ASTM E973-16(2020)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E973 − 16 (Reapproved 2020) An American National Standard
Standard Test Method for
Determination of the Spectral Mismatch Parameter Between
a Photovoltaic Device and a Photovoltaic Reference Cell
This standard is issued under the fixed designation E973; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
1.1 This test method provides a procedure for the determi-
nation of a spectral mismatch parameter used in performance
2. Referenced Documents
testing of photovoltaic devices.
2.1 ASTM Standards:
1.2 The spectral mismatch parameter is a measure of the
E490 Standard Solar Constant and Zero Air Mass Solar
error introduced in the testing of a photovoltaic device that is
Spectral Irradiance Tables
caused by the photovoltaic device under test and the photovol-
E772 Terminology of Solar Energy Conversion
taic reference cell having non-identical quantum efficiencies,
E948 Test Method for Electrical Performance of Photovol-
as well as mismatch between the test light source and the
taic Cells Using Reference Cells Under Simulated Sun-
reference spectral irradiance distribution to which the photo-
light
voltaic reference cell was calibrated.
E1021 TestMethodforSpectralResponsivityMeasurements
1.2.1 Examplesofreferencespectralirradiancedistributions
of Photovoltaic Devices
are Tables E490 or G173.
E1036 Test Methods for Electrical Performance of Noncon-
centrator Terrestrial Photovoltaic Modules and Arrays
1.3 The spectral mismatch parameter can be used to correct
Using Reference Cells
photovoltaic performance data for spectral mismatch error.
E1125 Test Method for Calibration of Primary Non-
1.4 Temperature-dependent quantum efficiencies are used to
Concentrator Terrestrial Photovoltaic Reference Cells Us-
quantify the effects of temperature differences between test
ing a Tabular Spectrum
conditions and reporting conditions.
E1362 Test Methods for Calibration of Non-Concentrator
1.5 This test method is intended for use with linear photo-
Photovoltaic Non-Primary Reference Cells
voltaic devices in which short-circuit is directly proportional to G138 Test Method for Calibration of a Spectroradiometer
incident irradiance.
Using a Standard Source of Irradiance
G173 TablesforReferenceSolarSpectralIrradiances:Direct
1.6 The values stated in SI units are to be regarded as
Normal and Hemispherical on 37° Tilted Surface
standard. No other units of measurement are included in this
SI10 Standard for Use of the International System of Units
standard.
(SI): The Modern Metric System
1.7 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the 3. Terminology
responsibility of the user of this standard to establish appro-
3.1 Definitions—Definitions of terms used in this test
priate safety, health, and environmental practices and deter-
method may be found in Terminology E772.
mine the applicability of regulatory limitations prior to use.
3.2 Definitions of Terms Specific to This Standard:
1.8 This international standard was developed in accor-
3.2.1 test light source, n—a source of illumination whose
dance with internationally recognized principles on standard-
spectral irradiance will be used for the spectral mismatch
ization established in the Decision on Principles for the
calculation. The light source may be natural sunlight or a solar
Development of International Standards, Guides and Recom-
simulator.
3.3 Symbols: The following symbols and units are used in
this test method:
This test method is under the jurisdiction of ASTM Committee E44 on Solar,
Geothermal and OtherAlternative Energy Sources and is the direct responsibility of
Subcommittee E44.09 on Photovoltaic Electric Power Conversion. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
CurrenteditionapprovedJune1,2020.PublishedJuly2020.Originallyapproved contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
in 1983. Last previous edition approved in 2016 as E973 –16. DOI: 10.1520/E0973- Standards volume information, refer to the standard’s Document Summary page on
16R20. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E973 − 16 (2020)
3.3.1 λ—wavelength (µm or nm). be tested differ from one another; these quantum efficiencies
vary with temperature.
3.3.2 D—as a subscript, refers to the device to be tested.
4.3 Determination of the spectral mismatch parameter M
3.3.3 R—as a subscript, refers to the reference cell.
requires six spectral quantities.
3.3.4 S—as a subscript, refers to the test light source.
4.3.1 The spectral irradiance distribution of the test light
3.3.5 0—as a subscript, refers to the reference spectral
source E (λ).
S
irradiance distribution.
4.3.2 The reference spectral irradiance distribution to which
3.3.6 A—active area, (m ).
the photovoltaic reference cell was calibrated E (λ).
–2
4.3.3 Photovolatic Reference Cell:
3.3.7 E—irradiance (W·m ).
4.3.3.1 The quantum efficiency at the temperature corre-
3.3.8 E (λ)—spectral irradiance, test light source
S
sponding to its calibration constant, Q (λT )
–2 –1 –2 –1
R 0
(W·m ·µm or W·m ·nm ).
4.3.3.2 The partial derivative of the quantum efficiency with
3.3.9 E (λ)—spectral irradiance, to which the reference cell
respect to temperature, Θ (λ)= ∂Q /∂T(λ).
R R
–2 –1 –2 –1
is calibrated (W·m ·µm or W·m ·nm ).
4.3.4 Device to be Tested:
4.3.4.1 The quantum efficiency at the temperature at which
3.3.9.1 Discussion—Following normal SI rules for com-
its performance will be reported, Q (λ,T ).
pound units (see Practice SI10), the units for spectral D D0
4.3.4.2 The derivative of the quantum efficiency with re-
irradiance, the derivative of irradiance, with respect to
–3
spect to temperature, Θ (λ)= ∂Q /∂T(λ)
wavelength, dE/dλ, would be W·m . However, to avoid R D
possible confusion with a volumetric power density unit and
4.4 Temperatures of both devices are measured, and M is
for convenience in numerical calculations, it is common
calculated using Eq 1 and numerical integration.
practice to separate the wavelength in the compound unit. This
5. Significance and Use
compound unit is also used in Tables G173.
3.3.10 I—short-circuit current (A).
5.1 The calculated error in the photovoltaic device current
–2
determined from the spectral mismatch parameter can be used
3.3.11 J —light-generated photocurrent density (A·m ).
L
to determine if a measurement will be within specified limits
3.3.12 M—spectral mismatch parameter (dimensionless).
before the actual measurement is performed.
3.3.13 Q(λ,T)—quantum efficiency (electrons per photon or
5.2 The spectral mismatch parameter also provides a means
%).
of correcting the error in the measured device current due to
3.3.14 Θ(λ)—partial derivative of quantum efficiency with
spectral mismatch.
–1 –1
respect to temperature (electrons per photon·°C or %·°C ).
5.2.1 The spectral mismatch parameter is formulated as the
–1
3.3.15 R(λ)—spectral responsivity (A·W ).
fractional error in the short-circuit current due to spectral and
temperature differences.
3.3.16 T—temperature (°C).
5.2.2 Error due to spectral mismatch is corrected by multi-
3.3.17 T —temperature, at which the reference cell is
R0
plying a reference cell’s measured short-circuit current by M,a
calibrated (°C).
technique used in Test Methods E948 and E1036.
3.3.18 T —temperature, to which the short-circuit current
D0
5.3 Because all spectral quantities appear in both the nu-
of the device to be tested will be reported (°C).
merator and the denominator in the calculation of the spectral
3.3.18.1 Discussion—When reporting photovoltaic perfor-
mismatch parameter (see 8.1), multiplicative calibration errors
mance to Standard Reporting Conditions (SRC), it is common
cancel, and therefore only relative quantities are needed
for T = T = 25°C.
R0 D0
(although absolute spectral quantities may be used if avail-
3.3.19 q—electron charge (C).
able).
3.3.20 h—Planck constant (J·s).
5.4 Temperature-dependent spectral mismatch is a more
–1
3.3.21 c—speed of light (m·s ).
accurate method to correct photovoltaic current measurements
compared with fixed-value temperature coefficients.
3.3.22 ∆T—temperature difference (°C).
3.3.23 ɛ—measurement error in short-circuit current (di-
6. Apparatus
mensionless).
6.1 Quantum Effıciency Measurement Apparatus—As re-
quired by Test Method E1021 for spectral responsivity mea-
4. Summary of Test Method
surements.
4.1 Spectral mismatch error occurs when a calibrated refer-
6.2 Spectral Irradiance Measurement Equipment—A spec-
ence cell is used to measure total irradiance of a test light
troradiometer as defined and required by Test Method G138
source (such as a solar simulator) during a photovoltaic device
and calibrated according to Test Method G138.
performance measurement, and the incident spectral irradiance
of the test light source differs from the reference spectral
irradiance distribution to which the reference cell is calibrated. Osterwald,C.R.,Campanelli,M.,Moriarty,T.,Emery,K.A.,andWilliams,R.,
“Temperature-Dependent Spectral Mismatch Corrections,” IEEE Journal of
4.2 Themagnitudeoftheerrordependsonhowthequantum
Photovoltaics, Vol 5, No. 6, November 2015, pp. 1692–1697. DOI:10.1109/
efficiencies of the photovoltaic reference cell and the device to JPHOTOV.2015.2459914
E973 − 16 (2020)
6.2.1 The wavelength resolution shall be no greater than 10 where ∆T = T – T and ∆T = T –T . Use an
R R R0 D D D0
nm. appropriate numerical integration scheme such as that de-
6.2.2 It is recommended that the wavelength pass-bandwith scribed in Tables G173. Appendix X1 provides the derivation
be no greater than 6 nm. of Eq 1.If ?∆T ? ≤ 0.5°C and ?∆T ? ≤ 0.5°C, then Θ (λ) and
R D R
6.2.3 The wavelength range should be wide enough to Θ (λ) may be omitted and Eq 1 simplified to:
D
include the quantum efficiencies of both the photovoltaic λ2 λ4
λQ λ,T E λ dλ λQ λ,T E λ dλ
* ~ ! ~ ! * ~ ! ~ !
D D0 S R R0 0
device to be tested and the photovoltaic reference cell. λ1 λ3
M 5 3 , (2)
λ4 λ2
6.2.4 The spectroradiometer must be able to scan the
* λQ ~λ,T !E ~λ!dλ * λQ ~λ,T !E ~λ!dλ
R R0 S D D0 0
λ3 λ1
required wavelength range in a time period short enough such
that the spectral irradiance at any wavelength does not vary 8.1.1 The wavelength integration limits λ1 and λ2 shall
more than 65 % during the entire scan. correspond to the spectral response limits of the photovoltaic
6.2.5 Test Methods E948, E1036, and E1125 provide addi- device.
tional guidance for spectral irradiance measurements. 8.1.2 The wavelength integration limits λ3 and λ4 shall
correspond to the spectral response limits of the photovoltaic
6.3 Temperature Measurement Equipment—As required by
reference cell.
Test Method E948 or Test Methods E1036.
8.2 Optional—Calculate the measurement error due to spec-
7. Procedure
tral mismatch using:
7.1 Obt
...