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Commercially technologies available on the market are now mainly a-Si:H (amorphous, including tandem and triple junction), CiS and CdTe modules.

There is no consensus up to now in the PV community about the general modeling of these new modules.

Several experimental works have observed significantly different behaviours of amorphous with respect to standard Crystalline cells. Mertens & al 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 1998, Holley et al 2000 and Mertens et al 2000 report experimental analysis of model parameter dependencies as function of temperature and spectral irradiance contents in amorphous simple and double junctions. Betts &al 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

In order to clarify these observations and to establish an approached model useable in PVsyst - including the necessary proposal of default parameters - we have performed an 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 Report 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 draw the error distributions for our 3 indicators. We assess that the precision of the model is mainly represented by the RMSE (named sigma) of these error distributions, i.e; the model response dispersion over 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 We used it mainly as a calibration of our method and experimental set-up, and especially as a reference for the study of the spectral effects.

As a by-product, this yields a validation of the standard model for this technology. Surprisingly, the pure standard model did not reproduce well our measurements. The model strongly underestimates the PMax data at low irradiances, giving a MBE of 6% and a RMSE of 3.9%.

This could be very well corrected by applying an exponential correction for the Rshunt, as for the amorphous modules: with an appropriate Rsho 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%.

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

Nevertheless we strongly feel that the Rshunt exponential correction is a general feature which 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 an analogous correction on Rshunt, our CIS module (Shell  ST40) behaves quasi perfectly according to the standard model. The error distributions are far better than with our mono-crystalline module.

With an optimal Rsho parameter, we observe on PMax MBE = 0.0% and RSME = 2.1%;  and on Voc, MBE = 0.0% and RSME = 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 of the SHR-17 had already been tested during the whole summer in 2001, when the second one had never been exposed to the sun. The parameter and performances of these two modules were quasi identical, and very surprisingly we didn't observe any initial degradation on the "new" module!

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

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

For correcting the standard model results (which underestimate the power by about 8% to 10% when applied over all our 3-months measurements) we identified 3 dominant corrections: