Figure 8: Inverse apparent shunt resistancesR Sh.Slope derived from theI -V -curve slopes between I SC and 450 mV/cell, plotted as a function of illumination intensity in Suns. Each graph represents one type of reverse bias characteristics (see Fig. 6), and each curve refers to one photogeneration inhomogeneity distribution +/- 0.4%, +/- 1.0%, and +/- 2.0%.
The lower right graph in Fig. 8 features an additional fourth curve with a dotted red line, showing for the case of +/- 2% photogeneration inhomogeneity the difference between a module circuit with and without bypass diodes. In the other cases of this study, the difference due to the bypass diodes is small and is therefore not shown explicitly here.
We can clearly see in Fig. 8 that cell photogeneration inhomogeneities of the cells in the module circuit cause the emergence of an intensity dependent apparent shunt R Sh.Slope, even though all individual cells have an identical and intensity independent shunt. The magnitude of the apparent shunt R Sh.Slopedoes not only depend on the illumination intensity and inhomogeneity, but also on the cells’ reverse bias characteristics. Generally, the more efficiently the cells are able to conduct current in reverse bias direction, the more pronounced is the illumination intensity dependence of the apparent shunt conductance 1/R Sh.Slope. Note that towards zero illumination intensity the value of 1/R Sh.Slope converges towards the value of 1x10-4 1/(Ωcm²). This value corresponds to the forward-bias shunt value of 10 kΩcm² that all cells in these simulations share (see also Table I).
Fig. 9 provides a closer look at simulated module I -V curves for the case of +/- 2.0% inhomogeneity of the photogenerationI PH of the cells in the module circuit. Note that all four module I -V curves were generated with a set of cell definitions that have completely identical forward-bias characteristics. Nevertheless, the forward characteristics of the moduleI -V curves are different for a wide range of forward voltages up to close to the maximum power voltageV MP at the MPP. Very unlike a real shunt, this effect ends in a sharp kink as all I -V curves merge rather abruptly into the grey dotted I -V curve, representing a module with homogeneous I PH for the cells.
Note that despite clearly visible I -V curve differences in Fig. 9, the four curves agree perfectly well with each other in the voltage range of the MPP. Thus, despite differentR Sh.Slope values, the maximum power production of these four different modules is identical and unaffected by different values of the apparent shunt R Sh.Slope.