solar energy collector orientation and tracking mode

$olar Energy, Vol. 20, pp. 7-11. P e r g a m o n P r e s s 1 9 7 8 . P f i n t e d i n G r e a t B r i t a i n

SOLAR ENERGY COLLECTOR ORIENTATION AND TRACKING MODE

RICHARD C. NEVILLE Department of Electrical Engineering and Computer Science, University of California, Santa Barbara, CA 93106,

U.S.A.

(Received 27 September 1976; in revised form 20 February 1977)

Abstract--The maximum solar energy available to an Earth-surface collector is examined as a function of latitude, the north-south tilt of the collector from the Earth's surface (~), and whether the collector is an ideal tracker (follows the Sun both north-south and east-west), an east-west tracker (follows the Sun east-west but is fixed in the north-south direction) or a fixed type. It is shown that the ideal tracker gives maximum potentially available energy, the use of an east-west tracking device results in 5-10 per cent degradation in potential performance, while performance, while performance of fixed collectors is degraded by close to 50 per cent. Insolation data by season of the year is also provided.

I N T R O D U C T I O N

The observed solar spectrum is not a smooth function of wavelength and exhibits both a time variation (solar flares, Sun-spot activity, etc. [1]) and a variation in output with wavelength. For our purposes the solar spectral irradiance may be presented as a time- and wavelength- smoothed envelope [2-4]. This is done in Fig. 1 where two curves are presented. The outer envelope is for solar irradiance above the atmosphere at a distance from the Sun comparable to an astronomical unit, the air mass zero condition. The inner curve is the solar irradiance at sea level, the air mass one condition. The solar insolation under air mass zero conditions is 0.135 W/cm 2, while the insolation under air mass one (after the light has been filtered through an atmosphere containing water vapor, carbon dioxide, oxygen, ozone and other gases) is 0.107W/cm214]. It is this difference, together with a potential 24hr insolation period under air-mass zero (AM0) conditions, which prompts discussion of space stations with solar energy collectors.

The ground-based solar energy collector is still at-

~ 1 v l ~ l l l ~ i i i r l l l r i i i i i i i

I 0 0 0,124

t ~ i a n n o s p ne re

0 , | | I I I I I I ' i l i , * , , t , , l t ' ' ' ' ' ' 12.42

ID "~ IO "z I0- ' I.o

Sdar spectral irmdlmce, W crn -2 p.m -I

Fig. 1. Solar spectral irradiance for AM0 and AMI conditions.

tThis paper is written assuming a northern hemisphere lo- cation. Techniques for transference to southern hemisphere lo- cations will be clear from the text.

tractive, however, since such a facility does not require the technology and effort required in construction and maintenance of a space facility. This paper will con~ider the effect of latitude, Earth axial tilt and the Earth's rotation on the amount of effective solar insolation at the Earth's surface. In this paper no attempt at delineating a particular type of solar collector will be made, no~ will local weather effects be considered; the emphasis will be on the ideal solar insolation available. By considering the effects of weather, climate and latitude for any given locale, the reader can then determine an optimum solar collector orientation scheme.

T H E O R E T I C A L A P P R O A C H

The solar insolation under air mass one is 1.07 kW/m 2. This condition implies a vertical orientation for the Sun and a horizontal orientation (relative to the Earth's surface) for the collector. The Earth rotates with ani axis angle of 23.5 ° and a period of close to 24 hr. This iniplies that the Sun is seldom, if ever, directly overhead. Should the Sun make an angle ~b with the normal of a detector lying flat upon the Earth's surface (Fig. 2), the available solar power, P, is

P = a(~b) cos ~b (1)

where a is 1.07 kW/m 2 under air mass one conditioas. In general, the factor a is a function of ~. As light traverses the atmosphere it is partially absorbed and scattered. The greater the angle with the normal, the greater the length of atmosphere which must be traversed and the mote the light is scattered and absorbed, thus the value iof a decreases. Table 1 lists values of a as a function of the angle ~[5].

The angle ~ varies daily from sunrise to sunset, and on a monthly basis as the Sun angle at noon (defined aS that time of day when the Sun angle ~ is smallest) varies from L-23.50 (June) to L + 23.5 ° (January) where L is the latitude in degrees.f It is possible to eliminate the geometric portion (cos ~b) of eqn (l) by tilting the detector until the Sun is on the collector normal, but such an

R. C. NEVILLE

I • /

-, ,Qx - \ \

\ \

\ \

Normal

Det~'tor I

Eor~ s u r g e

Fig. 2. Sun, detector, Earth geometrical relationships.

Normal Normal

Sun I~ l

C I

I Earth's surface North

Fig. 3. Sun, detector, Earth geometric relationships for a tilted detector in the northern hemisphere.

Table 1. Atmospheric effects on solar insolation

Solar angle

~b 0 10 20 30 40 45 50 55 a 1.07 1.06 1.05 1.03 0.993 0.968 0.939 0.903 ~b 60 70 75 80 85 87 88 a 0.855 0.717 0.603 0.451 0.233 0.142 0.095

action will not reduce the length of the atmospheric path and, hence, the effect on a(~).

The average year is 365 and a fraction days. The average month is 30.437 days. The appendix contains average values of solar angle, ~b', at noon and the average length of day (sunrise to sunset) for each average month. The year is assumed to start with the winter solstice. Using these average values the solar insolation can be computed for each "month" from 1-12 using numerical integration and the following expression for solar insolation, SI

f T/2

SI = 2 a(O) cos 0" dt (2) , ; ' 0

where T is the average length of day for each month, a is taken from Table 1 and ~b depends on ~', the monthly average north-south solar angle at noon, and 0, the angle with the surface normal made by the Sun as it traverses the east-west direction. These angles are related by

direction and

~"= 0 (5c)

for a collector which follows the Sun in both north-south and east-west directions.

The insolation is computed for (a) a collector lying horizontally upon the ground, (b) a collector equipped with a tracking device operational in both north-south and east-west planes and, hence, capable of the maximum possible insolation, (c) a series of collectors erected at some north-south angle, 4', to the ground but non- tracking, and (d) a series of collectors erected at some angle, 4', to the ground and possessed of an east-west tracking capability. For these cases the latitude on the Earth's surface is varied from 0 (the equator) to 7& north, and the fixed north-south angle 4' varies from 0 ° to 80 °, facing southward. Corrections are made for light obstruction by high ang]*, (4'), non-tracking structures at low latitudes, but no correction has been made for scattered light impinging on the collector. It is realized that clouds and weather will reduce these insolation values to a greater or lesser extent depending on the precise conditions at a specific locality. Additionally, sunlight is scattered by the atmosphere, buildings, the ground, etc. This diffuse component can dominate the energy input to a solar collector at large solar angles from the vertical where a is small. However, these data provide an upper bound for the solar insolation under any conditions.

tan 2 ~b = tan 2 ~b' + tan 2 0 (3)

and where, with t = 0 corresponding to sunrise

O=2(1-2t/T) for O<-t<-T[2 (4)

and for 4, equal to the north-south angle of the detector relative to the ground (Fig. 3)

tan 2 ~b" = t a n : ( ~ ' - 4,) + tan 2 0 (5a)

for a fixed collector

4," = 0 ' - 4' (Sb)

for a collector which tracks the Sun in an east-west

RESULTS AND DISCUSSION

The computed annual solar energy available (SI) can be presented in several ways. In Fig. 4 the annual energy input is presented as a function of latitude, with collector angle (from the horizontal-facing south) and tracking mode as parameters. No tracking implies that the solar collector would be fixed in position; ideal tracking implies that the collector moves, at all times holding the Sun on the normal to the collector plane, and east-west tracking utilizes a solar collector with fixed north-south angle but with the ability to move in an east-west plane, thus tracking the Sun from sunrise to sunset. Study of these figures shows that the use of east-west tracking results in a collected energy which is a close ap- proximation to the ideal case, provided that the proper north-south angle is picked, while fixed collectors provide much less output.

Solar energy collector orientation and tracking mode

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Flat collector

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Collector 3(~ South 4KXX) , n , , , ,

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Lat., (leg Fig. 4. Solar insolation in kW/hr/m 2 for no tracking and east-west tracking modes as a function of latitude and

collector angle (4~), and for an ideal tracker as a function of latitude.

10 R. C. NEVILLE

Table 2. Seasonal available insolation (kW/hr/m z) (Winter is months 11-2, Summer is months 5-8)

W

W

W

W

W

(N-S angle) 0 10 20 30 40 50 60 70 80 lat. of 0 °

Ideal 1220 No Tracking 850 880 890 880 850 800 730 630 510 E--WTracking 1160 1210 1210 1200 1150 1050 930 780 600


lat. of 10 ° Ideal 1170 No Tracking 770 810 840 850 840 810 760 690 600 E--WTracking 1020 1100 1150 1160 1150 1090 1000 880 740


lat. of 20 ° Ideal 1090 No Tracking 650 710 760 780 790 780 750 710 640 E--WTracking 840 950 1030 1070 1080 1070 1020 940 830

Ideal 1330 No Tracking 970 960 930 870 800 700 570 420 230 E--W Tracking 1320 1310 1280 1190 1060 880 680 470 240

lat. of 30 ° Ideal 990 No Tracking 520 590 640 680 700 710 700 680 640 E-W Tracking 650 770 860 940 980 980 980 930 850

Ideal 1390 No Tracking 1000 1000 990 960 910 830 730 600 440 E-W Tracking 1360 1380 1370 1310 1200 1010 900 700 490

lat. of 400 Ideal 850 No Tracking 360 440 500 550 580 600 600 600 580 E-W Tracking 430 550 660 740 830 840 840 830 800

S Ideal 1460 No Tracking 1010 1040 1050 1040 1000 950 870 760 620 E-W Tracking 1370 1440 1450 1440 1380 1270 1130 950 740

W lat. of 500 Ideal 650 No Tracking 200 280 340 380 420 440 450 460 450 E--W Tracking 230 340 430 510 570 620 640 640 640


W lat. of 60 ° Ideal 340 No Tracking 60 100 140 170 200 220 230 230 240 E-W Tracking 70 130 180 230 270 300 320 330 330


W lat. of 700 Ideal 140 No Tracking 10 20 30 30 40 50 50 50 50 E--W Tracking 10 40 60 80 100 110 120 130 130

S Ideal 1940 No Tracking 1010 1040 1080 1160 1210 1220 1210 1160 1090 E--W Tracking 1240 1480 1680 1820 1910 1930 1910 1820 1680

W = winter, S = summer.

Figure 5 plots the optimum north-south angle and optimum power for the tracking modes considered as a function of latitude. The optimum angle plotted is that angle which produces the maximum annual collectable insolation. For some climatic situations this may not be

the ideal angle, as it may be desired to optimize winter (months 11-2) or summer (months 5-8) energy collec- tion. To facilitate this the following table is included. In Table 2 is presented the solar insolation for winter and summer for the full tracking, east-west tracking, and

Solar energy collector orientation and tracking mode

4 O O O

.,~50 '~ x ' ' " ~ x ~ ' s i ~ "~ x ~ ...Y

20 /.//~" I 1000

'° / I J ' J ' I I I I I I I0 20 30 40 50 GO 7'0

Lot, deg Fig. 5. Optimum angle for installation for fixed and east-west tracking solar energy collectors, and the maximum annual energy (kW/hr/m 2) available to a solar collector of ideal, fixed, or east-

west tracking type as a function of latitude.

non-tracking strategies as a function of latitude and the

angle of the detector installation, 4, (see Fig. 3). In conclusion it must be realized that the optimum

detector installation depends not only on the potential

solar energy collectable (as a function of latitude, track-

ing mode and collector angle (40), but on weather[6], climate (in southern Arizona the emphasis would be on cooling in the summer, in northern Arizona, on heating in the winter), and type of energy converter (thermal panel,

thermoelectric, solar cell or other). For example, a solar- thermal converter such as those discussed in Meinel and

Meinel[7] can utilize long-wavelength scattered radiation

from the ground and can thus operate in a fixed (i.e. non-tracking) mode much more conveniently than a solar-

cell converter which requires direct radiation. Selection

would also depend on the use to which the collected energy would be put, if the collected energy would be used immediately or stored, and if stored, the charac- teristics of the storage techniques. The selection of an

optimum collector, then, is a systems decision with the material presented in this paper a crucial portion of the input data providing knowledge of the maximum energy available.

REFERENCES

1. J. A. Hynek (editor), Astrophysics. McGraw-Hill, New York (1951).

2. E. G. Gibson, The Quiet Sun, p. 14 and Appendices. NASA (1973).

3. Int. Symp. on Solar Radiation Simulation. Institute of En- vironmental Sciences, Washington, D.C. (1965).

4. M. P. Thekaekara, Solar Energy 14, 109 (1973). 5. A. M. Zarem and D. D. Erway, Introduction to the Utilization

of Solar Energy. McGraw-Hill, New York (1963). 6. D. M. Chapin, For example, the energy available to a solar cell

can decrease sharply with cloud cover. In Introduction to the Utilization o[ Solar Energy (1963).

7. A. B. Meinel and M. P. Meinel, For an excellent review of solar-thermal systems. Applied Solar Energy, An Introduction. Addison-Wesley, New York (1976).

APPENDIX A

SOLAR ANGLE AND DAY LENGTH The appendix contains the average angle, ~', made at noon by

the Sun with the normal to a horizontal detector as a function of latitude and month. The year is divided into 12 equal periods and is considered to begin on the winter solstice. Also contained in this appendix is the day length, T, for each monthly period. Average data are drawn from U.S. Weather Bureau tables.

Lat. (°) Month 0 10 20 30 40 50 60 70

1 & 12 ~b'(°) 22.4 32.4 42.4 52.4 62.4 72.4 82.4 88 T (hr) 12 11.5 10.9 10.3 9.3 8.0 5.4 1.4

2 & 11 ~b'(°) 16.4 26.4 36.4 46.4 56.4 66.4 76.4 85 T(hr) 12 11.7 11.3 10.8 10.1 9.3 7.7 5.2

3 & 10 ~b'(°) 6.0 16 26 36 46 56 66 76 T(hr) 12 11.9 11.8 11.7 11.5 11.2 10.6 9.7

4 & 9 6'(°) - 6.0 7.0 14 24 34 44 54 64 T (hr) 12 12.1 12.2 12.3 12.5 12.8 13.4 14.3

5 & 8 ~'(°) - 16.4 - 6.4 3.6 13.6 23.6 33.6 43.6 53.6 T (hr) 12 12.3 12.7 13.2 13.9 14.7 16.3 18.8

6 & 7 ~'(°) - 22.4 - 12.4 - 2.4 7.6 17.6 27.6 37.6 47.6 T (hr) 12 12.5 13.1 13.7 14.7 16.0 18.6 22.6

Positive solar angles indicate the Sun is to the south in the northern hemisphere; negative indicate the Sun is north of the normal to the Earth's surface.

Hours are average for the month and are from sunrise to sunset.

angles

Resumen--El m~ximo de energia solar obtenible sobre la superficie de la tierra por un colector es examinada como funci6n de la latitud, de la inclinaci6n norte-sud (~), sea el colector seguidor ideal del Sol (tanto norte-sur como este-oeste), o bien sigui6ndolo de este a oeste (fijo en la direcci6n norte-sur) o de tipo fijo. Se muestra que el sequidor ideal da potencialmente la mayor energfa obtenible, el seguidor este-oeste da una degradaci6n del rendimiento potencial del 5 al 10%, mientras que el comportamiento de los colectores fijos degrada cerca del 50%. Adem~s es provista la insolacibn para distintas estaciones del afio.

R6sum6--Le maximum d'6nergie solaire disponible pour un collecteur plac6 h la surface de la terre est 6tudi6 en fonction de la latitude, de l'inclinaison Nord-Sud du collecteur par rapport/t la surface terrestre (40, en consid6rant spit un collecteur qui est un suiveur id6al (qui suit le soleil/~ la fois dans sa course Nord-Sud et Est-Ouest), spit un suiveur Est-Ouest (qui suit le soleil dans sa course Est-Ouest mais qui est fixe dans la direction Nord-Sud), ou encore un type de collecteur fixe. On montre que le suiveur id6al donne le maximum d'6nergie disponible potentiellement, que l'utilisation d'un syst6me d'orientation Est-Ouest a pour cons6quence 5/x 10% de d6gradation dans les performances potentielles, alors que celles des collecteurs fixes sont r6duites ~ 50%. On fournit aussi les donn6es d'insolation par saison durant l'ann6e.

solar energy collector orientation and tracking mode

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