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3. Photovoltaic Irrigation Systems Components 303

The sharper the characteristic curve of the cell is, the higher the FF will be.
(9.2)
PP ¼ FF i SC V OC

• Energy conversion efficiency, h: The ratio between the maximum power
delivered (PP) and the input radiant power to the PV module, calculated as the
2
product of panel area times the reference irradiance (A$1000 W/m ).
FF i SC V OC
h ¼ (9.3)
1000 A
If the efficiency is considered constant for any irradiance value, the following
relationship can be written:
I b $PP
PPV ¼ (9.4)
1000
The curve in Fig. 9.4 can be fitted to the following mathematical equation:

eðV OC VÞ
i ¼ i sc 1 exp (9.5)
mkT
where “e” is the charge of the electron, “m” is the so-called diode ideality factor
l < m < 2, “k” is the Boltzman constant, and T is the absolute temperature.

3.1.1.1 Photovoltaic Modules Arrangement
The modules are electrically arranged into different series-parallel or parallel-series
combinations to obtain the intensity and voltage values suitable for each application.
The set of modules with its own connections, framework, etc. constitutes the PV
generator.
Both the modules and the cells are not always identical and knowing the ieV
characteristic of the set or generator can become a difficult problem. With N p and
N s being the number of modules connected in parallel and series, respectively, as
shown in Fig. 9.5, the current supplied by the generator should be N p times higher
than that of a module (i G ¼ i$N p ) and the voltage of the generator should be N s times
higher (V G ¼ V$N). Thus, the characteristic curve of the generator i G eV G is given by
Eq. (9.6):

eðV OC V G =N S Þ
i G ¼ N P i sc 1 exp (9.6)
mkT
The ieV response of the PV generator as a function of the temperature is
described by three coefficients. These coefficients are called a, b, and g, respec-
tively, and their typical values for monocrystalline silicon modules are given below:
a ¼ vI SC =vT ¼þ 0:04%; b ¼ vV oc =vT ¼ 0:37%; g ¼ vPP=vT ¼ 0:44%.
(9.7)