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: