Page 268 - Advances in Renewable Energies and Power Technologies

5. Modeling and Simulation of Photovoltaic Systems 241

FIGURE 7.4
An equivalent circuit representing the five-parameter model of the solar cell.

The IeV characteristic of the solar cell is given by an implicit and nonlinear
equation as follows [46]:

0 1

VþRs I
nV t C V þ R s I
I ¼ I PH I o@e 1A (7.12)
B
R sh
where I o and n are the reverse saturation current and ideality factor of the diode,
respectively, and V t is the thermal voltage.
The photo-generated current, I PH , can be evaluated for any arbitrary value of irra-
diance, G, and cell temperature, T c , using the following equation:
G
I PH ¼ I sc þ k i ðT c T ref Þ (7.13)
G ref
where G ref and T ref are, respectively, the irradiance and cell temperature at STC, ki
(A/oC) is the temperature coefficient of the current, and I sc is the solar cell short-
circuit current at STC.
On the other hand, the reverse saturation current, I o , is given by the following
equation:

Ego Eg

V to V t 3
I sc e T c
(7.14)

I o ¼
Voc T ref
e nNs V to 1
where I sc and V oc are the short-circuit current and the open-circuit voltage of solar
cell, respectively, V to is the thermal voltage at STC, E g is the energy bandgap of
the semiconductor, and E go is the energy bandgap at T ¼ 0K.
The value of the energy bandgap of the semiconductor at any cell temperature,
T c , is given by:
agap T c 2
E g ¼ E go (7.15)
bgap þ T c
where a gap and b gap are characteristic parameters of the semiconductor.