For an adjustment of the six unknown parameters of the two-diode model to measured data, the error function of the measured currents at a given voltage, irradiance and temperature and of the simulated currents must be minimised.
Ф = ^£(( – )2 (514)
With little mathematical effort, i. e. a linear regression, only the parameters Iph, STC and aI can be calculated from the linear irradiance-dependence and temperature-dependence of the short circuit current. The remaining parameter set can only be determined by gradient, raster or genetic procedures (Pukrop, 1997).
Example 5.3
|
Calculation of the parameters Iph_ STC and aI of a Siemens M55 module from the following table of values measured.
To be able to carry out a linear regression of the temperature dependence of the short circuit current using Equation (5.13), the irradiance G must be eliminated from the equation, so that only the temperature difference from standard test conditions remains as an independent parameter. The short circuit current is thus divided by the irradiance, and the regression for ISC/G against TPV-TPy STC is carried out. |
|
Current/irradiance Iph, sTC/GSTC [AW 1m2] |
Temperature difference TPV—TPVSTC [K] |
|
3.364 x 10—3 |
5 |
|
3.373 x 10—3 |
16 |
|
3.388 x 10—3 |
29 |
|
3.400 x 10—3 |
35 |
|
The linear regression produces as axis intercept Iph, STC/GSTC = 0.0034 AW 1m2, i. e. a short circuit current IphSTC of 3.4A, and as a gradient IphSTC/GSTCaI = 1 x 10-6 AW-1m2K-1, i. e. aI = 3 x 10-4 K—1 (+0.03%/K). |
