Model for Thin film and other new technologies

The commercially available technologies on the market are now primarily a-Si:H (amorphous, including tandem and triple junction), CIS and CdTe modules.

There is currently no consensus in the PV community regarding general modeling of these new modules.

Several experimental works have observed significantly different behaviours of amorphous with respect to standard Crystalline cells. Mertens & al¹ propose taking recombinations in the i-layer into account , resulting in a modification of the equivalent circuit, and a related modified "One-diode" analytical expression. Gottschalg et al 1998², Holley et al 2000³ and Mertens et al 2000⁴ report experimental analysis of model parameter dependencies as function of temperature and spectral irradiance contents in amorphous simple and double junctions. Betts & al⁵ have studied the spectral contents if the irradiance according to weather in central UK (Loughborough) and propose a correlation for correcting the response of amorphous modules.

Modelling in PVsyst: Research project at CUEPE

To clarify these observations and establish a usable model in PVsyst—including the necessary default parameters—we conducted experimental research at the University of Geneva, with the financial support of the SIG-NER fund (SIG - Services Industriels de Genève - is the Electricity and Gas Utility of Geneva). Details of this project may be found in the Final Report⁶ of this project, unfortunately only available in French at the moment.

The study is based on detailed outdoor I/V measurements of 6 PV modules, every 10 minutes over a period of 3 months. This yields a data sample covering all environmental conditions, with irradiances ranging from 40 to 1000 W/m² and temperatures between 0 and 70°C.

Methodology

We followed a phenomenological approach, by closely comparing the measured set of data with the model results. We used 3 indicators, easily identified on each I/V measured characteristics: the Pmax (MPP power), Voc and Isc values.

All our modeling attempts start from the standard one-diode model. The model main parameters are determined from one chosen I/V characteristics among the measured data. Knowing one complete I/V characteristics, the model parameters (Iph, Ioref, Gamma, Rs, Rsh) may all be determined accurately.

With this set of parameters, we can now determine the error distributions for our 3 indicators. We consider that the model precision is primarily represented by the RMSE (designated sigma) of these error distributions—that is, the model response dispersion across all operating conditions. Around the optimum, the MBE (Mean Bias Error) values, noted mu) are rather related to the basic input parameter uncertainties (Vco, Isc, Vmp, Imp) at the reference conditions Gref and Tref (i.e. the position of the reference I/V characteristics inside the distribution).

Standard model validation on Mono-Crystalline module

One of our measured modules was a Siemens M55 monocrystalline module. We used it primarily as a calibration reference for our method and experimental setup, and especially as a reference for studying spectral effects.

As a by-product, this yields a validation of the standard model for this technology. Surprisingly, the standard model alone did not accurately reproduce our measurements. The model significantly underestimated the Pmax data at low irradiances, with an MBE of 6% and an RMSE of 3.9%.

This was effectively corrected by applying an exponential correction for Rshunt, similar to amorphous modules: with an appropriate Rsh0 value, the MBE on Pmax reduced to 1.1% and the RMSE to 2.3%. This correction also strongly improves the Voc behaviour, the RMSE passing from 6.0% to 1.0%.

It is important to note that our test module is very old (15 years) and shows significant corrosion around the collector grid. We cannot say to what extent this Rsh behaviour could be related to these module deficiencies.

Nevertheless, we firmly believe that the Rshunt exponential correction is a general feature that should be applied to any PV module for proper modeling. But the required parameter Rsho (and even the basic Rshunt value at reference conditions!) cannot be determined from manufacturer data sheets.

Standard model applied to the CIS module

With a similar correction on Rshunt, our CIS module (Shell ST40) behaves nearly perfectly according to the standard model. The error distributions are far better than with our mono-crystalline module.

With an optimal Rsh0 parameter, we observe for Pmax MBE = 0.0% and RMSE = 2.1%; and for Voc, MBE = 0.0% and RMSE = 0.5%.

Measurements on a-Si:H triple-junction

Our 4 other modules were amorphous: 2 identical "tiles" Unisolar SHR-17 with triple junction, a Solarex MST43-MV (not yet produced) and a RWE Asiopak 30SG, both with tandem cells.

One SHR-17 had already been tested throughout the summer of 2001, while the second one had never been exposed to the sun. The parameters and performance of these two modules were nearly identical, and surprisingly, we observed no initial degradation on the new module!

Our first observation was that for any I/V characteristic, it is always possible to find a set of standard model parameters (Iph, Ioref, Gamma, Rs, Rsh) that exactly matches the I/V curve. The RMSE between the 30 measured current points and the model is always less than 0.3–0.4% of Isc (i.e., 0.5 mA at 40 W/m², 4 mA at 800 W/m²).

This means that the electrical (diode) behavior of amorphous junctions is quite similar to that of crystalline modules. The problem is now to determine these parameter dependencies according to irradiation and temperature.

To correct the standard model results (which underestimated power by about 8% to 10% when applied across all our 3-month measurements), we identified 3 dominant corrections:

• RSh exponential correction. On all our data - including Si-crystalline and CIS modules - we observe an exponential increase of the Rsh when irradiance decreases. This correction has a moderate effect on technologies with high Rsh, but strong in amorphous. This is the main contribution of our corrections.
• Recombination losses. This additional current loss occurs in the intrinsic layer of amorphous junctions. The correction proposed by Mertens et al.⁷ involves a distortion of the I/V curve that no longer matches our I/V measurements, but dramatically improves the Voc voltage behavior of the model.
• Spectral corrections. Applying the spectral correction established at Loughborough, UK for single amorphous modules (Betts et al.⁸) improves the error distributions by a factor of 10 to 20%. It is unclear whether this correction is suitable for our double and triple junctions.

NB: PVsyst does not account for the well-known initial degradation due to Staebler-Wronski effects. PVsyst results are assumed to apply to stabilized module performance after 2–3 months of sun exposure.