Back to Main Page: Effects of snow on photovoltaic performance

The purpose of this page is to outline current development of radiative transfer modelling and its applications to the prediction and modelling of PV performance

## Radiative Transfer Models (RTM)

[1] V.E. Cachorro, A.M. de Frutos, J.L. Casanova, Comparison between various models of solar spectral irradiance and experimental data, Appl. Opt. 24 (1985) 3249-3253.

* labert-beer-bouger law
* methods to determine preciptable water
* good overview of spectral transmittance data


The following is a breif list of available RTM codes

--SEDES2

Empirical program meant for PV applications, uses direct and diffuse irradiation as inputs


[1] B. Houshyani Hassanzahed, W.G.J.H.M. van Sark, A.C. de Keizer, N.H. Reich, The Effect of a Varying Solar Spectrum on the Energy Performance of Solar Cells, (2007).

[1] S.A. Khalil, Parameterization models for solar radiation and solar technology applications, Energy Conversion and Management. 49 (2008) 2384-2391.

[1] D.R. Myers, Terrestrial solar spectral distributions derived from broadband hourly solar radiation data, in: Proceedings of SPIE, San Diego, CA, USA, 2009: p. 74100A-74100A-11.

• errors of ~20% in use of SEDES2
• Expected measurement uncertainty in the measured data is 15% for wavelengths < 400 nm, 5% for wavelengths from 400 nm to 1000 nm, and 10% for wavelengths > 1000 nm. [1,2,3].
• SEDES is semi-empirical, using the SPECTRL model for clear sky conditions, and empirical cloud coefficients for cloud modelling
• SEDES uses Cloud Cover Modifiers. Liu and Jordan[14] clearness index, kt. CCM's exist as a function of Kt, zenith angle and wavelength.
• E(λ) = Ec(λ) *[ A1(λ) + A2(λ)/cos(z) + B1(λ)* Kt + B2( λ)*Kt/cos(z) + C1(λ)*Kt2 + C2(λ )*(Kt2 )/Cos(z).
• constant errors of ~28% in wintertime
• TMYSPEC does not include albedo in wintertime.
• wavelength dependent spectral errors
• The incorporation of methods of obtaining cloud optical depths from broadband data, such as described in Barnard et al. [18]
• More investigation required for wintertime spectral effects.

[1] S. Nann, K. Emery, Spectral effects on PV-device rating, Solar Energy Materials and Solar Cells. 27 (1992) 189-216. SEDES2 program used for prediction of terrestrial spectra

• Two-diode model for energy prediction
It has been reported by field experiments that photovoltaic modules do not
meet their name-plate power rating under actual operating conditions by 10% to
30% on an annual average [3,4]. This discrepancy is caused by the following effects
[51: S. Nann, K. Emery/Spectral effects on PV-device rating 191
(1) Modules operate at cell temperatures ranging from the ambient temperature
to temperatures which are about 40°C above the ambient temperature
(non-concentrating).
(2) The incident irradiance varies between 0 and 1200 W/m 2 standard.
(3) In addition, there are changes in the relative spectral distribution which
lead to higher or lower efficiencies compared to the efficiency under the AM1.5
reference spectrum.
(4) At high angles of incidence the incoming light is more reflected than at
direct normal incidence indoors under the light of the solar simulator [6]. Additional
transmission losses are caused by soiling.
(5) The name-plate rating itself is guaranteed by the manufacturers only within
a certain range (module-to-module variability).
(6) Partly, the discrepancies are caused by module degradation.
(7) Maximum power point tracking is off by some percent in most cases

• Inputs to SEDES2: Direct, Diffuse, RH
• Inputs to module energy model: Fuentes, POA, Tamb, Ws , array height, anemometer height, INOCT
• Data quality control, physical limits, consistency checks. 40W/m2 limit on irradiaiton, selected out 30% of daylight values.
• Riordan and Hulstrom [24,25], reveiw of spectral effects on PV-device performance
• Heidler et al. [23] "A new approach for the performance evaluation of solar cells under realistic reporting conditions,"
• good graphs of spectral effects on efficiency of various cells
• 20%-10% drop in wintertime efficiency due to red shift of modules.
• Calls for generation of standard day energy output comparisons.
• Created a software package to predict PV output /

[1] W.G.J.H.M. van Sark, Simulating performance of solar cells with spectral downshifting layers, Thin Solid Films. 516 (2008) 6808-6812.

[1] B. Houshyani, SEDES2 Spectral Model Validation;A comparative study of spectral radiative transfer models for clear and cloudy sky conditions using SMARTS, SPCTRL2 and MODTRAN, (2007).

--MODTRANS

Computationally heavy simulations package which is considered to be a reference for these measurements


--SBDART

Lightweight simulations package capable of simulating cloudy sky information


[1]Comparison of Modeled and Measured Shortwave Broadband Radiative Fluxes at the SGP and NSA Sites (with Special Emphasis on Diffuse Radiation), (n.d.).

[2] J.C. Barnard, D.M. Powell, A comparison between modeled and measured clear-sky radiative shortwave fluxes in Arctic environments, with special emphasis on diffuse radiation, J. Geophys. Res. 107 (2002) 10 PP.

-SMARTS2

Developed my NREL and used to generate ASTM AM1.5 standard spectra. Currently only performs calculations for clear sky phenomena.


[1]Description and availability of the SMARTS spectral model for photovoltaic applications, (n.d.).

• Clear-sky predictions, cloud modifiers fron Nann and Riordan

Line-by line models use quantum properties of radiation, accessed from the HITRAN database. Band models are simplified LBL models described by Fenn et al. MODTRANS is a band model models based on parametrizations of transmittance and absorbtin functions are simpler advantages of SMARTS

i) accurate and reg. updated spectral transmittance functions

ii) improved spectral resolution over existing transmittance models

iii) produces spectral irradiances comparable to MODTRAN

iv) predictions can be easily and directly compared to spectroradiometric measurements Anderson et. al. defines LOWTRAN spectra spectra are scaled by air term, RH, average temp Show sensitivity of PV systems to atmospheric constituents.

[1] C.A. Gueymard, Interdisciplinary applications of a versatile spectral solar irradiance model: A review, Energy. 30 (2005) 1551-1576.

[1] C.A. Gueymard, Direct solar transmittance and irradiance predictions with broadband models. Part II: validation with high-quality measurements, Solar Energy. 74 (2003) 381-395.

[2] C.A. Gueymard, Direct solar transmittance and irradiance predictions with broadband models. Part I: detailed theoretical performance assessment, Solar Energy. 74 (2003) 355-379.

[1] C.A. Gueymard, Parametrized transmittance model for direct beam and circumsolar spectral irradiance, Solar Energy. 71 (2001) 325-346.

--LBLRTM

Developed by ARM, it is a line-by line radiative transfer model


--[Streamer]

Based on the DISTORT code, can handle multiple cloud layers


--[Modtran5]

Developed by U.S air force, extensively validated spectral modelling code.


--RRTM

The rapid radiative transfer model (RRTM) is a validated, correlated k-distribution band model for the calculation of longwave and shortwave atmospheric radiative fluxes and heating rates. The Rapid Radiative Transfer Model for GCMs is an accelerated version of RRTM that provides improved efficiency with minimal loss of accuracy for application to general circulation models.


[1]Cloudy Sky RRTM Shortwave Radiative Transfer and Comparison to the Revised ECMWF Shortwave Model, (n.d.).

[2]RRTM validation, (n.d.).

[3] E.J. Mlawer, S.J. Taubman, S.A. Clough, RRTM: A Rapid Radiative Transfer Model, (n.d.).

[4] E.J. Mlawer, S.A. Clough, S. Kato, Shortwave clear-sky model-measurement intercomparison using RRTM, in: Proceedings of the Eighth ARM Science Team Meeting, 1998: pp. 23–27.

[5] S.A. Clough, M.W. Shephard, E.J. Mlawer, J.S. Delamere, M.J. Iacono, K. Cady-Pereira, et al., Atmospheric radiative transfer modeling: a summary of the AER codes, Journal of Quantitative Spectroscopy and Radiative Transfer. 91 (2005) 233-244.

## Modelling and retreiving atmospheric paramters

[1] C.A. Gueymard, Importance of atmospheric turbidity and associated uncertainties in solar radiation and luminous efficacy modelling, Energy. 30 (2005) 1603-1621.

[1] C. Gueymard, Critical analysis and performance assessment of clear sky solar irradiance models using theoretical and measured data, Solar Energy. 51 (1993) 121-138.

[1] C. Gueymard, Mathematically integrable parametrization of clear-sky beam and global irradiances and its use in daily irradiation applications, Solar Energy. 50 (1993) 385-397.

[1]Measurement and modelling of broadband and spectral global irradiance in southern saskatchewan canada, (n.d.).

[1] R.E. Bird, R.L. Hulstrom, A.W. Kliman, H.G. Eldering, Solar spectral measurements in the terrestrial environment, Appl. Opt. 21 (1982) 1430-1436.

• Formulation for homogeneous band transmission and air mass (AM) by Kasten
• sun photometer filters at 368,500,778,864 nm according to WMO, with FOV of 2-3 degrees, as of 1983
• Beer's law defines optical depth
• Rayleigh scattering is a function of surface pressure, defined by young
• molecular absorption is primarily ozone absorption. ref 23 gives estimations of ozone amounts
• look up fraundhaufer lines
Beginning at 300-nm wavelength, there is a broad ozone (03) absorption band called the Hartley-Huggins band that extends to 350-nm wavelength. The Chapuis03 band then extends from 500- to 700-nm wavelength. Water vapor (H20) absorption occurs throughout the spectrum from 570 nm to the end of the plot at 2300 nm. The strength of this absorption varies a great deal from wavelength to wavelength and is negligible at some wavelengths. Absorption from carbon dioxide (C0 2) occurs at several wavelengths longer than 1000 nm, but the effect of CO2 is relatively small. Narrow absorption features for oxygen (02) are dispersed throughout the spectrum with the major ones occurring near the 688- and 762-nm wavelengths. Other absorbers shown that have very little effect are methane (CH 4) and nitrous oxide (N2 0), which absorb several wavelengths between 1900 nm and the end of the plot, 2300 nm.

• Coulsen defines optical FOV
• Talks about difficulty of predicting a cloudy spectra
• turbidity is the most important component
• Water vapor is responsible for the steep drops in spectrum

## Aerosol Optical Depth

### Retreival

#### Sattellite

[1]GACP: Global Aerosol Climatology Project, (n.d.).

[1]Glory, (n.d.).

• Very high resolution Aerosols...crashed in ealy 2011

[1]Langley ASDC - Data Pool, (n.d.).

[2]NASA: TERRA (EOS AM-1) - About Terra, (n.d.).

#### Ground Based

[1] C.A. Gueymard, J.D. Garrison, Critical evaluation of precipitable water and atmospheric turbidity in Canada using measured hourly solar irradiance, Solar Energy. 62 (1998) 291-307.

[1] C.A. Gueymard, Turbidity Determination from Broadband Irradiance Measurements: A Detailed Multicoefficient Approach, J. Appl. Meteor. 37 (1998) 414-435.

[1] J. Lorente, A. Redañ, X. de Cabo, Influence of Urban Aerosol on Spectral Solar Irradiance., Journal of Applied Meteorology. 33 (1994) 406-415.

[1] K.M. Latha, K.V.S. Badarinath, Spectral solar attenuation due to aerosol loading over an urban area in India, Atmospheric Research. 75 (2005) 257-266.

[1] C.P. Jacovides, M.D. Steven, D.N. Asimakopoulos, Spectral Solar Irradiance And Some Optical Properties For Various Polluted Atmospheres, Solar Energy. 69 (2000) 215-227.

[1] C.P. Jacovides, M.D. Steven, D.N. Asimakopoulos, Solar Spectral Irradiance under Clear Skies around a Major Metropolitan Area, J. Appl. Meteor. 39 (2000) 917-930.

## Error Analysis

[1] C.A. Gueymard, Importance of atmospheric turbidity and associated uncertainties in solar radiation and luminous efficacy modelling, Energy. 30 (2005) 1603-1621.

[1] C. Gueymard, Analysis of monthly average atmospheric precipitable water and turbidity in Canada and Northern United States, Solar Energy. 53 (1994) 57-71.

## Column Water Vapour

### Retreival

#### Sattellite

[1]GEWEX - Global Energy and Water Cycle Experiment, (n.d.).

#### Ground Based

[1] C.A. Gueymard, J.D. Garrison, Critical evaluation of precipitable water and atmospheric turbidity in Canada using measured hourly solar irradiance, Solar Energy. 62 (1998) 291-307.

[1] C. Gueymard, Analysis of monthly average atmospheric precipitable water and turbidity in Canada and Northern United States, Solar Energy. 53 (1994) 57-71.

[1] C. Gueymard, Assessment of the Accuracy and Computing Speed of Simplified Saturation Vapor Equations Using a New Reference Dataset, J. Appl. Meteor. 32 (1993) 1294-1300.

[1] J. Garrison, G. Adler, Estimation of precipitable water over the United States for application to the division of solar radiation into its direct and diffuse components, Solar Energy. 44 (1990) 225-241.

## Cloud Cover

### Retreival

#### Ground Based

[1] J.C. Barnard, C.N. Long, A Simple Empirical Equation to Calculate Cloud Optical Thickness Using Shortwave Broadband Measurements, J. Appl. Meteor. 43 (2004) 1057-1066.

[2] R. Boers, A. van Lammeren, A. Feijt, Accuracy of Cloud Optical Depth Retrievals from Ground-Based Pyranometers, J. Atmos. Oceanic Technol. 17 (2000) 916-927.

[3] E. Leontyeva, K. Stamnes, Estimations of Cloud Optical Thickness from Ground-Based Measurements of Incoming Solar Radiation in the Arctic, J. Climate. 7 (1994) 566-578.

• Uses broadband measurements (0.3-4um)from an eppley pyranometer.
• Calculate available solar resource, iterate until finiding correct optical thickness. Good discussion of spectral snow albedo.

[4]A method to account for surface albedo heterogeneity and its application in the retrieval of cloud optical depth from ground-based measurements of irradiance, (n.d.).

• Addresses the isssues associted with mutliple rebounds of albedo radiation in areas where albedo is non-constant. Not necesarily needed for this project.

[5]Cloud optical thickness retrievals from ground-based pyranometer measurements, (n.d.).

• Optical thickness from pyranometer readings, incorperating aerosols.

[6]A Simple Empirical Equation to Calculate Cloud Optical Thickness from Shortwave Broadband Measurements, (n.d.).

• Empircial curve fit, very simple, only valid to albedos of 0.3
• optical thickness is a function of broadband iradiation
• To construct the cloud optical thickness, either the Min algorithm or SBDART (Barnard et. al derived in 2001) are used.
• Hu and Stammes, 1993 found that optical thickness is relatively constant over visible wavelengths.
• Min and SBDART produce same result except for optical thikness<10
• Error of ~1 for t=2, and decreases to 0 around 10
• Min chosen becasue of computational efficiecny
• t related to T (transmission) which is downwelling diffuse irradiance D/at the top of the atmosphere, Io. Io is solar constant times u0, min error of D is ~5w/m^2
• Can measure C instead of I0, giving a modified transmission of D/C, C is clear-sky total irradiance, measured with the same device. (Lonk and Long and Ackerman. Using this method reduces seasonal dependance on aerosols.
• r is of the form (D/Cu^alpha), with alpha chosen experimentally to be .25
• D is corrected for IR loss according to Dutton, 2001 and Long,2003
• Multi-Filter Rotating Shadowband Radiometer (MFRSR; Harrison et al. 1994)
• cloud fraction (Long algorithm, Long 2001)
• Sensitivity analysis using SBDART, Errors due to water vapour fraction are lowered by using C, because it takes this into account from the previous day's water content.
• t e 5 exp[2.15 1 A 1 1.91 arctanh(1 2 1.74r)],

[7]Development and Evaluation of a Simple Algorithm to Find Cloud Optical Depth with Emphasis on Thin Ice Clouds, (n.d.).

## Geographic Distribution of spectra

[1] G. Seckmeyer, B. Mayer, G. Bernhard, R.L. McKenzie, P.V. Johnston, M. Kotkamp, et al., Geographical differences in the UV Measured by intercompared spectroradiometers, Geophys. Res. Lett. 22 (n.d.) PP. 1889-1892.

[2] T. Huld, M. Šúri, E.D. Dunlop, Geographical variation of the conversion efficiency of crystalline silicon photovoltaic modules in Europe, Progress in Photovoltaics: Research and Applications. 16 (2008) 595-607.

[3] K. Bücher, Site dependence of the energy collection of PV modules, Solar Energy Materials and Solar Cells. 47 (1997) 85-94.

## Effects of spectrum on PV technologies

[1] B. Houshyani Hassanzahed, W.G.J.H.M. van Sark, A.C. de Keizer, N.H. Reich, The Effect of a Varying Solar Spectrum on the Energy Performance of Solar Cells, (2007).

[1] R. Shimokawa, Y. Miyake, Y. Nakanishi, Y. Kuwano, Y. Hamakawa, Effect of atmospheric parameters on solar cell performance under global irradiance, Solar Cells. 19 (1986) 59-72.

• Used an RTM to show the effects of turbidity and air mass on the response of PV cells. Good graphs.

## Spectral Mismatch Factor (MMF)

[1]Buy IEC 60904-7 ed3.0 - Photovoltaic devices - Part 7: Computation of the spectral mismatch correction for measurements of photovoltaic devices | IEC Webstore | Publication Abstract, Preview, Scope, (n.d.).

[2]A sensitivity analysis of the spectral mismatch correction procedure using wavelength-dependent error sources [solar cell testing], (1991) 459-465 vol.1.

[3]A new approach for the performance evaluation of solar cells under realistic reporting conditions, (1990) 1017-1022 vol.2.

[4] C.H. Seaman, Calibration of solar cells by the reference cell method--The spectral mismatch problem, Solar Energy. 29 (1982) 291-298.

[5] H. Müllejans, A. Ioannides, R. Kenny, W. Zaaiman, H.A. Ossenbrink, E.D. Dunlop, Spectral mismatch in calibration of photovoltaic reference devices by global sunlight method, Meas. Sci. Technol. 6 (2005) 1250-1254.

[6] N. Martín, J.M. Ruiz, A new method for the spectral characterisation of PV modules, Prog. Photovolt: Res. Appl. 7 (1999) 299-310.

[8] D.L. King, B.R. Hansen, A sensitivity analysis of the spectral mismatch correction procedure using wavelength-dependent error sources [solar cell testing], Photovoltaic Specialists Conference, 1991. (1991) 459-465 vol.1.

[9] IEC, Photovoltaic devices - Part 7: Computation of the spectral mismatch correction for measurements of photovoltaic devices, 2008.

[10] C.A. Gueymard, The sun's total and spectral irradiance for solar energy applications and solar radiation models, Solar Energy. 76 (2004) 423-453.

## Spectral effects on amorphous PV cells

--Effect of atmospheric parameters on the silicon solar cells performance, M. Chegaar, P. Mialhe Spectral effects simulated for Algeirs

effects in short-circuit current due to turbidity, decrease of: 4.41%, 4.7%, 7.34% for mono multi and amorphous. Turbidity decreases UV radiaiton

Increasing water vapour leads to decrease of 4.57%,4.4%, o.2% for same

Efficiency increase with air mass for crystalline, decrease for amorphous

-- [1. Rüther R, Kleiss G, Reiche K. Spectral effects on amorphous silicon solar module fill factors. Solar Energy Materials and Solar Cells 2002 Feb;71(3):375-385.]

amorphous silicon is more efficient in the summer

crystalline more efficient in winter

A:Si matches very well with indoor illumination spectra, they are more efficient indoors

Spectral mismatch factor: ratio between Isc rated and Isc extrapolated to 1000W/m2

Does not neccesarily hold true for a:Si cells: "However, in amorphous silicon solar cells, the proposition of the non-dependence of sðlÞ on the operating voltage does not hold. It is known that in p-i-n structures a typical blue-dispersion of the spectral response occurs for higher bias voltages [14]. Since the field-driven transport is the dominant mechanism with respect to diffusion, and since the electrical field is extended over practically the whole cell, the generation profile inside the cell produces a feedback on the internal quantum efficiency. In a-Si cell modelling, one takes advantage of this effect by application of the DICE method [12,15,16] to yield for a spatially resolved description of the field distribution inside the cell."

FF is the ratio between Imp and Isc

Used a filtered pyranometer to find "Red" and "Blue" spectra

Plots of FF vs Isc,shows much scatter in the central area of Isc.

Attrubited to the spectral effect, blue increasing FF, red to decrease it

Shows curves of spectral senstivity as a function of irradiation

Outdoors testing of A:Si generally leads to better efficiency in summer, worse in winter

Attributed to thermal annealing and seasonal spectral variations

Conclusion of this paper is that spectral effects are dominating

first cells utilized indoors in calculators

power efficiency from 71% in winter to 83% in summer

bandgap from 360-780

Crystal silicon is better in the winter

therefore, the seasonal variatoin is likely due to the seasonal changes in spectrum, not annealing. Does not really support this with numbers

useful fraction can very in the range of +6 to -9% from annual average

spectral mismatch factor: Fabero and Chenlo [7] and Merten [8] model the spectral mismatch with a spectral mismatch factor for the short circuit current of crystalline and amorphous silicon

Hirata and Tani [9], who used a pyranometer and 6 filters up to a maximum wavelength of 1200 nm and investigated the effect of the spectral changes on a-Si and c-Si devices.

Difficult to quantify the effects on multijunction units because it will cause a mismatch in the series connectes cells, leading to non-linear effects [13]

spectral effects though air mass and cloud cover(clearness index)

Annual fluctiations in useful fractions ~10%

Panels set at 35.5 degrees due south

Calculated output based upon global irradiaiton

Compared this to actual output: 20% variation in A:Si, derived a 3.7% increase in output over predicted

clearness index: H/H0/Hmax/Ho

I-V Curve at 10 min intervals

Use silver paste to T/C measurements

Spectral effect is ~16% increase in summer

The fraction of the specturm falling into spectrally useful ranges is 10% to -15%

Previous studies utilize clear sky models of irradiance for spectral disribution

< 10W/m2 ignored

Use a custom detector with spectral range 300-1700nm

Useful fraction is defined as ratio of irradiaion within useful range to total irradiaiton (300-780 nm)

UF for 300-1700nm is 60.4%

--[http://www.stefankrauter.com/info/23rd_EU_PVSEC_Krauter_Preiss_et%20al.pdf S. Krauter,, PV YIELD PREDICTION FOR THIN FILM TECHNOLOGIES AND THE EFFECT OF INPUT PARAMETERS INACCURACIES, (n.d.).] Outlines the errors in measurement for various PV technologies. Quantifies error due to albedo byt hrouwing out a number

Has created a computer program to simulate the performance of an a:Si PV module, however up to 20% inaccuracy due to innacuracy of inputs.

Good list of inputs for PV simulation

Outdoors measurement of amorphous, crystalline and CIS modules

Using eppley spectroradiometer, 5 min scans up to 2500nm with integrating sphere

Air pressure utilized to measure pressure corrected air mass

Uses an ESTI reference cell, divided in two sections, one shorted with a shunt resistor and one open circuit. Cell temperature derived from open circuit voltage

Temperature coefficient for Voc

Contains equations for translating the Isc, Impp and Vmpp to STC, omitting curve correction factor

Shows mismatch factor for measurement of c-si, a-si and CIS with pyran and reference cell as reference. graphs show high mismatch factors for a-si when using both techniques. shows that using a pyranometer with MMF correction can remove spectral effects

spectral mismatch factor, calculations included

Tests performed on days with <20% diffuse fraction therefore spectrum mismatch was largely dependent upon AM

Very comprehensive spectral evaluation resource

## Spectral effects on solar cells

• Defines Weighted Useful fractoin
Page data
Authors Rob Andrews 2011 CC-BY-SA-4.0 511 No main image Rob Andrews (2011). "Atmospheric radiation transfer for PV applications". Appropedia. Retrieved August 18, 2022.
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