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