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Lab 7 The Photovoltaic Characterization
171
To determine the equivalent circuit of the solar cells in a static regime (continuous
current) the analyses will start from simplified hypotheses. The solar cell can be
considered a current generator Iph, with a current that decreases due to the current
through the diode Id.
The diode is thus in parallel with the current generator. I is the current passing
through a resistance of charge R (see Figure 7-3, a). In order to consider the
internal losses in the equivalent circuit, the parasite resistances must also be
included: the series resistance, Rs and the shunt resistance, Rsh (see Figure 7-3 b)).
The current-voltage dependence for a solar cell can be expressed by the double
exponential model. This model is based on an equivalent circuit with two diodes
(see Figure 7-3, c)). In the equation that mathematically renders the model, the first
term represents the diffusion process of the minority carriers from the depletion
layer. The second term of the equation represents the recombination of the carriers
in the space charge region of the junction.
If the current caused by thermionic emission is also taken into consideration, the
mathematical model as well as the equivalent circuit modifies. In the mathematical
model another exponential term appears, and the equivalent circuit is given in
Figure 7-3 d).
The considerations regarding the mathematical models and the equivalent circuits
presented here start from the presumption that the solar cell is illuminated. If the
performances of the solar cell in the dark are under observation, Iph disappears from
the mathematical models. The most general mathematical model for most of the
solar cells studied in the dark becomes Equation (86), where the third term can be
neglected, given that the recombination component is much higher than the
thermionic component [Stutenbaeumer, Mesfin].
⎛
⎛
⎛ q (V + IRs ) ⎞ ⎞
⎛ q (V + IRs ) ⎞ ⎞ V + IRs
⎟⎟ − 1⎟ + I or ⎜ exp⎜⎜
⎟⎟ ⎟ +
I = I od ⎜⎜ exp⎜⎜
⎟
⎜
⎟
m
kT
m
kT
Rsh
1
2
⎝
⎠ ⎠
⎝
⎠⎠
⎝
⎝
(86)
The Solar Panel
A Si solar cell generates a typical open-circuit voltage of 0.6 V, regardless of its
area. The short-circuit current is proportional to the area and generally has values in
the range from 30 to 40 mA/cm2. The maximum power generated by the solar cell
is lower than Voc*Isc, as can be seen in Figure 7-2. This leads to the need to raise
the maximum power generated. We can raise the generated power if