Page 38 - Applied Photovoltaics

where ȡ is the ground reflectivity, the ratio R / R is correlated with K as
d o T
discussed in Section 1.8.3.1, and R is the ratio between the daily direct insolation
b
on the tilted surface to that on the horizontal. The latter ratio is approximated by the
same ratio of the corresponding extraterrestrial values. For the southern hemisphere,
the ratio is given by

ij
ij
cos ȕ cos įsin Ȧ * s, ȕ § ¨ ʌ · ¸ * s, ȕ sin Ȧ ȕ sin į
R © 180 ¹ (1.24a)
b § ʌ ·
cos ijcos įsin Ȧ * ¨ ¸ Ȧ * sin ijsin į
s, ȕ s, ȕ
© 180 ¹
where
­ cos 1 ijtan į tan
°
Ȧ * s, ȕ min ® (1.24b)
°cos 1 ij ȕ tan į tan
¯
is the sunset hour angle on the tilted surface for the characteristic day of the month.
For the northern hemisphere

ij
ij
cos ȕ cos įsin Ȧ * s, ȕ § ¨ ʌ · ¸ * s, ȕ sin Ȧ ȕ sin į
R © 180 ¹ (1.24c)
b § ʌ ·
cos ijcos įsin Ȧ * ¨ ¸ Ȧ * sin ijsin į
s, ȕ s, ȕ
© 180 ¹
where
­ cos 1 ijtan į tan
°
Ȧ * s, ȕ min ® (1.24d)
°cos 1 ij ȕ tan į tan
¯
Duffie and Beckman (1991) tabulate and plot values of R for various tilt angles.
b

1.9 SOLAR ENERGY AND PHOTOVOLTAICS
Photovoltaics is inextricably linked with the development of quantum mechanics.
Solar cells respond to light particles or quanta, although the wave-particle duality of
light cannot be overlooked in cell design.
Sunlight itself approximates ideal blackbody radiation outside the earth’s atmosphere.
The inability to explain such blackbody radiation by classical theory was itself
responsible for the development of quantum mechanics, which in turn was needed to
understand solar cell operation. As well as reflecting light from the sun, the earth
itself emits radiation similar to that of a blackbody, but centred at much greater
wavelengths because of its lower temperature.

Absorption and scattering of light by the earth’s atmosphere reduce the intensity and
wavelength distribution of light reaching the earth’s surface. They also interfere with
energy being radiated by the earth, resulting in higher terrestrial temperatures than on
the moon and a sensitivity of terrestrial temperature to ‘anthropogenic’ greenhouse
gases. Owing to the variability of the intensity and wavelength distribution of

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