Page 26 - Applied Photovoltaics

2. Evaluating the horizontal direct and diffuse components from the global
values.
3. Estimating these components for a tilted plane from the horizontal values.

1.8.1 Extraterrestrial radiation
R 0 , the extraterrestrial radiation on a horizontal surface, may be calculated from J E ,
the solar constant expressed as energy incident in one hour

Ȗ E 6 . 3 Ȗ kJm 2 1 (1.6)
h
and the geometry of the sun and earth (Iqbal, 1983, p. 65)

§ 24 · ª § ʌȦ s · º
R ¨ ¸ eȖ cos ijcos į sin Ȧ ¨ ¸cos Ȧ » (1.7)
«
0 E 0 s s
© ʌ ¹ ¬ © 180 ¹ ¼
where
§ 2 dʌ ·
0
e |1 033 cos ¨ ¸ (1.8)
.
0
© 365 ¹
is the orbital eccentricity (the reciprocal of the square of the radius vector of the
earth) (Iqbal, 1983) (a more accurate expression for the eccentricity is also available
in Lorenzo, 1989), Ȧ s is the sunrise hour angle, defined by
cos Ȧ tan ijtan į (1.9)
s
d is the day number starting with 1 January as d = 1 (February is always assumed to
have 28 days, introducing a small error in leap years), and į is the declination of the
sun as given by
­ 81 ª d 360 ½ º 81 ª d 360 º
İ
į | sin 1 ® sin İ . sin « ¾ » | sin « » (1.10)
¯ ¬ 365 ¿ ¼ ¬ 365 ¼
where İ = 23.45q. The declination is the angle between a line joining the earth and
sun centres and the earth’s equatorial plane and is zero at the equinoxes (Iqbal, 1983).
More complicated and accurate expressions are also available (see Appendix B).
The corresponding monthly average of extraterrestrial daily global radiation on a
horizontal surface is given by

§ 24 · * * ª * § ʌȦ * s · * º
R ¨ ¸ eȖ cosij cosį «sin Ȧ ¨ ¸ cosȦ » (1.11)
0 E 0 s ¨ ¸ s
© ʌ ¹ « ¬ © 180 ¹ » ¼
1.8.2 Terrestrial global radiation on a horizontal surface

Various instruments exist for measuring insolation levels (Iqbal, 1983; Tindell &
Weir, 1986). The simplest is a heliograph, which measures the hours of bright
sunshine by using focussed light to burn a hole in a rotating chart. Silicon solar cells
themselves are used in the next most sophisticated group of equipment. The

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