Page 64 - Advances in Renewable Energies and Power Technologies

5. The PV Arrays 37

FIGURE 1.32
Equivalent circuit of the module.

Because the cells are identical, they have the same output voltage V c , and
because they are connected in series, they have the same terminal current I st .As
V c ¼ V j þ I st R s ; V j ¼ V c I st R s ; and I st ¼ I ph I d ;

it follows that
!
ðVc þI st Rs Þ
I st ¼ I ph I s e nV T 1 (1.49)

The overall module voltage is the sum of cell voltages in the module
n e
X
V m ¼ V c ¼ n e V c (1.50)
1
Substituting Eq. (1.50) in (1.49), we get the IeV of the string
!
ðV m =n e þI st R s Þ
I st ¼ I ph I s e nV T 1 (1.51)

This equation is very simple. To pass the same current in the string, the string
voltage must be exactly a multiple of n e of the cell voltage.
Now let us pay our attention to the parallel connection of n s strings. Because all
cells are identical, the string current is the same in each string while the string volt-
ages are the same, i.e., V m . Hence,

n s
X
I m ¼ I st ¼ n s I st (1.52)
1
The IeV characteristics of the module can be obtained by substituting Eq. (1.52)
in (1.51), i.e.,
!
ðVm =ne þI st Rs Þ
I m ¼ n s I ph n s I s e nV T 1 (1.53)