Page 66 - Advances in Renewable Energies and Power Technologies

5. The PV Arrays 39

For a given I m , I stj are determined and V m is calculated from Eqs. (1.54) and
(1.55).
These equations can be solved numerically using the mathematical library or
Ò
Matlab . Another elegant approach to this problem is to use the circuit simulator
PSpice to solve the module circuit under any operating condition and illumination.
In addition to the solar cell mismatch, there is another serious problem of
decreasing the output from the module. This problem arises when the module is sub-
jected to nonhomogeneous solar radiation. This problem is termed the partial shad-
owing of the module [30]. According to the degree of shadowing, photocurrent of
some cells is reduced significantly. Partial shadowing comes from flying objects
and from moving clouds. If the photocurrent of a cell in a string is made zero,
i.e., the cell is dark, no current can pass in the string. This type of shadowing is
the most severe one and has two serious consequences:
1. One string cannot deliver power to the load and becomes outage
2. The second is more serious, namely, the shadowed cell will be reverse biased. If
this reverse bias is large, it can lead to defective shadowed solar cell by a
phenomenon called hot-spot formation.

To see the reverse bias of a shadowed cell, let us estimate the voltage drop on
such cell. Referring to Fig. 1.32 and assuming that the kth cell has I ph ¼ 0, according
to the second Kirchhoff’s law
n e
X
V sc ¼ V m V oci (1.59)
i¼1
where n e sk: Because I ph of the kth cell ¼ 0, the string is interrupted and all cells in
the string operate under open circuit condition; hence, V c ¼ V oci for all cells except
i ¼ k. Inspecting Eq. (1.59), we can differentiate the cases:
1. V m is that of the maximum power from the module
V m w FF V oc . n e ¼ 0.8 0.6 36 ¼ 17.28 V.
Assuming n e ¼ 36, V oc ¼ 0.6 V, and FF ¼ 0.8.
n
P e
V oci ¼ 36 0:6 ¼ 21 V, where n e sk:
i¼1
Substituting these values in Eq. (1.59), we get
V cs ¼ 17:28e21w 4V:
This means that the shadowed cell is reverse biased by 4V.
2. V m ¼ 0, short circuited-module. Then V cs ¼ 17.28 V. The shadowed cell is
reverse biased with even a much larger voltage of 17.28 V.

5.3 FORMATION OF HOT SPOTS

When we have a diode with soft reverse characteristics and we reverse bias it, hot-
spots will be formed. Hot-spots are hotter regions with higher current densities than