND DAILY SOLAR RADIATION COMPONENTS IN BOTSWANA, NAMIBIA, AND ZIMBABWE
N. N&gomdov Department of Physics, University of Botswana,
Private Bag 0022, Gaborone, Jhtsvana
ASHRAE model empirical coefficients A, B and C are obtained for clear days in Botswana from analysis of different solar radiation componenfs recorded at the University of Botswana, Botswana Technology Centre and some synoptic stations. Investigations show that the direct normal radiation in Botswana usually reveals a specific diurnal profile. For example 30 minutes before sunset, 1,radiation could be above 600 W m-* while at sunset and sunrise (half of the solar disc is under the horizon) it can be as high as 100 Wm-*. Such big values of direct normal solar radiation at sunset and sunrise are not only due to low humidity and turbidity but also due to small values of the relative air mass, m, which can be obtained with the help of a new formula developed by Nijegorodov et aL(1995). By using the ASHRAE empirical coefficients obtained, isotropic and anisotropic sky models and the new formula for the relative air mass a computer program to predict hourly and daily beam, diffuse and ground-reflected radiation on tilted, variously oriented surfaces is developed. This computer program can be used in Botswana, Namibia and Zimbabwe.
KEYWORDS: ASHRAE model, Empirical coefficients, Relative air mass
Based on the analysis of mean experimental data, obtained in the USA ASHRAE has suggested the method for estimating the hourly variation of different solar radiation components on a horizontal and tilted surfaces on a clear day. The method is based on an exponential attenuation model in which the direct normal beam radiation decreases with increase in the distance travelled through the atmosphere. According to the ASHRAE model (1972) dire&normal and diffuse radiation for a clear cloudless day are given by:
I,, = Aexp(-B/co&J,) I, = CI,
where A, B and C are mean monthly empirically chosen constants determined from the analysis of experimental data for USA. The method is simple and provides satisfactory results when applied not only in the USA, but in any country in the Northern hemisphere with meteorological conditions similar to meteorological conditions of the USA. To the authors knowledge the ASHRAE model has never been used in countries of southern Africa. The objectives of this article are: i) to analyse experimental data of different solar radiation components obtained in Botswana; ii) to determine ASHRAE model empirical constants to predict hourly and daily radiation components in Botswana.
EXPERIMENTAL DATA AND ITS ANALYSIS
Daily global radiation on a horizontal surface were recorded continuously at some synoptic stations and at the University of Botswana. Daily total radiation on a tilted surface (fi=-30) was recorded at the Botswana Technology Centre over a period of several years. Hourly direct normal, global and diffise components are continuously recorded at the University of Botswana. For these measurements standard EPLAB Normal Incidence Pyrheliometer (Model NIP), Solar Tracker (Model ST-3) and Precision Spectra1 Pyranometers (Model PSP), with Electronic Integrators were used.
Investigations show that the direct normal radiation in Botswana usually reveal a specific diurnal profile. For example, at solar noon the instantaneous direct normal radiation can be as high as 1150 W/m. 30 minutes before sunset it can be above 600 W/m2 and at sunset and sunrise (when half of the solar disc is under the horizon) it can be still above 100 W/m*. Such big values of direct normal radiation are not only due to low humidity and turbidity, but also due to small values of relative air mass, m, which have to be calculated with the help of the new formula (Nijegorodov et , 1995):
m= + 2r) + r%oe%,-lcose,
where: r - radius of the earth, 0, - zenith angle, H - effective thickness of the Atmosphere, M - average molecular weight of air, g - acceleration due to gravity, T - temperature in K and A - altitude in m. Equation (3) gives a finite value for m at sunset (sunrise) and depends on A and meteorological conditions. Analysis of daily solar radiation components, obtained in Botswana, are shown in Fig. 1. Solid curves give mean daily values for clear cloudless days. From this figure, it is clear that, depending on meteorological conditions, daily solar radiation components can vary within 20 - 25%. The mean daily total radiation on a tilted surface (P=-30) does not vary significantly. Hence this angle can be considered as the mean annual optimum slope of an absorber plate for Botswana. ASHBAE model empirical constants were chosen in such a way that: i) equation (1) must provide a correct value of I,, at solar noon, and it must fit experimental profile of I,,,,; ii) equation (2) must give proper values of hourly diffuse radiation; iii) daily direct normal, global and diffuse components simulated must fit experimental values given by curves 1, 2 and 4 in Fig. 1. Empirical co#istants chosen for Botswana are shown in Table I and constants for USA are given for comparison. ASHBAE empirical constants for Botswana presented earlier (Nijegorodov and Saubi, 1995) are slightly adjusted in this paper in such a way that they can be used in Zimbabwe and Namibia. By using empirical constants obtained, isotropic and anisotropic sky models and equation (3) for the relative air mass a computer program to predict hourly and daily direct normal, beam, diffuse and ground-reflected solar radiation components on a tilted, variously-oriented surfaces in Botswana is developed. An example of simulation done with the help of this program is shown in Fig. 2.
Since latitudes and mean monthly meteorological conditions of Zimbabwe and Namibia do not differ very much from meteorological conditions of Botswana the computer program
- z 35
;: cn 15
zl 10 u P
1 31 59 90 120 151 181 2x2 243 273 304 334 3
; DAY OF A YEAR
Variation of experimental daily solar radiation components with a day of a year and meteorological conditions. (1) - Direct normal; (2 and 4) - global and diffuse on a horizontal surface; (3) - total on a tilted surface (~3=-309.
1200 I Gaborone December 21
1 , I I
I @I - 6:oo 8:oo 1o:oo 1290 14:oo 16:OO l&o0
TIME, HOURS Fig.2: Simulated hourly solar radiation components (clear, cloudless day). (1) - Direct
normal; (2, 3 and 4) - beam, global and diffuse on a horizontal surface.
developed can be used in Zimbabwe and Namibia as well as in Botswana. Preliminary application of the program showed that the discrepancy between simulated and experimental mean daily solar radiation component values for different locations in Botswana, Namibia and Zimbabwe do not exceed 3-5 56.
Table I. ASHRAE model empirical coefficients
Jan. 21 I 1228 0.058
Apr. 21 1134 I
July 21 I 1084 0.207 0.136 1158 Aug. 21 I 1106 1152 0.164
Nov. 21 1219 0.063 1167
Dec. 21 1232 0.142 1169
I would like to thank Dr. A. Adedoyin for useful discussions on the influence of meteorological parameters on solar radiation in Botswana and Mr. B. Saubi for assistance in measurements of Ibn and help in the preparation of this paper.
1. American Society and Heating, Refrigerating and Airconditioning Engineers (ASHRAE), Handbook of Fundamentals, pp. 385443 (1972)
2. N. Nijegorodov, P. V. C. Luhanga, (1995). Analytical and empirical investigation of the effective thickness of the atmosphere; a new formula for air mass, Proc. of the Second International Conference on New Energy Systems and Convention, 31 July - 3 August, Istanbul, Turkey.
3. N. Nijegorodov and B. H. Saubi, (1995) ASHRAE model empirical coefficients to estimate solar radiation on a clear in Botswana, Abstracts of the International Solar Energy Society, Solar World Congress, September 11-15, Harare, Zimbabwe.