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.
5 REFERENCES
[1] W. De Soto, S.A. Klein and W.A. Beckman, “Improvement and
validation of a model for photovoltaic array performance”, Solar Energy
80 (2006), p. 78-88.
[2] A. Mermoud and T. Lejeune, “Performance assessment of a
simulation model for PV modules of any available technology”, 25th
EU-PVSEC (2010), Valencia, Spain.
[3] G.E. Bunea, K.E. Wilson, Y. Meydbray, M.P. Campbell and D.M. De
Ceuster, “Low light performance of mono-crystalline silicon solar
cells”, IEEE 4th WC-PEC, 2006, pp. 1312-1314..
[4] S. J. Robinson, A. G. Aberle, and M.A. Green, “Departures from
the principle of superposition in silicon solar cells”, Journal of
Applied Physics 76, (1994), p. 7920-7930.
[5] O. Breitenstein, “An alternative one-diode model for
illuminated solar cells”, Energy Procedia 55 (2014) p. 30 – 37.
[6] K. Ramspeck, C. Böhmer, and M. Meixner, “Measurement
Uncertainty Analysis for Large Area High-Efficiency Modules”,
40th European Photovoltaic Solar Energy Conference,
(2023), p. 020213-001 - 020213-005.
[7] N.-P. Harder, and J. Cano Carcia, “TOPCon module
characterization at different temperatures and intensities: Revision of
shunt parameterization by De Soto and PVsyst”, 52ndIEEE Photovoltaics Specialists Conference (2024), proceedings in print.
[8] C.E. Clement, J. Prakash Singh, E. Birgersson, Y. Wang, and Y.
Sheng Khoo, “Illumination Dependence of Reverse Leakage Current in
Silicon Solar Cells”, IEEE Journal of Photovoltaics, Vol. 11(5), 2021,
p. 1285.