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Research Papers

Evaluation and Validation of Equivalent Circuit Photovoltaic Solar Cell Performance Models

[+] Author and Article Information
Matthew T. Boyd, Sanford A. Klein, Douglas T. Reindl

Solar Energy Laboratory, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI 53706klein@engr.wisc.edu

Brian P. Dougherty

 National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899

Named after the collective work of Hay, Davies, Klucher, and Reindl.

J. Sol. Energy Eng 133(2), 021005 (Mar 22, 2011) (13 pages) doi:10.1115/1.4003584 History: Received February 17, 2010; Revised June 23, 2010; Published March 22, 2011; Online March 22, 2011

The “five-parameter model” is a performance model for photovoltaic solar cells that predicts the voltage and current output by representing the cells as an equivalent electrical circuit with radiation and temperature-dependent components. An important feature of the five-parameter model is that its parameters can be determined using data commonly provided by module manufacturers on their published datasheets. This paper documents the predictive capability of the five-parameter model and proposes modifications to improve its performance using approximately 30 days of field-measured meteorological and module data from a wide range of cell technologies, including monocrystalline, polycrystalline, amorphous silicon, and copper indium diselenide (CIS). The standard five-parameter model is capable of predicting the performance of monocrystalline and polycrystalline silicon modules within approximately 6% RMS but is slightly less accurate for a thin-film CIS and an amorphous silicon array. Errors for the amorphous technology are reduced to approximately 5% RMS by using input data obtained after the module underwent an initial degradation in output due to aging. The robustness and possible improvements to the five-parameter model were also evaluated. A sensitivity analysis of the five-parameter model shows that all model inputs that are difficult to determine and not provided by manufacturer datasheets such as the glazing material properties, the semiconductor band gap energy, and the ground reflectance may be represented by approximate values independent of the PV technology. Modifications to the five-parameter model tested during this research did not appreciably improve the overall model performance. Additional dependence introduced by a seven-parameter model had a less than 1% RMS effect on maximum power predictions for the amorphous technology and increased the modeling errors for this array 4% RMS at open-circuit conditions. Adding a current sink to the equivalent circuit to better model recombination currents had little effect on the model behavior.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 15

Six-parameter current sink modeling errors using the January–unshaded periods data set for (a) mono-Si and (b) 2-a-Si technologies

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Figure 16

Effect of the χ parameter in the six-parameter current sink model on the behavior of the modeled I-V curve

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Figure 1

Distribution of days of data selected for the clear days 9:30–4 EST data set

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Figure 2

Histograms of the (a) clear days 9:30–4 EST and (b) January–unshaded periods data sets used for model validation

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Figure 3

Equivalent circuit of a photovoltaic solar cell used in the five-parameter model

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Figure 4

Effect of the five parameters in the five-parameter model on the behavior of the modeled I-V curve

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Figure 5

Effect of the POA correction factor R on the five-parameter modeling errors for the mono-Si module for two different data sets

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Figure 6

Statistical modeling errors of the five-parameter model for the six backside insulated arrays using two different data sets ((a) mono-Si, (b) poly-Si (glass glazing), (c) poly-Si (ETFE glazing), (d) poly-Si (PVDF glazing), (e) 2-a-Si, and (f) CIS)

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Figure 7

Statistical modeling errors of the five-parameter model for the 2-a-Si array using the clear days 9:30–4 EST data set and different sets of STC data measured at progressively longer periods of solar exposure

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Figure 8

The change in modeling errors from using accepted values to using characteristic values of Eg,ref, K⋅L, nglaz, and ρg and setting C and αIsc to zero. The modeling errors are calculated for the mono-Si module using the clear days 9:30–4 EST data set.

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Figure 9

Five- and seven-parameter modeling errors using the clear days 9:30–4 EST data set for (a) mono-Si and (b) 2-a-Si technologies

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Figure 10

Five- and seven-parameter modeling errors using the January–unshaded periods data set for (a) mono-Si and (b) 2-a-Si technologies

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Figure 11

Five- and six-parameter modeling errors for 2-a-Si using the January–unshaded periods data set. The six-parameter model errors in (a) are when m=0, while those in (b) are when δ=0.

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Figure 12

Effect of parameter m in the seven-parameter model on the behavior of the modeled I-V curve

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Figure 13

Effect of parameter δ in the seven-parameter model on the behavior of the modeled I-V curve

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Figure 14

Equivalent circuit of a photovoltaic solar cell used in the five-parameter model with an added current sink shown in dotted lines

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