Page 352 - Advances in Renewable Energies and Power Technologies

4. Modeling and Simulation of Photovoltaic Irrigation System 325

The total irradiance on a sloped plane is then given by the following equation:
cos q 1 þ cos b 1 cos b
I b ¼ I b $ þ I d þðI d þ I b Þ$r$ (9.45)
cos q z 2 2
Considering that the position of the PVarray at a specific moment is described by
!
the vector n , normal to the collector plane:
! !
cos q ¼ n $ s (9.46)
!
!
cos b ¼ n $ k (9.47)
The equation for estimating the irradiance is:
!
!
! !
!
!
! ! 1 þ n $ k 1 n $ k
n $ s
I b ¼ I b $ þ I d þðI d þ I b Þ$r$ (9.48)
cos q z 2 2
!
If the PV array is mounted on a one-axis tracker, vector n moves and, in this
case, its instantaneous expression is given by Eq. (9.49).
0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 0 1
s s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
! ! 2
! ð e $ s Þ A ! 1 A !
n ¼ @ cos c sin c e þ @ sin c s (9.49)
! ! 2 ! ! 2
1 ð e $ s Þ 1 ð e $ s Þ
!
where the e and c values depend on the type of tracking, as shown in Table 9.3.
For a two-axis tracker:
! !
n ¼ s (9.50)
4.1.4 Power Calculations
The main objective of a PV installation is to produce the power required by the
pumps to lift or inject the water into the irrigation system.
4.1.4.1 Electric Power Generated by the Photovoltaic Modules
This power can be calculated by applying the following equation:

I b $PP
P PV ¼ (9.51)
1000
!
Table 9.3 e and c for Different Types of One-Axis Tracking
e
Tracking Type ! c
Vertical axis ! ! ! b
0 i þ 0 j þ 1 k
EeW horizontal axis ! ! ! p 2
1 i þ 0 j þ 0 k =
NeS horizontal axis ! ! ! p 2
0 i þ 1 j þ 0 k =
NeS inclined axis ! ! ! p 2
0 i sins j þ coss k =
Polar ! ! ! p 2
0 i sin 4 j þ cos 4 k =