Environmental Engineering Reference
In-Depth Information
cell is given in a closed form:
f ( V , I ) = 0
(4.36)
The corresponding current I or voltage V should be estimated for a given
voltage V g or a given current I g . Any solution will result in a zero value for the
function f ( V , I ). The following iteration procedure is suitable to find this
solution:
(4.37)
Starting with an initial value V 0 or I 0 , the solution of the implicit equation
with a given current I g or voltage V g , respectively, will be found if the iteration
is performed until the difference between two iteration steps is smaller than a
predefined limit
ε
. The stopping conditions for the iteration are: | V i
- V i-1 |<
ε
.
The Newton method tends to convergence very quickly; however, the speed
of convergence depends strongly on the chosen initial value V 0 or I 0 . A pre-
iteration using another method could be useful near the range of the diode
breakdown voltage.
The iteration for estimating the current I of the solar cell for a given
voltage V g according to Equation 4.37 is:
or | I i - I i-1 |<
ε
(4.38)
Two-diode model
The two-diode (Figure 4.18) model provides an even better description of the
solar cell in many cases. A second diode is therefore connected in parallel to
Figure 4.18 Two-diode Model of a Solar Cell
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