Page 65 - Advances in Renewable Energies and Power Technologies

38 CHAPTER 1 Solar Cells and Arrays: Principles, Analysis, and Design

This relationship is the required IeV of the module. It has the form of a
single solar cell, with the current multiplied by n s , the number of strings, and the
cell voltage is multiplied by n e , the number of cells in the string. Because the power
output ¼ IV, the power output of a single cell will be multiplied by (n e n s ).
Solar cells with the same type are not identical because of fabrication toler-
ances. Basically, the produced solar cells from a production line must be sorted
to select the matched cells. Matched cells have very high tolerances. On the other
hand, if the solar cells are not matched, the string short circuit current will be the
smallest short cell current, and the module output voltage under open circuit con-
dition will be equal to the smallest open circuit voltage of the strings connected in
parallel and the curve factor of the overall module becomes smaller because of the
larger internal losses in the module. Hence, cell mismatch leads to additional in-
ternal losses and reduces the efficiency of the array in comparison to that of the
single cells [29].

5.2 THE IeV CHARACTERISTICS OF MISMATCHED CELLS IN THE
MODULE

Now each cell i has its own parameters, I sci , V oci , FF i , n i , I si , I phi , and R si . For a string
current I st , the voltage developed on the ith cell can be expressed according to
Eq. (1.49) as

I ph I st I si
V ci ¼ n i V T ln þ I st R si (1.54)
I si
The total string voltage is then

n e
X
V m ¼ V ci (1.55)
1
If n s unmatched strings are connected in parallel with the jth string, which is para-
metric, then

V m1 ¼ V rn2 ¼ V m3. ¼ V mj. ¼ V mns ¼ V m (1.56)
The string currents I st1 , I st2 , I st3 ., I stj , ., I sns are different. From Eqs. (1.54) and
(1.55), the jth string has the characteristics:
n e;j
X
V mj ¼ V ci ¼ V m (1.57)
i¼1
This equation can split into (n s l) equations in I stj . One needs one additional
equation to determine I stj . This equation is the output node equation

n s
X
I m ¼ I stj (1.58)
i¼1