Pergamon Energy Conuers. Mgmr Vol. 38, No. 8, pp. 779-185, 1997

0 1997 Elsevier Science Ltd

PJ.k so1%-89oq%)ooo8a-x Printed in Great Britain. All rights reserved

0196-8904/97 $17.00 + 0.00

ESTIMATION OF HOURLY GLOBAL SOLAR RADIATION IN THE PLANE AREAS

OF UTTAR PRADESH, INDIA

0. P. SINGH, S. K. SRIVASTAVA and G. N. PANDEY Department of Applied Sciences (Energy Laboratory), Institute of Engineering and Technology,

Lucknow 226 021, (U.P.), India

(Received IO October 1995)

Abstract-The hourly global radiation on a horizontal surface can be evaluated for the plane areas of Uttar Pradesh using regression constants based on the model proposed by Al-Sadah et al. (1990). Comparison between estimated and measured values shows that the constants derived for Lucknow (latitude 26.75”N, longitude 80SO”E) provide good estimates of the hourly global radiation except for the sunrise and sunset hours. The present results are comparable with the estimates of the Liu and Jordan (1960) and Collares-Pereira and Rabl (1979) models which also correlate hourly values and daily totals of the global radiation. 0 1997 Elsevier Science Ltd. All rights reserved

Hourly global radiation Uttar Pradesh

INTRODUCTION

The design of any solar energy system requires knowledge of the availability of solar radiation data at the location of interest. The average distribution of solar radiation over the day is of fundamental importance in many areas of solar energy. It provides the basis for predicting instantaneous solar radiation from the commonly available monthly averages of daily insolation. Unfortunately, there are only a few solar radiation measuring stations in Uttar Pradesh, India. However, for locations where measured data are not available, empirical correlations developed by various investigators can be used to estimate the solar radiation.

Sometimes, the design of solar energy devices needs accurate estimations of hourly solar radiation values. At places where hourly radiation values are not available, it has to be estimated from the daily values. There are various methods which allow the conversion of daily solar radiation into hourly values. The distribution of total radiation on a horizontal surface over a day was examined by Liu and Jordan [l], who showed that the ratio of hourly to daily radiation could be correlated with the local day length and hour angle. The hours were designated by the time for the mid point of the hour, and the days were considered to be symmetrical about solar noon. The results of Liu and Jordan were confirmed by Collares-Pereira and Rabl[2], using a wider data base. A model for hourly solar radiation has also been developed by Al-Sadah et al. [3], which is correlated with the local time of day. There are some other models [4, 51 to estimate the hourly solar radiation. As the availability of solar radiation for a place depends upon the climatic conditions of the locality, a correlation for a place may not be suitable for other places of different climatic conditions.

The purpose of this paper is to present an analysis of hourly solar radiation data and to develop new regression constants for estimating the hourly global solar radiation on a horizontal surface, which is based on the solar model proposed by Al-Sadah et al. [3]. The present results are compared to the data from direct measurements and the predictions from Liu and Jordan [l] and Collares-Pereira and Rabl[2] methods.

779

780 SINGH et al.: HOURLY SOLAR RADIATION IN UTTAR PRADESH

EXPERIMENTAL SET-UP

The measurements of global solar radiation on a horizontal surface were made by using a precision pyranometer (calibration constant: 5.5 mV/cal/cm*/min) at Lucknow (latitude 26.75”N, longitude: 80.50”E, altitude 120 m above sea level), Uttar Pradesh. A potentiometric chart recorder was used to record the output of the pyranometer. The potentiometric chart recorder had a range of O-10 mV, a chart width of 160 mm and a normal chart speed of 20 mm/hour. Radiation data from April 1991 to March 1992 have been taken for the present study. The hourly data values, as well as daily total values, of the radiation were computed from the record obtained from the potentiometric chart recorder.

MATHEMATICAL MODELS TO ESTIMATE HOURLY GLOBAL RADIATION ON HORIZONTAL SURFACE

Liu and Jordan [l] proposed the following correlation to estimate the monthly mean hourly global radiation (r> on a horizontal surface from the monthly mean daily radiation (Z?) on a horizontal surface.

I//A = (n/24)(cos W - cos Ws) sin W, - (2n W,/360) cos W,

where W is the hour angle in degrees for the midpoint of the hour for which the calculation is to be made, and W, is the sunset hour angle.

To estimate the monthly mean hourly radiation on a horizontal surface, Collares-Pereira and Rabl[2] proposed the following correlation:

r/Z? = (a + b cos W) (rr/24)(cos W - cos W,)

sin Ws - (271 W,/360) cos W, (2)

Al-Sadah et al. [3] developed the following correlation to estimate the ratio of the monthly mean hourly (0 to monthly mean daily (m global radiation on a horizontal surface:

T/Z? = al + b, t + cl t* (3)

for 6.00 < t < 18.00, where al, bl and cl are constants and t is the local time in hours. The relative percentage deviation (6) was calculated using the formula defined as:

where (f//R>,,, and (r/g), are measured and calculated ratios of (r/m, respectively.

Table 1. Regression constants al, bl and CI for each month of the year

Month Year

Regression constants

al b, Cl

April May June July August September October November December January February March

1991 - 0.3748 0.0825 1991 - 0.4356 0.0930 1991 - 0.3244 0.0724 1991 - 0.4172 0.0892 1991 - 0.4976 0.1055 1991 - 0.5017 0.1067 1991 - 0.5434 0.1143 1991 - 0.6067 0.1265 1991 - 0.6356 0.1310 1992 - 0.7344 0.1440 1992 - 0.6763 0..1349 1992 - 0.5247 0.1091

- 0.0034 - 0.0038 - 0.0030 - 0.0037 - 0.0044 - 0.0045 - 0.0048 - 0.0053 - 0.0055 - 0.0059 - 0.0055 - 0.0045

SINGH et a/.: HOURLY SOLAR RADIATION IN UTTAR PRADESH 781

0.14 - Month-April 91

0.12- h

;s O.lO-

j O.OS-

8 ‘a 0.06 -

1 0.04-

0.02 -

- Measured

--•-- New constants

- Eqn. (4) - - O- - Collares-Pereira

I t%o I I I I I I 8.00 IO.00 12.00 14.00 16.00 18.00

Time (hours)

‘i 0.08 -

8 ‘i 0.06 - a 2 0.04-

#’

- Measured

--•-- New constants

Time (hours)

0.14 - Month-June 91

0.12 -

0.10 -

0.08 - - Measured

0.06 - --.-- New constants

e Eqn. (4) 0.04 - - - o- - Collares-Pereira

0.02 -

I &o I I I I 1 I

8.00 10.00 12.00 14.00 16.00 18.00

Time (hours)

Figs 1, 2 and 3. Measured and estimated ratios of monthly mean hourly to daily global radiation (r/H) for the months of April, May and June 1991.

RESULTS AND DISCUSSION

Least squares regression analysis was used to fit equation (3) to the data for each hour of the day to obtain values of the regression constants al, b, and cl for each month of the year. The regression constants al, b, and cl for each month of the year are given in Table 1. Verification of the present constants was made by comparing the estimated ratios of hourly to daily global

182 SINGH et al.: HOURLY SOLAR RADIATION IN UTTAR PRADESH

radiation (f/R) with the measured values. The estimated values of the monthly mean ratios (r/R), along with the measured values, as a function of the local time t for all the months of the year are plotted (Figs 1-12).

A close agreement has been observed between the experimental and theoretical values of the hourly global radiation. The agreement is more pronounced between 9.00 and 15.00 hours.

- Measured

- -. - - New constants

++ Eqn. (4) - - O- - Collares-Pereira

I 4 6qoo

I I I I I I 8.M) lO.OO IZOO 14.OO 16.00 18.00

Time (hours)

0.16b

- Measured

--.-- New constants

m Eqn. (4) - -O- - Cokes-Pereira

Time (hours)

Figs 4, 5 and

0.14 -

0.12 -

0.10 -

0.08 -

0.06 -

0.04 -

0.02 -

- Measured --.-- New constants

- Eqn. (4) - - o- - Collares-Pereira

1 i 6qoo I I I I I I

8.00 10.00 12.00 14.00 16.00 18.OO

Time (hours)

6. Measured and estimated ratios of monthly mean hourly to daily global radiation for the months of July, August and September 1991.

SINGH et al.: HOURLY SOLAR RADIATION IN UTTAR PRADESH 783

- Measured

- - ??- - New constants

+ Eqn. (4) - - o- - CoIlares-Pereira

Time (hours)

0.16.

0.14

- 0.12 IX I= - 0.10 .o 3 n ml

- Month-Nov

-

--c Measured

- - ??- - New constants

- -O- - Collares-Pereira

I/ &IO

I I I I I 8.00 IO.00 12.00 14.00 16.00 18.00

Time (hours)

---c Measured

--a-- New constants

- -0- - Collares-Pereira

Time (hours)

Figs 7, 8 and 9. Measured and estimated ratios of monthly mean hourly to daily global radiation for the months of October, November and December 1991.

184 SINGH et al.: HOURLY SOLAR RADIATION IN UTTAR PRADESH

a deviation of 0.01-0.45% has only been observed for this period using the new constants. The estimated values of hourly radiation for the period lO.O(_L14.00 hours are less than the respective measured values. A significant deviation in the estimated values has been observed at low sun angles (morning and evening hours), which is of little consequence for solar energy operated systems,

0.16

0.14

0.12

0.10

0.081

- Month-Jan

- Measured

--•-- New constants

- - o- - Collares-Pereira

I I I I I ‘c , 8.00 10.00 12.00 14.00 16.00 18.00

Time (hours)

- Measured

--•-- New constants

--o- Eqn. (4)

- - o- - Collares-Pereira

Time (hours)

0.14 - Month-March

0.12 -

$ 0.08 -

.: 0.06- z G 2 0.04-

- Measured

- - ??- - New constants

+3- Eqn. (4) --O-- Collares-Pereira

LO I I I

[ 1, 8.00 10.00 12.00 14.00 16.00 18.00

Time (hours)

Figs 10, 11 and 12. Measured and estimated ratios of monthly mean hourly to daily global radiation (I/R) for the months of January, February and March 1992.

SINGH et al.: HOURLY SOLAR RADIATION IN UTTAR PRADESH 785

because the global radiation during morning and evening hours is very small and constitutes only a small part of the radiation for the day. The present results are also compared with the theoretical estimates of Liu and Jordan [l] and Collares-Pereira and Rabl[2], while in the figures the values estimated using the Liu and Jordan model have not been shown due to overlapping with other calculations. The comparison shows that the present constants produce comparative results to the predictions of the Liu and Jordan and Collares-Pereira and Rable models. In addition, the new constants predict more effectively the hourly radiation during the summer between 10.30 and 14.30 hours.

The whole year data for each hour of the day was also regressed to fit equation (3). The following relationship is established to evaluate the hourly global radiation on a horizontal surface.

f/I? = - 0.5090 + 0.1069t - 0.0044r2 (4)

for 6.00 < t < 18.00. Comparison of the hourly radiation values evaluated by equation (4) with the measured values for each hour of the day for each month shows that the estimates of equation (4) provide satisfactory results (Figs 1-12). The estimated values, calculated by using equation (4), shows that equation (4) is more appropriate than the other correlations for the period when there is a partially cloudy sky. The estimated values of the ratios (r/Z?), calculated by using the constants for each month and equation (4) were also compared (results are not shown) with the observed values for individual days of the respective months, which show that the estimated and measured values are in good agreement, provided days of almost clear sky are chosen for the comparison. The presence of fogs and clouds severely effects the results.

CONCLUSIONS

The hourly global radiation on a horizontal surface can be satisfactorily estimated for the plane areas of Uttar Pradesh, India, by using the new regression constants. A comparison of the present results with existing measurements (shown for. Lucknow) shows that the estimated and measured values are in close agreement, except for low sun angles. The agreement is more pronounced for the peak radiation hours. The present constants produce comparable results to the predictions of the Liu and Jordan and Collares-Pereira and Rabl models. The new constants predict more accurately the hourly global radiation during the summer and winter, while equation (4) may be used for partially cloudy conditions.

Acknowledgemenf-One of the authors (O.P.S.) is thankful to CSIR, New Delhi, for providing financial assistance.

REFERENCES

I. Liu, B. Y. H. and Jordan, R. C., The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy, 1960, 4, 19.

2. Coilares-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.

3. Al-Sadah, F. H., Ragab, F. M. and Arshad, M. K., Hourly solar radiation over Bahrain. Energy, 1990, 15(S), 395. 4. Justus, C. L. and Paris, V., A model for solar irradiance and radiance at the bottom and top of a cloudless atmosphere.

J. Clim. App. Meteor., 1985, 24, 193. 5. Bird, R. and Riordan, C., Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes

at the earth’s surface for cloudless atmospheres. U.S. Solar Energy Research Institute Technical Report TR-215-2436, Golden, Colorado, 1984.