Page 269 - Advances in Renewable Energies and Power Technologies

242 CHAPTER 7 Strategies for Fault Detection and Diagnosis

There are simplified versions of this model. The simplest one includes only the
controlled current source giving the photo-generated current and the diode: the
three-parameter model [47]. These parameters are I PH , I o , and n. Moreover, because
the shunt resistance, R sh , included in the five-parameter model normally has a very
high value, it can be neglected and the power losses are then just modeled by R s . This
model is called the four-parameter model [48]. As mentioned above, the most
commonly used is the five-parameter model; however, the three- and four-
parameter models can achieve similar or better accuracies in some cases [49].
Commercial PV modules are composed by association of solar cells in series
forming a branch and in some cases also include several branches in parallel connec-
tion. Considering N s solar cells in series in each branch, and a number of N p branches
for a PV module, Eq. (7.12) can be conveniently scaled to obtain a similar equation
for the IeV characteristic of a PV module, taking into account the following equa-
tions [46,49,50]:
I m ¼ N p I (7.16)

V m ¼ N s V (7.17)
N s
R sm ¼ R s (7.18)
N p
N s
R shm ¼ R sh (7.19)
N p
where parameters with subscript m stands for the PV module.
The same procedure can be applied to scale up the model of the PV module to the
model of a PVarray by taking into account the number of PV modules connected in
series by string, N sm , and the number of parallel strings in the PVarray, N pm [46]. The
coordinates of the MPP of a PVarray, I mg and V mg , of arbitrary series-parallel, N sm x
N pm , connection of PV modules can be calculated for any condition of G and T c us-
ing the following equations that include parameters of the PV modules forming the
PV array [46]:

I mm dI scm
I mg ¼ N pm G þ ðT c T ref Þ (7.20)
1000 dT
!! !
I scm I mm Vocm
N
V mg ¼ N sm N s V T ln 1 þ e s V T 1 I mm R sm (7.21)
I scm
where I scm and V ocm are the short-circuit current and open-circuit voltage of the PV
modules included in the array, respectively.
On the other hand, the ambient air temperature, T air , can be used to find the oper-
ating PV module temperature, T c , at any irradiance conditions using the following
equation [51]:
NOCT 20
T c ¼ T air þ G (7.22)
800