Electrical insulating materials - A.C. voltage endurance evaluation (IEC 61251:2015)

This International Standard describes many of the factors involved in voltage endurance tests
on electrical insulating materials and systems. It describes the voltage endurance graph, lists
test methods illustrating their limitations and gives guidance for evaluating the sinusoidal a.c.
voltage endurance of insulating materials and systems from the results of the tests. This
International Standard is applicable over the voltage frequency range 20 Hz to 1 000 Hz. The
general principles can also be applicable to other voltage shapes, including impulse voltages.
The terminology to be used in voltage endurance is defined and explained.

Elektrische Isolierstoffe und -systeme - Ermittlung der Wechselspannungsbeständigkeit

Matériaux isolants électriques - Evaluation de l'endurance à la tension alternative

L'IEC 61251:2015 décrit plusieurs des facteurs intervenant dans les essais d'endurance à la tension de systèmes et de matériaux isolants électriques. Elle décrit le graphe d'endurance à la tension, donne une liste des méthodes d'essai en indiquant leurs limites et donne des lignes directrices pour évaluer l'endurance à la tension alternative de systèmes et de matériaux isolants à partir des résultats des essais. La présente Norme internationale est applicable sur la plage de fréquences de la tension allant de 20 Hz à 1 000 Hz. Les principes généraux peuvent également être applicables à d'autres formes de tension, y compris les tensions de chocs. La terminologie à utiliser dans le cadre de l'endurance à la tension est définie et expliquée. Cette première édition de l'IEC 61251 annule et remplace la deuxième édition de l'IEC TS 61251 parue en 2008. Cette édition constitue une révision technique. Cette édition inclut les modifications techniques majeures suivantes par rapport à la deuxième édition de l'IEC TS 61251: a) transformation d'une Spécification technique en Norme internationale; b) clarification des questions soulevées depuis la publication de l'IEC TS 61251.

Elektroizolacijski materiali - Ocenjevanje vzdržljivosti pri izmenični napetosti (IEC 61251:2015)

V tem mednarodnem standardu so opisani številni dejavniki, ki so vključeni v preskuse napetostne vzdržljivosti na elektroizolacijskih materialih in sistemih. Opisuje graf napetostne vzdržljivosti, navaja preskusne metode in prikazuje njihove omejitve ter na podlagi rezultatov preskusov podaja navodila za ocenjevanje sinusne vzdržljivosti pri izmenični napetosti za izolacijske materiale in sisteme. Ta mednarodni standard se uporablja za frekvenčno območje napetosti 20–1000 Hz. Splošna načela se lahko uporabljajo tudi za druge oblike napetosti, vključno z impulznimi napetostmi. Opredeljeni in razloženi so izrazi, ki se uporabljajo za napetostno vzdržljivost.

General Information

Status
Published
Publication Date
13-Mar-2016
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
03-Mar-2016
Due Date
08-May-2016
Completion Date
14-Mar-2016

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SLOVENSKI STANDARD
SIST EN 61251:2016
01-maj-2016

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Electrical insulating materials - A.C. voltage endurance evaluation (IEC 61251:2015)

Matériaux isolants électriques - Evaluation de l'endurance à la tension alternative

Ta slovenski standard je istoveten z: EN 61251:2016
ICS:
17.220.99 Drugi standardi v zvezi z Other standards related to
elektriko in magnetizmom electricity and magnetism
29.035.01 Izolacijski materiali na Insulating materials in
splošno general
SIST EN 61251:2016 en

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

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SIST EN 61251:2016
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SIST EN 61251:2016
EUROPEAN STANDARD EN 61251
NORME EUROPÉENNE
EUROPÄISCHE NORM
February 2016
ICS 17.220.99; 29.035.01
English Version
Electrical insulating materials and systems - A.C. voltage
endurance evaluation
(IEC 61251:2015)

Systèmes et matériaux isolants électriques - Évaluation de Elektrische Isolierstoffe und -systeme - Ermittlung der

l'endurance a la tension alternative Wechselspannungsbeständigkei
(IEC 61251:2015) (IEC 61251:2015)

This European Standard was approved by CENELEC on 2015-12-23. 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, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,

Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, 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: Avenue Marnix 17, B-1000 Brussels

© 2016 CENELEC All rights of exploitation in any form and by any means reserved worldwide for CENELEC Members.

Ref. No. EN 61251:2016 E
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SIST EN 61251:2016
EN 61251:2016
European foreword

The text of document 112/338/FDIS, future edition 1 of IEC 61251, prepared by IEC/TC 112

"Evaluation and qualification of electrical insulating materials and systems" was submitted to the

IEC-CENELEC parallel vote and approved by CENELEC as EN 61251:2016.
The following dates are fixed:
(dop) 2016-09-23
• latest date by which the document has to be
implemented at national level by
publication of an identical national
standard or by endorsement
• latest date by which the national (dow) 2018-12-23
standards conflicting with the
document have to be withdrawn

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

patent rights. CENELEC [and/or CEN] shall not be held responsible for identifying any or all such

patent rights.
Endorsement notice

The text of the International Standard IEC 61251:2015 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 60243-1 NOTE Harmonized as EN 60243-1.
IEC 60243-2 NOTE Harmonized as EN 60243-2.
IEC 60243-3 NOTE Harmonized as EN 60243-3.
IEC 60343 NOTE Harmonized as EN 60343.
IEC 61649 NOTE Harmonized as EN 61649.
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SIST EN 61251:2016
EN 61251:2016
Annex ZA
(normative)
Normative references to international publications
with their corresponding European publications

The following documents, in whole or in part, are normatively referenced in this document and are

indispensable for its application. For dated references, only the edition cited applies. For undated

references, the latest edition of the referenced document (including any amendments) applies.

NOTE 1 When 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 62539 - Guide for the statistical analysis of - -
electrical insulation breakdown data
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SIST EN 61251:2016
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SIST EN 61251:2016
IEC 61251
Edition 1.0 2015-11
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Electrical insulating materials and systems – AC voltage endurance evaluation
Systèmes et matériaux isolants électriques – Évaluation de l'endurance à la
tension alternative
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 17.220.99; 29.035.01 ISBN 978-2-8322-2990-3

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
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SIST EN 61251:2016
– 2 – IEC 61251:2015 © IEC 2015
CONTENTS

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

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

1 Scope .............................................................................................................................. 6

2 Normative references ...................................................................................................... 6

3 Terms, definitions and symbols........................................................................................ 6

3.1 Terms and definitions .............................................................................................. 6

3.2 Symbols .................................................................................................................. 7

4 Voltage endurance .......................................................................................................... 7

4.1 Voltage endurance testing ...................................................................................... 7

4.2 Electrical stress ...................................................................................................... 7

4.3 Voltage endurance (VE) graph ................................................................................ 8

4.4 Short-time electric strength ..................................................................................... 8

4.5 Voltage endurance coefficient (VEC) ....................................................................... 9

4.6 Differential VEC (n ) ............................................................................................... 9

4.7 Electrical threshold stress (E ) ................................................................................ 9

4.8 Voltage endurance relationship ............................................................................. 10

5 Test methods ................................................................................................................. 11

5.1 Introductory remarks ............................................................................................. 11

5.2 Tests at constant stress ........................................................................................ 11

5.2.1 Conventional VE test ..................................................................................... 11

5.2.2 Diagnostic measurements .............................................................................. 12

5.2.3 Detection of an electrical threshold ................................................................ 12

5.3 Tests at higher frequency...................................................................................... 12

5.4 Progressive stress tests ........................................................................................ 13

5.5 Preliminary tests to determine the initial part of the VE line ................................... 15

5.6 Recommended test procedure .............................................................................. 15

6 Evaluation of voltage endurance .................................................................................... 15

6.1 Significance of the VEC ........................................................................................ 15

6.2 Significance of the electrical threshold stress ........................................................ 16

6.3 Dispersion of data and precision requirements ...................................................... 16

6.4 Presentation of the results .................................................................................... 16

Annex A (informative) The Weibull distribution ..................................................................... 18

A.1 Weibull distribution times to dielectric breakdown ................................................. 18

A.2 Weibull distribution dielectric breakdown stresses ................................................. 18

A.3 Generalized Weibull distribution of the dielectric breakdown stresses ................... 18

A.4 Inverse power model for the time to dielectric breakdown ..................................... 19

Bibliography .......................................................................................................................... 20

Figure 1 – General voltage endurance line .............................................................................. 8

Figure 2 – Determination of the differential VEC n at a generic point P of the VE line ............ 9

Figure 3 – Plotting the VE line in a progressive stress test using different rates of

stress rise ............................................................................................................................. 14

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SIST EN 61251:2016
IEC 61251:2015 © IEC 2015 – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTRICAL INSULATING MATERIALS AND SYSTEMS –
AC VOLTAGE ENDURANCE EVALUATION
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 61251 has been prepared by IEC technical committee 112:

Evaluation and qualification of electrical insulating materials and systems.

This first edition of IEC 61251 cancels and replaces the second edition of IEC TS 61251,

published in 2008. This edition constitutes a technical revision.

This edition includes the following significant technical changes with respect to the second

edition of IEC TS 61251:
a) upgrade from Technical Specification to an International Standard;
b) clarification of issues raised since publication of IEC TS 61251.
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SIST EN 61251:2016
– 4 – IEC 61251:2015 © IEC 2015
The text of this standard is based on the following documents:
FDIS Report on voting
112/338/FDIS 112/347/RVD

Full information on the voting for the approval of this standard can be found in the report on

voting indicated in the above table.

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

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

the stability date indicated on the IEC website under "http://webstore.iec.ch" in the data

related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
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SIST EN 61251:2016
IEC 61251:2015 © IEC 2015 – 5 –
INTRODUCTION

This International Standard covers insulating materials and systems. Voltage endurance tests

are used to compare and evaluate insulating materials and systems. It is complex to

determine the capability of electrical insulating materials and systems to endure a.c. voltage

stress. The results of voltage endurance tests are influenced by many factors. Therefore this

International Standard can be considered as an attempt to present a unified view of voltage

endurance for simplified planning and analysis.
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SIST EN 61251:2016
– 6 – IEC 61251:2015 © IEC 2015
ELECTRICAL INSULATING MATERIALS AND SYSTEMS –
AC VOLTAGE ENDURANCE EVALUATION
1 Scope

This International Standard describes many of the factors involved in voltage endurance tests

on electrical insulating materials and systems. It describes the voltage endurance graph, lists

test methods illustrating their limitations and gives guidance for evaluating the sinusoidal a.c.

voltage endurance of insulating materials and systems from the results of the tests. This

International Standard is applicable over the voltage frequency range 20 Hz to 1 000 Hz. The

general principles can also be applicable to other voltage shapes, including impulse voltages.

The terminology to be used in voltage endurance is defined and explained.
2 Normative references

The following documents, in whole or in part, are normatively referenced in this document and

are indispensable for its application. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any
amendments) applies.

IEC 62539, Guide for the statistical analysis of electrical insulation dielectric breakdown data

3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1.1
voltage endurance
measures of the capability of a solid insulating material to endure voltage

Note 1 to entry: In this International Standard, only a.c. voltage is considered.

Note 2 to entry: This note only applies to the French language.
3.1.2
life
time to dielectric breakdown
3.1.3
voltage endurance coefficient
VEC

numerical value of the reciprocal of the slope of a straight line log-log VE plot

Note 1 to entry: This note only applies to the French language.
3.1.4
specimen

representative test object for assessing the value of one or more physical properties

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SIST EN 61251:2016
IEC 61251:2015 © IEC 2015 – 7 –
3.1.5
sample

group of nominally identical specimens extracted randomly from the same manufacturing

batch
3.2 Symbols
c, c′ constants in the inverse-power model
E electric stress
E short-time electric strength
E electric threshold stress
f frequency
h, k constants in the exponential model
L life
m scale parameter in the Weibull distribution (one variable)
M scale parameter in the generalized Weibull distribution (two variables)
n exponent of stress in the inverse-power model coinciding with the VEC
n differential VEC
R dimensional ratio
t time
t time to dielectric breakdown at constant stress
t time to dielectric breakdown at constant stress E
o o
t time to dielectric breakdown with progressive stress
tan δ dissipation factor

α scale parameter (63,2 percentile) in the Weibull distribution of times to dielectric

breakdown at constant stress

β shape parameter in the Weibull distribution of times to dielectric breakdown at

constant stress

γ shape parameter of the Weibull distribution of the dielectric breakdown stresses from a

progressive stress test
4 Voltage endurance
4.1 Voltage endurance testing

To evaluate the voltage endurance of insulating materials or systems, a number of specimens

are subjected to a.c. voltage and their times to dielectric breakdown are measured. In practice,

several samples of many specimens are tested at different voltages to reveal the effect of the

applied voltage on the time to dielectric breakdown. The arithmetic mean time to dielectric

breakdown of each sample is the average time to dielectric breakdown of all specimens tested

at that voltage. The time at which a certain percentage of specimens break down is the

estimated time to dielectric breakdown with a probability equal to this percentage.

The statistical treatment of the data (either by analytical or graphical methods) allows the

extraction of additional data such as other failure percentiles or confidence bounds and,

possibly, determination of the distribution (Gaussian, Weibull, lognormal, etc.).

4.2 Electrical stress

In general, reference to electrical stress (voltage per unit thickness) instead of voltage is

required. For a uniform field, electrical stress is given by the voltage (effective value) divided

by the thickness of specimens.
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SIST EN 61251:2016
– 8 – IEC 61251:2015 © IEC 2015

If the electric field is not uniform, the maximum value shall be considered by the relevant

equipment committees.
4.3 Voltage endurance (VE) graph

The VE graph represents the time to dielectric breakdown (life) versus the corresponding

value of electrical stress. In the VE graph, the electrical stress is plotted as the ordinate with

either a linear or logarithmic scale. The times to dielectric breakdown are plotted on the

abscissa with a logarithmic scale. The voltage endurance line on this graph gives the final

result of the VE tests as it allows clear and complete evaluation of voltage endurance of the

specimens under the specified test conditions. For maximum significance, materials or

systems shall be compared at equal thickness and using the same type of electrodes,

temperature, humidity and ambient gas, or as agreed by the relevant equipment committees.

An accurate plotting of the line requires more than three tests at different voltages and one or

more tests are required at voltages which result in times to failure longer than 1 000 h. In any

case, a minimum number of three tests is required to draw the VE graph.

The voltage endurance line is straight or curved. In the latter case, its trend can often be

approximated by a few straight regions: sometimes a first part for short times with a low slope,

a middle region (which can extend to long times) with a steeper slope and finally a further

trend of the line showing a tendency to become horizontal (see Figure 1, where a general VE

line is shown). It is likely that the shape of the VE graph changes significantly from one

material or system to another. With a curve as shown in Figure 1, the VEC is not constant,

and the VEC will be different at different times (see n in Figure 2).
Log E
t Log time to breakdown
IEC
Figure 1 – General voltage endurance line
4.4 Short-time electric strength

The short-time electric strength is measured using a linearly increasing voltage. The duration

of such a test, as used in this International Standard, is of the order of one minute up to some

tens of minutes. The arithmetic mean value of the breakdown field for the tested sample is E .

The results of electric strength tests (or, in general, of tests with increasing voltage) are not

represented directly in the VE graph. Instead, a constant voltage test at the same stress as

the mean electric strength, E (or very close to it, 0,9E or as agreed), is made to determine

o o

the time to dielectric breakdown, t , with constant stress. The point (E , t ) is the origin of the

o o o

VE line. More details on this procedure are given in 5.5. However, when this procedure is

used, the following precautions shall be taken.
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SIST EN 61251:2016
IEC 61251:2015 © IEC 2015 – 9 –

a) The electric strength tests shall be carried out under the same conditions (humidity,

temperature, etc.), in the same test cell and with the same procedures as for the voltage

endurance tests.

b) The test specimens, the breakdown path and the conditions of the specimen after

dielectric breakdown shall be examined and recorded for future use in the analysis of the

results. The latter is to ensure that the mode of failure at high stress is the same as that of

the other specimens tested later at lower stress.
4.5 Voltage endurance coefficient (VEC)

The slope of the VE line, n, is an indicator of the response of a material or system to electrical

stress. The parameter n is dimensionless. With a small slope of the VE line (i.e. a large value

of VEC), even a small reduction of stress produces a great increase in life. The reciprocal of

the slope is taken to be consistent with the numerical value of the exponent n in Formula (1).

A large value of the VEC does not correspond necessarily to high electric strength. It can

happen that the material with lower VEC has a longer time to dielectric breakdown at a given

stress if its short-time electric strength is so high that its poorer endurance is compensated for.

The value of n shall be associated with a high mean electric strength before attributing a high

endurance to the material. What is most significant is the retention of usable electric

strength for long periods of time.
4.6 Differential VEC (n )

If the VE line is curved in log-log coordinates, its slope is measured by means of the tangent

at any point. For any electrical stress, and thus for any point on the line, the differential

, can be defined as the absolute value of the reciprocal of
voltage endurance coefficient, n

the slope of the curve at that point (Figure 2) according to the life model described in

Clause 5.
Log
VE line
Line for determining n
1,0
Log time to breakdown
IEC

Figure 2 – Determination of the differential VEC n at a generic point P of the VE line

4.7 Electrical threshold stress (E )

If the VE line tends to become horizontal with decreasing stress within the test stress-times,

this indicates the presence of a limiting stress, E , below which electrical ageing becomes

negligible. This limit is called the electrical threshold stress. The tendency of the line to

become horizontal is detected by means of tests of suitable duration. However, the tests do

not always succeed in revealing such a trend in a reasonable time. Some insulating materials

or systems do not show any electrical threshold stress even for very long test times.

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SIST EN 61251:2016
– 10 – IEC 61251:2015 © IEC 2015
4.8 Voltage endurance relationship

The VE relationship is the mathematical model of life under electrical stress or voltage, i.e.

the formula relating electrical stress and time to dielectric breakdown, whose graphical

representation is given by the VE line. If this line is straight on log-log graph paper, the

formula is of the type:
L = c E (1)
where
L is the time to dielectric breakdown or time to failure or life;
E is the electrical stress;

c and n are constants dependent on temperature and other environmental parameters.

Formula (1) constitutes the so-called inverse-power model, which is the voltage-life model

often encountered with voltage endurance data on solid electrical insulation. In this case the

VEC is n, and it is constant. When data are available for time to dielectric breakdown at two

constant-voltage stresses, this model shall be used to get a rough estimate of the value of n

by using Formula (2):
L  E 
1 1
 
= (2)
 
L E
2 2
 

If the VE test data do not form a straight line on log-log paper, the use of the inverse-power

, other models have
model is incorrect. If the line approaches an electrical threshold stress, E
been proposed, among them
L = c′ (E – E ) , (3)

which becomes the inverse-power model if E tends to 0 and is preferably used when the data

for short and medium times fit a straight line on log-log coordinates. Alternatively, another

model is
k exp (− h E)
L = , (4)
E − E

which derives from the exponential model, corresponding to an approximately straight line in

semilog coordinates for E > E but gives infinite time to dielectric breakdown when E tends to

E . In Formulas (3) and (4), constants c′, n, k, h and E depend on temperature and other

t t
environmental conditions.

Formulas (3) and (4) generate two new formulas which define the trend of the VE line

, E ) and (L , E ). The following formulas are obtained:
between any two points, (L
1 1 2 2
 E − E 
1 1 t
 
= , (5)
 
L E − E
2  2 t 
L exp {− h (E − E )}
1 1 2
= . (6)
L (E − E )/ (E − E )
2 1 t 2 t
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SIST EN 61251:2016
IEC 61251:2015 © IEC 2015 – 11 –

The formulas of the VE line for a straight line or a straight-line segment on log-log plot are

Formulas (1) and (2). When there is a tendency toward a threshold after an approximately

linear trend on log-log or semilog graph paper, Formulas (3), (4), (5) and (6) apply.

By taking the logarithms, the inverse-power model, Formula (1), becomes
ln (L) = ln (c) − n ln (E) . (7)

This is the formula of the straight VE line in log-log coordinates. Its slope is −1/n. As the

numerical value of the reciprocal of the slope is equal to n, the VEC can also be defined as

the exponent n in the inverse-power model.
5 Test methods
5.1 Introductory remarks

Different methods of carrying out the VE test can be used. The differences concern the way of

applying voltage (constant or increasing with time), the frequency (service or higher) and the

time
...

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