Figure 7: I -V curves at 1 Sun (upper range of curves) and 0.5 Sun (lower range of curves), plotted forI SC-matched cells in the module circuit shown in Fig. 3, with different assumptions for the R Shuntdistribution amongst the individual cells.
We can see in Fig. 7 that inhomogeneous shunt distributions across the different cells in the module circuit all produce I -V curve shapes that clearly cannot be described by a simple shunt model. No single value of a voltage-independent effective shunt can produce such I -V curve shapes. However, apart from a minor series resistance effect, the slopes of the curves are identical when comparing 1 Sun to 0.5 Sun curves. We can therefore conclude that also shunt distributions cannot create I -V curve shapes that could be interpreted as some kind of illumination dependent shunt resistance.
3.1 Modules with I SC mismatched cells
In this section we show simulation results for modules where each individual cell is described by the standard model parameters of Table I, except for a variation of the photogeneration currentI PH. The photogeneration current distribution amongst the cells is according to the inhomogeneity map shown in Fig. 4. We scale the inhomogeneity distribution of this map to three different levels of maximum-to-minimum variations: +/- 0.4%, +/- 1.0%, and +/- 2.0%. Since photogeneration current inhomogeneities amongst the cells will drive some cells into reverse bias, we explore the effect of the four different reverse bias characteristics shown in Fig. 6.
Fig. 8 shows four plots, each representing a module where all cells in the module have one of the four different reverse bias characteristics of Fig. 6. In each plot there are different curves that correspond to different degrees of inhomgeneities of the photogeneration across the cells in the module circuit: +/- 0.4%, +/- 1.0%, and +/- 2.0%. The quantity plotted in these graphs is the slope of the simulatedI -V curves between I SC and 450 mV/cell. (Very similar results are obtained for other choices, such as the slope between I SC and 300 mV/cell.) The inverse of these slopes is the apparent shunt resistanceR Sh.Slope. The horizontal axis of the graphs in Fig. 8 is the illumination intensity expressed in Suns (1 Sun = 1000 W/m²).