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324 CHAPTER 9 Design Principles of Photovoltaic Irrigation Systems

where the diffuse and direct components are:
(9.39)
I d ¼ r d H d
I b ¼ðrH r d H d Þ (9.40)

4.1.3.1 Irradiance on a Fixed or Tracked Collector Plane
To calculate the irradiance on a collector plane, direct, diffuse, and global irradiance
must be calculated on a horizontal surface every short period of time on a character-
istic day of each month. The following input parameters must be defined to perform
these calculations: Julian day, latitude, irradiation (H), and timer. The global irradi-
ance in a horizontal plane is the sum of direct irradiance and diffuse irradiance:
Then, both the direct and diffuse irradiance on the tilted PV modules must be
!

calculated taking into account both the unit solar vector s and the unit vector
of the collector plane (n).

• Direct irradiance received by the modules I bb : The most widely accepted
approach for estimating the direct daily radiation on a sloped surface considers
the geometric position of the Sun and the collector and is based on the hy-
pothesis of proportionality between the fractions of direct and extraterrestrial
radiation.
cos q
I bb ¼ I b $ (9.41)
cos q Z

• Diffuse irradiance received by the modules I db : The estimation of this
parameter is based on the isotropic model, which assumes that the distribution
of the diffuse radiation is independent of the azimuth and the zenith angle;
therefore radiation from any point in the celestial hemisphere has the same
intensity.

1 þ cos b
I db ¼ I d (9.42)
2

• Reflected irradiance received by the modules I rb : It is usually assumed that the
terrain behaves as a horizontal and infinite surface that reflects radiation in an
isotropic way.

1 cos b
I rb ¼ðI d þ I b Þ$r$ (9.43)
2
where r is the albedo of the ground, which is highly variable and depends on the
soil type. A constant value (r ¼ 0.2) is supposed in many works.
• Total irradiance received by the modules (I b ): It is the sum of the three radiation
components:

(9.44)
I b ¼ I bb þ I db þ I rb