EN IEC 62836:2024

SLOVENSKI STANDARD
01-junij-2024
Merjenje notranjega električnega polja v izolacijskih materialih - Metoda širjenja
tlačnega vala (IEC 62836:2024)
Measurement of internal electric field in insulating materials - Pressure wave propagation
method (IEC 62836:2024)
Messung des inneren elektrischen Feldes in Isoliermaterialien - Methode der
Druckwellenausbreitung (propagation method) (IEC 62836:2024)
Mesurage du champ électrique interne dans les matériaux isolants - Méthode de l'onde
de pression (IEC 62836:2024)
Ta slovenski standard je istoveten z: EN IEC 62836:2024
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
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD EN IEC 62836

NORME EUROPÉENNE
EUROPÄISCHE NORM April 2024
ICS 17.220.99; 29.035.01
English Version
Measurement of internal electric field in insulating materials -
Pressure wave propagation method
(IEC 62836:2024)
Mesurage du champ électrique interne dans les matériaux Messung des inneren elektrischen Feldes in
isolants - Méthode de l'onde de pression Isoliermaterialien - Methode der Druckwellenausbreitung
(IEC 62836:2024) (IEC 62836:2024)
This European Standard was approved by CENELEC on 2024-04-03. 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.
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Türkiye 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
© 2024 CENELEC All rights of exploitation in any form and by any means reserved worldwide for CENELEC Members.
Ref. No. EN IEC 62836:2024 E
European foreword
The text of document 112/627/FDIS, future edition 1 of IEC 62836, 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 IEC 62836:2024.
The following dates are fixed:
• latest date by which the document has to be implemented at national (dop) 2025-01-03
level by publication of an identical national standard or by endorsement
• latest date by which the national standards conflicting with the (dow) 2027-04-03
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 shall not be held responsible for identifying any or all such patent rights.
Any feedback and questions on this document should be directed to the users’ national committee. A
complete listing of these bodies can be found on the CENELEC website.
Endorsement notice
The text of the International Standard IEC 62836:2024 was approved by CENELEC as a European
Standard without any modification.

IEC 62836 ®
Edition 1.0 2024-02
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Measurement of internal electric field in insulating materials – Pressure wave

propagation method
Mesurage du champ électrique interne dans les matériaux isolants – Méthode

de l'onde de pression
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 17.220.99, 29.035.01 ISBN 978-2-8322-8338-7

– 2 – IEC 62836:2024 © IEC 2024
CONTENTS
FOREWORD . 5
INTRODUCTION . 7
1 Scope . 8
2 Normative references . 8
3 Terms, definitions and abbreviated terms . 8
3.1 Terms and definitions . 8
3.2 Abbreviated terms . 8
4 Principle of the method . 9
5 Samples . 12
6 Electrode materials . 12
7 Pressure pulse wave generation . 12
8 Set-up of the measurement. 13
9 Calibrating the electric field . 14
10 Measurement procedure . 14
11 Data processing for experimental measurement . 15
12 Space charge distribution measurement . 16
13 Impact of coaxial geometry . 16
13.1 Measuring set-up of pressure wave propagation method for the coaxial
geometry sample . 16
13.2 Physical model in coaxial geometry . 17
13.3 Measuring conditions . 18
13.4 Calibration of electric field for a coaxial sample . 19
13.4.1 Summary . 19
13.4.2 Linearity verification . 19
13.4.3 Validity verification of the ratio between two current peaks . 19
13.4.4 Method for retrieving internal electric field from the measured current
signal . 20
Annex A (informative) Preconditional method of the original signal for the PWP
method on a planar sample . 22
A.1 Simple integration limitation . 22
A.2 Analysis of the resiliency effect and correction procedure . 23
A.3 Example of the correction procedure on a PE sample . 24
A.4 Estimation of the correction coefficients . 25

A.5 MATLAB® code . 27
Annex B (informative) Linearity verification of the measuring system . 29
B.1 Linearity verification . 29
B.2 Sample conditions. 29
B.3 Linearity verification procedure . 29
B.4 Example of linearity verification. 29
Annex C (informative) Measurement examples for planar plaque samples . 32
C.1 Samples. 32
C.2 Pressure pulse generation . 32
C.3 Calibration of sample and signal . 32
C.4 Testing sample and experimental results . 33
C.4.1 Measurement results . 33

IEC 62836:2024 © IEC 2024 – 3 –
C.4.2 Internal electric field distribution in the testing sample . 34
C.4.3 Distribution of space charge density in the testing sample . 36
Annex D (informative) Measurement examples for coaxial geometry samples . 38
D.1 Example of linearity verification of coaxial geometry . 38
D.1.1 Sample conditions . 38
D.1.2 Linearity verification procedure . 38
D.1.3 Example of linearity verification . 38
D.2 Verification of the current peak area ratio between the outer and inner
electrodes . 39
D.2.1 Verification principle . 39
D.2.2 Example of verification of the current peak area ratio . 40
D.3 Testing sample and experimental results . 40
D.3.1 Raw results of measurements . 40
D.3.2 Electric field distribution in the coaxial sample . 42
D.3.3 Space charge distribution in the coaxial sample . 44
Bibliography . 46

Figure 1 – Principle of the PWP method . 11
Figure 2 – Measurement set-up for the PWP method . 13
Figure 3 – Sample of circuit to protect the amplifier from damage by a small discharge
on the sample . 13
Figure 4 – Diagram of the pressure wave propagation method set-up for a coaxial
sample . 17
Figure 5 – Diagram of wave propagation of PWP for a coaxial geometry sample . 17
Figure 6 – Diagram of the propagation of pressure wave on the section of a cylinder . 19
Figure 7 – Flowchart for the computation of the electric field in a coaxial sample from
PWP measured currents . 21
Figure A.1 – Comparison between practical and ideal pressure pulses . 22
Figure A.2 – Original signal of the sample free of charge under moderate voltage . 23
Figure A.3 – Comparison between original and corrected reference signals with a
sample free of charge under moderate voltage . 24
Figure A.4 – Electric field in a sample under voltage with space charge calculated from
original and corrected signals . 25
Figure A.5 – Geometrical characteristics of the reference signal for the correction
coefficient estimation . 26
Figure A.6 – Reference signal corrected with coefficients graphically obtained and
adjusted . 26
Figure A.7 – Electric field in a sample under voltage with space charge calculated with
graphically obtained coefficient and adjusted coefficient . 27
Figure B.1 – Voltage signals obtained from the oscilloscope by the amplifier with
different amplifications . 30
Figure B.2 – Current signals induced by the sample, considering the input impedance
and the amplification of the amplifier . 30
Figure B.3 – Relationship between the measured current peak of the first electrode and
applied voltage . 31
Figure C.1 – Measured current signal under −5,8 kV . 32
Figure C.2 – First measured current signal (< 1 min) . 33
Figure C.3 – Measured current signal after 1,5 h under −46,4 kV . 33

– 4 – IEC 62836:2024 © IEC 2024
Figure C.4 – Measured current signal without applied voltage after 1,5 h under
−46,4 kV . 34
Figure C.5 – Internal electric field distribution under −5,8 kV . 34
Figure C.6 – Internal electric field distribution under −46,4 kV, at the initial state . 35
Figure C.7 – Internal electric field distribution after 1,5 h under −46,4 kV . 35
Figure C.8 – Internal electric field distribution without applied voltage after 1,5 h under
−46,4 kV . 36
Figure C.9 – Space charge distribution after 1,5 h under –46,4 kV . 37
Figure C.10 – Space charge distribution without applied voltage after 1,5 h under
−46,4 kV . 37
Figure D.1 – Measured currents from the LDPE coaxial sample under different applied
voltages in a few minutes . 39
Figure D.2 – Relationships between the peak amplitude of the measured current at
outer and inner electrodes and applied voltage . 39
Figure D.3 – First measured current signal (< 1 min) for the coaxial sample . 40
Figure D.4 – Measured current signals for the coaxial sample at beginning and after
2 h under −90,0 kV . 41
Figure D.5 – Measured current signals for the coaxial sample after 2 h under −90,0 kV,
and without applied voltage after 2 h under high voltage . 41
Figure D.6 – Internal electric field distribution under –22,5 kV for the coaxial sample . 42
Figure D.7 – Internal electric field distribution under –90,0 kV for the coaxial sample, at
the initial state . 43
Figure D.8 – Internal electric field distribution after 2 h under –90,0 kV . 43
Figure D.9 – Internal electric field distribution without applied voltage after 2 h under
−90,0 kV . 44
Figure D.10 – Space charge distribution with and without applied voltage after 2 h
under −90,0 kV . 45

Table A.1 – Variants of symbols used in the text . 27
Table D.2 – Analysis of ratio between theoretical and measured peak area for
measured current signal . 40

IEC 62836:2024 © IEC 2024 – 5 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MEASUREMENT OF INTERNAL ELECTRIC FIELD IN INSULATING
MATERIALS – PRESSURE WAVE PROPAGATION METHOD

FOREWORD
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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) IEC draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). IEC takes no position concerning the evidence, validity or applicability of any claimed patent rights in
respect thereof. As of the date of publication of this document, IEC had not received notice of (a) patent(s), which
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the latest information, which may be obtained from the patent database available at https://patents.iec.ch. IEC
shall not be held responsible for identifying any or all such patent rights.
IEC 62836 has been prepared by IEC technical committee 112: Evaluation and qualification of
electrical insulating materials and systems. It is an International Standard.
This first edition cancels and replaces IEC TS 62836 published in 2020.
This edition includes the following significant technical changes with respect to IEC TS 62836:
a) addition of Clause 12 for the measurement of space charge distribution in a planar sample;
b) addition of Clause 13 for coaxial geometry samples;
c) addition of Annex D with measurement examples for coaxial geometry samples;
d) addition of a Bibliography;
e) measurement examples for a planar sample have been moved from Clause 12 in
IEC TS 62836 to Annex C.
– 6 – IEC 62836:2024 © IEC 2024
The text of this International Standard is based on the following documents:
Draft Report on voting
112/627/FDIS 112/632/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/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, or
• revised.
IMPORTANT – The "colour inside" logo on the cover page of this document indicates
that it contains colours which are considered to be useful for the correct understanding
of its contents. Users should therefore print this document using a colour printer.

IEC 62836:2024 © IEC 2024 – 7 –
INTRODUCTION
High-voltage insulating structures, especially high-voltage DC cables and capacitors etc., are
subjected to charge accumulation and this can lead to electrical breakdown if the electric field
produced by the charges exceeds the electrical breakdown threshold. With the trend to multiply
power plants, especially green power plants such as wind or solar generators, more cables will
be used for connecting these power plants to the grid and share the electric energy between
countries. Therefore, a standardized procedure for testing how the internal electric field can be
characterized has become essential for the materials used for the cables, and even the structure
of these cables when considering electrodes or the junction between cables. The measurement
of the internal electric field provides a tool for comparing materials and helps to establish
thresholds on the internal electric field for high-voltage applications in order to avoid risks of
breakdown as much as possible. The pressure wave propagation (PWP) method has been used
by many researchers to measure the space charge distribution and the internal electric field
distribution in insulators. However, since experimental equipment, with slight differences, is
developed independently by researchers throughout the world, it is difficult to compare the
measurement results between the different equipment.
The procedure outlined in this document provides a reliable point of comparison between
different test results carried out by different laboratories in order to avoid interpretation errors.
The method is suitable for a planar plaque sample as well as for a coaxial sample, with
homogeneous insulating materials of thickness from 0,5 mm to 5 mm.

– 8 – IEC 62836:2024 © IEC 2024
MEASUREMENT OF INTERNAL ELECTRIC FIELD IN INSULATING
MATERIALS – PRESSURE WAVE PROPAGATION METHOD

1 Scope
This document provides an efficient and reliable procedure to test the internal electric field in
the insulating materials used for high-voltage applications, by using the pressure wave
propagation (PWP) method. It is suitable for a planar and coaxial geometry sample with
homogeneous insulating materials of thickness larger or equal to 0,5 mm and an electric field
higher than 1 kV/mm, but it is also dependent on the thickness of the sample and the pressure
wave generator.
2 Normative references
There are no normative references in this document.
3 Terms, definitions and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following
addresses:
• IEC Electropedia: available at https://www.electropedia.org/
• ISO Online browsing platform: available at https://www.iso.org/obp
3.1.1
pressure wave propagation
procedure where a pressure wave is propagated in a material containing electric charges and
the induced electric signal from electrodes is measured.
3.1.2
interface charge
net layer of charges between two different materials, either two different insulators or a
conductor and an insulator
3.1.3
space charge
net charge inside an insulating dielectric material
3.2 Abbreviated terms
CB carbon black
EVA ethylene vinyl acetate
LDPE low density polyethylene
LIPP laser induced pressure pulse
PE polyethylene
PIPP piezoelectric induced pressure pulse
PMMA poly methyl methacrylate
PWP pressure wave propagation
S/N signal to noise ratio
IEC 62836:2024 © IEC 2024 – 9 –
4 Principle of the method
The principle of the PWP method is shown schematically in Figure 1, which is for a planar
sample. Figure 1 a) shows the principle and the relation between the current measured with the
PWP method and the electric field distribution in the sample without space charge. Figure 1 b)
shows the principle and the relation between the current measured with the PWP method and
the space charge distribution in the sample without applied voltage. Figure 1 c) shows the
measuring schematics of the PWP method. In Figure 1, x is the position of pulse front, d is the
f 0
original thickness of sample, and d ≈d in the case of a narrow pulse.
The space charge in the dielectric and the interface charge are forced to move by the action of
a pressure wave. The charge displacement then induces an electric signal in the circuit which
is an image of the charge distribution in short-circuit current measurement conditions. The
expression for the short-circuit current signal with time t is
d
∂p xt,
( )
i(t)= C BE( x) dx (1)
∫
∂t
where
E(x) is the electric field distribution in the sample at position x;
d is the thickness of sample;
p(x, t) is the pressure wave in the sample, which depends on the electrode materials,
dielectric sample material, the condition of coupling on the interface, etc.;
C is the sample capacitance with the action of a pressure wave. The active area is the

area on which the pressure wave acts, and it shall be less than the area of the
measuring electrode.
C depends on the thickness of the sample, and its surface area which is equal to the
area of action of the pressure wave.
The constant B χ 1/−a ε only depends on the characteristics of the dielectric materials. In
( )
this formula, χ is the coefficient of compressibility of the material, Ɛ is the permittivity of the
material and a is the coefficient of electrostriction of the material. For heterogeneous dielectric
materials, B is a function of position. For homogeneous dielectric materials, B is thus put outside
the integral as it does not depend on positions. However, B depends on the measurement
conditions. The measurement is carried out in given environmental conditions so B shall be
determined during the calibration in the same conditions (temperature, humidity and pressure).
In this document, only homogeneous dielectric materials are considered, so B is a constant.
In Equation (1), the electric field distribution can be obtained if it is deconvolved.
=
– 10 – IEC 62836:2024 © IEC 2024

a) Applied pressure pulse and measured short-circuit current
with applied voltage but without space charge

b) Applied pressure pulse and measured short-circuit current
with space charge but without applied voltage

IEC 62836:2024 © IEC 2024 – 11 –

c) Measuring schematics
Key
x position of pulse front
f
d original thickness of sample
≈ d in the case of a narrow pulse
d
Figure 1 – Principle of the PWP method
The applied pressure wave can be generated by different techniques, but the same kind of
analysis can be done for any of these techniques. The main practical PWP method can be
divided into two ways: a pressure pulse is induced by a powerful laser pulse, a technique called
LIPP method, and a pressure pulse generated by a piezoelectric device, a technique called
PIPP. The sensibility and resolution of the PWP method depends mainly on the amplitude and
duration of the pressure pulse. The advantage of the LIPP method is to produce highly sensitive
measurements without contact. The advantage of the PIPP method is to obtain the
measurement with a high measuring rate and allow a low-cost measurement system.
In the case of a narrow pulse, for example when the duration of the pressure pulse is much
smaller than the transit time of the pressure wave in the sample, τ is the pressure pulse duration
with τ<<mindv,d / ,
( )
0sx

t d

 i t′′dt = C BE x p x,dt x
( ) ( ) ( )

∫∫
(2)


x=vt

 s
where
v is the sound speed in the sample;
s
E x ,x=vt is the mean electric field during the pressure pulse width at the position x. For
( )
s
simplicity, it is shown as in this document.
E(x=vt)
s
– 12 – IEC 62836:2024 © IEC 2024
Because of sound loss and sound dispersion in polymer dielectrics, the amplitude of p( x,t) will
decrease, and the width of p x,t will increase during the propagation of a pressure pulse in
( )
the sample. For polymer dielectrics, the sound dispersion is dominant, therefore, even if p x,t
( )
d
is not a constant in the dielectrics, its integral pxx,t d remains constant during its propagation
( )
∫
in the sample.
From Equation (2), if the signal is obtained with a sample free of charges and submitted to an
d
intermediate voltage U , B p x,t dx can be obtained since the electric field E x vt E is
( ) ( )
0 ∫ s0
uniform in this case and the sample capacitance C is inversely proportional to the thickness of
the sample. This can be used as a calibration base for the other measurements.
5 Samples
A dielectric insulating material is suggested, for example polyethylene, with a thickness of 1 mm
or 2 mm planar plaque sample with a diameter sufficiently large to avoid edge discharges,
typically larger than 200 mm with 50 mm disc form centred electrodes for 60 kV.
6 Electrode materials
The selection of electrode materials depends on the method of the generation of the pressure
pulse wave. Usually, semi-conductive electrodes with ethylene-vinyl acetate (EVA) + carbon
black (CB) or polyethylene (PE) + carbon black (CB) are used. For laser PWP (also called LIPP),
the suitable thickness of the semi-conductive electrode is about 0,5 mm, and it shall be less
than 1 mm. If the acoustic impedances are different for the electrode and the insulator, the
transit time of the pressure wave through the electrode should be at least half the one in the
insulator to avoid spurious echoes.
It is important to keep good contact between the electrode and the insulator. It is recommended
to use the hot-press method for marking the electrode on the sample.
NOTE The hot-press method is an effective and simple way for bonding semi-conductive electrode(s) and the PE
sample to achieve good interfacial contacts between them. It involves the application of a uniaxial pressure at a
temperature in a time duration which depend on the materials of the sample and electrodes.
7 Pressure pulse wave generation
The suggested pressure pulse wave should have a 20 ns to 50 ns duration, and a 1 MPa to
10 MPa amplitude for a sample of 0,5 mm to 5 mm thickness. It can be produced by a
piezoelectric driven device, or by a powerful pulsed laser. If a powerful laser is used, the
suggested energy is about 300 mJ to 500 mJ per pulse with a 3 ns to 7 ns duration.
NOTE The pressure amplitude, the duration, and the energy of the laser can be adjusted depending on the material
tested.
==
IEC 62836:2024 © IEC 2024 – 13 –
8 Set-up of the measurement
The practical set-up of the measurement is shown in Figure 2. In the practical set-up, the length
l (the length of the connection between the sample and the output connector, i.e., between a
ab
and b) shall be less than 0,5 m. The length l of the connection cable with the characteristic
bc
impedance of 50 Ω between the output and the protection circuit (between b and c) should be
less than 0,5 m. In addition, the length l of the connection cable with the characteristic
de
impedance of 50 Ω between the protection circuit and the amplifier (between d and e) should
be less than 0,5 m. The total length of l + l (between b and e) should be less than 0,5 m
bc de
too. This is the principal suggestion to avoid any reflection effect of the measured signal
between the amplifier and the sample, in the case where the input impedance of the amplifier
is not the perfect match with the signal cable. An amplifier with a 40 dB and 200 MHz bandwidth
is suitable. The input impedance of the amplifier should be strictly 50 Ω to avoid the unwanted
reflecting signal. The resistance of the resistor R in Figure 2 depends on the conditions of
applied voltage, but it shall be in the range of 100 MΩ to 1 GΩ to limit the current in the case
of the sample being discharged.

Key
a, b, c, d and e indicate the real positions in the measuring system.
Figure 2 – Measurement set-up for the PWP method
The practical protection circuit is shown in Figure 3. Diodes in the protection circuit should have
a fast recovery time to overcome a quick overvoltage. It is recommended to use a 5 Ω resistor
without residual induction in the protection circuit.

Figure 3 – Sample of circuit to protect the amplifier from damage
by a small discharge on the sample

– 14 – IEC 62836:2024 © IEC 2024
9 Calibrating the electric field
For a planar plaque sample with a thickness of 1 mm to 2 mm, the applied field for calibration
is about 5 kV/mm to 10 kV/mm during a short period of time (typically less than 1 min) in order
to avoid space charge injection and accumulation. If space charges already exist in the sample
prior to the calibration measurement, it is possible to construct the calibration measurement
from a measurement under voltage and to subtract from it the signal measured under short-
circuit just before or just after the measurement under voltage.
10 Measurement procedure
To implement the same dielectric insulating materials, the same electrode materials, and the
same interface condition between the electrode and insulator, one sample with a thickness d
is used as the calibrating sample, and another sample with a thickness d is used as the testing
x
sample.
For the calibrating sample with the thickness d , voltage U is applied during a short period of
0 0
time that is quick enough so as to not induce space charge accumulation in the sample. See
also Annex C. The internal electric field in the sample is E =−Ud in the absence of space
0 00
charge. With the action of the pressure pulse wave, the measured short-circuit current signal
will be
d
∂p x, t
( )
i t = CB E dx (3)
()
c 00
∫
∂t
Applying an integration over time on this current signal, one obtains
d
t
′
i t'dt = C BE p x, t dx (4)
( ) ( )
∫∫c 00
where EE= since the electric field is uniform.
For the testing sample with the thickness d , the measured short-circuit signal is
x
d
x
∂p x, t
( )
i t = CB E x dx (5)
() ( )
m0
∫
∂t
Now, the internal electric field depends on the applied voltage and space charge. It is therefore
no longer a uniform field but varies as a function of the space position. After integration over
time, one has
d
t
x
'
i t'dt C BE x vt p x,t dx (6)
( ) ( ) ( )
msx
∫∫
==
IEC 62836:2024 © IEC 2024 – 15 –

11 Data processing for experimental measurement
The integral of the pressure pulse is the same for the testing sample and for the calibrating
sample, i.e.
dd
0 x
p( x, t)dx= p( x, t)dx (7)
∫∫
If the active area of the pressure pulse is S , then
εεS εεS U
0r 0 0r 0 0
CC＝＝, , E =−
(8)
00x
d d d
00x
So, one has
εεS d
x
0r 0
t
' BE x=vt p x, tdx
( ) ( )
s
′ ∫
it( )dt
m −=d E x vtd
∫ d ( )
0 s0
0 x
＝ =
(9)
t
d
εεS U
' dU
0r 0 0 0
x 0
′
i t dt
( ) − B px, tdx
( )
c
∫
∫
dd
The following can be obtained
t
− it' d't
( )
m dU
∫
00x
E x vt ×
( ) (10)
s
t 2
d
i t' d't 0
( )
∫ c
If the thickness and tested area are equal for the testing sample and for the calibrating sample,
or if the testing sample is also used as the calibrating sample d = d
0 x
tt
it( ')d't it( ')d't
mm
U ∫∫
00 0
E x= vt =− ×=E ×
( ) (11)
s0
tt
d
i t' d't i t' d't
( ) ( )
cc
∫∫
Therefore, the internal electric field can be obtained from the above Equation (11). The method
is suitable both for the sample under voltage and for the sample in short-circuit containing space
charge.
It can be noticed that the denominator of that expression should be a constant since the electric
field is uniform in the case of the calibration measurement. In order to improve the signal to
==
– 16 – IEC 62836:2024 © IEC 2024
noise ratio, the denominator can be safely replaced by the amplitude of the integral once
calculated, or by the integral of the first peak as
tt
it' d't it' d't
( ) ( )
U mm
∫∫
00 0
E x= vt =− ×=E ×
( ) (12)
s0
55ττ
d
i t' d't i t' d't
( ) ( )
∫∫cc
In Equation (12), τ is the duration of the pressure pulse in the sample, the denominator of the
equation is no longer a function of time, but the definite integral of the first peak of the measured
current. The upper limit of the integral is set to 5τ to ensure that the first peak of current is
completely included. The upper limit can be adjusted according to the conditions.
12 Space charge distribution measurement
With Equation (12), pressure wave velocity x=vt and Poisson’s equation for one dimension
s
∂E
ρ(x)=εε , the space charge distribution can be obtained as follows:
0r
∂x
∂ εε E
E
0r 0
ρ x=vt=εε =⋅ ⋅it=γ⋅it
( ) () ()
m s 0r m m
5τ (13)
∂xv
s
i t′′dt
( )
c
∫
εε E
0r 0
where ⋅=γ is a constant depending only on the properties of the sample.
5τ
v
s
′′
i (t)dt
c
∫
Equation (13) is suitable for any applied measuring voltage, and γ can be determined by the
measured current signal under lower applied voltage. See also Clause 9.
13 Impact of coaxial geometry
13.1 Measuring set-up of pressure wave propagation method for the coaxial geometry
sample
For coaxial geometry samples like a cable etc., the measurement is not exactly the same as in
the case of a planar plaque sample.
Figure 4 shows the diagram of the set-up of the pressure wave propagation method for a coaxial
sample such as a shortened cable. If the sample is cut from a real long cable, its semiconducting
layer at both ends shall be removed to avoid the occurrence of flashovers, which length is
dependent on the applied voltage during the testing. The semiconductor layer is kept in the
middle part of the cable to maintain a well-defined electric field at the measuring position. The
length L shall be plus 10 times the diameter of active area and plus 10 times the insulation
thickness. A high-voltage DC power source is connected to one side of the cable conductor
through a high-voltage resistor. The pressure wave can be induced by a powerful pulsed laser
or a piezoelectric pressure wave generator, which is the same as that described in Clause 7.

IEC 62836:2024 © IEC 2024 – 17 –

Key
The black part on the sample represents the outer semi-conductive shield layer.
Figure 4 – Diagram of the pressure wave propagation
method set-up for a coaxial sample
The signal passes through a coupling capacitor, protection circuit, amplifier, to be received by
a digital oscilloscope and finally, further data processing is carried out on a computer.
13.2 Physical model in coaxial geometry
In the physical model shown in Figure 5, the inner and outer radius of the dielectric of a coaxial
sample are respectively r and r . Considering one
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