Figure 1: Measured efficiencies of a TOPCon module (symbols)
and calculated efficiencies by the 1-diode model (solid lines), with a
fixed shunt R Sh, and using a simple series
resistance R S, independent of temperature and
intensity, from reference [7]. The dashed and dotted lines are
calculated efficiencies based on PVsyst’s [2] (dashed lines), or De
Soto’s [1] (dotted lines) approach, which both use an intensity
dependent shunt.
Importantly, and as has been discussed already in our recent module
characterization study [7], using R Sh.Slopeas shunt resistance in an equivalent circuit model for theI -V curve of modules leads to physical inconsistencies:R Sh.Slope typically has a rather low value, but
(as this present paper will show in detail) does not represent an actual
shunt conductance. Using this value R Sh.Slopenevertheless for the shunt in equivalent circuit models (e.g. a 1-diode
model) and trying to reproduce V OC and MPP
values, leads to needing to use a too low ideality factor value for the
module I -V curve. In our recent characterization study of
a TOPCon module [7] we found exactly such phenomenon: PAN file
specified low shunt values that correspond to the measuredR Sh.slope, in combination with an implausibly low
ideality factor in the PAN file. Note that a wrong (too low) ideality
factor in turn, affects the temperature-dependency of the modeled module
performance. As a consequence, the simulation software PVsyst introduces
without physical basis a temperature dependency for the ideality factor
(by using a temperature coefficient “muGamma”).
It shall be pointed out that a simple model, that neither uses the
complication of an intensity-dependent shunt nor an unphysical feature
such as a temperature dependent ideality factor, is not only
advantageous by virtue of its simplicity and better physical
interpretability. As is shown here in Fig. 1, taken from reference
[7], such simpler model also leads to accurate (and seemingly even
more accurate) module performance parameterization over a wide range of
illumination intensities and temperatures.
We set out in this paper to explore the origin of the intensity
dependent I -V curve slope from I SConwards (i.e. the intensity dependent R Sh.Slope)
by using a simple 1-diode model for the individual cells, connected in
series to a 60-cell module. This simple model obviously (and
deliberately) does not contain the effects of the apparent shunt
discovered by Robinson [4] and explained by Breitenstein [5]. We
make this choice for two reasons:
Firstly, Robinson’s “photoshunt” is very small and affects in no
conditions known to us the MPP. In consequence, it is typically not
considered at all in equivalent circuit models that seek to describe
power production by solar cells [3]. It is nevertheless fair to say
that to some small degree Robinson’s photoshunt will have some
contribution to the appearance of an illumination intensity dependence
of the module I -V curve slope in the quasi-linear region
from I SC onwards. However, we deem this
contribution to be marginal in practice for PV modules.
Secondly, and more importantly, by focusing on a simple model, we can
highlight in a very pointed manner the main origin of the
intensity-dependent R Sh.Slope. In this way we can
show how by combining individual cells that each do not feature an
intensity dependent shunt, the phenomenon of an intensity dependent
apparent shunt R Sh.Slope emerges in a module.
2 MODEL DESCRIPTION
We represent individual solar cells by the “1-Diode model” equivalent
circuit model, shown in Fig. 2. The I -V curve of the
1-Diode model is given in equation 1: