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318 CHAPTER 9 Design Principles of Photovoltaic Irrigation Systems

Another complementary way to regulate the system and to optimize the use of
the generated energy for irrigating the crop is to design more than one irrigation
sector. When the farm is divided into a number of sectors (n s ) greater than 1, the
discharge and power needed to irrigate each sector can be obtained by dividing
the maximum discharge and the maximum power by n s .
In this case, the system can start irrigating with a shaft power that is n s times
lower than when only one sector is considered. Two different strategies can be
applied in this type of system:

1. To irrigate with only one irrigation sector in operation
2. To irrigate with multiple irrigation sectors in operation simultaneously
In the first scenario, only one pump is required as the same pump would be used
to irrigate all the irrigation sectors. In the second scenario, the number of pumps
would have to be equal to the number of sectors that are irrigated simultaneously.
Generalizing, when a number “n j ” of sectors out of n s are operating simulta-
neously, the net power generated by the PV system (P) must be distributed among
the n j pumps in operation (P i ¼ P/n j ). Thus, the total discharge of the system is rep-
resented by Eq. (9.27):

P P m 9
aÞ If < 0 Q i ¼ 0 >
>
>
n j n s >
>
>
>
>
>
!
1=3 >
=
P m P P M Q M P i n s
bÞ If 0 Q i ¼ n j (9.27)
n s n j n s n s n j P M >
>
>
>
>
>
P P M Q M >
>
cÞ If > 0 Q i ¼ $n j >
>
;
n j n s n s
For the sake of illustration, Fig. 9.20 depicts the discharge of the pumping system
as a function of the incoming power for an irrigation system composed of a total
of four sectors. In this example, the type of greenhouse farm considered was 1 ha
2
in size, using emitters with a discharge equal to 3 L/h and 2 emitters/m , which is
a very common arrangement in greenhouse irrigation systems in the south of Spain.
This results in a total discharge per hectare (Q M ) equal to 60,000 L/h or 16.67 L/s.
The total head (H M ) assumed for this maximum discharge is 40 m (including
the three terms in Eq. 8). The pumping efficiency has been considered equal to
0.75. The maximum power (P M ) per hectare proves to be equal to 8720 W. It was
supposed that the ratio between minimum and maximum working pressure of
the emitter was equal to 1/4 (5/20 m/m). Applying affinity laws in Eq. (9.19),
the minimum power required per hectare (P m ) is found to be equal to one-eighth
of the maximum power (P M /8). With these data, and applying Eq. (9.22),
the discharge has been calculated for a number of sectors in operation ranging
from 1 to 4.
Dashed lines represent the variation of the discharge of the system as a function
of the incoming power when only one, two, three, or all four sectors are in operation.