Figure 11: Short-circuit current density of the modules, normalized by the illumination intensity, plotted as a function of illumination intensity. For increasing inhomogeneity, the quality of the proportionality between short-circuit current I SCand illumination intensity is reduced, even though every single cell in the module circuit features liner I PH-Suns relation and hence a near-perfect proportionality(linearity) of cellI SC and illumination intensity.
We can see from the variation of the ratioI SC/Suns in Fig. 11 that theI SC of modules is not linear with illumination intensity if the photogeneration I PH of the individual cells is not homogeneous across the module. This is an interesting observation and potentially of importance in situations where one may be tempted to use the module I SC as a measure for the average photogeneration, such as when analyzing soiling of modules in the field. In such cases it is actually better to observe the maximum power, or the current at the maximum power point. This is demonstrated in Fig. 9, where all curves shared the same MMP, which is also shared by the grey dotted I -V curve that features in all cells the average photogeneration of the inhomogeneous distribution of the other curves.
The non-linearity of I SC with (average) intensity of the illumination, as explored in Fig. 11, does not mean a model for power production of PV systems would need to take into account such non-linearity. Instead, Fig. 9 has shown that the MPP, which lies for reasonable non-degenerate cell photogeneration distributions well outside the voltage range affected by cell I SCcurrent mismatch, can be well described with using the average photogeneration. The average photogeneration I PHscales well with the illumination intensity. Hence, the results presented here rather underline that an equivalent circuit model (e.g. 1-Diode model) for PV system power production simulation can and should scale the photogeneration I PH linearly with illumination intensity. The challenge lies only in determining a suitable 1-Diode parameterization of the module I -V curve, including the average cell I PH ( \(\approx\)I SC ) for use in the 1-Diode model parameterization of the module.
4 CONCLUSIONS
We have shown how an apparent shunt emerges in a moduleI -V curve from combining cells with different photogeneration in the module circuit. Since the difference of photogeneration scales with illumination intensity, this apparent shunt in the module I -V curve scales with illumination intensity. However, this effect is not at all an actual shunt conductance and appears only when applying a method for shunt analysis that is only appropriate for single cells: The slope of the moduleI -V curve in the quasi-linear range fromI SC towards larger voltages is not a good indication a shunt conductance in the module. When the cells in the module have different photogeneration, which can be caused by illumination inhomogeneities or by cell production variations, this slope is strongly influenced by current mismatch effects.
We show that this mismatch induced slope in the quasi-linear range of the I -V curve has no influence on the I -V curve near MPP. However, interpreting this slope as a shunt (or rather: “pseudo shunt”) and using this value as shunt conductance in an equivalent circuit model for the module, such as the 1-Diode model, does affect the MPP. Consequently, the slope-derived pseudo shunt value should not be used as shunt conductance in equivalent circuit models for representing the module power production performance.
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