Technical Report

NREL/TP-520-47277

March 2010

Preliminary Investigation of 

Methods for Correcting for 

Variations in Solar Spectrum 

under Clear Skies

B. Marion
National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393

303-275-3000 • www.nrel.gov

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

Contract No. DE-AC36-08-GO28308

Technical Report

NREL/TP-520-47277

March 2010

Preliminary Investigation of 

Methods for Correcting for 

Variations in Solar Spectrum 

under Clear Skies

B. Marion

Prepared under Task No. PVD9.1460
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iii

Acknowledgements

This work was performed under DOE Contract No. DE-AC36-08GO28308 and Task No. 

PVD9.1460. The author acknowledges the efforts of Jose Rodriguez, Ed Gelak, and Matt Muller 

at the National Renewable Energy Laboratory (NREL) for installation and operation of the test 

equipment; the efforts of Gobind Atmaram and Jim Roland at the Florida Solar Energy Center 

for coordinating the collection of data at their location; and the efforts of Chris Gueymard (Solar 

Consulting Services), David King (Sandia National Laboratories-Retired), Joshua Stein (Sandia 

National Laboratories), Kevin Fok (United Solar Ovonic), Joe del Cueto (NREL), and Matt 

Muller (NREL) for reviewing this report and providing helpful suggestions.
iv

List of Acronyms and Abbreviations

AM air mass

AMa absolute air mass

ASTM American Society for Testing and Materials

CREST Centre for Renewable Energy Systems Technology 

f(AM) function of air mass

FSEC Florida Solar Energy Center

Isc short-circuit current 

NREL National Renewable Energy Laboratory 

POA plane-of-array 

PV photovoltaic 

SAM Solar Advisor Model

SRC Standard Reporting Conditions

Tpv PV module temperature 
v

Abstract

Two types of methods were evaluated for correcting the short-circuit current of photovoltaic

(PV) modules for variations in the solar spectrum under clear skies: (1) empirical relationships 

based on air mass, and (2) use of spectral irradiance models and PV module spectral response 

data. Methods of the first type were the Sandia absolute air-mass function, or f(AMa

For predicting the short-circuit current for a multi-crystalline silicon PV module and an 

amorphous silicon PV module, the methods using spectral irradiance models and PV module 

spectral response data performed better than the empirical air mass methods. This is attributed to 

the empirical air mass methods not accounting for variations of aerosols and water vapor. For the 

multi-crystalline silicon PV module, applying a correction with any of the methods was not

significantly beneficial when compared to not applying a correction.

), and the 

CREST air-mass function, or f(AM). The second type used SEDES2 and SMARTS spectral 

irradiance models. The methods were evaluated using data recorded during June, September, and 

December 2008 at the National Renewable Energy Laboratory and during June 2008 at the 

Florida Solar Energy Center. 
vi

Table of Contents

Acknowledgements ...................................................................................................................... iii

List of Acronyms and Abbreviations......................................................................................... iv

Abstract.......................................................................................................................................... v

Table of Contents......................................................................................................................... vi

List of Tables............................................................................................................................... vii

List of Figures.............................................................................................................................. vii

1 Introduction ......................................................................................................................... 1

2 Spectral Correction Methods............................................................................................. 2

2.1 Empirical Methods Using Air Mass............................................................................. 2

2.1.1 Sandia Method .......................................................................................................... 2

2.1.2 CREST Method......................................................................................................... 4

2.2 Method Using Spectral Irradiance Models and PV Module Spectral Response .......... 5

2.2.1 Spectral Mismatch Correction .................................................................................. 5

2.2.2 SEDES2 Model ......................................................................................................... 6 

2.2.3 SMARTS Model....................................................................................................... 6

2.2.4 PV Module Spectral Response.................................................................................. 7

2.2.5 Method Variation for Multi-Junction PV Modules .................................................. 7

3 Design of Experiment and Data ......................................................................................... 9

3.1 Equipment..................................................................................................................... 9

3.2 Solar Geometry............................................................................................................. 9

3.3 Data Screening............................................................................................................ 12

3.4 Temperature Corrections............................................................................................ 13

3.5 Additional Data for Spectral Models.......................................................................... 13

3.5.1 SMARTS Model..................................................................................................... 13

3.5.2 SEDES2 Model....................................................................................................... 15

4 Results ................................................................................................................................ 16

5 Analysis of Results............................................................................................................. 27

5.1 Variations in Solar Spectrum...................................................................................... 27

5.1.1 Influence of Air Mass............................................................................................. 27

5.1.2 Influence of Aerosols.............................................................................................. 28

5.1.3 Influence of Water Vapor ....................................................................................... 29

5.1.4 Influence of Aerosol and Water Vapor Combinations ........................................... 30

5.1.5 Geographical and Seasonal Considerations............................................................ 31

5.2 Comparison of Air Mass Function and Spectral Mismatch ....................................... 32

5.3 Effects of Diffuse Radiation on AM Functions.......................................................... 35

6 Summary............................................................................................................................ 36

7 References.......................................................................................................................... 38

Appendix A: Plots...................................................................................................................... 40
vii

List of Tables

Table 2-1. Sandia AMa Polynomial Coefficients for a Multi-Crystalline Silicon and an a-Si/a-Si/aSi:Ge PV Module .......................................................................................................................3

Table 3-1. Summary of Days Used for Model Evaluations ...................................................................12

Table 3-2. Isc Correction Factors for PV Module Temperature.............................................................13

Table 3-3. Additional Input Values for the SMARTS Model ..................................................................14

Table 4-1. Results of Least-Square-Fits of Temperature Corrected Isc Versus Effective Irradiance 

When Using Various Spectral Correction Methods.............................................................26

List of Figures

Figure 2-1. Sandia AMa function for a multi-crystalline silicon and an a-Si/a-Si/a-Si:Ge PV module 

as a function of the pressure corrected air mass....................................................................................3

Figure 2-2. PVSYST spectral correction as a function of air mass and clearness for amorphous 

silicon PV modules. ....................................................................................................................................4

Figure 2-3. Spectral response for the multi-crystalline silicon PV module and the G-173-03 

reference spectrum.....................................................................................................................................8

Figure 2-4. Spectral response for the top, middle, and bottom cells of the a-Si/a-Si/a-Si:Ge PV 

module, and the G-173-03 reference spectrum........................................................................................8

Figure 3-1. Relationship between air mass (pressure corrected) and the PV module’s angle-ofincidence of the direct beam radiation for the test dates at NREL and FSEC and the PV module tilt 

angles from horizontal..............................................................................................................................10

Figure 3-2. BP Solar model SX5M (top) and UNI-SOLAR model US-11 (bottom) PV modules with 

plane-of-array pyranometer at NREL for June 7-9, 2008. PV modules are south-facing and tilted 

12° from the horizontal. The enclosure behind the PV modules contains the data logger...............11

Figure 3-3. BP Solar model SX5M and UNI-SOLAR model US-11 PV modules with plane-of-array 

pyranometer at FSEC for June 14-19, 2008. PV modules are mounted horizontal and viewed from 

the north.....................................................................................................................................................11

Figure 4-1. Temperature-corrected Isc versus POA irradiance, without spectral correction, multicrystalline silicon PV module. .................................................................................................................17

Figure 4-2. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance, 

without spectral correction, multi-crystalline silicon PV module........................................................17

Figure 4-3. Temperature-corrected Isc versus POA irradiance corrected with Sandia AMa function, 

multi-crystalline silicon PV module. .......................................................................................................18

Figure 4-4. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with Sandia AMa function, multi-crystalline silicon PV module. ........................................18

Figure 4-5. Temperature-corrected Isc versus POA irradiance corrected with spectral mismatch 

using SEDES2 model and PV module spectral response data, multi-crystalline silicon PV module.

....................................................................................................................................................................19

Figure 4-6.. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with spectral mismatch using SEDES2 model and PV module spectral response data, 

multi-crystalline silicon PV module. .......................................................................................................19

Figure 4-7. Temperature-corrected Isc versus POA irradiance corrected with spectral mismatch 

using SMARTS model and PV module spectral response data, multi-crystalline silicon PV 

module........................................................................................................................................................20

Figure 4-8. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with spectral mismatch using SMARTS model and PV module spectral response data, 

multi-crystalline silicon PV module. .......................................................................................................20
viii

Figure 4-9. Temperature-corrected Isc versus POA irradiance, without spectral correction, a-Si/aSi/a-Si:Ge PV module................................................................................................................................21

Figure 4-10. Fit slopes of individual data sets for temperature-corrected Isc versus POA 

irradiance, without spectral correction, a-Si/a-Si/a-Si:Ge PV module.................................................21

Figure 4-11. Temperature-corrected Isc versus POA irradiance corrected with Sandia AMa

function, a-Si/a-Si/a-Si:Ge PV module. ...................................................................................................22

Figure 4-12. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with Sandia AMa function, a-Si/a-Si/a-Si:Ge PV module. ....................................................22

Figure 4-13. Temperature-corrected Isc versus POA irradiance corrected with CREST AM 

function, a-Si/a-Si/a-Si:Ge PV module. ...................................................................................................23

Figure 4-14. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with CREST AM function, a-Si/a-Si/a-Si:Ge PV module.......................................................23

Figure 4-15. Temperature-corrected Isc versus POA irradiance corrected with spectral mismatch 

using SEDES2 model and PV module spectral response data, a-Si/a-Si/a-Si:Ge PV module. .........24

Figure 4-16. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with spectral mismatch using SEDES2 model and PV module spectral response data, aSi/a-Si/a-Si:Ge PV module........................................................................................................................24

Figure 4-17. Temperature-corrected Isc versus POA irradiance corrected with spectral mismatch 

using SMARTS model and PV module spectral response data, a-Si/a-Si/a-Si:Ge PV module. ........25

Figure 4-18. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with spectral mismatch using SMARTS model and PV module spectral response data, aSi/a-Si/a-Si:Ge PV module........................................................................................................................25

Figure 5-1. Comparison of spectra for air mass values 1.0 and 2.0 with the G173-03 hemispherical 

spectrum. Other model inputs are the same as that for the G173-03 hemispherical spectrum.......28

Figure 5-2. Comparison of spectra for aerosol optical depth values of 0.055 and 0.300 with the 

G173-03 hemispherical spectrum. Other model inputs are the same as that for the G173-03 

hemispherical spectrum...........................................................................................................................29

Figure 5-3. Comparison of spectra for precipitable water vapor amounts of 0.2 cm and 3.4 cm 

with the G173-03 hemispherical spectrum. Other model inputs are the same as that for the G173-

03 hemispherical spectrum......................................................................................................................30

Figure 5-4. Comparison of two spectra with the G173-03 hemispherical spectrum. One spectra 

with an aerosol optical depth of 0.055 and a precipitable water vapor amount of 0.2 cm, and the 

other spectra with an aerosol optical depth of 0.300 and a precipitable water vapor amount of 3.4 

cm. Other model inputs are the same as that for the G173-03 hemispherical spectrum. .................31

Figure 5-5. Sandia AMa function and spectral mismatch, calculated using SMARTS model, versus 

AMa for the multi-crystalline silicon PV module....................................................................................33

Figure 5-6. Sandia AMa function and spectral mismatch, calculated using SMARTS model, versus 

AMa for the a-Si/a-Si/a-Si:Ge silicon PV module....................................................................................33

Figure 5-7. Spectral mismatch for the a-Si/a-Si/a-Si:Ge PV module and each of its cells for June 

14-19 at FSEC. Performance is limited by the middle cell. ...................................................................34

Figure 5-8. Spectral mismatch for the a-Si/a-Si/a-Si:Ge PV module and each of its cells for 

December 19 and 21 at NREL. Performance is limited by the top cell. ...............................................34

Figure 5-9. Sandia AMa function and spectral mismatch values, calculated using SMARTS 

modeled direct normal spectra, versus AMa for the a-Si/a-Si/a-Si:Ge silicon PV module. ...............35
1

1 Introduction

This report presents results of a preliminary investigation of methods for correcting the shortcircuit current (Isc

The performance of a PV module is rated at Standard Reporting Conditions (SRC), where one of 

the conditions stipulates that the spectral distribution of the solar radiation conforms to the 

American Society for Testing and Materials (ASTM) standard for hemispherical spectrum, ASTM 

G 173-03.

) of photovoltaic (PV) modules for variations in the solar spectrum. Correcting 

PV output for variations in the solar spectrum is included in certain PV performance software 

applications, and is under consideration for developing energy rating standards.

1 However, PV modules perform under a variety of conditions where the spectral 

distribution varies from the ASTM spectrum. Spectral distribution is primarily influenced by the 

path length through the atmosphere and the amounts of atmospheric water vapor and aerosols. 

These factors cause diurnal, seasonal, and geographic variations in spectral distribution that can 

increase or decrease Isc

Variations in spectral distribution are more likely to impact the performance of PV modules that 

respond to a narrower wavelength range of solar radiation, such as amorphous silicon, than those 

that respond to a wider wavelength range of solar radiation, such as crystalline silicon. This work 

evaluated methods that represent two approaches for correcting for variations in spectral 

distribution: (1) empirical relationships based on air mass (AM) or path length through the 

atmosphere, and (2) use of spectral irradiance models and PV module spectral response data.

from expected values when spectral effects are not considered.

The methods were evaluated using data recorded at the National Renewable Energy Laboratory 

(NREL) and the Florida Solar Energy Center (FSEC) for a range of air mass, water vapor, and 

aerosol values under mostly clear sky conditions. The data included one-minute average values 

of Isc and PV module temperature (Tpv

The following sections of this report describe the methods for correcting for variations in 

spectrum, the design of the experiment and data, the results, and analysis of the results.

) for both a multi-crystalline silicon PV module and a

triple-junction amorphous silicon PV module, along with coincident measurements of the planeof-array (POA) solar irradiance with a pyranometer.
2

2 Spectral Correction Methods

As mentioned previously, this work considered two approaches for correcting for variations in 

spectral distribution: (1) empirical relationships based on air mass or path length through the 

atmosphere, and (2) use of spectral irradiance models with PV module spectral response data.

2.1 Empirical Methods Using Air Mass

Two empirical air mass methods were evaluated for correcting for spectral variations: (1) the 

Sandia method developed by King et al.2, 3 and (2) the Centre for Renewable Energy Systems 

Technology (CREST) method developed by Betts et al.4

2.1.1 Sandia Method

This method uses an empirically based correction factor based on air mass, with polynomial 

coefficients that are determined using one or more days of outdoor performance measurements. 

The PV module is mounted on a two-axis tracker alongside a thermopile pyranometer. Isc and 

irradiance data are recorded from sunrise to sunset, thereby providing data for determining the 

polynomial coefficients that define the correction factor function. To determine a correction 

factor with this method, air mass is determined with Equation 1 and adjusted for altitude

(pressure) with Equation 2 to give an absolute value.

[ ( ) ( ) ] 1 1.634

s 08 Zs AM cos Z 0.5057 96. − − = + ⋅ − (1)

( ) AM e AM 0.0001184 h

a = ⋅ − ⋅ (2)

where:

Zs

h = site altitude, m.

= zenith angle of the sun, degrees

The correction factor as a function of absolute air mass, or f(AMa) is then given by Equation 3.

( ) ( ) ( ) ( )

4

4 a

3

3 a

2 f AMa = a 0 + a1 ⋅ AMa + a 2 ⋅ AMa + a ⋅ AM + a ⋅ AM (3)

where:

a0, a1, a2, a3, a4

This correction assumes that variations in spectrum are predominantly influenced by the path 

length through the atmosphere, and that variations in clouds, aerosols, and water vapor with 

season or location are of less influence. The correction has a value of one for AM

= empirically derived polynomial coefficients.

a

For the two PV modules in this study, polynomial coefficients for similar PV modules of the 

same manufacturer from the Sandia module data base

= 1.5.

5 were used. The values of the coefficients 

are provided in Table 2-1 and the resulting functions of absolute air mass are shown graphically 

in Figure 2-1. The air mass functions exhibit different air mass dependencies for these two 

modules, with dependency values increasing along with increasing air mass for the multicrystalline silicon PV module. However, dependency values decreased with increasing air mass 

for the a-Si/a-Si/a-Si:Ge PV module. These results are consistent with the theory that increasing 
3

the air mass shifts the spectral distribution to longer wavelengths, which are more beneficial to 

crystalline silicon PV modules than to amorphous silicon PV modules that are more responsive 

to shorter wavelengths (especially for multi-junction amorphous silicon PV modules).

Table 2-1. Sandia AMa

PV Module

Polynomial Coefficients for a Multi-Crystalline Silicon

and an a-Si/a-Si/a-Si:Ge PV Module

a0 a1 a2 a3 a

BP SX3150

4

0.9415 0.05272800 -0.009588 0.00067629 -1.8111E-05

Uni-Solar US211.0470 0.00082115 -0.025900 0.00317360 0.00011026

Air mass function values greater than 1.0 indicate spectral distributions that are more favorable 

than for the AMa = 1.5 condition. The values also indicate that the Isc will be proportionally 

greater than expected based on the integrated spectral or broadband irradiance, such as measured 

by a thermopile pyranometer. (The converse applies if air mass function values are less than 1.0.) 

To apply a spectral correction, the broadband irradiance is multiplied by the air mass function 

value to obtain an “effective irradiance” where Isc is considered proportional to the “effective 

irradiance” if the PV temperature is constant. The “effective irradiance” may also include a 

multiplier to account for angle-of-incidence effects. But to examine spectral effects more 

precisely for this work, the analysis restricted angle-of-incidences to less than 50° where angleof-incidence effects are small or nonexistent.

Figure 2-1. Sandia AMa

Sandia has developed air mass polynomial coefficients for numerous PV modules and 

technologies, and several PV system design and/or performance software applications use this 

function for a multi-crystalline silicon and an a-Si/a-Si/a-Si:Ge PV module

as a function of the pressure corrected air mass.

0 1 2 3 4 5 6

Air Mass (pressure corrected)

0.6

0.7

0.8

0.9

1.0

1.1

S

a

n

dia

A

Ma F

u

n

ctio

n

m-Si

a-Si/a-Si/a-Si:Ge
4

method to correct for variations in spectral distribution. These software applications include: PVDesignPro by Maui Solar Energy Software Corporation6

; NREL’s Solar Advisor Model (SAM)7; 

and the University of Wisconsin-Madison’s 5-Parameter model8 which is used by the California 

Energy Commission’s PV Calculator.9

2.1.2 CREST Method

Unlike the other two applications, the 5-Parameter model 

uses coefficients for a multi-crystalline PV module for all PV modules and technologies because 

the results obtained from using module and technology-specific coefficients did not show 

significant differences.

This method also uses an empirically based correction factor. Using a year of spectroradiometer 

measurements for a south-facing latitude-tilt (52°) orientation, CREST parameterized the 

spectral correction as a function of air mass (optical, per Eqn. 1) and clearness, where clearness 

is the ratio of global radiation to the global radiation for clear skies. This approach for correcting 

for spectral distribution is used by the PV system software package PVSYST.

10 For amorphous 

silicon, the PVSYST spectral correction is shown in Figure 2-2. The same correction for 

amorphous silicon can also be selected in PVSYST for cadmium telluride (CdTe) PV modules. 

Betts et al.4 at CREST did not see an improvement in error statistics when applying spectral 

corrections for crystalline silicon PV modules; consequently, PVSYST does not apply spectral 

corrections for these PV modules.

Figure 2-2. PVSYST spectral correction as a function of air mass and clearness for amorphous 

silicon PV modules.

Because only data recorded under primarily clear skies were used for this study, only the 

empirical function for a clear sky (Ktcd = 1.0) was evaluated. It is similar to the Sandia air mass 

function in that it has a value of 1.0 for an air mass of 1.5, but different in that it is a function of 
 5 

optical air mass instead of pressure-corrected air mass and its rate of change with respect to air 

mass is only about half that of the Sandia method. For cloudy skies, the values of the function are 

increased. This seems reasonable because the presence of clouds shifts the diffuse spectrum to 

shorter wavelengths,11

For ease of implementation, and to provide the spectral correction factor as a function of air mass 

(optical) for clear skies, the information in Figure 2-2 was digitized as:

 which would provide a more favorable spectrum for amorphous silicon 

PV modules.

( ) ( )

2 f AM = 1.0491− 0.031243⋅ AM − 0.000948⋅ AM (4)

2.2 Method Using Spectral Irradiance Models and PV Module Spectral Response

Another approach for accounting for spectral variations is to model the solar spectrum, and use it 

with the PV module’s spectral response to calculate a spectral mismatch correction, similar to 

principles developed by Osterwald12 for translating device performance to reference conditions. 

This method more directly addresses the influence of aerosols and water vapor on the solar 

spectrum, but introduces additional error sources because of uncertainties associated with the 

modeled solar spectrum and the PV module spectral response data. This method was applied 

using two different spectral irradiance models: (1) SEDES213 and (2) SMARTS.

14

 This method is 

fairly complex and computationally intense, and it isn’t currently used in PV system design or 

performance software. However, it has been recommended in the past to model the spectral 

irradiance with SEDES2 for a proposed energy rating methodology.

2.2.1 Spectral Mismatch Correction

15

The general form of the spectral mismatch correction M is represented by Equation 5. A value of 

M = 1.0 indicates that there is no spectral mismatch with regard to the reference spectrum. A 

value greater than 1.0 indicates that the spectral distribution of the incident radiation for the 

device being tested is more favorable than if the incident radiation were the reference spectral 

condition; consequently, the Isc

∫ λ ⋅ λ λ

∫ λ ⋅ λ λ

⋅

∫ λ ⋅ λ λ

∫ λ ⋅ λ λ

= d

c

ref t

d

c

inc t

b

a

inc r

b

a

ref r

E ( ) S ( )d

E ( ) S ( )d

E ( ) S ( )d

E ( ) S ( )d

M

is increased proportionally (the converse applies for values less 

than 1.0). 

(5)

where:

λ = wavelength

a,b = integration limits, should include response range of reference device

c,d = integration limits, should include response range of device being tested

Eref

E

(λ) = spectral irradiance for reference condition

inc

S

(λ) = spectral irradiance incident device being tested

r

S

(λ) = spectral response of reference device

t(λ) = spectral response of device being tested.
 6 

SEDES2 is an adaption of the model SEDES1 developed by Nann and Riordan.11 SEDES2 more 

readily calculates solar spectral irradiance for clear and cloudy skies from site-specific data.

Meteorological inputs to the model are: global horizontal irradiance; diffuse horizontal or direct 

normal irradiance; dew point temperature, or relative humidity and dry bulb temperature; and 

atmospheric pressure or site elevation. The clear-sky approximation is based on SPCTRAL216

NREL’s SEDES2 code models spectra from 300 to 2,500 nanometers (nm). This upper limit is 

less than the upper limit of the Kipp & Zonen CM11 pyranometer (spectral range from 310 nm 

to 2,800 nm) which is used for the reference device in Equation 5. Consequently, when using the 

SEDES2 spectra an error is introduced because any variations in spectral distribution in the 

2,500-2,800 nm range are not addressed. However, the error is insignificant because of the small 

amount of solar radiation within that range (only 0.04 W/m

and then, depending on the broadband irradiance values input to the model, cloud cover 

modifiers are applied to the spectral irradiance. The cloud cover modifiers were derived from 

measured spectra.

2

Derived from Equation 5, Equation 6 is the formula for M for calculating spectral mismatch 

when using the SEDES2 model and the Kipp & Zonen CM11 pyranometer for the reference 

device. By assuming the black detector of the pyranometer has a constant spectral response 

within its spectral range, the S

when integrating the spectral 

irradiance of the G173-03 hemispherical spectrum from 2,500 nm to 2,800 nm). 

r(λ) parameter may be removed from the first term of Equation 5 if 

the integration limits are within the response range of the pyranometer. Furthermore, the 

numerator of the first term may be replaced by the integrated solar irradiance of the G 173-03 

reference spectrum from 310 to 2500 nm, or 992.39 W/m2

∫ λ ⋅ λ λ

∫ λ ⋅ λ λ

⋅

∫ λ λ

= 2500

300

G173 t

2500

300

SEDES2 t

2500

310

SEDES2

2

E ( ) S ( )d

E ( ) S ( )d

E ( )d

992.39W / m M

. 

(6)

where:

λ = wavelength, nm

EG173(λ) = G173-03 hemispherical spectrum, W m-2nm

E

-1

SEDES2(λ) = SEDES2 spectral irradiance, W m-2

 nm-1

Similar to the use of the Sandia or CREST correction factor, multiplying the broadband 

irradiance measurement of the pyranometer by M from Equation 6 provides an “effective 

irradiance” that is corrected for variation in spectral distribution from the reference spectrum.

. 

2.2.3 SMARTS Model

The Simple Model of the Atmospheric Radiative Transfer of Sunshine Version 2 (SMARTS)

was also used to model spectral irradiance for calculating the spectral mismatch correction. 

Developed by Gueymard,17 SMARTS provides direct normal, global and diffuse horizontal, and 

global tilted spectral irradiances for clear skies and for 2002 wavelengths from 280 to 4,000 nm. 

It has been shown to be more accurate than the SPCTRAL2 model, and as accurate as more 

complex models such as Air Force MODTRAN.

18

2.2.2 SEDES2 Model
 7 

SMARTS allows nearly 30 input parameters for defining atmospheric constituents and site and 

application conditions. This work uses SMARTS Version 2.9.5. An earlier Version 2.9.2 was 

used to develop the G173-03 reference solar spectral irradiances. Compared to Version 2.9.2, the 

primary difference is that Version 2.9.5 allows the use of a more up-to-date extraterrestrial 

spectrum. This increases the spectral irradiance by a few percent from 400 nm to 550 nm and 

decreases it by a few percent from 550 nm to 700 nm and from 850 to 1,300 nm. Algorithms for 

diffuse irradiance were also streamlined in Version 2.9.5.

Similar to the derivation of the spectral mismatch correction when using the SEDES2 model, 

Equation 7 is the formula for M for calculating spectral mismatch when using the SMARTS

model and the Kipp & Zonen CM11 pyranometer for the reference device. The numerator of the 

first term, 992.43 W/m2

∫ λ ⋅ λ λ

∫ λ ⋅ λ λ

⋅

∫ λ λ

= 4000

280

G173 t

4000

280

SMARTS2 t

2800

310

SMARTS2

2

E ( ) S ( )d

E ( ) S ( )d

E ( )d

992.43W / m M

, is the integrated solar irradiance of the G 173-03 reference spectrum 

from 310 to 2,800 nm, which includes the complete spectral range of the Kipp and Zonen 

pyranometer.. 

(7)

where:

ESMARTS(λ) = SMARTS spectral irradiance, W m-2nm-1

2.2.4 PV Module Spectral Response

.

The spectral response data for the multi-crystalline PV module and the a-Si/a-Si/a-Si:Ge PV 

module were selected from previous measurements at NREL, rather than from performing 

spectral response measurements of the individual PV modules. The data were judged as being 

representative of the technology and manufacture. Figures 2-3 and 2-4 provide the spectral 

response data used for the multi-crystalline PV module and the a-Si/a-Si/a-Si:Ge PV module, 

respectively.

2.2.5 Method Variation for Multi-Junction PV Modules

For series-connected multi-junction PV modules where one junction may limit the current of 

another, the Isc of the PV module is considered to be the Isc provided by the junction that 

produces the least current. Consequently, for the a-Si/a-Si/a-Si:Ge PV module, the second term 

of Equations 6 and 7 is evaluated by using the spectral response of the cell that gives the smallest 

numerator (current at test conditions) for the numerator. The spectral response of the cell that 

gives the smallest denominator (current at reference conditions) is used for the denominator. 

Depending on test conditions, the numerator and denominator may require spectral responses of 

different cells.
8

Figure 2-3. Spectral response for the multi-crystalline silicon PV module and 

the G-173-03 reference spectrum.

Figure 2-4. Spectral response for the top, middle, and bottom cells of the a-Si/a-Si/a-Si:Ge PV 

module, and the G-173-03 reference spectrum.

0 500 1000 1500 2000 2500

Wavelength (nm)

0.0

0.5

1.0

1.5

2.0

S

p

e

ctral Irra

dia

n

c

e (W/m2/n

m)

G 173-03 Global Spectrum

m-Si Spectral Response

0.0

0.5

1.0

1.5

2.0

S

p

e

ctral R

e

s

p

o

n

s

e (A/W)

0 500 1000 1500 2000 2500

Wavelength (nm)

0.0

0.5

1.0

1.5

2.0

S

p

e

ctral Irra

dia

n

c

e (W/m2/n

m)

G 173-03 Global Spectrum

Top Cell Spectral Response

Middle Cell Spectral Response

Bottom Cell Spectral Response

0.0

0.2

0.4

0.6

0.8

1.0

S

p

e

ctral R

e

s

p

o

n

s

e (A/W)
9

3 Design of Experiment and Data

Impacts of the spectral distribution on PV module Isc were measured to show geographic 

variations (i.e., NREL in Golden, Colorado versus FSEC in Cocoa, Florida) and seasonal 

variations (summer, fall, and winter at NREL). To provide consistent measurements, the same 

PV modules and data acquisition equipment were used for both locations and all time periods. 

Additionally, data were screened to remove times with unstable irradiance and times when 

reflection losses at high incidence angles of the direct beam radiation could be confused with 

changes in Isc

3.1 Equipment

caused by variations in spectral distribution. 

The two PV modules used for the experiment were:

• A multi-crystalline silicon PV module – BP Solar Model SX5M, S/N C1020522 2146292

• An a-Si/a-Si/a-Si:Ge PV module – UNI-SOLAR Model US-11, S/N US-11-015754.

The a-Si/a-Si/a-Si:Ge PV module had been sun-exposed for several years; consequently, the 

initial light-induced degradation occurred prior to this experiment. Seasonal changes in the 

efficiency of amorphous silicon PV modules occur from temperature-induced annealing, but the 

changes primarily affect the fill-factor, not the Isc.

19

I

Furthermore, the deployment times were 

minimized in order to minimize any exposure or aging effects.

sc

3.2 Solar Geometry

values were measured with current shunts connected to the module leads. PV module 

temperatures were measured with type T “cement-on” thermocouples taped to the module backsurface, near the center. The plane-of-array irradiance was measured with a Kipp & Zonen 

CM11 pyranometer. A Campbell Scientific datalogger performed measurements every second 

and stored the data as one-minute averages.

The PV modules were deployed with a south-facing fixed-tilt orientation, with the tilt angle 

adjusted, for a particular period and location, so that the angle-of-incidence of the direct beam 

radiation would be near zero at solar noon. This was to ensure that the sun’s position with respect 

to the PV modules was as similar as possible for all locations and test periods, thereby 

facilitating the comparison of test data.
10

Figure 3-1 presents the relationship between the pressure-corrected air mass and the PV 

module’s angle-of-incidence of the direct beam radiation. Except for the December dates, 

adjusting the tilt angle provided very similar air mass versus angle-of-incidence relationships. In 

Figure 3-1, the distance between symbols represents one hour, with the leftmost symbol 

coinciding with solar noon.

Figure 3-1. Relationship between air mass (pressure corrected) and the PV module’s 

angle-of-incidence of the direct beam radiation for the test dates at 

NREL and FSEC and the PV module tilt angles from horizontal.

Figures 3-2 and 3-3 show the PV modules deployed at NREL June 7-9, 2008 and at FSEC June 

14-19, 2008. To have similar solar geometries with respect to the PV modules, the tilt angles for 

the two deployments differ by 12° to accommodate their difference in latitude.

0 20 40 60 80 100

Angle-of-Incidence of Direct Beam Radiation (°)

0

2

4

6

8

10

Air M

a

s

s (pre

s

s

ure

c

orre

cte

d)

Tilt Angles and Dates of Data Collection

Jun 7, 8, and 9 at NREL, 12° tilt

Jun 14-19 at FSEC, 0° tilt

Jun 29, 30 at NREL, 12° tilt

Sep 15, 17 at NREL, 40° tilt

Dec 19, 21 NREL, 60° tilt
11

Figure 3-2. BP Solar model SX5M (top) and UNI-SOLAR model US-11 (bottom) PV modules with 

plane-of-array pyranometer at NREL for June 7-9, 2008. PV modules are south-facing and tilted

12° from the horizontal. The enclosure behind the PV modules contains the data logger.

Figure 3-3. BP Solar model SX5M and UNI-SOLAR model US-11 PV modules with 

plane-of-array pyranometer at FSEC for June 14-19, 2008. PV modules are 

mounted horizontal and viewed from the north.
12

3.3 Data Screening

Prior to analysis, the data were screened to remove data with the potential to create errors in the 

results. The removed data included: (a) data with an angle-of-incidence of direct beam radiation 

greater than 50°, (b) data with a plane-of-array irradiance below 600 W/m2 or greater than 1,150 

W/m2, and (c) data where the plane-of-array irradiance had changed by more than 5 W/m2

For angle-of-incidences greater than 50°, I

from 

the previous minute’s value.

sc is reduced because of increased reflection losses. By 

limiting data to angle-of-incidences of 50° or less, effects of variations in spectral distribution on 

Isc

Calibration records for the pyranometer show its responsitivity varying less than 1% for anglesof-incidence of 50° or less, using both morning and afternoon calibration data. The “b” and “c”

criteria ensured that data are for mostly clear-sky conditions and conditions are reasonably stable 

with respect to the plane-of-array irradiance. A rapidly changing irradiance might impact results 

because the response of the thermopile detector in the pyranometer is significantly slower than 

that of the PV modules.

may be considered separately from the effects of angle-of-incidence, which can be 

considerably larger. This also ensured that irradiance measurements using the Kipp & Zonen 

CM11 pyranometer were accurate. 

The deployments at NREL afforded the opportunity to collect data for a two- to three-week 

period, and then select two or three days that typified clear-sky conditions, to which the 

screening criteria were then applied. The FSEC deployment was of shorter duration, and 

screening criteria were applied to all recorded data. Table 3-1 summarizes the measurement days 

selected for model evaluation. Appendix A shows data passing selection and screening criteria.

Table 3-1. Summary of Days Used for Model Evaluations

Location Period Tilt Angle 

(°)

NREL June 7-9, 2008 12

FSEC June 14-19, 2008 0

NREL June 29-30, 2008 12

NREL Sept 15 and17, 

2008

40

NREL Dec 19 and 21, 

2008

60
13

3.4 Temperature Corrections

Besides spectral and angle-of-incidence effects, Isc is also dependent on PV module temperature. 

To prevent temperature effects from impacting the study, the Isc measurements were corrected 

for temperature by using Equation 8 to translate Isc values at the measured PV module 

temperature to Isc





 



















 ⋅ − ° ° = ÷ + α + E 25 C

1000W / m

2.5 C I I 1 T 2 sc25 sc pv

values for a temperature of 25°C.

(8)

where:

α = Isc correction factor for PV module temperature, °C

T

-1

pv

E = plane-of-array irradiance, W/m

= PV module back-surface temperature, °C

2

In Equation 8, the middle term within the parentheses accounts for the temperature gradient that 

exists from the PV module back-surface to the PV cell. Values of α for similar PV modules of 

the same manufacturer from the Sandia module data base

.

5

Table 3-2. I

were used. The values of the 

coefficients are provided in Table 3-2.

sc

PV Module

Correction Factors for PV Module Temperature

Technology α (°C-1

BP SX3150

)

multi-crystalline silicon 0.000404

Uni-Solar US21a-Si/a-Si/a-Si:Ge 0.000850

3.5 Additional Data for Spectral Models

The empirical air mass methods may be implemented by calculating the sun’s position and 

resulting air mass. Sun position may be determined from the site coordinates and the date and 

time. Air mass is determined from Equation 1, or with Equation 2 if pressure corrected. The 

methods using the spectral irradiance models require additional information for modeling the 

spectral irradiance. This additional information is described in the following paragraphs.

3.5.1 SMARTS Model

Like the air mass methods, the spectral irradiance models use the site coordinates and the date 

and time to calculate the sun’s position. SMARTS allows additional input parameters for 

defining atmospheric constituents and site and application conditions. Besides date and time, the

inputs that we used with SMARTS Version 2.9.5 are listed in Table 3-3. 
14

Table 3-3. Additional Input Values for the SMARTS Model

Parameter June 7-9, 

2008

June 14-19, 

2008

June 29-30, 

2008

Sept 15 and 

17, 2008

Dec 19 and 

21, 2008

Location NREL FSEC NREL NREL NREL

Latitude (°N) 39.74 28.39 39.74 39.74 39.74

Longitude (°W) 105.18 80.75 105.18 105.18 105.18

Altitude (km) 1.80 0.01 1.80 1.80 1.80

Time Zone -7 -5 -7 -7 -7

Reference Atmosphere* U.S. Standard U.S. Standard U.S. Standard U.S. Standard U.S. Standard

Solar Constant* (W/m2) 1367 1367 1367 1367 1367

Ozone*(atm-cm) 0.3438 0.3438 0.3438 0.3438 0.3438

Carbon Dioxide* (ppm) 370 370 370 370 370

Gaseous Absorption* Default 

Vertical Profile

Default 

Vertical Profile

Default 

Vertical 

Profile

Default Vertical 

Profile

Default Vertical 

Profile

Extraterrestrial Spectrum Option =0, 

new synthetic

Option =0, 

new synthetic

Option =0, 

new synthetic

Option =0, new 

synthetic

Option =0, new 

synthetic

Aerosol Model* S&F Rural S&F Rural S&F Rural S&F Rural S&F Rural

Aerosol Optical Depth at 

500 nm 0.060 0.300 0.105 0.100 0.055

Precipitable Water Vapor 

(cm) 0.7 3.4 1.1 1.2 0.2

PV Module Tilt(°) 12 0 12 40 60

PV Module Azimuth (°) 180 180 180 180 180

Far-Field Albedo File 51 – Dry long 

grass

64 – Open sea 

water

51 – Dry long 

grass

51 – Dry long 

grass

30 – Granular 

snow

Near-Field Albedo File 51 – Dry long 

grass

29 – Green 

rye grass

51 – Dry long 

grass

51 – Dry long 

grass

30 – Granular 

snow

Receiver Slope, View, 

and Limit Half-Angles*(°) 0, 2.9, 0 0, 2.9, 0 0, 2.9, 0 0, 2.9, 0 0, 2.9, 0

*These parameters are the same as those for the G173-03 hemispherical spectrum.
15

In Table 3-3, parameters that are the same as for the G173-03 hemispherical spectrum are 

identified with an asterisk. Precipitable water vapor amounts were determined from the daytime 

average dew point temperatures and the method of Wright et al.,20 except for the December 

NREL data, which are precipitable water data that were available from NREL’s Solar Radiation 

Research Laboratory21 (SRRL). Aerosol optical depth data for the NREL location and test 

periods were also from SRRL, and average daytime values for the period. For the FSEC location, 

no aerosol optical depth data were available. Consequently, it was estimated using information 

from the National Solar Radiation Data Base.22

3.5.2 SEDES2 Model

In hindsight, a far-field albedo for the FSEC 

location should have included a mix of green grass or trees and water, rather than just water. The 

near-field albedo is of no consequence for the horizontal PV modules at FSEC.

Compared to SMARTS, SEDES2 has a reduced set of allowable inputs. Besides the site 

coordinates and the date and time to calculate the sun’s position, the input requirements are:

global horizontal irradiance; diffuse horizontal or direct normal irradiance; and dew point 

temperature, or relative humidity and dry bulb temperature. For NREL, nearby SRRL data were 

used to provide global horizontal, diffuse horizontal, and direct normal irradiance data. These 

data were not available for FSEC; consequently, the SEDES2 model was not evaluated using the 

FSEC data. In place of dew point temperature, SEDES2 code was modified to use the 

precipitable water vapor amounts from Table 3-3, instead of calculating it internal to SEDES2

from dew-point temperature. This allowed identical precipitable water vapor amounts to be used 

by both SMARTS and SEDES2.
16

4 Results

For the data that met screening criteria, air mass correction factors were determined using 

Equations 3 and 4 for the Sandia and CREST methods, respectively, and spectral mismatch 

corrections were determined using Equations 6 and 7 and the SEDES2 and SMARTS models, 

respectively. For each method and data point, the plane-of-array irradiance was then multiplied 

by the resulting factor or correction to determine an “effective” irradiance.

The methods were compared by performing linear least-square fits through the origin for the 

temperature-corrected Isc

Figures 4-1 through 4-18 present the results graphically. Odd numbered figures show plots with 

data displayed using all data sets and the resulting regression line and RMSE of the fit. Even 

numbered figures show the same regression line as well as the regression lines for the leastsquare fits of the individual data sets. The slopes of the regression lines for the individual data 

sets are provided as the percent change from the slope of the regression line when using all data. 

Differences in the slopes of the regression lines may indicate geographical or seasonal 

dependencies. This information is summarized in Table 4-1.

values versus the “effective” irradiances. The least-square fits were 

performed for the five individual data sets and also for the complete data set consisting of all test 

data. The root-mean-square-error (RMSE) of the complete data set was used to judge overall 

performance, and differences in the slopes of the regression lines for the five individual data sets 

were an indication of how well the method accommodated geographical and seasonal differences 

in the data sets. To judge the benefit of the methods relative to not performing a spectral 

correction, similar least-square fits were also performed using irradiances measured by the 

pyranometer with no correction applied.

For the multi-crystalline silicon PV module, the method using the SEDES2 model yielded the 

smallest RMSE and the smallest range of slope differences for the least-square fits of the 

individual data sets, which was a small improvement over not applying a spectral correction. The 

method using the SMARTS model was a close second. The method using the Sandia f(AMa

For the a-Si/a-Si/a-Si:Ge PV module, all methods provided some improvement. The SEDES2 

and SMARTS performed best, and about equal to each other. The Sandia and CREST air mass 

methods performed about the same as each other, but compared to the methods using the 

SEDES2 and SMARTSs models, they had greater RMSE and the differences in the slopes of the 

regression lines of the individual data sets were larger. As described previously, results for the 

SEDES2 model do not include the Florida data because that data set did not include all 

parameters required for the SEDES2 model. However, it doesn’t appear that this compromised 

the results. Results determined for the SMARTS model, with and without the FSEC data, were 

the same. Both the SEDES2 and SMARTS model exhibited similar results in that the fit slope for 

the June 7-9 data at NREL was the smallest, and the fit slope for the June 29-30 data at NREL 

was the largest.

) 

function yielded errors that were somewhat greater than when no corrections were applied. 
17

Figure 4-1. Temperature-corrected Isc versus POA irradiance, without 

spectral correction, multi-crystalline silicon PV module.

Figure 4-2. Fit slopes of individual data sets for temperature-corrected Isc

600 800 1000 1200

POA Irradiance (W/m2)

0.16

0.20

0.24

0.28

0.32

0.36

Is

c25 (A)

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Through Origin: Y = 0.0002884 * X

Number of data points used = 2727

Average X = 945.5

Average Y = 0.2728

RMSE = 0.0029 A or 1.1% of average

versus POA irradiance, 

without spectral correction, multi-crystalline silicon PV module.

600 800 1000 1200

POA Irradiance (W/m2)

0.16

0.20

0.24

0.28

0.32

0.36

Is

c25 (A)

All Data

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Slope Relative to All Data Slope

-1.3%

+0.9%

+0.1%

+0.7%

-0.4%
18

Figure 4-3. Temperature-corrected Isc versus POA irradiance corrected with Sandia AMa function, 

multi-crystalline silicon PV module.

Figure 4-4. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with Sandia AMa

600 800 1000 1200

f(AMa) x POA Irradiance (W/m2)

0.16

0.20

0.24

0.28

0.32

0.36

Is

c25 (A)

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Through Origin: Y = 0.0002905 * X

Number of data points used = 2727

Average X = 938.8

Average Y = 0.2728

RMSE = 0.00472 A or 1.7% of average

function, multi-crystalline silicon PV module.

600 800 1000 1200

f(AMa) x POA Irradiance (W/m2)

0.16

0.20

0.24

0.28

0.32

0.36

Is

c25 (A)

All Data

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Slope Relative to All Data Slope

-0.3%

+1.2%

+1.1%

+1.0%

-2.4%
19

Figure 4-5. Temperature-corrected Isc versus POA irradiance corrected with spectral mismatch 

using SEDES2 model and PV module spectral response data, multi-crystalline silicon PV module.

Figure 4-6.. Fit slopes of individual data sets for temperature-corrected Isc

600 800 1000 1200

M x POA Irradiance (W/m2)

0.16

0.20

0.24

0.28

0.32

0.36

Is

c25 (A)

Jun 7, 8, 9 at NREL

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Results Through Origin: Y = 0.0002924 * X

Number of data points used = 2375

Average X = 940.5

Average Y = 0.2750

RMSE = 0.0022 A or 0.8% of average

versus POA irradiance 

corrected with spectral mismatch using SEDES2 model and PV module spectral response data, 

multi-crystalline silicon PV module.

600 800 1000 1200

M x POA Irradiance (W/m2)

0.16

0.20

0.24

0.28

0.32

0.36

Is

c25 (A)

All Data

Jun 7, 8, 9 at NREL

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Slope Relative to All Data Slope

-0.4%

+0.5%

+0.2%

-0.3%
20

Figure 4-7. Temperature-corrected Isc versus POA irradiance corrected with spectral mismatch 

using SMARTS model and PV module spectral response data, multi-crystalline silicon PV module.

Figure 4-8. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with spectral mismatch using SMARTS model and PV module spectral response data, 

multi-crystalline silicon PV module.

600 800 1000 1200

M x POA Irradiance (W/m2)

0.16

0.20

0.24

0.28

0.32

0.36

Is

c25 (A)

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Through Origin: Y = 0.0002930 * X

Number of data points used = 2727

Average X = 930.8

Average Y = 0.2728

RMSE = 0.0028 A or 1.0% of average

600 800 1000 1200

M x POA Irradiance (W/m2)

0.16

0.20

0.24

0.28

0.32

0.36

Is

c25 (A)

All Data

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Slope Relative to All Data Slope

+0.0%

+0.4%

+0.8%

+0.1%

-1.0%
21

Figure 4-9. Temperature-corrected Isc versus POA irradiance, without spectral correction, a-Si/aSi/a-Si:Ge PV module.

Figure 4-10. Fit slopes of individual data sets for temperature-corrected Isc versus POA 

irradiance, without spectral correction, a-Si/a-Si/a-Si:Ge PV module.

600 800 1000 1200

POA Irradiance (W/m2)

0.40

0.60

0.80

1.00

Is

c25 (A)

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Through Origin: Y = 0.0007467 * X

Number of data points used = 2727

Average X = 945.5

Average Y = 0.706

RMSE = 0.027 A or 3.8% of average

600 800 1000 1200

POA Irradiance (W/m2)

0.40

0.60

0.80

1.00

Is

c25 (A)

All Data

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Slope Relative to All Data Slope

-2.3%

+3.8%

+2.8%

+1.8%

-5.5%
22

Figure 4-11. Temperature-corrected Isc versus POA irradiance corrected with 

Sandia AMa function, a-Si/a-Si/a-Si:Ge PV module.

Figure 4-12. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with Sandia AMa

600 800 1000 1200

f(AMa) x POA Irradiance (W/m2)

0.40

0.60

0.80

1.00

Is

c25 (A)

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Through Origin: Y = 0.0007395 * X

Number of data points used = 2712

Average X = 956.6

Average Y = 0.708

RMSE = 0.016 A or 2.3% of average

function, a-Si/a-Si/a-Si:Ge PV module.

600 800 1000 1200

f(AMa) x POA Irradiance (W/m2)

0.40

0.60

0.80

1.00

Is

c25 (A)

All Data

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Slope Relative to All Data Slope

-4.0%

+2.9%

+1.0%

+0.9%

-1.4%
23

Figure 4-13. Temperature-corrected Isc versus POA irradiance corrected with 

CREST AM function, a-Si/a-Si/a-Si:Ge PV module.

Figure 4-14. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with CREST AM function, a-Si/a-Si/a-Si:Ge PV module.

600 800 1000 1200

f(AM) x POA Irradiance (W/m2)

0.40

0.60

0.80

1.00

Is

c25 (A)

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Through Origin: Y = 0.0007480 * X

Number of data points used = 2711

Average X = 945.5

Average Y = 0.708

RMSE = 0.017 A or 2.4% of average

600 800 1000 1200

f(AM) x POA Irradiance (W/m2)

0.40

0.60

0.80

1.00

Is

c25 (A)

All Data

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Slope Relative to All Data Slope

-3.5%

+2.4%

+1.4%

+1.3%

-2.2%
24

Figure 4-15. Temperature-corrected Isc versus POA irradiance corrected with spectral mismatch 

using SEDES2 model and PV module spectral response data, a-Si/a-Si/a-Si:Ge PV module.

Figure 4-16. Fit slopes of individual data sets for temperature-corrected Isc

600 800 1000 1200

M x POA Irradiance (W/m2)

0.40

0.60

0.80

1.00

Is

c25 (A)

Jun 7, 8, 9 at NREL

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Through Origin: Y = 0.0007478* X

Number of data points used = 2348

Average X = 952.0

Average Y = 0.712

RMSE = 0.012 A or 1.7% of average

versus POA irradiance 

corrected with spectral mismatch using SEDES2 model and PV module spectral 

response data, a-Si/a-Si/a-Si:Ge PV module.

600 800 1000 1200

M x POA Irradiance (W/m2)

0.40

0.60

0.80

1.00

Is

c25 (A)

All Data

Jun 7, 8, 9 at NREL

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Slope Relative to All Data Slope

-2.2%

+1.6%

-0.6%

-0.9%
25

Figure 4-17. Temperature-corrected Isc versus POA irradiance corrected with spectral mismatch 

using SMARTS model and PV module spectral response data, a-Si/a-Si/a-Si:Ge PV module.

Figure 4-18. Fit slopes of individual data sets for temperature-corrected Isc versus POA irradiance 

corrected with spectral mismatch using SMARTS model and PV module spectral response data, aSi/a-Si/a-Si:Ge PV module.

600 800 1000 1200

M x POA Irradiance (W/m2)

0.40

0.60

0.80

1.00

Is

c25 (A)

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Through Origin: Y = 0.0007354 * X

Number of data points used = 2704

Average X = 962.7

Average Y = 0.708

RMSE = 0.013 A or 1.8% of average

600 800 1000 1200

M x POA Irradiance (W/m2)

0.40

0.60

0.80

1.00

Is

c25 (A)

All Data

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Fit Slope Relative to All Data Slope

-2.2%

-0.6%

+1.5%

-0.7%

+0.7%
26

Table 4-1. Results of Least-Square-Fits of Temperature Corrected Isc

Spectral Correction 

Method

Versus Effective Irradiance 

When Using Various Spectral Correction Methods.

Multi-Crystalline Silicon

PV Module

a-Si/a-Si/a-Si:Ge

PV module

RMSE (%) Slope Delta 

(%)*

RMSE (%) Slope Delta 

(%)*

None 1.1 -1.3 to 0.9 3.8 -5.5 to 3.8

Sandia f(AMa) 1.7 -2.4 to 1.2 2.3 -4.0 to 2.9

CREST f(AM) -- -- 2.4 -3.5 to 2.4

SEDES2 w/ Spectral 

Response Data

0.8 -0.4 to 0.5 1.7 -2.2 to 1.6

SMARTS w/Spectral 

Response Data

1.0 -1.0 to 0.8 1.8 -2.2 to 1.5

* Difference of slope of regression line for individual data set from that when using all 

data.
27

5 Analysis of Results

From the results presented in Section 4, the methods using spectral irradiance models and PV 

module spectral response data performed better than the empirical air mass methods. This is 

attributed to the spectral models accounting for the influence of aerosols and water vapor on the 

distribution of the spectral irradiance, but also may be a consequence of how the empirical air 

mass functions are determined and implemented.

5.1 Variations in Solar Spectrum

For clear skies, variations in spectrum are predominantly influenced by the air mass, aerosols, 

and water vapor. To illustrate their effects, the SMARTS model was used to model spectra to 

compare with the G173-03 hemispherical spectrum. The same inputs used to model the G173-03 

hemispherical spectrum were used, except air mass, aerosol, and water vapor amounts were 

varied singularly and in combination to show their effects. Like the G173-03 hemispherical 

spectrum, the spectra modeled with SMARTS include both the direct and diffuse solar radiation 

components.

5.1.1 Influence of Air Mass

Figure 5-1 illustrates spectra for air mass values of 1.0 and 2.0 for comparison with the G173-03 

hemispherical spectrum with air mass of 1.5. Other model inputs are the same, including a sunfacing 37° tilted-surface; consequently, the angle-of-incidence of direct beam radiation to the PV 

module surface is increased and the hemispherical radiation is decreased for both air mass values 

of 1.0 and 2.0. Nevertheless, the change in spectral distribution from shorter to longer 

wavelengths with increasing air mass is evident. This is the fundamental reasoning for the 

empirical air mass methods.
28

Figure 5-1. Comparison of spectra for air mass values 1.0 and 2.0 with the G173-03 hemispherical 

spectrum. Other model inputs are the same as that for the G173-03 hemispherical spectrum.

5.1.2 Influence of Aerosols

Figure 5-2 illustrates spectra for aerosol optical depths of 0.055 and 0.300 for comparison with 

the G173-03 hemispherical spectrum with aerosol optical depth of 0.084. The value of 0.055 

corresponds to the NREL December 19 and 21 data, and the value of 0.300 corresponds to the 

FSEC June 14-19 data. Compared to the G173-03 spectrum, decreasing the aerosol optical depth 

to 0.055 increased the broadband radiation by about 12 W/m2, which mostly occurred over 

wavelengths less than 500 nm. Increasing the aerosol optical depth to 0.300 decreased the 

broadband radiation by about 40 W/m2

0 500 1000 1500 2000 2500

Wavelength (nm)

0.0

0.5

1.0

1.5

2.0

S

p

e

ctral Irra

dia

n

c

e (W/m2/n

m)

G 173-03 AM 1.5, incidence = 11.2°, 1000.4 W/m2

AM 1.0, incidence = 37.0°, 931.1 W/m2

AM 2.0, incidence = 23.1°, 867.3 W/m2

, which is noticeable over a broader range of wavelengths, 

but primarily for wave lengths less than 800 nm.
29

Figure 5-2. Comparison of spectra for aerosol optical depth values of 0.055 and 0.300

with the G173-03 hemispherical spectrum. Other model inputs are the same as 

that for the G173-03 hemispherical spectrum.

5.1.3 Influence of Water Vapor

Figure 5-3 illustrates spectra for precipitable water vapor amounts of 0.2 cm and 3.4 cm for 

comparison with the G173-03 hemispherical spectrum with precipitable water vapor amount of 

1.4164 centimeters (cm). The value of 0.2 cm corresponds to the NREL December 19 and 21 

data, and the value of 3.4 cm corresponds to the FSEC June 14-19 data. Compared to the G173-

03 spectrum, decreasing the precipitable water vapor to 0.2 cm increased the broadband radiation 

by about 83 W/m2. Increasing the precipitable water vapor to 3.4 cm decreased the broadband 

radiation by about 46 W/m2

Water vapor absorption bands are centered at 724; 824; 938; 1,120; 1,400; 1,860; and 2,700 nm. 

Water vapor absorption in bands outside the spectral response range of the PV module impact 

the spectral mismatch factor more than those within the spectral response range of the PV 

module because they do not change the integrated current output of the PV module (numerator of 

the second term of Equations 6 and 7), but they still change the value of the integrated spectral 

irradiance (denominator of the first term of Equations 6 and 7). Changes in water vapor amounts 

will cause more variability in the spectral mismatch factor for an amorphous silicon PV module 

than for a crystalline silicon PV module because the spectral response range of the amorphous 

silicon PV module includes fewer water vapor absorption bands. Additionally, a multi-junction

amorphous silicon PV module should be expected to have greater variability in spectral 

mismatch factor than a single-junction amorphous silicon PV module because its individual 

junctions encompass smaller spectral response ranges and fewer water vapor absorption bands.

.

0 500 1000 1500 2000 2500

Wavelength (nm)

0.0

0.5

1.0

1.5

2.0

S

p

e

ctral Irra

dia

n

c

e (W/m2/n

m)

G 173-03, AOD = 0.084, H2O = 1.4164 cm, 1000.4 W/m2

AOD = 0.055, 1011.6 W/m2

AOD = 0.300, 960.4 W/m2
30

Figure 5-3. Comparison of spectra for precipitable water vapor amounts of 0.2 cm and 3.4 cm

with the G173-03 hemispherical spectrum. Other model inputs are the same as 

that for the G173-03 hemispherical spectrum.

5.1.4 Influence of Aerosol and Water Vapor Combinations

Figure 5-4 illustrates spectra for two combinations of aerosol optical depth and precipitable 

water vapor amounts. One spectra has an aerosol optical depth of 0.055 and a precipitable water 

vapor amount of 0.2 cm (which corresponds to the NREL December 19 and 21 data), and the 

other spectra has an aerosol optical depth of 0.300 and a precipitable water vapor amount of 3.4 

cm (which corresponds to the FSEC June 14-19 data).

Compared to the G173-03 spectrum, decreasing the aerosol optical depth and the precipitable 

water vapor increased the broadband radiation by about 91 W/m2. Increasing the aerosol optical 

depth and the precipitable water vapor decreased the broadband radiation by about 88 W/m2

. 

These amounts are similar, but a few W/m2

0 500 1000 1500 2000 2500

Wavelength (nm)

0.0

0.5

1.0

1.5

2.0

S

p

e

ctral Irra

dia

n

c

e (W/m2/n

m)

G 173-03, AOD = 0.084, H2O = 1.4164 cm, 1000.4 W/m2

H2O = 0.2, 1083.6 W/m2

H2O= 3.4 cm, 954.7 W/m2

different, than if the accumulative effects of Figures 

5-2 and 5-3 are considered where aerosol optical depth and the precipitable water vapor amounts 

are varied singularly.
31

Figure 5-4. Comparison of two spectra with the G173-03 hemispherical spectrum. One spectra 

with an aerosol optical depth of 0.055 and a precipitable water vapor amount of 0.2 cm, and the 

other spectra with an aerosol optical depth of 0.300 and a precipitable water vapor amount of 

3.4 cm. Other model inputs are the same as that for the G173-03 hemispherical spectrum.

5.1.5 Geographical and Seasonal Considerations

For the multi-crystalline silicon PV module, the error statistics for Sandia AMa function were 

larger than if no correction were applied. This may be a result of seasonal variations in aerosols 

and water vapor compensating for seasonal changes in air mass. For the United States, 

precipitable water vapor is about three times greater in the summer than the winter.

23 Similarly, 

aerosol amounts are also greater in summer than winter, partly because the aerosols are larger 

because of the presence of water vapor. Decreased water vapor and aerosol amounts in winter 

may be offsetting any spectral benefit of increased air mass. Consequently, by only addressing 

one parameter that influences spectrum, the Sandia AMa

Another consideration is using a pressure-corrected airmass to adjust for elevation. Equation 2 

provides an AM

function may be introducing error 

instead of removing it.

a value representing an absolute path length through the atmosphere for clean 

dry air, whose constituents are generally considered uniformly mixed. If aerosols and water 

vapor were also uniformly mixed in the atmosphere, their effects might also be related to AMa, 

but this is not the situation. Aerosol concentrations vary with altitude; likewise for precipitable 

water vapor where about one-half is concentrated in the first 2 kilometers (km) above sea level.23

For our test data, comparing the June 29-30 data at NREL with the June 14-19 data at FSEC 

yields AMa values for NREL’s elevation that are 81% of those at FSEC, but the aerosol optical 

depth and precipitable water vapor amounts are only 35% and 32%, respectively, of those at 

FSEC. Gueymard24

0 500 1000 1500 2000 2500

Wavelength (nm)

0.0

0.5

1.0

1.5

2.0

S

p

e

ctral Irra

dia

n

c

e (W/m2/n

m)

G 173-03, AOD = 0.084, H2O = 1.4164 cm, 1000.4 W/m2

AOD = 0.055, H2O = 0.2 cm, 1091.4 W/m2

AOD = 0.300, H2O = 3.44 cm, 912.4 W/m2

presents similar information and recommends that a pressure-corrected 
32

airmass not be used because the extinction of solar radiation by aerosols, water vapor, or ozone is 

not proportional to pressure.

5.2 Comparison of Air Mass Function and Spectral Mismatch

Figures 5-5 and 5-6 compare the Sandia AMa function for the multi-crystalline silicon PV 

module and the a-Si/a-Si/a-Si:Ge PV module with spectral mismatch values calculated for each 

set of test data using the SMARTS model and the PV module spectral response data. For 

comparison, spectral mismatch values are plotted versus AMa

In general, for the NREL and FSEC data sets the calculated spectral mismatch values change less 

with AM

.

a than the Sandia AMa functions, and while the Sandia AMa functions equal 1 when the

AMa

For the a-Si/a-Si/a-Si:Ge PV module, only the spectral mismatch values for the NREL December 

19 and 21 data resembled the Sandia AM

equals 1.5, the spectral mismatch is less than 1 for the multi-crystalline silicon PV module 

(from 0.98 to 0.995) and greater than 1 for the a-Si/a-Si/a-Si:Ge PV module (from 1.025 to 1.07).

a function. This is likely a consequence of which cell in 

the multi-junction construction was limiting the performance. Figures 5-7 and 5-8 provide the 

spectral mismatch for the PV module and each of its cells for two data sets: June 14-19 at FSEC 

and December 19 and 21 at NREL. For June at FSEC, the mismatch for the middle cell in Figure 

5-7 has the same profile as the mismatch for the PV module; consequently, the middle cell is 

determining performance. (Performance is determined by the cell producing the least current, but 

current is not shown in the figures.) For December at NREL, the top cell in Figure 5-8 is limiting 

performance, which provided results similar to the Sandia AMa function.
33

Figure 5-5. Sandia AMa function and spectral mismatch, calculated using SMARTS model, 

versus AMa for the multi-crystalline silicon PV module.

Figure 5-6. Sandia AMa function and spectral mismatch, calculated using SMARTS model, 

versus AMa for the a-Si/a-Si/a-Si:Ge silicon PV module.

0 1 2 3 4 5 6

Air Mass (pressure corrected)

0.90

0.95

1.00

1.05

A

Ma F

u

n

ctio

n

or S

p

e

ctral Mis

m

atc

h

M

Spectral Mismatch M

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Sandia AMa

0 1 2 3 4 5 6

Air Mass (pressure corrected)

0.70

0.80

0.90

1.00

1.10

A

Ma F

u

n

ctio

n

or S

p

e

ctral Mis

m

atc

h

M

Spectral Mismatch M

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL Sandia AMa
34

Figure 5-7. Spectral mismatch for the a-Si/a-Si/a-Si:Ge PV module and each of its cells for 

June 14-19 at FSEC. Performance is limited by the middle cell.

Figure 5-8. Spectral mismatch for the a-Si/a-Si/a-Si:Ge PV module and each of its cells for 

December 19 and 21 at NREL. Performance is limited by the top cell.

0 1 2 3 4 5 6

Air Mass (pressure corrected)

0.70

0.80

0.90

1.00

1.10

1.20

S

p

e

ctral Mis

m

atc

h

M

Spectral Mismatch M

PV Module

Top cell

Middle cell

Bottom cell

0 1 2 3 4 5 6

Air Mass (pressure corrected)

0.70

0.80

0.90

1.00

1.10

1.20

S

p

e

ctral Mis

m

atc

h

M

Spectral Mismatch M

PV Module

Top cell

Middle cell

Bottom cell
35

5.3 Effects of Diffuse Radiation on AM Functions

Solar radiation received by a flat-plate PV module consists of both direct beam and diffuse 

radiation. The spectral distribution of these two components is quite different. Direct beam 

radiation has more energy at longer wavelengths, which shifts further with increasing air mass. 

Diffuse radiation has more energy at shorter wavelengths, as represented by a blue sky. The 

presence of clouds further shifts the diffuse spectrum to shorter wavelengths.

Consequently, besides the influence of aerosols and water vapor, determining an air mass 

function for a PV module is affected by the proportions of direct beam and diffuse radiation. The 

Sandia and CREST air mass functions were derived using two different PV module orientations, 

and achieved two different results for the a-Si/a-Si/a-Si:Ge PV module. The CREST method 

employs a fixed-tilt orientation and their function was less dependent on air mass because of the 

presence of more diffuse radiation. The Sandia method mounts the PV module on a two-axis 

tracker, thereby ensuring a high percentage of direct beam radiation and more dependence on air 

mass. In fact, the Sandia results may be similar to those in which only direct beam radiation is 

present. Figure 5-9 compares the Sandia AM

11

a function for the a-Si/a-Si/a-Si:Ge PV module with 

spectral mismatch values calculated for each set of test data using direct normal spectra from the 

SMARTS model and the PV module spectral response data. When only modeled direct normal 

radiation is considered, the calculated spectral mismatch values are more similar to the Sandia 

AMa function.

Figure 5-9. Sandia AMa function and spectral mismatch values, calculated using SMARTS

modeled direct normal spectra, versus AMa for the a-Si/a-Si/a-Si:Ge silicon PV module.

0 1 2 3 4 5 6

Air Mass (pressure corrected)

0.40

0.60

0.80

1.00

1.20

A

Ma F

u

n

ctio

n

or S

p

e

ctral Mis

m

atc

h

M

Spectral Mismatch M

Jun 7, 8, 9 at NREL

Jun 14-19 at FSEC

Jun 29, 30 at NREL

Sep 15, 17 at NREL

Dec 19, 21 at NREL

Sandia AMa
36

6 Summary

This report presents the results of a preliminary investigation of methods for correcting the Isc of 

PV modules for variations in solar spectrum under clear skies. We evaluated two types of 

methods: (1) empirical relationships based on air mass, and (2) use of spectral irradiance models 

and PV module spectral response data. Methods of the first type were the Sandia f(AMa

The methods were evaluated using data recorded during June, September, and December, 2008 

at NREL and during June, 2008 at FSEC. The data included one-minute average values of I

) 

function and the CREST f(AM) function. The second type used SEDES2 and SMARTS spectral 

irradiance models.

sc

Data used for analysis were screened to remove data when the presence of clouds or large angleof-incidences of direct beam radiation created the potential for errors in the results. The angle-ofincidence screening limited data to within about three or three and one-half hours either side of 

solar noon, the peak energy producing part of the day. AM

and 

PV module temperature for both a multi-crystalline silicon PV module and an a-Si/a-Si/a-Si:Ge 

PV module, along with coincident measurements of the plane-of-array solar irradiance with a 

pyranometer. The same equipment was used for all measurements at both locations. The PV 

modules were deployed south-facing at a fixed-tilt, with the tilt angle adjusted, for a test period 

and location, so that the angle-of-incidence of the direct beam radiation would be near zero at 

solar noon.

a

For predicting I

values of the screened data ranged 

from 0.8 to 1.5 for the June and September data, and from 1.8 to 3.3 for the December data.

sc, the methods using spectral irradiance models and PV module spectral 

response data performed better than the empirical air mass methods. This is attributed to the 

empirical air mass methods not accounting for variations of aerosols and water vapor, which 

have also been identified by Emery et al.25

For the multi-crystalline silicon PV module, the Sandia f(AM

as a limitation of these methods.

a

A satisfactory solution might be to apply a general derate factor of 0.98 or 0.99 to bring the 

performance with the reference spectrum closer to these experimental results. (Interestingly, PV 

modules with conventional bulk silicon cells rated under the G173-03 hemispherical spectrum 

have their I

) function yielded errors that were 

somewhat greater than when no corrections were applied. Decreased water vapor and aerosol 

amounts in winter may have offset any spectral benefit from increased air mass predicted by the 

method. The methods using spectral irradiance models improved results compared to when not 

applying a spectral correction, but not significantly when considering the larger modeling errors 

that can exist with plane-of-array irradiance models or PV module temperature models. 

sc increased 0.6% to 1.0% when compared to a rating under the previous reference 

spectrum.26

For the a-Si/a-Si/a-Si:Ge PV module, all methods provided some improvement compared to no 

spectral correction. The SEDES2 and SMARTS performed best, and about equal to each other. 

The Sandia and CREST air mass functions performed about the same as each other, but with 

increased error. Not properly accounting for diffuse radiation by these methods may have 

Consequently, the previous reference spectrum would give a general derate factor 

closer to one for this PV module.)
37

influenced results. This module’s f(AMa

Future work will evaluate the use of a spectral irradiance model and PV module spectral 

response data for other PV technologies and for all sky conditions. The SEDES2 model already 

accommodates the influence of clouds and can be used without modification. The SMARTS

models spectra for only clear skies, but the ability to provide spectra for direct and diffuse 

components may afford the opportunity to extend its capabilities, or cloud cover modifiers 

similar to that used for SEDES2 might be derived.

) function was strongly dependent on air mass and 

indicated that performance was top cell limited, consistent with a characterization performed on 

a tracker with a large direct beam component. However, the test data were for fixed-tilt operation 

with a smaller direct beam component and a larger diffuse component. For the June data, the 

method using the SMARTS model, which accounts for the proportions of direct and diffuse 

components, indicated only a small sensitivity to air mass and that performance was limited by 

the middle cell.

A worthwhile effort might also be to perform an inter-comparison between SEDES2, SMARTS, 

and experimental data using spectroradiometer measurements at NREL. Better input data to the 

models might also improve results. For example, this study used the same ozone amount as the 

G173-03 spectrum, but satellite-derived amounts are available that would provide seasonal and 

location-specific values. 

Work is also underway at NREL to provide better estimates of aerosol and water vapor amounts, 

which could improve spectral modeling results. Detailed spectral albedo measurements have also 

been identified by Gueymard as important for modeling spectral irradiances for steeply tilted 

surfaces.27
38

7 References

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th

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18. D. Myers; K. Emery, ;C. Gueymard. “Terrestrial Solar Spectral Modeling Tools and 

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Osaka, 2003.

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40

Appendix A: Plots

This appendix contains plots of the plane-of-array irradiance versus time of day for data passing 

the screening criteria for the days selected for the model evaluations. For ease of view, only every 

fifth data point is displayed in the figures.
41

Figure A-1. Irradiance profiles using data passing screening criteria for June 7-9, 2008 at NREL.

Figure A-2. Irradiance profiles using data passing screening criteria for June 14-19, 2008 at FSEC.

6 8 10 12 14 16 18

Time of Day (Hour)

0

200

400

600

800

1000

1200

P

O

A Irra

dia

n

c

e (W/m2)

Jun 7 at NREL

Jun 8 at NREL

Jun 9 at NREL

6 8 10 12 14 16 18

Time of Day (Hour)

0

200

400

600

800

1000

1200

P

O

A Irra

dia

n

c

e (W/m2)

Jun 14 at FSEC

Jun 15 at FSEC

Jun 16 at FSEC

Jun 17 at FSEC

Jun 18 at FSEC

Jun 19 at FSEC
42

Figure A-3. Irradiance profiles using data passing screening criteria for June 29-30, 2008 at NREL.

Figure A-4. Irradiance profiles using data passing screening criteria for 

September 15 and 17, 2008 at NREL.

6 8 10 12 14 16 18

Time of Day (Hour)

0

200

400

600

800

1000

1200

P

O

A Irra

dia

n

c

e (W/m2)

Jun 29 at NREL

Jun 30 at NREL

6 8 10 12 14 16 18

Time of Day (Hour)

0

200

400

600

800

1000

1200

P

O

A Irra

dia

n

c

e (W/m2)

Sep 15 at NREL

Sep 17 at NREL
43

Figure A-5. Irradiance profiles using data passing screening criteria for 

December 19 and 21, 2008 at NREL.

6 8 10 12 14 16 18

Time of Day (Hour)

0

200

400

600

800

1000

1200

P

O

A Irra

dia

n

c

e (W/m2)

Dec 19 at NREL

Dec 21 at NREL
F1147-E(10/2008)

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1. REPORT DATE (DD-MM-YYYY)

March 2010

2. REPORT TYPE

Technical Report

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Preliminary Investigation of Methods for Correcting for Variations in 

Solar Spectrum under Clear Skies

5a. CONTRACT NUMBER

DE-AC36-08-GO28308

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

B. Marion

5d. PROJECT NUMBER

NREL/TP-520-47277

5e. TASK NUMBER

PVD9.1460

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Renewable Energy Laboratory

1617 Cole Blvd.

Golden, CO 80401-3393

8. PERFORMING ORGANIZATION

REPORT NUMBER

NREL/TP-520-47277

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NREL

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National Technical Information Service

U.S. Department of Commerce

5285 Port Royal Road

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13. SUPPLEMENTARY NOTES

14. ABSTRACT (Maximum 200 Words)

This report presents results of a preliminary investigation of methods for correcting the short-circuit current of 

photovoltaic modules for variations in the solar spectrum. Two types of methods were evaluated: (1) empirical 

relationships based on air mass, and (2) use of spectral irradiance models and PV module spectral response data. 

The report describes the methods of correction, the design of the experiment and data, the results, and analysis of 

the results.

15. SUBJECT TERMS

short-circuit current; photovoltaic modules; solar spectrum; spectral irradiance;spectral irradiance models;spectral 

response data

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OF ABSTRACT

UL

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