23 g belluardo_sensitivity_analysis_and_uncertainty_evaluation_of_simulated_clear-sky_solar_spectra

Sensitivity Analysis and Uncertainty Evaluation
of Simulated Clear-Sky Solar Spectra
Using Monte Carlo Approach
Giorgio Belluardo
EURAC Research
Institute for Renewable Energy, Bolzano (Italy)

4th PV Performance Modelling and Monitoring Workshop
Cologne – 2015, October 22th
Grazia Barchi, David Moser
EURAC Research
Institute for Renewable Energy, Bolzano (Italy)
2
Collaborators
Philipp Weihs
University of Natural Resources and Life Sciences
Institute of Meteorology, Vienna (Austria)
Marcus Rennhofer
AIT Austrian Institute of Technology GmbH
Energy Department, Vienna (Austria)
Dietmar Baumgartner
University of Graz
Institute of Physics, Kanzelhöhe Observatory
for Solar and Environmental Research,
Treffen (Austria)

3
Content
• Introduction
• Methodology
• Radiative Transfer Models
• Monte Carlo technique – description and application
• Results
• Spectral & broadband uncertainty
• Sensitivity analysis and uncertainty limits
• Impact on PV device calibration (Isc and MM)
• Conclusions

part of PV modelling chain
4
Introduction
Why this study?
Richter et al., 2015. Performance Plus project
 simulation of (spectral) irradiance: many tools available
 accuracy proven to be good
 what about uncertainty?
 modelling of (spectral) irradiance useful
when:
 no direct measurement available
 radiation information on a spec. area
 information on spectrum (spectral
effect on PV)
bankability of solar energy projects

Radiative Transfer Models - SDISORT
5
Evaluate uncertainty of SDISORT model using Monte Carlo technique
(GUM-JCGM 101:2008)
 clear-sky conditions
 spectral range: 280-2500nm
 global, diffuse, direct horizontal
(spectral) irradiance
Assumptions:
Includes SR of PV technologies
Includes sensitivity of spectroradiometers
, , Ω , , , ,
π
, , Ω
Not linear and not differentiable  general law of error propagation not applicable
, , : specific intensity [W/(m2 Hz sr)] : emission coefficient :scattering cross section:absorption cross section : solid angle : light speed
Methodology

6
Methodology
Monte Carlo
1
, 2
, … ,
1, … , ≫ 1
if Probability Density Function (PDF) of Q is known 
abs. uncertainty(Q) = σ(PDF(Q))
1. Assign PDF to reference values of input quantities
2. Make N>>1 random draws of input quantities according to their PDF
3. Feed each of the N>>1 input vectors into the model
4. Obtain N>>1 outputs
5. Statistical analysis of outputs to obtain uncertainty of Q
“method for the propagation of
distributions by performing random
sampling from probability distributions”
(GUM-JCGM 101:2008)

7
Methodology
Which one?
values correspond to meteorological and climatological measurements which is not possible
to perform directly under repeatability conditions.
Principle of Maximum Entropy (GUM-JCGM 101:2008): select one of the most probable PDFs
among those which comply with the restrictions imposed by the available information
What is the available information?
Error bound, d: the maximum error reasonably attributed to an input quantity. It is chosen
according to the experience or from literature.
Cordero (2007): when only error bound is available, the most probable PDF is rectangular
σ
3
pj pj+dpj-d
d d

8
Methodology
= assign a shape + reference value + limits (error bounds)
parameter symbol reference value source error bound source
extraterrestrial spectrum S ‐ Gueymard (2004) 5% Gueymard (2004)
solar zenith angle θ 35.85° SolPos 0.03° SolPos
surface albedo A 0.12 CM‐SAF (AVHRR) 25% Xia et al. (2007)
total ozone column o 321.27 DU WDC (GOME‐2) 5% Valks et al. (2011)
total precipitable water w 7.43 mm aeronet 10% Holben et al. (2001); Perez‐Ramirez et al. (2014)
Ångström exponent α 1.13 aeronet 0.08 Schuster et al. (2006); Toledano et al. (2007)
Ångström turbidity coefficient β 0.025 aeronet 0.025 Cordero et al. (2007)
single scattering coefficient ω 0.99 aeronet 0.05 Dubovik et al. (2000)
aerosol asymmetry factor g 0.67 aeronet 0.05 Xia et al. (2007); Andrews et al. (2006)
Reference values:
Kanzelhöhe Observatory
(Austria, 1526 m asl)
10:00 on April 25th, 2013
MAE: -8.7 W/m2
MBE: 31.5 W/m2
RMSE: 39.5 W/m2
Gmeas: 611.4 W/m2
Gsimul: 606.7 W/m2

9
Methodology
Option 1: let one input parameter change (the rest as reference value)  influence of
uncertainty of a specific input parameter to the output uncertainty
2. Make N>>1 random draws of input quantities according to their PDF
3. Feed each of the N>>1 input vectors into the model
Use of software (Statistics 101): N = 500 values generated for each input parameter
Option 2: let all Npar input parameters change simultaneously  combination of
uncertainty of all input parameter to the output uncertainty
4. Obtain N>>1 outputs
500 generated spectra = 500 values at every wavelength between 280 and 2500nm
5. Statistical analysis of outputs to obtain uncertainty of Q
Relative uncertainty %
.
on the pool of 500 values

10
Methodology
Option 1

11
Methodology
Option 2

Results – spectral uncertainty
extraterrestrial spectrum S
solar zenith angle θ
surface albedo A
total ozone column o
total precipitable water w
Ångström exponent α
Ångström turbidity coefficient β
single scattering coefficient ω
aerosol asymmetry factor g
Ozone: only at UV-B region (280-315nm)
Extr. spectrum: constant unc. contribution
Water vapour: only at absorption bands
Surface albedo
UV-B UV-A VISUV VIS NIR SWIR

surface albedo A
Ozone, extr. spectrum, water vapour: like GHI case
Ångström turbidity coefficient β: higher than GHI
UV VIS NIR SWIR UV-B UV-A VIS

surface albedo A
Ångström turbidity coefficient β: considerable influence
UV VIS NIR SWIR UV-B UV-A VIS
Surface albedo, Single scattering albedo and asymmetry factor
Ozone, extr. spectrum, water vapour: like previous cases

Results – broadband uncertainty
parameter symbol DiffHI DirHI GHI
extraterrestrial spectrum S 2.95% 2.95% 2.95%
solar zenith angle θ 0.01% 0.03% 0.02%
surface albedo A 1.29% n.a.* 0.12%
total ozone column o 0.08% 0.03% 0.04%
total precipitable water w 0.06% 0.20% 0.18%
Ångström exponent α 0.82% 0.10% 0.01%
Ångström turbidity coefficient β 22.20% 2.62% 0.31%
single scattering albedo ω 1.37% n.a.* 0.13%
aerosol asymmetry factor g 0.59% n.a.* 0.06%
combination ‐ reference 22.47% 3.98% 2.99%
280 nm – 2500 nm
*: not affected by this parameter

parameter symbol variation range, step min unc. max unc. value @ min unc. value @ max unc.
extraterrestrial spectrum S ‐ 2.95% 2.95% ‐ ‐
solar zenith angle θ 10°‐70°, 10° 0.01% 0.10% 10° 70°
surface albedo A 0.05‐0.95, 0.10 0.05% 0.91% 0.05 0.75
total ozone column o 250DU‐500DU, 25DU 0.03% 0.05% 250 DU 500 DU
total precipitable water w 5mm‐50mm, 5mm 0.00% 0.32% 0 50
Ångström exponent α 0.5‐2.5, 0.25 0.01% 0.04% 0.5 2.5
Ångström turbidity coefficient β 0‐0.5, 0.05 0.16% 0.36% 0 0.5
single scattering coefficient ω 0.6‐1, 0.05 0.12% 0.14% 1 0.6
aerosol asymmetry factor g 0.5‐0.9, 0.05 0.04% 0.06% 0.9 0.5
16
Results – sensitivity analysis only GHI
combination
max uncertainty
surface albedo
combination
min uncertainty

17
Results – uncertainty limits
Broadband uncertainty:
2.9% ÷5.9%
sum of squares: 3.1%
Typical values of
uncertainty from
outdoor measurements
(Vasiliki et al., 2013):
2.5%
only GHI

extrat. spec. sol. zen. ang. surf. alb. ozone col. water vap. Ång. exp. Ång. turb. coeff. single sc. albedo asymm. factor combined combined combined
Technology S θ A o w α β ω g reference min max
c‐Si 2.95% 0.02% 0.10% 0.03% 0.11% 0.01% 0.31% 0.13% 0.06% 2.985% 2.94% 7.74%
mc‐Si 2.95% 0.02% 0.10% 0.03% 0.11% 0.01% 0.30% 0.13% 0.06% 2.984% 2.94% 7.77%
2j‐a‐Si 2.95% 0.02% 0.17% 0.07% 0.02% 0.02% 0.38% 0.17% 0.07% 3.003% 2.94% 12.38%
CIGS 2.95% 0.02% 0.09% 0.04% 0.11% 0.01% 0.29% 0.13% 0.06% 2.982% 2.94% 7.76%
CdTe 2.95% 0.02% 0.13% 0.05% 0.04% 0.02% 0.34% 0.15% 0.06% 2.992% 2.94% 10.00%
CZTS 2.95% 0.02% 0.11% 0.05% 0.07% 0.01% 0.31% 0.14% 0.06% 2.985% 2.94% 9.04%
organic 2.95% 0.02% 0.21% 0.07% 0.01% 0.02% 0.42% 0.18% 0.07% 3.014% 2.94% 14.54%
18
Results – uncertainty on PV device calibration
parameters
λ
Uncertainty higher with technologies with SR at lower wavelengths
2.985%
2.984%
3.003%
2.982%
2.992%
2.985%
3.014%
only GHI
Uncertainty of SRdut(λ) neglected
: simulated spectrum
: technology spectral response (measured in lab)

19
Results – uncertainty on PV device calibration
parameters
λ
λ
λ
λ
Uncertainty of SRdut(λ) neglected
extrat. spec. sol. zen. ang. surf. alb. ozone col. water vap. Ång. exp. Ång. turb. coeff. single sc. albedo asymm. factor combined combined combined
Technology S θ A o w α β ω g reference min max
c‐Si n.a. <0.01% 0.02% <0.01% 0.08% <0.01% <0.01% <0.01% <0.01% 0.080% 0.01% 2.13%
mc‐Si n.a. <0.01% 0.02% <0.01% 0.08% <0.01% <0.01% <0.01% <0.01% 0.080% 0.01% 2.16%
2j‐a‐Si n.a. <0.01% 0.05% 0.03% 0.16% 0.01% 0.08% 0.04% 0.01% 0.185% 0.03% 7.16%
CIGS n.a. <0.01% 0.03% <0.01% 0.07% <0.01% 0.01% <0.01% <0.01% 0.081% 0.01% 2.14%
CdTe n.a. <0.01% 0.01% 0.01% 0.14% <0.01% 0.03% 0.02% 0.01% 0.142% 0.01% 4.61%
CZTS n.a. <0.01% 0.02% 0.01% 0.11% <0.01% 0.01% 0.01% <0.01% 0.114% 0.01% 3.56%
organic n.a. <0.01% 0.09% 0.03% 0.17% 0.01% 0.11% 0.05% 0.02% 0.231% 0.04% 9.45%
Uncertainty higher with technologies with SR at lower wavelengths
Higher uncertainty variability
0.080%
0.080%
0.191%
0.078%
0.147%
0.115%
0.234%
0.978
0.976
1.015
0.970
0.987
0.971
1.051
MM (absolute mean value)
only GHI
: simulated spectrum
: technology spectral response (measured in lab)
: reference spectrum
1 at every wavelength (pyranometer)

20
Conclusions
 Monte Carlo useful when dealing with not linear and not differentiable equations (like RTE)
 SDISORT uncertainty (reference input parameters):
 influence of extraterrestrial spectrum (constant), ozone column (UV-B), Ångström
turbidity coefficient (UV-VIS), precipitable water (absorption bands – NIR-SWIR)
 GHI: 3.0%, DirHI: 4.0%, DiffHI: 22.5% (high contribution of Ångström turbidity
coefficient)
 Uncertainty limits on GHI: 2.9% to 5.9% (vs. 2.5% spectroradiometers)
 Effect on PV device calibration:
 Isc: values of uncertainty around 3%, less variability (0.032% span)
 MM: values between 0.08% and 0.23%  higher variability
 Higher uncert. for c/mc-Si, CIGS
 Lower uncert. for a-Si, organic, CdTe

21
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measurement: Propagation of distributions using a Monte Carlo method
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Clark, D., Frouin, R., Halthore, R., Karneli, A., O’Neill, N., Pietras, C., Pinker, R., Voss, K., ibordi, G., 2001. An emerging ground-based aerosol climatology: Aerosol optical depth from aeronet.
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Andrews, E., Sheridan, P. J., Fiebig, M., McComiskey, A., Ogren, J. A., Arnott, P., Covert, D., Elleman, R., Gasparini, R., Collins, D., Jonsson, H., Schmid, B., Wang, J., 2006. Comparison of
methods for deriving aerosol asymmetry parameter. J. Geophys. Res- Atmos. 111, D05S04.
Richter, M., De Brabandere, K., Kalisch, J., Schmidt, T., Lorenz, E., 2015. Best practice guide on uncertainty in PV modelling. Performance Plus WP2 deliverable 2.4
Vasiliki, P., Norton, M., Hadjipanayi, M., Georghiou, G., 2013. Calibration of spectroradiometers for outdoor direct solar spectral irradiance measurements. In: 28th European Photovoltaic Solar
Energy Conference and Exhibition, Paris, France. pp. 3466–3471.

European Regional Development Fund (ERDF)
project 2-1a-97 ”PV Initiative”
22
Acknowledgements
Stiftung Südtiroler Sparkasse
project 5-1a-232 ”Flexi-BIPV”
European Union’s Horizon 2020
research and innovation programme
project ”Solar Bankability”
Roberto Galleano
Joint Research Center
Thomas Eck
NASA

Thank you for the attention
Giorgio Belluardo
giorgio.belluardo@eurac.edu

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