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.