Solar Energy Vol. 28, No. 4. pp. 303-306. 1982 0038-092Xl821040303..04,~3.00/0 Printed in Great Britain. © 1~2 Pergamon Press Ltd.

A SIMPLE MODEL FOR SKY RADIATION MEASUREMENTS

M. PosPi~IL and L. POSPi~ILOVA Astronomical Institute CSAV, 25165 Ond~ejov, Czechoslovakia

(Received 29 May 1981; accepted 18 August 1981)

AINtraet--In the proposed model the sky hemisphere as a radiating source has been replaced by a single point radiating source and a diffuse background. The point source produces insolation H on a horizontal surface, its beam coming from direction (a, ~0), a being the azimuth and q~ the zenith angle. The diffuse radiation comes from all directions equally and produces insolation D on a horizontal surface. For estimating all four parameters H, a, ~ and D of the model, a four-segment photo-cell was developed and tested. The method is suitable for calculating the optimal orientation (azimuth and tilt) of a solar collector, depending on local conditions.

I. INTRODUCTION

At the majority of locations, where a solar system is to be built, it is necessary to consider the whole sky hemisphere as a source of radiated energy. In in- dustrialized countries there are nearly no places where the "astronomical" sun is sufficient as the only source of energy. In Czechoslovakie, for example, two thirds of the solar insolation are diffuse and only one third direct, on an annual average.

To measure the sky hemisphere as a source of radia- tion is a rather complicated task--it is necessary to measure the brightness of each element of the sky at every moment. It is, of course, possible to conduct such an experiment--to project the sky onto a semiconductor CCD sensor with a fish-eye objective, to introduce data reduction, to record the data on magnetic tape and to rectify the projection of the sky hemisphere into the plane of the sensor during further data processing in a computer. The "simplified" TV mode, e.g. 300 x 300 pic- ture elements and 128 or less levels of grey, is easier than that developed and used for processing of Landsat pic- tures. But to conduct such measurements for the design of each solar system would be unnecessarily accurate, too complicated and expensive.

McArthur and Hay[l] described a simplified measurement of this type. They used a pyranometer and in addition to it they measured the density of all-sky photographs. They investigated up to 2629 picture ele- ments (approx. 60 ×60 points). Their method is rather time consuming.

Designers usually exploit the data from weather sta- tions, which are mostly average values of global in- solation on a horizontal surface. According to some of the modqs[2-4] the beam and diffuse components are calculated from these data, which are then reduced to obtain the tilted-surface values. Steinm011er[5] estimates the inaccuracies at 25 per cent on an average, but up to 50 per cent in the worst case. The result of the cal- culation is the energy which the collector is able to deliver during a given interval. The orientation of the collector is very often only set by estimate--in the northern hemisphere it is faced south with a tilt of 10 ° more than the latitude of the location ([6], p. 7).

If flat collectors are used, the inaccuracies in orien-

tation are usually not critical. The energy collected by a plane collector, irradiated by one stationary source, varies by less than -+ 3 per cent if the orientation varies by -+ 150 from the optimum, perpendicular to the incident beam (assuming cosinusoidal dependence of the collector output power on the angle of incident radiation). If the movement of the sun along the sky and diffuse radiation are considered, the permissible limits in which the angle may vary, would be even larger. For 3 per cent devia- tions from maximum energy Hamakar and deWitt[7] give azimuths of 30°E-22.5°W and tilts in the region of 35-72 °.

But if a large solar system or many systems at one location are to be built, or if focusing devices or collec- tors with reflectors are to be used, one must respect local conditions such as shadowing by the horizon, reflection of water or snow[8] surfaces, typical morning fogs or evening cloudiness. Interpolation between weather sta- tions sometimes leads to substantial inaccuracies, and in some countries the density of the station network is insufficient. And reducing the data from global to beam and diffuse, and from horizontal to tilted surfaces intro- duces further errors. Therefore, measurements at the construction site are sometimes necessary.

In this case one usually measures: --global insolation on a horizontal surface by pyranometer, - -beam insolation on a horizontal surface by pyr- heliometer (with the mechanical diaphragm controlled by a clockwork), --ambient temperature and the wind vector ([6], p. 16). The advantage of the method is the possibility of using commercially available instruments, the disadvantage the small amount of information for calculating the optimal orientation of the collector and the necessity of reducing the horizontal data to the tilted surface.

2. THE MODEL

In designing a solar system it is necessary to estimate the optimal orientation of the collector, i.e. the angles of azimuth and tilt in such a way that the power delivered by the collector is as large as possible and at the proper time (during the day and the year). Further it is neces- sary to estimate the performance of the collector, i.e. the

303

304 M. POSPLqlL and L. POSPiglLOVA

power delivered per I m 2 of its area (which makes it possible to calculate the area of the collector given the demand) and the capacity of the accumulator.

Let us assume that the time dependence of the power demand is given and that the qualities of the system and the location make the measurement in situ necessary. In a first approximation we tried to replace the real sky hemisphere by the sum of the single point source and a diffuse background.

The point source is in the direction a (azimuth) and (the angle between the beam and the zenith direction). This source produces insolation H (Wm -2) on the horizontal surface.

The diffuse radiation comes from all directions in equal intensity and produces insolation D (Wm -2) on the horizontal surface.

The direction (a, ,p) of the direct beam need not be the same as the direction of the "astronomical" sun. (But on sunny days it is the same, of course.) The direction (a, ,p) determines the strongest source of radiation in the sky at the time of measurement.

3. FOUR-SEGMENT CELL

A circular silicon cell, 29 mm in diameter, is divided into four rectangular segments with one common con- tact. Two crossed diaphragms are situated above the boundaries of the segments. The whole system is moun- ted under an air-tight hemispherical cover. In the space under the base plate there are load resistors, desiccator and a thermistor for measuring the temperatures in the device (see Figs. 1 and 2).

The output voltage of each segment in the "short- circuit regime" depends linearly on the radiation from the point source (see the preceding section), which depends on the insolation H and on the irradiated area. The latter is the area of the segment less its part shadowed by the diaphragm. This part of the output voltage depends on H, a and ¢. The voltage generated by the diffuse insolation D over the whole area of the segment is added to it.

The four parameters H, a, ¢ and D of the model can be calculated from the four output voltages of the four- segment cell.

Fig. I. Complete measuring device with the four-segment cell.

Fig. 2. Four-segment cell. Above the boundaries between the segments are crossed diaphragms.

A simple model for sky radiation measurements 305

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Fig. 3. Output voltage of the individual segments and the temperature in the device on a sunny day.

4. RESULTS

Figure 3 shows the output voltages of the cell on a sunny day; the anisotropy is quite distinct. The fifth picture of the group illustrates the run of the temperature in the device. Figure 4 shows the quantities on a cloudy day.

The points were measured at 12-sec intervals, the sequences being repeated every 144sec. The measured values were recorded on a paper-strip recorder. The preparation of the data recorded during 1 day for com- puter processing took two people 2 hr of tedious work. This is the reason why only some typical days have been processed so far.

$. CONCLUSIONS

The measurements proved the usefulness of the pro- posed model and the suitability of the four-segment cell

for calculating the model parameters. The silicon cell made it possible to construct this simple device and, due to its relatively high output voltage (100 mV at a 3-ohm load) to use simple electronics.

In comparison to the thermo-electric pyranometers the silicon cell has ([9], p. 24): --a great spectral efficiency dependence (see also [101, p. 122), --a great efficiency dependence on the angle of incidence ([10], p. 124).

In this first approximation the spectral dependence was neglected, but it can be accounted for in the data processing. The dependence on the angle of incidence is measured during calibration. For this purpose only the cell, without the diaphragm, is measured. This result is included in the data processing program.

The optimal shape of the diaphragm is under

306 M. POSPi~IL and L. POSPff;ILOV,i.

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Fig. 4. Output voltage and temperature on a cloudy day.

development now; bet ter ways of recording and storing

the data are necessary in future.

Acknowledgements--The authors are very grateful to Dr. M. Ko~:andrle of the Faculty of Mathematics and Physics of the Charles University in Praha for valuable discussions and com- ments.

REFERENCES

I. L. B. McArthur and J. E. Hay, An assessment of the tech- niques for determining the distribution of diffuse solar radi- ance for the sky hemisphere. Solar Energy 25, 573-574 (1980).

2. T. M. Klucher, Evaluation of models to predict insolation on tilted surfaces. Solar Energy 23, I I 1-114 (1979).

3. B. Goldberg, W. H. Klein and R. D. McCartness, A corn-

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4. M. Iqbal, The influence of collector azimuth on solar heating of residential buildings and the effect of anisotropic sky- diffuse radiation. Solar Energy 26, 249-257 (1981).

5. B. Steinmiiller, The two-solarimeter method for insolation on inclined surfaces. Solar Energy 25, 449-460 (1980).

6. J. R. Williams, Solar Energy. Ann Arbor, Ann Arbor (1977). 7. J. Jamaker and M. deWitt, Tilt, orientation and overshadow-

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8. R. E. Grojean, J. A. Sousa and M. C. Henry, The efficacy of solar conversion in a polar environment. Solar Energy 25, 537-542 (1980).

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