IEC 60891:2021

Photovoltaic devices - Procedures for temperature and irradiance corrections to measured I-V characteristics

IEC 60891:2021 defines procedures to be followed for temperature and irradiance corrections to the measured I-V (current-voltage) characteristics (also known as I-V curves) of photovoltaic (PV) devices. It also defines the procedures used to determine factors relevant to these corrections. Requirements for I-V measurement of PV devices are laid down in IEC 60904-1 and its relevant subparts.
This third edition cancels and replaces the second edition published in 2009. This edition includes the following significant technical changes with respect to the previous edition:
- adds guidance on which correction procedure shall be used depending on application;
- introduces translation procedure 4 applicable to c-Si technologies with unknown temperature coefficients;
- introduces various clarifications in existing procedures to improve measurement accuracy and reduce measurement uncertainty;
- adds an informative annex for supplementary methods that can be used for series resistance determination.
The content of the corrigendum 1 (2024-10) has been included in this copy.

Dispositifs photovoltaïques - Procédures pour les corrections en fonction de la température et de l'éclairement à appliquer aux caractéristiques I-V mesurées

IEC 60891:2021 définit des procédures à suivre pour les corrections en fonction de la température et de l'éclairement appliquées aux caractéristiques I-V (courant-tension) mesurées (également appelées courbes I-V) des dispositifs photovoltaïques (PV). Il définit également les procédures utilisées pour déterminer les facteurs appropriés pour ces corrections. Les exigences pour le mesurage I-V des dispositifs PV sont données dans l'IEC 60904-1 et ses sous-parties applicables.
Cette troisième édition annule et remplace la deuxième édition parue en 2009. Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition précédente:
- ajout de recommandations concernant la procédure de correction à utiliser selon l'application;
- introduction de la procédure de transposition 4 applicable aux technologies c-Si avec des coefficients de température inconnus;
- introduction de différentes classifications dans les procédures existantes afin d'améliorer la précision de mesure et de réduire l'incertitude de mesure;
- ajout d'une annexe informative qui présente des méthodes supplémentaires qui peuvent être utilisées pour déterminer la résistance-série.
Le contenu du corrigendum 1 (2024-10) a été pris en considération dans cet exemplaire.

General Information

• Status: Published
• Publication Date: 26-Oct-2021
• ICS: 27.160 - Solar energy engineering
• Technical Committee: TC 82 - Solar photovoltaic energy systems
• Drafting Committee: WG 2 - TC 82/WG 2
• Current Stage: PPUB - Publication issued
• Start Date: 27-Oct-2021
• Completion Date: 12-Nov-2021

Relations

• Corrected By: IEC 60891:2021/COR1:2024 - Corrigendum 1 - Photovoltaic devices - Procedures for temperature and irradiance corrections to measured I-V characteristics
• Effective Date: 05-Sep-2023
• Revises: IEC 60891:2009 - Photovoltaic devices - Procedures for temperature and irradiance corrections to measured I-V characteristics
• Effective Date: 05-Sep-2023

Standards Content (Sample)

IEC 60891 ®
Edition 3.0 2021-10
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Photovoltaic devices – Procedures for temperature and irradiance corrections to
measured I-V characteristics
Dispositifs photovoltaïques – Procédures pour les corrections en fonction de la
température et de l'éclairement à appliquer aux caractéristiques I-V mesurées

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form
or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from
either IEC or IEC's member National Committee in the country of the requester. If you have any questions about IEC
copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or
your local IEC member National Committee for further information.

Droits de reproduction réservés. Sauf indication contraire, aucune partie de cette publication ne peut être reproduite
ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique, y compris la photocopie
et les microfilms, sans l'accord écrit de l'IEC ou du Comité national de l'IEC du pays du demandeur. Si vous avez des
questions sur le copyright de l'IEC ou si vous désirez obtenir des droits supplémentaires sur cette publication, utilisez
les coordonnées ci-après ou contactez le Comité national de l'IEC de votre pays de résidence.

IEC Central Office Tel.: [phone]
3, rue de Varembé [e-mail]
CH-1211 Geneva 20 www.iec.ch
Switzerland
About the IEC
The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes
International Standards for all electrical, electronic and related technologies.

About IEC publications
The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the
latest edition, a corrigendum or an amendment might have been published.

IEC publications search - webstore.iec.ch/advsearchform IEC online collection - oc.iec.ch
The advanced search enables to find IEC publications by a Discover our powerful search engine and read freely all the
variety of criteria (reference number, text, technical publications previews. With a subscription you will always
committee, …). It also gives information on projects, replaced have access to up to date content tailored to your needs.
and withdrawn publications.
Electropedia - www.electropedia.org
IEC Just Published - webstore.iec.ch/justpublished
The world's leading online dictionary on electrotechnology,
Stay up to date on all new IEC publications. Just Published
containing more than 22 000 terminological entries in English
details all new publications released. Available online and
and French, with equivalent terms in 18 additional languages.
once a month by email.
Also known as the International Electrotechnical Vocabulary

(IEV) online.
IEC Customer Service Centre - webstore.iec.ch/csc
If you wish to give us your feedback on this publication or
need further assistance, please contact the Customer Service
Centre: [e-mail].
A propos de l'IEC
La Commission Electrotechnique Internationale (IEC) est la première organisation mondiale qui élabore et publie des
Normes internationales pour tout ce qui a trait à l'électricité, à l'électronique et aux technologies apparentées.

A propos des publications IEC
Le contenu technique des publications IEC est constamment revu. Veuillez vous assurer que vous possédez l’édition la
plus récente, un corrigendum ou amendement peut avoir été publié.

Recherche de publications IEC - IEC online collection - oc.iec.ch
webstore.iec.ch/advsearchform Découvrez notre puissant moteur de recherche et consultez
La recherche avancée permet de trouver des publications IEC gratuitement tous les aperçus des publications. Avec un
en utilisant différents critères (numéro de référence, texte, abonnement, vous aurez toujours accès à un contenu à jour
comité d’études, …). Elle donne aussi des informations sur adapté à vos besoins.
les projets et les publications remplacées ou retirées.

Electropedia - www.electropedia.org
IEC Just Published - webstore.iec.ch/justpublished
Le premier dictionnaire d'électrotechnologie en ligne au
Restez informé sur les nouvelles publications IEC. Just
monde, avec plus de 22 000 articles terminologiques en
Published détaille les nouvelles publications parues.
anglais et en français, ainsi que les termes équivalents dans
Disponible en ligne et une fois par mois par email.
16 langues additionnelles. Egalement appelé Vocabulaire

Electrotechnique International (IEV) en ligne.
Service Clients - webstore.iec.ch/csc

Si vous désirez nous donner des commentaires sur cette
publication ou si vous avez des questions contactez-nous:
[e-mail].
IEC 60891 ®
Edition 3.0 2021-10
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Photovoltaic devices – Procedures for temperature and irradiance corrections

to measured I-V characteristics

Dispositifs photovoltaïques – Procédures pour les corrections en fonction de la

température et de l'éclairement à appliquer aux caractéristiques I-V mesurées

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 27.160 ISBN 978-2-8322-1036-0

– 2 – IEC 60891:2021 © IEC 2021
CONTENTS
FOREWORD . 4
1 Scope . 6
2 Normative references . 6
3 Terms and definitions, symbols and abbreviated terms . 7
4 Correction procedures . 8
4.1 General . 8
4.2 Correction procedure 1 . 11
4.3 Correction procedure 2 . 12
4.4 Correction procedure 3 . 14
4.4.1 General . 14
4.4.2 Correction for the irradiance and temperature from two measured I-V
curves . 14
4.4.3 Correction to various irradiances and temperatures from three I-V
curves . 17
4.4.4 Correction to various irradiances and temperatures from four measured
I-V curves . 17
4.5 Correction procedure 4 . 18
5 Determination of temperature coefficients . 20
5.1 General . 20
5.2 Apparatus . 20
5.3 Procedure in natural or steady-state simulated sunlight . 22
5.4 Procedure with a pulsed solar simulator . 23
5.5 Calculation of temperature coefficients . 23
6 Determination of internal series resistance R and R′ . 24
S S
6.1 General . 24
6.2 Determination of R in correction procedures 1 and 4 . 25
S
6.3 Determination of B and B in correction procedure 2 . 27
1 2
6.4 Determination of R′ in correction procedure 2 . 28
S
6.5 Determination of R in correction procedure 4 . 30
S
7 Determination of the curve correction factor κ and κ′ . 31
7.1 General . 31
7.2 Procedure . 31
8 Reporting . 32
Annex A (informative) Alternative procedures for series resistance determination . 34
A.1 General . 34
A.2 Differential resistance at V against inverse irradiance method . 34
OC
Bibliography . 35

Figure 1 – Example of the correction of the I-V characteristics by formulae (10) and
(11) . 16
Figure 2 – Schematic diagram of the relation of G and T which can be chosen in the
3 3
simultaneous correction for irradiance and temperature, for a fixed set of T , G , T ,
1 1 2
and G by formulae (12) and (13) . 16
Figure 3 – Schematic diagram of the processes for correcting the I-V characteristics to
various ranges of irradiance and temperature based on three measured
characteristics . 17
Figure 4 – Schematic diagram of the processes for correcting the I-V characteristics to
various ranges of irradiance and temperature based on four measured characteristics . 18
Figure 5 – Example positions for measuring the temperature of the test module behind
the cells . 21
Figure 6 – Determination of internal series resistance . 26
Figure 7 – Determination of internal series resistance when the corrected I-V

characteristics intersect . 27
Figure 8 – Determination of irradiance correction factors B and B and internal series
1 2
resistance, R′ . 29
S
Figure 9 – Determination of internal series resistance of a PV module from a single I-V
curve . 31
Figure 10 – Determination of curve correction factor . 32
Figure A.1 – Determination of internal series resistance . 34

Table 1 – Overview of correction procedures for irradiance corrections (i.e. T = T ) . 9
1 2
Table 2 – Overview of correction procedures for temperature corrections (i.e. G = G ) . 10
1 2
– 4 – IEC 60891:2021 © IEC 2021
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
PHOTOVOLTAIC DEVICES – PROCEDURES FOR TEMPERATURE AND
IRRADIANCE CORRECTIONS TO MEASURED I-V CHARACTERISTICS

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international
co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and
in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports,
Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)”). Their
preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with
may participate in this preparatory work. International, governmental and non-governmental organizations liaising
with the IEC also participate in this preparation. IEC collaborates closely with the International Organization for
Standardization (ISO) in accordance with conditions determined by agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence between
any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent
rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60891 has been prepared by IEC technical committee 82: Solar
photovoltaic energy systems.
This third edition cancels and replaces the second edition published in 2009. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
– adds guidance on which correction procedure shall be used depending on application;
– introduces translation procedure 4 applicable to c-Si technologies with unknown
temperature coefficients;
– introduces various clarifications in existing procedures to improve measurement accuracy
and reduce measurement uncertainty;
– adds an informative annex for supplementary methods that can be used for series resistance
determination.
The text of this International Standard is based on the following documents:
FDIS Report on voting
82/1936/FDIS 82/1957/RVD
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/standardsdev/publications.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
– 6 – IEC 60891:2021 © IEC 2021
PHOTOVOLTAIC DEVICES – PROCEDURES FOR TEMPERATURE AND
IRRADIANCE CORRECTIONS TO MEASURED I-V CHARACTERISTICS

1 Scope
This document defines procedures to be followed for temperature and irradiance corrections to
the measured I-V (current-voltage) characteristics (also known as I-V curves) of photovoltaic
(PV) devices. It also defines the procedures used to determine factors relevant to these
corrections. Requirements for I-V measurement of PV devices are laid down in IEC 60904-1
and its relevant subparts.
The PV devices include a single solar cell with or without a protective cover, a sub-assembly of
solar cells, or a module. A different set of relevant parameters for I-V curve correction applies
for each type of device. The determination of temperature coefficients for a module (or sub-
assembly of cells) may be calculated from single cell measurements, but this is not the case for
the internal series resistance and curve correction factor, which should be separately measured
for a module or subassembly of cells. Refer to Annex A for alternative procedures for series
resistance determination.
The use of I-V correction parameters is valid for the PV device for which they have been
measured. Variations may occur within a production lot or the type of class.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies.
For undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60904-1, Photovoltaic devices – Part 1: Measurements of photovoltaic current-voltage
characteristics
IEC TS 60904-1-2, Photovoltaic devices – Part 1-2: Measurement of current-voltage
characteristics of bifacial photovoltaic (PV) devices
IEC 60904-2, Photovoltaic devices – Part 2: Requirements for reference solar devices
IEC 60904-7, Photovoltaic devices – Part 7: Computation of the spectral mismatch correction
for measurements of photovoltaic devices
IEC 60904-8, Photovoltaic devices – Part 8: Measurement of spectral responsivity of a
photovoltaic (PV) device
IEC 60904-9, Photovoltaic devices – Part 9: Classification of solar simulator characteristics
IEC 60904-10:2020, Photovoltaic devices – Part 10: Methods of linear dependence and linearity
measurements
IEC 61215-2, Terrestrial photovoltaic (PV) modules – Design qualification and type approval –
Part 2: Test procedures
IEC TS 61836, Solar photovoltaic energy systems – Terms, definitions, and symbols

3 Terms and definitions, symbols and abbreviated terms
For the purposes of this document, the terms and definitions given in IEC TS 61836, together
with the following, apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
3.1
B
irradiance correction factor for open-circuit voltage which is linked with the diode thermal
voltage, V of the p-n junction and n
t S
Note 1 to entry: It is used in correction procedure 2.
3.2
B
irradiance correction factor for open-circuit voltage which accounts for non-linearity of V with
OC
irradiance scaling
Note 1 to entry: It is used in correction procedure 2.
3.3
DUT
device under test
3.4
R
S
internal series resistance of the DUT employed by correction procedures 1 and 4
3.5
R′
S
internal series resistance of the DUT employed by correction procedure 2
Note 1 to entry: Although determined by a different method than R , both quantities share the same physical
S
meaning and therefore their values for the same DUT are similar.
3.6
n
S
number of cells serially connected in the DUT
3.7
a
interpolation constant employed in correction procedure 3, that has a relation with the irradiance
and temperature
3.8
ε
product of ideality factor of the DUT with the bandgap of the photovoltaic material divided by
electron’s elementary charge
Note 1 to entry: It is used in correction procedure 4.

– 8 – IEC 60891:2021 © IEC 2021
4 Correction procedures
4.1 General
This document provides four procedures for correcting measured current-voltage
characteristics to other conditions of temperature and irradiance, such as Standard Test
Conditions (STC), that can be applied. The first procedure describes a system of linear
equations for current and voltage, which is best applicable for irradiance corrections within
±40% of the target irradiance. The second procedure is an alternative algebraic correction
method which yields better results for large irradiance corrections (exceeding ±40 %). Both
procedures require that correction parameters of the PV device are known. If not known they
need to be determined prior to performing the correction. The third procedure is an interpolation
method which does not require correction parameters as input. It can be applied when a
minimum of two current-voltage curves have been measured for the DUT. This correction
method is applicable in the temperature and irradiance range spanned by the two current
voltage curves. The fourth procedure is based on the single-diode model and provides a
methodology for determining a correction parameter R from a single I-V curve, when the
S
parameter is unknown. The method is best applicable to irradiance corrections when the
2 2
measured and target irradiance are both in the range 300 W/m to 1 200 W/m and the series
resistance R is unknown. It is suitable for translations when the characteristics under STC
S
have to be estimated from a single experimental I-V curve.
Table 1 and Table 2 provide an overview of the four different correction procedures, and
describe qualitatively the advantages, disadvantages and required correction parameters for
each procedure. The purpose of these tables is to provide guidance to the user of this document
on which correction procedure to use for different applications.
For simultaneous corrections of irradiance and temperature, the benefits and limitations listed
in Table 1 and Table 2 apply concurrently.
Common to all procedures is that I-V characteristics of the PV device are to be measured in
accordance with IEC 60904-1 and its relevant subparts.
All PV devices should be linear at least within the range of irradiances and device temperature
over which corrections are made. Details on how to assess the deviation from the ideal linear
dependence are described in IEC 60904-10.
An estimate of the translation accuracy is required (see Clause 8).
Usually, the total irradiance G shall be calculated from the measured short-circuit current of the

PV reference device (I ) as defined in IEC 60904-2, and its calibration value at STC (I ).
RC RC,STC
A correction should be applied to account for the actual temperature of the reference device
T using the specified relative temperature coefficient of short-circuit current of the reference
RC
device (𝛼𝛼 ) which is given at 25 °C and 1 000 W/m .
RC,rel
−2
1000 𝑊𝑊𝑚𝑚 ×𝐼𝐼
RC
𝐺𝐺 =
(1)
𝐼𝐼 ×�1 +𝛼𝛼 × (𝑇𝑇 − 25°𝐶𝐶)�
RC,STC RC,rel RC
Ideally, the reference device shall be linear in short-circuit current over the entire irradiance
range of interest, as defined in IEC 60904-10. In practice, even for linear devices it is
recommended to apply a correction for linearity of the reference device according to
IEC 60904-10. If the device is not linear according to IEC 60904-10 over the entire irradiance
range of interest, then corrections shall be applied to avoid errors in the corrections of its I-V
characteristics. The PV reference device shall either be spectrally matched to the DUT, or a
spectral mismatch (SMM) correction shall be performed in conformance with IEC 60904-7.
Since the spectral responsivity of the device can vary with temperature, the apparent change
in temperature coefficient with spectra should be taken into account in the correction. An
interpolation method of temperature against SMM correction can minimize the error sources.
Table 1 – Overview of correction procedures for irradiance corrections (i.e. T = T )
1 2
Procedure 1
Correction parameter requirement: R
S
Advantages Disadvantages
• Suitable where R is determined (typically • Assumes superposition of current at all voltages
S
within ± 40 % of the irradiance at which R was
S
determined)
• Works reasonably well over a broader range of • Cannot produce complete I-V curves for higher
irradiance (typically within ± 80 % of the irradiance corrections (part of I-V curve between
irradiance at which R was determined) for
P and V is missing), when the I-V curve is not
S
max OC
devices that are linear with respect to measured sufficiently far into the negative current
irradiance according to IEC 60904-10. This is regime. In this case extrapolation for V is
OC
typically the case for c-Si.
necessary
Procedure 2
Correction parameter requirement: B , B , R′ . κ′ and β
1 2 S rel
Advantages Disadvantages
• Requires more parameters to be known than
• Suitable in the irradiance range where R′ is
S
procedures 1 and 4
determined (typically within ± 40 % of the
irradiance at which R′ was determined)
S
• Works reasonably well over a broader range of • Not recommended for I-V translation over
irradiance (typically within ± 80 % of the irradiance exceeding ± 40 % of the target
irradiance at which R′ was determined) for irradiance, when the DUT has significant leakage
S
current (low shunt resistance)
devices that are linear with respect to
irradiance according to IEC 60904-10. This is
typically the case for c-Si.
• Can produce complete I-V curves for higher
irradiance corrections
• Provides information for relative comparison of
the DUT modelling parameters used in single-
diode model (ideality factor and R′ )
S
Procedure 3
Correction parameter requirement: None
Advantages Disadvantages
• Best accuracy for I-V corrections when • Requires knowledge of I-V curves at higher and
interpolating lower levels of irradiance compared to target
irradiance
• Fitting parameters not required • Not possible to perform comparison between
different technologies, because fitting parameters
cannot be extracted
• Least technology specific method • Interpolation gives better results than
extrapolation. Extrapolation should be practiced
with caution
– 10 – IEC 60891:2021 © IEC 2021
Procedure 4
Correction parameter requirement: None
Advantages Disadvantages
• Suitable when the correction parameter R is • Approximate R is determined from a single I-V
S S
unknown curve
• Does not require multiple I-V curves measured • Not suitable for technologies which do not follow
at different levels of irradiance for R the single-diode model
S
determination
Table 2 – Overview of correction procedures for temperature corrections (i.e. G = G )
1 2
Procedure 1
Correction parameter requirement: R , κ, α and β
S
Advantages Disadvantages
• Suitable as long as the measured irradiance is • Not recommended when the measured irradiance
within ± 30 % of the irradiance at which differs by more than ±30 % from the irradiance at
temperature coefficients were determined which the temperature coefficients were
determined
Procedure 2
Correction parameter requirement: B , B , R′ , κ′, α and β
1 2 S rel rel
Advantages Disadvantages
• Suitable as long as the measured irradiance is • Requires more parameters to be known than
within ± 30 % of the irradiance at which procedures 1 and 4
temperature coefficients were determined
• Applicable over the entire range of irradiance for • Not recommended for devices that are not linear
which the device is proven to be linear with with respect to irradiance when the measured
respect to irradiance according to IEC 60904-10. irradiance differs by more than ± 30 % from the
This is typically the case for c-Si. irradiance at which the temperature coefficients
were determined
Procedure 3
Correction parameter requirement: None
Advantages Disadvantages
• Best accuracy for I-V corrections when • Requires knowledge of I-V curves at higher and
interpolating lower temperatures
• Fitting parameters not required • Fitting parameters cannot be extracted
• Least technology specific method • Interpolation gives better results than
extrapolation. Extrapolation should be practiced
with caution
Procedure 4
Correction parameter requirement: ε, α and n
rel S
Advantages Disadvantages
• The same value of the device dependent • Not suitable for technologies which do not follow
constant, ε can be used for all c-Si PV devices the single-diode model

• ε is independent of temperature and irradiance

4.2 Correction procedure 1
The first procedure relies on the principle of superposition of the currents at all voltages, which
assumes that the diode current does not depend on photocurrent [1] . This is typically not the
case when the target irradiance is significantly different from the measured irradiance.
The current-voltage characteristic measured at condition 1 shall be corrected to STC or other
selected temperature and irradiance values (condition 2) by applying the following formulae:
𝐺𝐺
𝐼𝐼 =𝐼𝐼 +𝐼𝐼 ×� − 1� +𝛼𝛼 × (𝑇𝑇 −𝑇𝑇 )
(2)
2 1 SC1 2 1
𝐺𝐺
𝑉𝑉 =𝑉𝑉 −𝑅𝑅 × (𝐼𝐼 −𝐼𝐼 )−𝜅𝜅 ×𝐼𝐼 × (𝑇𝑇 −𝑇𝑇 ) +𝛽𝛽 × (𝑇𝑇 −𝑇𝑇 ) (3)
2 1 S 2 1 2 2 1 2 1
where:
I , V are coordinates of points on the measured characteristics;
1 1
I , V are coordinates of the corresponding points on the corrected characteristic;
2 2
G is the irradiance measured with the reference device, corrected for temperature
and linearity of the reference device and the SMM;
G is the target irradiance for the DUT;
T is the measured temperature of the DUT;
T is the target temperature of the DUT;
I is the measured short-circuit current of the DUT at G1 and T1;
SC1
α and β are the short-circuit current and open-circuit voltage temperature coefficients,
respectively, of the DUT at the target irradiance for correction and within the
temperature range of interest (e.g. β = –2,3 mV/°C);
R is the internal series resistance of the DUT;
S
is a curve correction factor.
κ
NOTE For crystalline silicon PV devices α is normally positive and β negative.
As the data point V will be shifted off the original axis when translating from lower to higher
OC1
irradiance, the translated V has to be determined by linear extrapolation near and above
OC2
V (i.e. for negative currents), or by linear extrapolation near V if there are no voltage
OC2 OC2
points above V . To minimize errors caused by extrapolation, it is recommended that I-V
OC2
curves shall be measured as far into forward bias beyond V as possible.
OC
V may be also extrapolated by polynomial fit of the I-V curve. In particular, this is
OC2
recommended if measured V is translated to an I-V data point with current offset. For the
OC1
polynomial curve fit all I-V data points in the voltage range larger than V shall be considered.
Pmax
The resulting curve shall be plausible in the whole voltage range V to V . Alternative
Pmax OC
methods to linear extrapolation (such as diode fitting) are also allowed.
___________
Numbers in square brackets refer to the Bibliography.

– 12 – IEC 60891:2021 © IEC 2021
The extrapolation method used has to be stated in the report together with a statement of its
estimated uncertainty on the translated V .
OC2
Procedures for determination of the I-V correction parameters of the DUT are described in
Clauses 5 to 7.
Formula (2) is only applicable for I-V curves measured at irradiances which are constant during
the acquisition of the entire I-V curve. For pulsed solar simulators with decaying irradiance, or
any other kind of irradiance fluctuations during I-V measurement, formula (2) is not applicable
as such. In this case, each measured I-V curve has to be corrected to an equivalent I-V curve
at constant irradiance which requires an additional scaling factor in front of I . For practical
SC1
reasons, this scaling factor is related to the irradiance corresponding to measured I . For
SC1
non-constant irradiance, formula (2) will become the following translation formula.
′
𝐺𝐺 𝐺𝐺
(4)
𝐼𝐼 = 𝐼𝐼 + ×𝐼𝐼 × � − 1� +𝛼𝛼 × (𝑇𝑇 −𝑇𝑇 )
2 1 SC1 2 1
′
𝐺𝐺 𝐺𝐺
SC1 1
G′
where G is the irradiance value at the time of I measurement and is the irradiance
SC1 SC1
measured at time of data acquisition of individual I-V data points.
Correction procedure 1 assumes that the normalized spectra corresponding to G and G are
1 2
identical. If they are not, an additional uncertainty component is required to account for the
variation of 𝛼𝛼 with spectrum by calculating the effect based on the measured spectral
responsivity of the DUT as a function of temperature or of irradiance and on the measured
spectral irradiance. Spectral mismatch corrections shall be implemented in accordance with
IEC 60904-7.
4.3 Correction procedure 2
This procedure is based on the simplified one-diode model of PV devices [2]. The semi-
empirical translation formulae contain six I-V curve correction parameters which can be
determined by measurement of I-V curves at different temperature and irradiance conditions
(see Clauses 5 to 7). Besides the relative temperature coefficients for short-circuit current (α )
rel
and open-circuit voltage (β ) an additional temperature coefficient (κ′) is commonly used which
rel
accounts for changes of the internal series resistance (and fill factor) with temperature.
Furthermore, correction procedure 2 introduces a quadratic irradiance factor f(G) with
coefficients B and B , which accounts for the non-linear scaling of diode’s ideality factor with
1 2
irradiance. The correction procedure is defined by the following formulae for current and voltage:
( )
𝐺𝐺 �1 +𝑎𝑎 × 𝑇𝑇 − 25°𝐶𝐶�
2 rel 2
𝐼𝐼 = 𝐼𝐼 (5)
2 1
𝐺𝐺
�1 +𝑎𝑎 × (𝑇𝑇 − 25°𝐶𝐶)�
rel 1
′ ′
( ) ( )
𝑉𝑉 =𝑉𝑉 −𝑅𝑅 × 𝐼𝐼 −𝐼𝐼 −𝜅𝜅 ×𝐼𝐼 × 𝑇𝑇 −𝑇𝑇
2 1 𝑆𝑆1 2 1 2 2 1
(6)
1 1
[ ( ) ( ) ( ) ( )]
+𝑉𝑉 ×�𝛽𝛽 × 𝑓𝑓𝐺𝐺 × 𝑇𝑇 − 25°𝐶𝐶 −𝑓𝑓𝐺𝐺 × 𝑇𝑇 − 25°𝐶𝐶 + − �
OC,STC rel 2 2 1 1
𝑓𝑓(𝐺𝐺 ) 𝑓𝑓(𝐺𝐺 )
2 1
−2 −2
𝑉𝑉 1 000 𝑊𝑊𝑚𝑚 1 000 𝑊𝑊𝑚𝑚
𝑂𝑂𝑂𝑂,𝑆𝑆𝑆𝑆𝑂𝑂
( )
𝑓𝑓𝐺𝐺 = =𝐵𝐵 ×𝑙𝑙𝑙𝑙 � � +𝐵𝐵 ×𝑙𝑙𝑙𝑙� � + 1 (7)
2 1
𝑉𝑉 (𝐺𝐺) 𝐺𝐺 𝐺𝐺
𝑂𝑂𝑂𝑂
′ ′ ′
𝑅𝑅 =𝑅𝑅 +𝜅𝜅 × (𝑇𝑇 − 25°𝐶𝐶) (8)
𝑆𝑆1 𝑆𝑆 1
where:
I , V are coordinates of points on the measured I-V characteristic;
1 1
I , V are coordinates of the corresponding points on the corrected I-V curve;
2 2
G is the irradiance as measured with the reference device, corrected for
temperature and linearity of the reference device and the SMM;
G is the target irradiance for the corrected I-V characteristic;
T is the measured temperature of the DUT;
T is the target temperature of the DUT;
V is the open-circuit voltage at test conditions G and T ;
OC1 1 1
V is the open-circuit voltage at standard test conditions;
OC,STC
α and β are the relative short-circuit current and open-circuit voltage temperature
rel rel
coefficients, respectively, of the DUT measured at 1 000 W/m . They express
the relative change of short-circuit current and open-circuit voltage with respect
to their values at STC; both coefficients are expressed in percent per unit
temperature and should be scaled by a fraction of 100 when used in the
-1 -1
formulae (e.g. α = 0,045 % K = 0,00045 K );
rel
B is the irradiance correction factor for open-circuit voltage which is linked with
the diode thermal voltage D of the p-n junction and the number of cells n
S
serially connected in the DUT;
B is the irradiance correction factor for open-circuit voltage which accounts for
non-linearity of V with irradiance scaling;
OC
is the internal series resistance of the DUT determined at 25 °C;
R′
S
is the internal series resistance of the DUT at measured temperature T ;
R′
S1
′
κ′ is interpreted as temperature coefficient of the internal series resistance 𝑅𝑅 .
𝑆𝑆
Care should be taken that the numerical values for κ′ and R′ for procedure 2 can be different
S
from κ and R of correction procedure 1, as correction procedure 2 requires the series
S
resistance to be explicitly determined at 25 °C.
When unknown, V can be derived from the actual measurement using the following
OC,STC
expression:
( )
𝑉𝑉 ×𝑓𝑓𝐺𝐺
OC1 1
𝑉𝑉 = (9)
OC,STC
1 +𝛽𝛽 × (𝑇𝑇 − 25°C) ×𝑓𝑓 (𝐺𝐺 )
rel 1 1
NOTE 1 For c-Si modules when V scales with the irradiance term ln(1 000/G) linearly, a typical range for the
OC
irradiance correction factor B is 0,05 ± 0,01 while B is 0. When V scales non-linearly with the irradiance term
1 2 OC
ln(1 000/G), B typically varies in the range of 0,04 ± 0,01 and B in the range of 0,004 ± 0,001.
1 2
NOTE 2 A typical range for the temperature coefficient α of c-Si modules is from 0,03 %/°C to 0,06 %/°C with
rel
respect to the I at STC. A typical range for the temperature coefficient β of c-Si modules is from -0,35 %/°C
SC rel
to -0,2 %/°C with respect to the V at STC.
OC
– 14 – IEC 60891:2021 © IEC 2021
4.4 Correction procedure 3
4.4.1 General
This procedure may be applied only to devices proven to be linear according to IEC 60904-10.
It is based on the linear interpolation or extrapolation of two measured I-V characteristics [3].
The method uses a minimum of two I-V characteristics, and requires no correction parameters
or fitting parameters. The measured current-voltage characteristics shall be corrected to STC
or other target temperature and irradiance values by applying the following formulae:
(10)
( )
𝑉𝑉 =𝑉𝑉 +𝑎𝑎 × 𝑉𝑉 −𝑉𝑉
3 1 2 1
(11)
𝐼𝐼 =𝐼𝐼 +𝑎𝑎 × (𝐼𝐼 −𝐼𝐼 )
3 1 2 1
The pair of (I ,V ) and (I , V ) should be chosen so that 𝐼𝐼 −𝐼𝐼 =𝐼𝐼 −𝐼𝐼
1 1 2 2 2 1 SC2 𝑆𝑆𝑂𝑂1
where:
I , V are coordinates of points on the measured characteristics at an irradiance G and
1 1 1
temperature T .
I , V are coordinates of points on the measured characteristics at an irradiance G and
2 2 2
temperature T .
I , V are coordinates of the corresponding points on the corrected characteristics at an
3 3
irradiance G and temperature T .
3 3
I , I are the measured short-circuit current of the DUT at irradiances G and G .
SC1 SC2 1 2
𝑎𝑎 is a constant for the interpolation, which has the relation with the irradiance and
temperature as follows:
(12)
( )
𝐺𝐺 =𝐺𝐺 +𝑎𝑎 × 𝐺𝐺 −𝐺𝐺
3 1 2 1
(13)
𝑇𝑇 =𝑇𝑇 +𝑎𝑎 × (𝑇𝑇 −𝑇𝑇 )
3 1 2 1
This method should be applicable to most PV technologies. Formulae (10) to (13) can be used
for the irradiance correction, temperature correction, and simultaneous correction of irradiance
and temperature. This procedure assumes that the normalized spectra corresponding to G , G
1 2
and G are identical. If they are not, then there will be an additional source of uncertainty in G .
3 3
Measuring G and G with SMM corrections based upon the spectral responsivity measured at
1 2
T and T according to IEC 60904-8 will minimize these errors. If the spectral responsivity is
1 2
nonlinear in relation to irradiance then it should be measured at bias light intensities equal to
G and G .
1 2
4.4.2 Correction for the irradiance and temperature from two measured I-V curves
The procedure to correct the I-V characteristics to the irradiance and temperature (G , T ) from
3 3
two I-V characteristics measured at the irradiances and temperatures of (G , T ) and (G , T )
1 1 2 2
is as follows (Figure 1a) and 1b)):
a) Measure the two I-V characteristics at the irradiances and temperatures of (G , T ) and
1 1
(G , T ), respectively (solid lines in Figure 1a)). Find the values of I and I .
2 2 SC1 SC2
b) Calculate α by formula (12) or (13) choosing a target irradiance or temperature. For example,
when the two measured I-V curves were made at:
G = 1 000 W/m and T = 50 °C
1 1
G = 500 W/m and T = 40 °C.
2 2
and the target irradiance is G = 800 W/m :
then, using formula (12) α = 0,4
= 46 °C.
and using formula (13) T
c) Choose a point (V , I ) on the I-V curve 1. Find a point (V , I ) on the I-V curve 2, so that
1 1 2 2
the relation I – I = I – I is satisfied (Figure 1b)).
2 1 SC2 SC1
d) Calculate V and I by formulae (10) and (11).
3 3
e) Select multiple sets of data points (V , I ) on the I-V curve 1, and calculate (V , I ) for each
1 1 3 3
by the procedures c) and d).
f) The I-V characteristics 3 at the irradiance G and temperature T is given by the set of data
3 3
points (V , I ) (broken line in Figure 1 b)).
3 3
Figure 1a) and Figure 1b) show an example of an irradiance correction (T = T ). Figure 1c)
1 2
shows an example of a temperature correction (G = G ).Figure 1d) shows a simultaneous
1 2
correction of irradiance and temperature. When 0 ≤ α ≤ 1, the procedure is interpolation.
Otherwise, the procedure is extrapolation.
It should be noted that when G , G , T and T are fixed, G and T may not be chosen
1 2 1 2 3 3
independently, because they have the relationships given in formulae (12) and (13) (Figure 2).
2 2
For example, when G = 1 000 W/m , T = 20 °C, G = 0 W/m , T = 60 °C (dark I-V curve at
1 1 2 2
60 °C), and you wish to have the new curve at G = 750 W/m , α is calculated to be 0,25 by
formula (12). Therefore, T is 30 °C from formula (13).
≠ I and the corrected I-V characteristics around the open-circuit voltage is
When I
SC1 SC2
required, the measured characteristics should extend beyond V .
OC
When there are no measured data points which exactly satisfy I = I + (I – I ), the V
2 1 SC2 SC1 2
and I may be calculated from interpolation of the data points in the I-V curve 2.
This method is applicable to both interpolation (0 ≤ α ≤ 1) and extrapolation (α < 0 or α > 1).
Interpolation gives better results
...