1) NREL is a national laboratory operated by the Alliance for Sustainable Energy, LLC that focuses on energy efficiency and renewable energy. 2) The presentation discusses options for quantifying solar resource from measurements including horizontal and inclined surfaces, and methods for transposing horizontal irradiance data to plane of array irradiance. 3) It notes that isotropic models used to approximate this transposition can underestimate plane of array irradiance by 5-20% compared to using anisotropic physics models that better simulate cloud conditions and solar radiances.

1. NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.
The Future of Transposition
Models:
From Isotropic Approximation to
Physics Models
Yu Xie and Manajit Sengupta
EPRI/Sandia PV Systems Symposium
May 9, 2016

2. 2
Sensing, Measurement, and Forecasting
The right observations of
wind and solar resource
Measurements
Targeted predictions of
resources and
plant performance
Modeling
Raising everyone to
the same level and
enabling dialog
Standards
Provide high-quality meteorological and power data for energy
yield assessment, resource characterization, and grid
integration

3. 3
Options in quantifying solar resource
Thermopile on a horizontal
surface providing horizontal
irradiance
Reference cell or thermopile
on inclined surfaces: more
closely correlate with system
performance
Transpose horizontal
irradiance to POA irradiance:
horizontal data are easier to
document

4. 4
∫ Ω+×+= dIfGHIDNIPOAI 'cos'cos θσθ
Computation of POA irradiance
θʹ

5. 5
Isotropic approximation
• Liu and Jordan (1963):
• Koronakis (1986), Tian et al. (2001), Badescu (2002), etc.
• Models after 1963 may have a better agreement to surface
measurements (Noorian et al.(2008), Jakhrani et
al.(2012),Loutzenhiser, et al.(2007)).
Xie and Sengupta, submitted to Renewable Energy
2
cos1 β+
×= DHIPOAIdiffuse

6. 6
Isotropic vs. anisotropic models
Wm-2sr-1μm-1

7. 7
Isotropic vs. anisotropic models
• Radiative transfer
models can simulate
radiances.
• For each tilt angle,
POA irradiance can be
computed.
• Isotropic model may
dramatically
underestimate POA
irradiance.
λ=0.6μm

8. 8
Isotropic vs. anisotropic models
• The underestimation
increases with cloud
optical thickness, but
rapidly decreases
when cloud is thick.
• The underestimation
can reach >20%
(>200W/m2).
• For thick clouds,
isotropic model
overestimates POA
irradiance by ~5% (8-
15W/m2).
λ=0.6μm

9. 9
Empirical transposition models show bias
 Empirical transposition models consider a more detailed analysis of the
downwelling diffuse solar radiation by using empirically derived coefficients.
 Perez model is one of the models (in 21 models) with consistently best
performance (Hay, 1988).
 Sun et al. (2014) showed bias of Perez model depending on site.
Sun et al.(2014)

10. 10
Uncertainties in transposition models
 The accuracy of empirical transposition models varies
with the use of the coefficients.
 Decomposition model gives additional uncertainty in the
POA irradiance.
1-minute POA irradiances from 1-axis tracking measurements on 1/22/2015.
“Cape Canaveral 1988”
(Golden, CO)

11. 11
Uncertainties in surface albedo
 Transposition models use surface
albedo from climatology/TMY to
estimate surface reflection.
 The uncertainty becomes much larger
in winter because of snow.
1/22/2015
Golden, CO
7/30/2015
Golden, CO

12. 12
Current models lead to higher uncertainties
POA
Irradiance
GHI
DHI
DNI
Surface
data
Satellite
data
Spectral
GHI, DHI,
DNI
Radiative
Transfer
Spectral
Model
Decomposition
Transposition

13. 13
Future opportunities
 The spectral channels with better
temporal and spatial resolutions
will lead to more accurate cloud
and land surface products.
 Current models are hard to
benefit from future development
of satellite techniques.
GHI
Cloud optical thickness
http://nsrdb.nrel.gov

14. 14
Cloud transmittance and
reflectance of irradiance
AOD, θ, g, ω, PWV, P,
ozone,…
Clear-sky transmittance and
reflectance
REST2
Surface albedo
All-sky broadband
irradiances
Fast All-sky Radiation Model for Solar applications
(FARMS)
Xie et al., submitted to Solar Energy

15. 15
Empirical vs. physics models
Satellite
data
GHI DHI
DNI
Satellite
data
GHI
DHI
DNI
FARMS
Radiative
Transfer
Decomposition

16. 16
Future models
Satellite
data
POA
Irradiance
Spectral
GHI, DHI,
DNI
Spectral
POA
Irradiance
Radiative
Transfer
Decomposition
Transposition
Spectral
Model

17. 17
Conclusions and future work
• POA irradiance can be analytically solved using an
isotropic approximation.
• Isotropic model can underestimate POA irradiance by
5-20%.
• The accuracy of empirical transposition models
depends on empirical coefficients, decomposition
models, and surface albedo.
• Future transposition models can benefit from the
development of satellite remote sensing.
• The risk of accumulated uncertainties can be reduced
by using a physics model.

18. 18
Let’s talk!
yu.xie@nrel.gov
manajit.sengupta@nrel.gov
andrew.clifton@nrel.gov
The Energy Systems Integration Facility
Golden, CO. Image by Dennis Schroeder, NREL