ABSTRACT: It is common practice in PV system simulation to use the De
Soto model, which describes how to use the 1-diode equivalent circuit
model for modules. De Soto’s model scales the shunt with irradiance,
making it disappear towards zero W/m². Also, the commercial software
PVsyst uses a parameterization that reduces the shunt effect when the
irradiance goes down. However, the Si solar cells that make up a module
typically do not have an illumination dependent shunt. We therefore
investigate the origin of the intensity dependent apparent shunt in
modules. We show that this apparent shunt (derived from the slope of the
quasi-linear region from ISC onwards) is a
misinterpretation and has little to do with a shunt conductance.
Instead, the module I-V curve slope of the quasi-linear
region from ISC onwards stems fromISC mismatches between the cells. Such mismatch
can occur from small illumination inhomogeneity or cell production
variation. Abandoning the practice of using the I-V curve
slope to determine the shunt value for equivalent circuit models of
modules (and the corresponding shunt scaling in the De Soto model or
PVsyst), contributes to physically more meaningful I-Vcurve parameterizations and possibly also more accurate PV system energy
yield prediction.
Keywords: Module performance, I -V curve parameterization,
Shunt characterization.
1 INTRODUCTION
For single solar cells, the slope at I SC [or
rather: the slope between I SC and some mid-sized
voltage well before the maximum power point (MPP) where the
recombination current is still very small] can be interpreted as shunt
conductance ∆I / ∆V = 1 / R Sh. For
single cells, this shunt value can be used for equivalent circuit models
of such single cells, for example in a 1-diode or 2-diode model. We call
this quantity R Sh.Slope, as it is derived from
the I -V curve slope between I SC and
some mid-sized voltages before the curvature of the exponential term
becomes notable. By applying this type of analysis, De Soto et al.
[1] and Mermoud et al. [2], for example, observed that moduleI¬V curves have an intensity-dependentR Sh.Slope. De Soto et al. and Mermoud et al.
interpreted this slope as the shunt conductance and also provided
parameterizations of this slope as a function of illumination intensity
for their 1-diode model parameterization of modules. An intensity
dependent shunt in modules is surprising, or possibly even implausible,
because on cell level there is typically no indication that an
equivalent-circuit model would need an intensity-dependent shunt for
describing the maximum power point (MPP) of a solar cell, not even for
describing the MPP for a very wide range of intensities [3]. (Note
that the academically interesting and very small effect of a seemingly
intensity-dependent shunt, as described by Robinson [4], and later
explained by Breitenstein [5], is an effect of lightI -V curves that vanishes well before the MPP. This effect,
that we call “photoshunt”, is therefore of no relevance for an
equivalent circuit model that seeks to describe the power production of
a cell or module.)
We show in this paper the origin of the intensity dependence ofR Sh.Slope. For modules, this slope-derivedR Sh.Slope is not related to an actual shunt
conductance, and instead it is the result ofI SC-mismatches between the cells, combined with
their reverse-bias characteristics. Note that suchI SC mismatch might stem from an illumination
inhomogeneity in a module measurement [6], from variations in cell
manufacturing, or a combination of these two effects.