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).