Photovoltaic devices - Part 10: Methods of linear dependence and linearity measurements

This part of IEC 60904 describes the procedures used to measure the dependence of any
electrical parameter (Y) of a photovoltaic (PV) device with respect to a test parameter (X) and
to determine the degree at which this dependence is close to an ideal linear (straight-line)
function. It also gives guidance on how to consider deviations from the ideal linear
dependence and in general on how to deal with non-linearities of PV device electrical
parameters. Typical device parameters are the short-circuit current ISC, the open-circuit
voltage VOC and the maximum power Pmax. Typical test parameters are the temperature T and
the irradiance G. However, the same principles described in this document can be applied to
any other test parameter with proper adjustment of the procedure used to vary the parameter
itself.
Performance evaluations of PV modules and systems, as well as performance translations
from one set of temperature and irradiance to another, frequently rely on the use of linear
equations (see for example IEC 60891, IEC 61853-1, IEC 61829 and IEC 61724-1). This
document lays down the requirements for linear dependence test methods, data analysis and
acceptance limits of results to ensure that these linear equations will give satisfactory results.
Such requirements prescribe also the range of the temperature and irradiance over which the
linear equations may be used. This document gives also a procedure on how to correct for
deviations of the short-circuit current ISC from the ideal linear dependence on irradiance
(linearity) for PV devices, regardless of whether they are classified linear or non-linear
according to the limits set in 9.7. The impact of spectral irradiance distribution and spectral
mismatch is considered for measurements using solar simulators as well as under natural
sunlight.
The measurement methods described herein apply to all PV devices, with some caution to be
used for multi-junction PV devices, and are intended to be carried out on a device, or in some
cases on an equivalent device of identical technology, that is stable according to the criteria
set in the relevant part of IEC 61215. These measurements are meant to be performed prior
to all measurements and correction procedures that require a linear device or that prescribe
restrictions for non-linear devices.
The main methodology used in this document is based on a fitting procedure in which a linear
(straight-line) function is fitted to a set of measured data points {Xi,Yi}. The linear function
uses a least-squares fit calculation routine, which in the most advanced analysis also
accounts for the expanded combined uncertainty (k=2) of the measurements. The linear
function crosses the origin in the case of short-circuit current data versus irradiance. The
deviation of the measured data from the ideal linear function is also calculated and limits are
prescribed for the permissible percentage deviation.
Procedures to determine the deviation of the Y(X) dependence from the linear (straight-line)
function are described in Clause 6 (measurements under natural sunlight and with solar
simulator), Clause 7 (differential spectral responsivity measurements) and Clause 8
(measurements via two-lamp and N-lamp method). Data analyses to determine the deviations
from the linear function are given in Clause 9.
A device is considered linear for the specific measured dependence Y(X), when it meets the
requirements of 9.7.

Photovoltaische Einrichtungen - Teil 10: Messverfahren für die Linearität

Dispositifs photovoltaïques - Partie 10: Méthodes de mesure de la dépendance linéaire et de la linéarité

l’IEC 60904-10:2020 décrit les procédures utilisées pour mesurer la dépendance de tout paramètre électrique (Y) d’un dispositif photovoltaïque (PV) par rapport à un paramètre d’essai (X) et pour déterminer le degré de proximité de la dépendance par rapport à une fonction linéaire idéale (ligne droite). Elle fournit également des recommandations relatives à la prise en considération des écarts par rapport à la dépendance linéaire idéale et, de façon générale, sur le traitement des non-linéarités des paramètres électriques d’un dispositif PV. 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: a. Modification du titre. b. Ajout d’une Introduction qui explique les modifications apportées et les raisons de ces modifications. c. Ajout d’un nouvel Article Termes et définitions (Article 3) qui fait la distinction entre la dépendance linéaire générique et la dépendance linéaire de courant de court-circuit en fonction de l’éclairement (linéarité). d. Définition explicite de l’échantillon équivalent (Article 4). e. Révision technique de l’équipement (Article 5), des procédures de mesure (Article 6 à Article 8) et de l’analyse des données (Article 9), avec distinction entre analyse des données relative à une dépendance linéaire générique et analyse des données spécifique à l’évaluation de la linéarité (c’est-à-dire la dépendance du courant de court-circuit sur l’éclairement). De plus, ajout de l’impact des effets spectraux sur l’évaluation de la linéarité et de la dépendance linéaire. f. Introduction d’une analyse de données spécifique à la méthode à deux lampes, rendant celle-ci entièrement quantitative. Ajout d’une version étendue appelée méthode à N lampes. g. Modification du critère d’évaluation de la linéarité avec ajout d’une formule qui peut être appliquée pour corriger le relevé d’éclairement d’un dispositif PV de référence pour la non‑linéarité de son courant de court-circuit en fonction de l’éclairement. Un facteur de linéarité spécifique est nouvellement défini dans ce but. h. Révision des exigences relatives au rapport (Article 10) afin de préciser les informations qui sont toujours nécessaires et ce qui dépend de la procédure réellement suivie pour mesurer la dépendance linéaire, y compris le type de dépendance mesuré (générique ou linéarité).

Fotonapetostne naprave - 10. del: Metode merjenja linearne odvisnosti in linearnosti

General Information

Status
Published
Publication Date
08-Dec-2020
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
08-Dec-2020
Due Date
12-Feb-2021
Completion Date
09-Dec-2020

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SLOVENSKI STANDARD
SIST EN IEC 60904-10:2021
01-januar-2021
Nadomešča:
SIST EN 60904-10:2011
Fotonapetostne naprave - 10. del: Metode merjenja linearne odvisnosti in
linearnosti
Photovoltaic devices - Part 10: Methods of linear dependence and linearity
measurements
Photovoltaische Einrichtungen - Teil 10: Messverfahren für die Linearität

Dispositifs photovoltaïques - Partie 10: Méthodes de mesure de la dépendance linéaire

et de la linéarité
Ta slovenski standard je istoveten z: EN IEC 60904-10:2020
ICS:
27.160 Sončna energija Solar energy engineering
SIST EN IEC 60904-10:2021 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST EN IEC 60904-10:2021
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SIST EN IEC 60904-10:2021
EUROPEAN STANDARD EN IEC 60904-10
NORME EUROPÉENNE
EUROPÄISCHE NORM
November 2020
ICS 27.160 Supersedes EN 60904-10:2010 and all of its
amendments and corrigenda (if any)
English Version
Photovoltaic devices - Part 10: Methods of linear dependence
and linearity measurements
(IEC 60904-10:2020)

Dispositifs photovoltaïques - Partie 10: Méthodes de Photovoltaische Einrichtungen - Teil 10: Methoden zur

mesure de la dépendance linéaire et de la linéarité Messung der linearen Abhängigkeit und Linearität

(IEC 60904-10:2020) (IEC 60904-10:2020)

This European Standard was approved by CENELEC on 2020-10-23. CENELEC members are bound to comply with the CEN/CENELEC

Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration.

Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC

Management Centre or to any CENELEC member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translation

under the responsibility of a CENELEC member into its own language and notified to the CEN-CENELEC Management Centre has the

same status as the official versions.

CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Croatia, Cyprus, the Czech Republic,

Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the

Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,

Turkey and the United Kingdom.
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2020 CENELEC All rights of exploitation in any form and by any means reserved worldwide for CENELEC Members.

Ref. No. EN IEC 60904-10:2020 E
---------------------- Page: 3 ----------------------
SIST EN IEC 60904-10:2021
EN IEC 60904-10:2020 (E)
European foreword

The text of document 82/1759/FDIS, future edition 3 of IEC 60904-10, prepared by IEC/TC 82 "Solar

photovoltaic energy systems" was submitted to the IEC-CENELEC parallel vote and approved by

CENELEC as EN IEC 60904-10:2020.
The following dates are fixed:

• latest date by which the document has to be implemented at national (dop) 2021-07-23

level by publication of an identical national standard or by endorsement

• latest date by which the national standards conflicting with the (dow) 2023-10-23

document have to be withdrawn

This document supersedes EN 60904-10:2010 and all of its amendments and corrigenda (if any).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. CENELEC shall not be held responsible for identifying any or all such patent rights.

Endorsement notice

The text of the International Standard IEC 60904-10:2020 was approved by CENELEC as a European

Standard without any modification.

In the official version, for Bibliography, the following notes have to be added for the standards

indicated:
IEC 61829 NOTE Harmonized as EN 61829
IEC 61853-1 NOTE Harmonized as EN 61853-1
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SIST EN IEC 60904-10:2021
EN IEC 60904-10:2020 (E)
Annex ZA
(normative)
Normative references to international publications
with their corresponding European publications

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.

NOTE 1 Where an International Publication has been modified by common modifications, indicated by (mod),

the relevant EN/HD applies.

NOTE 2 Up-to-date information on the latest versions of the European Standards listed in this annex is available

here: www.cenelec.eu.
Publication Year Title EN/HD Year
IEC 60891 - Photovoltaic devices - Procedures for EN 60891 -
temperature and irradiance corrections to
measured I-V characteristics
IEC 60904-1 - Photovoltaic devices - Part 1: Measurement of EN IEC 60904-1 -
photovoltaic current-voltage characteristics
IEC 60904-1-1 - Photovoltaic devices - Part 1-1: Measurement EN 60904-1-1 -
of current-voltage characteristics of multi-
junction photovoltaic (PV) devices
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 EN 60904-2 -
for photovoltaic reference devices
IEC 60904-3 - Photovoltaic devices - Part 3: Measurement EN IEC 60904-3 -
principles for terrestrial photovoltaic (PV) solar
devices with reference spectral irradiance data
IEC 60904-7 - Photovoltaic devices - Part 7: Computation of EN IEC 60904-7 -
the spectral mismatch correction for
measurements of photovoltaic devices
IEC 60904-8 - Photovoltaic devices - Part 8: Measurement of EN 60904-8 -
spectral responsivity of a photovoltaic (PV)
device
IEC 60904-8-1 - Photovoltaic devices - Part 8-1: Measurement EN 60904-8-1 -
of spectral responsivity of multi-junction
photovoltaic (PV) devices
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SIST EN IEC 60904-10:2021
EN IEC 60904-10:2020 (E)
Publication Year Title EN/HD Year
IEC 60904-9 - Photovoltaic devices - Part 9: Classification of EN IEC 60904-9 -
solar simulator characteristics

IEC 61215 series Crystalline silicon terrestrial photovoltaic (PV) EN 61215 series

modules - Design qualification and type
approval
IEC 61724-1 - Photovoltaic system performance - Part 1: - -
Monitoring
IEC/TS 61836 - Solar photovoltaic energy systems - Terms, - -
definitions and symbols
ISO/TS 28037 - Determination and use of straight-line - -
calibration functions
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SIST EN IEC 60904-10:2021
IEC 60904-10
Edition 3.0 2020-09
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Photovoltaic devices –
Part 10: Methods of linear dependence and linearity measurements
Dispositifs photovoltaïques –
Partie 10: Méthodes de mesure de la dépendance linéaire et de la linéarité
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 27.160 ISBN 978-2-8322-8802-3

Warning! Make sure that you obtained this publication from an authorized distributor.

Attention! Veuillez vous assurer que vous avez obtenu cette publication via un distributeur agréé.

® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale
---------------------- Page: 7 ----------------------
SIST EN IEC 60904-10:2021
– 2 – IEC 60904-10:2020 © IEC 2020
CONTENTS

FOREWORD ........................................................................................................................... 3

INTRODUCTION ..................................................................................................................... 5

1 Scope .............................................................................................................................. 7

2 Normative references ...................................................................................................... 8

3 Terms and definitions ...................................................................................................... 8

4 Device selection .............................................................................................................. 9

5 Apparatus ...................................................................................................................... 10

5.1 General requirements common to all procedures .................................................. 10

5.2 Apparatus for measurement of all linear dependences under natural sunlight

or with a solar simulator ........................................................................................ 11

5.3 Apparatus for measurement of all linear dependences of short-circuit current

by differential spectral responsivity measurements ............................................... 12

5.4 Apparatus for linearity measurement of short-circuit current by two-lamp

method ................................................................................................................. 12

5.5 Apparatus for linearity measurement of short-circuit current by N-lamp

method ................................................................................................................. 12

6 Procedures to measure linearity and other linear dependences under natural

sunlight or with a solar simulator ................................................................................... 12

6.1 Additional general requirements for natural sunlight .............................................. 12

6.2 Mounting under natural sunlight ............................................................................ 13

6.3 Mounting with a solar simulator ............................................................................. 13

6.4 Linear dependence measurements versus irradiance ............................................ 13

6.5 Linear dependence measurements versus temperature ......................................... 16

7 Procedures to measure linearity and other linear dependence of short-circuit

current from differential spectral responsivity ................................................................. 17

7.1 Linearity measurements ........................................................................................ 17

7.2 Linear dependence measurements of short-circuit current versus

temperature .......................................................................................................... 18

8 Procedure for short-circuit current linearity measurement by the two-lamp or the

N-lamp methods ............................................................................................................ 18

8.1 Background........................................................................................................... 18

8.2 Measurement procedure by the two-lamp method ................................................. 19

8.3 Measurement procedure by the N-lamp method .................................................... 20

9 Calculation of linear dependence and linearity ............................................................... 21

9.1 General considerations ......................................................................................... 21

9.2 Measurement uncertainty evaluation ..................................................................... 21

9.3 Determination of deviations from a generic linear dependence .............................. 22

9.3.1 Generic case ................................................................................................. 22

9.4 Determination of the short-circuit current non-linearity versus irradiance ............... 22

9.5 Determination of the short-circuit current non-linearity versus irradiance

using the two-lamp method ................................................................................... 23

9.6 Determination of the short-circuit current non-linearity versus irradiance

using the N-lamp method ...................................................................................... 24

9.7 Requirements for maximum deviations from the ideal linear function ..................... 25

10 Report ........................................................................................................................... 26

Bibliography .......................................................................................................................... 27

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SIST EN IEC 60904-10:2021
IEC 60904-10:2020 © IEC 2020 – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
PHOTOVOLTAIC DEVICES –
Part 10: Methods of linear dependence and linearity measurements
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 60904-10 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:
a) Modification of title.

b) Inclusion of an Introduction explanatory of the changes and the reasoning behind them.

c) Inclusion of a new Clause Terms and Definitions (Clause 3), with distinction between

generic linear dependence and linear dependence of short-circuit current versus
irradiance (linearity).
d) Explicit definition of equivalent sample (Clause 4).
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SIST EN IEC 60904-10:2021
– 4 – IEC 60904-10:2020 © IEC 2020

e) Technical revision of the apparatus (Clause 5), of the measurement procedures (Clause 6

to Clause 8) and of the data analysis (Clause 9), with separation of the data analysis for a

generic linear dependence from the data analysis specific to linearity (i.e. short-circuit

current dependence on irradiance) assessment. Additionally, inclusion of impact of

spectral effects on both linearity and linear dependence assessment.

f) Introduction of specific data analysis for two-lamp method, making it fully quantitative.

Addition of extended version called N-lamp method.

g) Modification of the linearity assessment criterion with inclusion of a formula that can be

used to correct the irradiance reading of a PV reference device for non-linearity of its

short-circuit current versus irradiance. A linearity factor is specifically newly defined for

this purpose.

h) Revision of the requirements for the report (Clause 10) in order to improve clearness

about what information is always necessary and what is dependent on the procedure

actually followed to measure the linear dependence, including the type of dependence

measured (generic or linearity).
The text of this International Standard is based on the following documents:
FDIS Report on voting
82/1759/FDIS 82/1784/RVD

Full information on the voting for the approval of this International Standard can be found in

the report on voting indicated in the above table.

This document has been drafted in accordance with the ISO/IEC Directives, Part 2.

A list of all parts of the IEC 60904 series, under the general title Photovoltaic devices, can be

found on the IEC website.

The committee has decided that the contents of this document will remain unchanged until the

stability date indicated on the IEC website under "http://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.
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SIST EN IEC 60904-10:2021
IEC 60904-10:2020 © IEC 2020 – 5 –
INTRODUCTION
IEC 60904-10 is the reference document for several IEC standards when the linear

dependence of one or more electrical parameters of a photovoltaic (PV) device has to be

assessed in relation to a test parameter. Test parameters are usually either the device

temperature or the irradiance. In order to better reflect the different cases to be handled and

the peculiarities of the linear dependence of the short-circuit current of a PV device on the

irradiance, IEC 60904-10 has been extensively revised.

To avoid confusion, in this document the word “linearity” will be used only for the dependence

of the short-circuit current (I ) on the irradiance (G), while all the other dependences will be

referred to as generic linear dependence (when not explicitly described).

Three major technical changes have been included in this third edition compared to the

second edition.

The first main change is the split of the data analysis for the linearity from the one to be used

for a generic linear dependence (like for example V (T), which gives the open-circuit voltage

as function of temperature). The latter keeps the same approach already included in the

previous edition, i.e. the least squares fit method, with addition of the recommended use of

the measurement uncertainties within the data analysis. The former applies the proportionality

function that describes the dependence between I and G for an ideal linear PV device. It

also makes use of the calibration value of the I to establish a reference point towards which

the non-linearity is explicitly referred. Also, the impact of test spectra and spectral mismatch

on both linearity and generic linear dependence is now considered.

Following this new approach for the linearity assessment, the second major change involves a

modification of the definition of non-linearity (referred now explicitly to the calibration value)

and the inclusion of a formula to correct the measured irradiance for the non-linearity of the

PV device used to measure it. Such a PV device is usually a reference device. However,

IEC 61853-1 explicitly considers the case of using the short-circuit current of the PV device

itself to measure the irradiance when its linearity has been proved (Note in IEC 61853-1:2011:

8.1). A correction of the actual irradiance measurement to account for deviations of I from

linearity is therefore relevant when the irradiance is measured by a reference device as well

as by the device under test itself. In principle, this can be extended to non-linear devices as

well, provided that the non-linearity information is stated in addition to the calibration value of

the PV device itself. The irradiance correction for non-linearity is made in this document by

means of a multiplication factor, resembling the same approach used in the IEC 60904-7 for

the spectral mismatch correction. This formula has been introduced in order to address the

explicit reference of the other standards to IEC 60904-10 in terms of handling non-linear

devices. However, this formula can be useful to correct deviations from linearity within the

acceptance limits even in the case of reference devices classified as linear according to the

previous edition of this standard.

The third main change is the revision of the two-lamp method approach. This is achieved first

by the introduction of a specific data analysis for the two-lamp method, which was a simple

pass/fail test in the second edition and gains now the status of a quantitative method. This

change is crucial in order to have results, obtained by any procedure for linearity

measurements allowed by this standard, to be fully comparable to each other within their

stated measurement uncertainties. Thereby, the irradiance correction formula is also

applicable to the results from the two-lamp method. With these additions, the two-lamp

method becomes the simplest quantitative method to assess the linearity (i.e. dependence of

short-circuit current I on irradiance) of PV devices, not even requiring a reference device

when devices under test are single PV cells. An extended version called N-lamp method has

been included, which overcomes some limitations of the two-lamp method.

A secondary change, which was introduced to improve locating the necessary procedure

within the document, is the distinction between the cases of irradiance and of temperature as

test parameter, i.e. the parameter being varied and on which the dependence is checked.

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SIST EN IEC 60904-10:2021
– 6 – IEC 60904-10:2020 © IEC 2020

Furthermore, when the linear dependence of a device parameter (e.g. I ) has to be

assessed towards more than a single test parameter, intermediate steps applying the

procedures described by this standard can be followed if the device under test is stable

according to the criterion given in IEC 61215-1 and its relevant part. For example, the

measurement of a power matrix as defined by IEC 61853-1 requires the measurement of the

maximum power as a function of both irradiance and temperature. In this case, the most

convenient way of performing the power matrix measurement is usually to vary one parameter

(e.g. the temperature) while keeping the other (e.g. the irradiance) steady, and then to repeat

this procedure at different levels of the second parameter until the full matrix is completed. In

this view, the second parameter would be considered as the fixed one, and the first one would

be the test parameter towards which the linear dependence is evaluated according to this

standard. However, once the full power matrix has been measured, the subsequent data

analysis of the maximum power (as well as of any other relevant electrical parameter) of the

device under test can be done by considering either parameter as the test parameter as long

as the other one is kept constant. Therefore, a linear dependence can be assessed with

respect to one or the other parameter, independent of the measurement procedure used to

obtain the data.
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SIST EN IEC 60904-10:2021
IEC 60904-10:2020 © IEC 2020 – 7 –
PHOTOVOLTAIC DEVICES –
Part 10: Methods of linear dependence and linearity measurements
1 Scope

This part of IEC 60904 describes the procedures used to measure the dependence of any

electrical parameter (Y) of a photovoltaic (PV) device with respect to a test parameter (X) and

to determine the degree at which this dependence is close to an ideal linear (straight-line)

function. It also gives guidance on how to consider deviations from the ideal linear

dependence and in general on how to deal with non-linearities of PV device electrical

parameters. Typical device parameters are the short-circuit current I , the open-circuit

voltage V and the maximum power P . Typical test parameters are the temperature T and

OC max

the irradiance G. However, the same principles described in this document can be applied to

any other test parameter with proper adjustment of the procedure used to vary the parameter

itself.

Performance evaluations of PV modules and systems, as well as performance translations

from one set of temperature and irradiance to another, frequently rely on the use of linear

equations (see for example IEC 60891, IEC 61853-1, IEC 61829 and IEC 61724-1). This

document lays down the requirements for linear dependence test methods, data analysis and

acceptance limits of results to ensure that these linear equations will give satisfactory results.

Such requirements prescribe also the range of the temperature and irradiance over which the

linear equations may be used. This document gives also a procedure on how to correct for

deviations of the short-circuit current I from the ideal linear dependence on irradiance

(linearity) for PV devices, regardless of whether they are classified linear or non-linear

according to the limits set in 9.7. The impact of spectral irradiance distribution and spectral

mismatch is considered for measurements using solar simulators as well as under natural

sunlight.

The measurement methods described herein apply to all PV devices, with some caution to be

used for multi-junction PV devices, and are intended to be carried out on a device, or in some

cases on an equivalent device of identical technology, that is stable according to the criteria

set in the relevant part of IEC 61215. These measurements are meant to be performed prior

to all measurements and correction procedures that require a linear device or that prescribe

restrictions for non-linear devices.

The main methodology used in this document is based on a fitting procedure in which a linear

(straight-line) function is fitted to a set of measured data points {X ,Y }. The linear function

i i

uses a least-squares fit calculation routine, which in the most advanced analysis also

accounts for the expanded combined uncertainty (k=2) of the measurements. The linear

function crosses the origin in the case of short-circuit current data versus irradiance. The

deviation of the measured data from the ideal linear function is also calculated and limits are

prescribed for the permissible percentage deviation.

Procedures to determine the deviation of the Y(X) dependence from the linear (straight-line)

function are described in Clause 6 (measurements under natural sunlight and with solar

simulator), Clause 7 (differential spectral responsivity measurements) and Clause 8

(measurements via two-lamp and N-lamp method). Data analyses to determine the deviations

from the linear function are given in Clause 9.

A device is considered linear for the specific measured dependence Y(X), when it meets the

requirements of 9.7.
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SIST EN IEC 60904-10:2021
– 8 – IEC 60904-10:2020 © IEC 2020
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 60891, P
...

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