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4. Modeling and Simulation of Photovoltaic Irrigation System 323

1
0.8
K d
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1
H
K =
T
H 0
FIGURE 9.26
K d versus K T relationship.

could reach that location if there was no atmosphere (Eq. 9.31). K t measures the
transparency of the atmosphere and constitutes the basis of most methods for esti-
mating radiation on inclined surfaces.
H
K T ¼ (9.31)
H o
The fraction of diffuse radiation, K d , can be calculated from the K t fraction using
the relationships proposed by Erbs et al. O Collares-Pereira depicted in Fig. 9.26.
The direct and diffuse components of radiation can be estimated by applying
Eqs. (9.32) and (9.33).

H b ¼ð1 K d ÞH (9.32)
H d ¼ K d H (9.33)
The Collares-Pereira and Rabl formula is used to disaggregate the daily global
irradiation into hourly values (Eqs. 9.34e9.36).
p cos u cos u S
r ¼ ða þ b cos uÞ (9.34)
24 sin u S u S cos u S
p

a ¼ 0:409 þ 0:516 sin u S (9.35)
3
p

a ¼ 0:6609 0:4767 sin u S (9.36)
3
And for the diffuse irradiance, the equation by Liu and Jordan is used:
p

a ¼ 0:409 þ 0:516 sin u S (9.37)
3
Therefore, the instantaneous global irradiance (sum of direct and diffuse) is given by
the following equation:
I ¼ðI b þ I d Þ¼ rH (9.38)