BS EN
62226-3-1:2007

BRITISH STANDARD

+A1 :201 7

Exposure to electric or
magnetic fields in the
low and intermediate
frequency range —
Methods for calculating
the current density and
internal electric field
induced in the human
body —
Part 3-1: Exposure to electric fields —
Analytical and 2D numerical models

(IEC 62226-3-1 :2007)

ICS 1 7. 220.20

?? ? ? ????? ??????? ??? ?? ???????? ? ?? ? ?? ?? ?? ?????? ? ?? ? ? ?????? ? ???
?

?

?

?

?

?

?

?

?

?


BS EN 62226-3-1:2007+A1:2017

National foreword
This British Standard is the UK implementation of EN 62226-3-1:2007+A1:2017.
It is identical to IEC 62226-3-1: 2007, incorporating amendment 1 : 2016.
It supersedes BS EN 62226-3-1 : 2007 which is withdrawn.

The start and finish of text introduced or altered by amendment is
indicated in the text by tags. Tags indicating changes to IEC text carry
the number of the IEC amendment. For example, text altered by IEC
amendment 1 is indicated by
.

!"

The UK participation in its preparation was entrusted to Technical Committee

GEL/106, Human exposure to low frequency and high frequency
electromagnetic radiation.
A list of organizations represented on this committee can be obtained on
request to its secretary.
This publication does not purport to include all the necessary provisions of a
contract. Users are responsible for its correct application.

Compliance with a British Standard cannot confer immunity from
legal obligations.

This British Standard was
published under the authority
of the Standards Policy and

Amendments/corrigenda issued since publication
Date

Comments

28 February 201 7

Implementation of IEC amendment 201 6 with CENELEC

Strategy Committee
on 31 October 2007

© The British Standards

Institution 2017.
Published by BSI

Standards Limited 2017

ISBN 978 0 580 92814 7

endorsement A1: 2017


EN 62226-3-1 :2007+A1

EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM

January 201 7

ICS 1 7.220.20

English version

Exposure to electric or magnetic fields
in the low and intermediate frequency range Methods for calculating the current density
and internal electric field induced in the human body Part 3-1 : Exposure to electric fields Analytical and 2D numerical models
(IEC 62226-3-1 :2007)

Exposition aux champs électriques
ou magnétiques à basse
et moyenne fréquence Méthodes de calcul des densités
de courant induit et des champs électriques
induits dans le corps humain Partie 3-1 : Exposition
à des champs électriques Modèles analytiques et numériques 2D

(CEI 62226-3-1 :2007)

Sicherheit in elektrischen
oder magnetischen Feldern im niedrigen
und mittleren Frequenzbereich Verfahren zur Berechnung der induzierten
Körperstromdichte und des im menschlichen
Körpers induzierten elektrischen Feldes Teil 3-1 : Exposition gegenüber
elektrischen Feldern Analytische Modelle
und numerische 2D-Modelle
(IEC 62226-3-1 :2007)

This European Standard was approved by CENELEC on 2007-09-01 . 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 Central Secretariat 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 Central Secretariat has the same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Cyprus, the
Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.

CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung

Central Secretariat: rue de Stassart 35, B - 1 050 Brussels

© 2007 CENELEC -

All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 62226-3-1 :2007 E


BS EN 62226-3-1:2007+A1:2017
EN 62226-3-1:2007+A1:2017

–2–

Foreword
The text of document 1 06/1 25/FDIS, future edition 1 of IEC 62226-3-1 , prepared by IEC TC 1 06, Methods
for the assessment of electric, magnetic and electromagnetic fields associated with human exposure, was
submitted to the IEC-CENELEC parallel vote and was approved by CENELEC as EN 62226-3-1 on
2007-09-01 .
This European Standard is to be used in conjunction with EN 62226-1 :2005.
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
national standard or by endorsement

(dop)

2008-06-01

– latest date by which the national standards conflicting
with the EN have to be withdrawn

(dow)


201 0-09-01

__________

Endorsement notice
The text of the International Standard IEC 62226-3-1 :2007 was approved by CENELEC as a European
Standard without any modification.
__________

Foreword to amendment A1

The text of document 1 06/376/FDIS, future IEC 62226-3-1 :2007/A1 , prepared by IEC/TC 1 06
"Methods for the assessment of electric, magnetic and electromagnetic fields associated with human
exposure" was submitted to the IEC-CENELEC parallel vote and approved by CENELEC as
EN 62226-3-1 :2007/A1 :201 7.
The following dates are fixed:
•

latest date by which the document has to be
implemented at national level by
publication of an identical national
standard or by endorsement

(dop)

201 7-08-1 1

•


latest date by which the national
standards conflicting with the
document have to be withdrawn

(dow)

201 9-1 1 -1 1

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 62226-3-1 :2007/A1 :201 6 was approved by CENELEC as a
European Standard without any modification.


–3–

BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

CONTENTS
INTRODUCTION ..................................................................................................................... 6
1
2
3
4

5


6

7

Scope ............................................................................................................................... 7
Exposure to electric field .................................................................................................. 7
General procedure.......................................................................................................... 1 0
3.1 Shape factor.......................................................................................................... 1 0
3.2 Procedure ............................................................................................................. 1 0
Human body models ....................................................................................................... 1 1
4.1 General ................................................................................................................. 1 1
4.2 Surface area ......................................................................................................... 1 1
4.3 Semi-spheroidal model .......................................................................................... 1 2
4.4 Axisymmetrical body model ................................................................................... 1 4
Calculation of induced current ........................................................................................ 1 5
5.1 General ................................................................................................................. 1 5
5.2 Semi-spheroid ....................................................................................................... 1 5
5.3 Axisymmetrical models .......................................................................................... 1 9
5.4 Comparison of the analytical and numerical models .............................................. 2 6
Influence of electrical parameters ................................................................................... 2 6
6.1 General ................................................................................................................. 2 6
6.2 Influence of permittivity ......................................................................................... 2 6
6.3 Influence of conductivity ........................................................................................ 2 7
6.4 Non-homogeneous conductivity ............................................................................. 2 7
Measurement of currents induced by electric fields......................................................... 2 7
7.1 General ................................................................................................................. 2 7
7.2 Current flowing to the ground ................................................................................ 2 7

Annex A (normative) Analytical solutions for a spheroid in a uniform electric field ................ 29

Annex B (normative) Human body axisymmetrical model ..................................................... 3 2
Annex C (informative) Child body model .............................................................................. 3 7
Annex D (informative) Example of use of this standard ........................................................ 39
Annex E (informative) Numerical calculation methods .......................................................... 4 3
Bibliography.......................................................................................................................... 5 1
Figure 1 – Illustration of the phenomenon of currents induced by electric field in a
human body standing on the ground ........................................................................... . . .......... 9
Figure 2 – Potential lines of the electric field generated by an energised wire in the
absence of any objects (all distances in metres) .............................................................. . . ..... 9
Figure 3 – A realistic body model .......................................................................................... 1 1
Figure 4 – Scheme of the semi-spheroid simulating a human being standing on a zero
potential plane ...................................................................................................................... 1 2
Figure 5 – Equivalent spheroid radius, R, versus height, L , and for different mass, M .......... 1 4
Figure 6 – The axisymmetrical body model for the reference man (left) and woman
(right).................................................................................................................................... 1 4


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

–4–

Figure 7 – Conductive spheroid exposed to electric field ....................................................... 1 5
Figure 8 – Calculation of the shape factor for electric field KE for an spheroid exposed
to an unperturbed electric field.............................................................................................. 1 6
Figure 9 – Current density JS induced by an unperturbed electric field (1 kV/m, 50 Hz)
in a spheroid versus parameter L / R (values in µA/m²) ........................................................... 1 7
Figure 1 0 – Dimensions and mesh of the semi-spheroid ....................................................... 1 8
Figure 1 1 – Distortion of power frequency electric field lines close to the conductive
semi-spheroid ....................................................................................................................... 1 8

Figure 1 2 – Calculated induced current density JA (h) in the body standing in a vertical
50 Hz electric field of 1 kV/m ................................................................................................ 2 0
Figure 1 3 – Computation domain .......................................................................................... 2 2
Figure 1 4 – Mesh of the man body model and distortion of power frequency electric
field lines close to model....................................................................................................... 2 2
Figure 1 5 – Distribution of potential lines and 50 Hz electric field magnitude (man
model) .................................................................................................................................. 2 3
Figure 1 6 – Computation of induced currents JA along a vertical axis, and distribution
of induced currents in the man model at 50 Hz ..................................................................... 2 3
Figure 1 7 – Mesh of the woman body model and distortion of power frequency electric
field lines close to model....................................................................................................... 2 4
Figure 1 8 – Distribution of potential lines and 50 Hz electric field magnitude (woman
model) .................................................................................................................................. 2 5
Figure 1 9 – Computation of induced currents JA along a vertical axis, and distribution
of induced currents in the woman model at 50 Hz ................................................................. 2 5
Figure A.1 – Conductive spheroid exposed to electric field ................................................... 29
Figure B.1 – Normalised axisymmetrical models. Left: man, Right: woman ........................... 3 4
Figure C.1 – Computation of induced currents JZ along a vertical axis, and distribution
of induced currents in the 1 0 years reference child model ..................................................... 3 8
Figure E.1 – Spheroid model................................................................................................. 4 4
Figure E.2 – Space potential model ...................................................................................... 4 5
Figure E.3 – Exemple of charge simulation method using rings ............................................. 4 6
Figure E.4 – Superficial charges integral equation method, cutting of the body into N
elements ............................................................................................................................... 4 7
Figure E.5 – Mesh of the body using finite element method .................................................. 4 8
Figure E.6 – Impedance method ........................................................................................... 49
Figure E.7 – Yee-method: Electric and magnetic grids for spatial discretization .................... 5 0
Table 1 – Data for reference man and reference woman ....................................................... 1 2
Table 2 – Values of arcsin(e) / e for different values of L/R ................................................... 1 3
Table 3 – Derived data using spheroid model at 50 Hz ......................................................... 1 9

Table 4 – Electric field EBR required to produce basic restrictions JBR in the neck at
50 Hz .................................................................................................................................... 2 1
Table 5 – Comparison of values of the shape factor for electric field KE and
corresponding current densities for an unperturbed 50 Hz electric field of 1 kV/m ................. 2 6
Table B.1 – Measures from antropomorphic survey used to construct vertical
dimensions of axisymmetrical model [56] .............................................................................. 3 3


–5–

BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

Table B.2 – Measures from antropomorphic survey used to construct the radial
dimensions of axisymmetrical model [56] .............................................................................. 3 3
Table B.3 – Normalised model dimensions............................................................................ 3 5
Table B.4 – Axisymmetric model dimensions for reference man and reference woman
whose mass and height are defined by ICRP [38] and are given in Table 1 ........................... 3 6
Table C.1 – Reference values provided by ICRP for male and female children...................... 3 7
Table C.2 – Dimensions of the reference children (in m excepted SBR in m²) ....................... 3 7
Table C.3 – Results of analytical method for the reference children ...................................... 3 8
Table D.1 – Normalised dimensions of the women model...................................................... 4 0
Table D.2 – Calculation of the dimensions for a specific person ............................................ 4 1


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

–6–


INTRODUCTION
Public interest concerning human exposure to electric and magnetic fields has led
international and national organisations to propose limits based on recognised adverse
effects.
This standard applies to the frequency range for which the exposure limits are based on the
induction of voltages or currents in the human body, when exposed to electric and magnetic
fields. This frequency range covers the low and intermediate frequencies, up to 1 00 kHz.
Some methods described in this standard can be used at higher frequencies under specific
conditions.
The exposure limits based on biological and medical experimentation about these
fundamental induction phenomena are usually called “basic restrictions”. They include safety
factors.
The induced electrical quantities are not directly measurable, so simplified derived limits are
also proposed. These limits, called “reference levels” are given in terms of external electric
and magnetic fields. They are based on very simple models of coupling between external
fields and the body. These derived limits are conservative.
Sophisticated models for calculating induced currents in the body have been used and are the
subject of a number of scientific publications. These models use numerical 3D
electromagnetic field computation codes and detailed models of the internal structure with
specific electrical characteristics of each tissue within the body. However such models are still
developing; the electrical conductivity data available at present has considerable
shortcomings; and the spatial resolution of models is still progressing. Such models are
therefore still considered to be in the field of scientific research and at present it is not
considered that the results obtained from such models should be fixed indefinitely within
standards. However it is recognised that such models can and do make a useful contribution
to the standardisation process, specially for product standards where particular cases of
exposure are considered. When results from such models are used in standards, the results
should be reviewed from time to time to ensure they continue to reflect the current status of
the science.



–7–

BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

EXPOSURE TO ELECTRIC OR MAGNETIC FIELDS
IN THE LOW AND INTERMEDIATE FREQUENCY RANGE –
METHODS FOR CALCULATING THE CURRENT DENSITY AND
INTERN AL ELECTRIC FIELD INDUCED IN THE HUMAN BODY –
Part 3-1 : Exposure to electric fields –
Anal ytical and 2D numerical models

1

Scope

This part of IEC 62226 applies to the frequency range for which exposure limits are based on
the induction of voltages or currents in the human body when exposed to electric fields.
This part defines in detail the coupling factor K – introduced by the I EC 62226 series to
enable exposure assessment for complex exposure situations, such as non-uniform magnetic
field or perturbed electric field – for the case of simple models of the human body, exposed to
uniform electric fields. The coupling factor K has different physical interpretations depending
on whether it relates to electric or magnetic field exposure. It is the so called “shape factor for
electric field”.
This part of IEC 62226 can be used when the electric field can be considered to be uniform,
for frequencies up to at least 1 00 kHz.
This situation of exposure to a “uniform” electric field is mostly found in the vicinity of high
voltage overhead power systems. For this reason, illustrations given in this part are given for
power frequencies (50 Hz and 60 Hz).

2

Exposure to electric field

Alternating electric fields are generated by energised conductors (i.e. under voltage). I n the
immediate vicinity of domestic electrical equipment, such as lights, switches, food mixers and
irons, local electric-field strengths about 1 00 V/m may be found. Such fields are non-uniform,
but their strengths are far below the levels recommended in safety guidelines, so there is no
need of calculation of induced currents in such exposure situations.
Higher electric-field strengths may be found in the vicinity of high voltage equipment such as
electric power line. In the frequency range covered by this standard, it is considered that
exposure from power lines is the only significant exposure source for public regarding safety
guidelines limits.
Guidelines on human exposure to electric fields are generally expressed in terms of induced
current density or internal electric field. These quantities cannot be measured directly and the
purpose of this document is to give guidance on how to assess these quantities induced in the
human body by external (environmental) electric fields E0 .


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

–8–

The induced current density J and the internal electric field Ei are closely linked by the simple
relation:
J = σ. Ei

(1 )


where σ is the conductivity of the body tissue under consideration.

some guidelines on human exposure to electric fields adopt internal electric field as
! aAlthough
limiting parameter, for reason of simplification, the content of this standard is presented
mainly in terms of induced current densities J, from which values of internal electric field Ei
can be easily derived using the previous formula."

All the calculation developed in this document use the low frequency approximation in which
displacement currents are negligible, such that εω/ σ is less than 1 in the body. This
approximation has been checked using published tissue data [29,31 ] 1 ) in the low frequency
range and it has been found to be valid for frequencies up to at least 1 00 kHz and is probably
valid at higher frequencies.
Computations based on sophisticated numerical models of the human body [24] also
demonstrate that this assumption is valid at frequencies up to more than 1 00 kHz by showing
that the relationship between the induced current density in the body and the product of
frequency and external electric field hardly varies at all between 50 Hz and 1 MHz, and is only
slightly altered at 1 0 MHz.
Analytical models can be used for simple cases of calculations.
Electric fields cause displacement of electric charges in conductive objects (including living
bodies) and, because these fields are alternating, the electric charges move backwards and
forwards. The result is an “induced” alternating current inside the conductive object. This
current depends only on:
– the shape and size of the conducting object;
– the characteristics (magnitude, polarisation, degree of non-uniformity, etc.) of the
unperturbed field (field which is measured in the absence of any conducting object);
– the frequency of the field
– the variation of conductivity of the object (in homogeneous media, the current density
induced by electric fields does not depend on conductivity).
Figure 1 illustrates this induction phenomenon for the case where the body is in electrical

contact with the ground.

—————————
1 ) Figures in square brackets refer to the Bibliography.


–9–

BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

Electric fields
Induced currents

IEC 750/07

Figure 1 – Illustration of the phenomenon of currents induced by an electric field in a
human body standing on the ground
The typical case of public exposure to an electric field is under high voltage power
transm ission lines. I n this case, the distance between the source of field and the hum an bod y
is large and the field in the zone close to the ground, in the absence of an y conductive obj ect,
can be considered to be uniform (see Figure 2).
12

Height from ground m

10

8


6

4

2

2

4

6
8
10
Horizontal distance m

12

14

16
IEC 751/07

Figure 2 – Potential lines of the electric field generated by an energised wire in the
absence of any objects (all distances in metres)


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017
3


– 10 –

General procedure

3.1

Shape factor

In the low and intermediate frequency range, the relation between the induced current in the
human body ( J) and a uniform electric field ( E0 ) can be reduced to:

J = K E . f. E

(2)

0

Where:

f is the frequency;
E0 is the magnitude of the unperturbed electric field;
KE is defined as the “ shape factor for the electric field”.
KE is dependant on the size, the conductivity, the form and the position of the model of the

human body. It is also dependant on the location within the body where the induced current
density is evaluated. KE is independent of the frequency for analytical assessment of the
induced current produced by electric fields (see Annex A).

KE is given in units of A⋅ s ⋅ V -1 ⋅ m -1 or Farad per metre (F/m), which relates to the fact that the


!

exposure to the electric field corresponds physically to a capacitive coupling between the field
source and the conductive object exposed to the field.

N OTE

Th e

co n d u cti v i ty

3.2

i n t e rn a l

of

th e

e l e c t ri c

human

fi e l d

m od el

E

ca n


be

"

ca l cu l a te d

i

(see

e q u a ti o n

fr o m

th e

c u rre n t

d e n s i ty

J

as

E

=
i


Jσ
/

,

w h e re

σ

i s

th e

(1 )).

Procedure

The current density inside an individual can be estimated analytically, following a three stage
process. The first stage is to compute the current density in a semi-spheroid, whose
dimensions are chosen to best represent the particular body. As it will be shown in 5.3 of this
standard, the current density is uniform throughout the spheroid but depends on the ratio L/R
of its semi-major axis and semi-minor axis.

!

The second stage is to use a realistic axisymmetrical model of a human body to determine the
current density as a function of vertical position within the body.
Th e

t h i rd


c u rre n t
r e fe r

th e

s ta g e

d e n s i ty

s p e c i fi c a l l y

p a rt i c u l a r

c ro s s

is
in

"

s e cti o n

to

a re a
of

to
th e


c o n v e rt

c u rre n t

of

th e

th e

d i ffe re n t

d e n s i ty

i n t e re s t
n e ck,

c u rre n t

ti s s u e s
(or

w i th i n

wh i ch

at

d e n s i ty

th a t

i n t e rn a l

th e

bod y

a v e ra g e d

h e i g h t.
e l e c tri c

is

c o n c e n t ra t e s

th e
th e

at

H e a l th
fi e l d )

spin al

a

in


th e

c o rd

c u rre n t

p a rt i c u l a r

g u i d el in es

(or

in

c e n t ra l

th e

heigh t

on

n e rv o u s

n e ck,

i n t e rn a l

to


th e

e x p o s u re

due

e l e c t ri c

l o ca l

to

EMF

s ys te m ,

to

th e

fi e l d )

so

small

in

th a t


re g i o n .

Induced currents are calculated for men and women as well as children using reference
values for their height, mass and surface area published by ICRP [38]. Sufficient information
is given here to apply the method to persons of any weight and height.
Numerical calculations are also presented demonstrating the validity of the analytical
procedure.


– 11 –

4
4.1

BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

Human body models
General

In scientific literature, many models of different complexity have been used for the
assessment of currents and internal fields induced by electric or magnetic field (Figure 3).
Examples of such sophisticated calculations are given in the bibliography. It must be
emphasised that these computations have been performed using dedicated softwares which
require highly specialised competences and are not widely available. Therefore, it is
considered that such computational techniques are not relevant with regard to standardisation
objectives.

IEC 752/07


Figure 3 – A realistic body model

Analytical calculations are possible when using simple models, such as the model of a
spheroid in a uniform electric field.
4.2

Surface area

The surface area of a body ( SB ) is used to scale both the spheroidal and the axisymmetrical
body models for different sized bodies. It depends on the height and the mass of the body.
The report of the ICRP [38], Basic Anatomical and Physiological Data for Use in Radiological
Protection: Reference Values, provides an algorithm giving the total surface area ( SB T ) of a
person as a function of its height L (in metres) and mass M (in kg):
SB T = 0,1 64 4 M 0,51 4 56 L0, 422 46

(3)

In our case, only the outwards-facing surface area of the body is considered, which is
approximately 82 % of the total surface area SB T . The 1 8 % reduction comprises 3 % for
excluding the soles of the feet, 6 % for excluding the touching surface of the legs, and 8 % for
excluding the inner surface of the arms and hands and 1 % for the perineum. The reduced
surface area ( SB R ) is therefore:
SBR = 0, 82 SB T

(4)

Table 1 gives the results for the reference man and the reference woman which are
introduced in 4.4 and Annex B.



BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

– 12 –

Table 1 – Data for reference man and reference woman

H eig ht, m
Mass, kg
Total su rface area SB T , m

2

Red u ced su rface area SB R , m

4.3

2

Reference
man

Reference
woman

1 , 76

1 , 63


73

60

1 , 889

1 , 662

1 , 557

1 , 363

Semi-spheroidal model

To calculate the induced current density inside a hum an standing on a conducting plane it is
necessary to m odel the reflection of the bod y in the ground. Thus the body is represented by
half of the spheroid (Figure 4) and the reflection by the other half (Figure 7). The semi-major
axis L of the spheroid is set to the height of the person being represented.
z

E0 Z

L

R
y
Ground plane

x


IEC 753/07

Figure 4 – Scheme of the semi-spheroid simulating a human being standing
on a zero potential plane
The sem i-m inor axis (i. e. the rad ius) R is chosen to give the same total current flowing into the
ground through the feet when the bod y is grounded as for the bod y it represents. This is
achieved by ensuring that the spheroid has the sam e outward-facing surface area SB R as the
bod y it represents.
The surface area SB S of a half spheroid of height L and radius R is given by:

SBS = πR 2 ⎡⎢ 1 +
⎣

where e is the eccentricity:

L arcsin (e ) ⎤
R
e ⎥⎦

(5)


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

– 13 –
R2

e= 1−


L2

R is determ ined from the m ass M and L by solving equation (5) for R , with SB S = SB R and
where SB R is given by equations (3) and (4). Thus
,

R=−

B

2

⎛
⎜
⎝

±

B

2

⎞
⎟
⎠

2

+


SB S
π

(6)

where
B=L

arcsin( e )
e

B is a function of R , but as arcsin (e ) /e varies onl y slowl y with L/R , as shown in Table 2, B also
varies onl y slowl y with L/R , and therefore B can be determ ined using an approxim ate value for
L/R . .

Table 2 – Values of arcsin (e)
L /R

Arcsi n (e) /e

/e

for different values of L /R

9, 0

9, 2

9, 4


9, 6

9, 8

10

1 , 469

1 , 471

1 , 473

1 , 474

1 , 476

1 , 478

Using L/R = 9, 8 gives
B = 1, 476 L

This is substitu ted into equation (6) to give the equation for R in term s of
R = −0,738 L + 0,545 L2 +

SBS
π

L

and SB S:

(7)

Figu re 5 presents the result graphicall y. I t can be used to find the radius R from the height L
and mass M of a person. For example, the reference man, whose mass is 73 kg and height is
1 . 76 m , the radius R is 0, 1 78 m and L/R is 9, 86.


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

– 14 –

0,35

0,30

1 20
110
1 00
90
80
70
60
50

0,20

0,1 5

M kg


R m

0,25

40
30

0,1 0
1 ,0

1 ,5

2,0

L m

IEC 754/07

Figure 5 – Equivalent spheroid radius, R , versus height, L ,
and for different mass, M
4.4

Axisymmetrical body model

The axisymmetrical bod y m odel represents the essential features of the bod y: its height, total
surface area, neck d imensions, and approximate vertical profile. However it cannot be a
perfect representation of the bod y because the bod y is not axisymm etrical. Figure 6 illustrates
the radial cross section of the axisymmetrical model for the reference man and woman.
1 . 80

1 ,80

1 .80
1 ,80

1 . 60
1 ,60

1 .60
1 ,60

1 . 40
1 ,40

1 ,40
1 .40

1 . 20
1 ,20

1 ,20
1 .20

1 . 00
1 ,00

1 ,00
1 .00

0. 80

0,80

0,80
0.80

0. 60
0,60

0,60
0.60

0. 40
0,40

0,40
0.40

0. 20
0,20

0.20
0,20

0,00
0. 00
0.0
0,0

0.2
0,2


0,00
0.00
0,0
0.0

0,2
0.2
IEC 755/07

Figu re 6 – The axisymmetrical body model for the reference
man (left) and woman (right)


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

– 15 –

Annex B describes how data from an anthropometric survey of 2 208 women and 1 1 74 men,
chosen as a representative sample from the U S Army, were used to develop the
axisymmetrical model. The model is defined by 1 3 (radius, height) coordinates.

5

Calculation of induced current

5.1

General


Analytical models to quantify the relationship between induced currents in conductive bodies
and external electric fields are generally based upon the most simple assumption that the
external fields are uniform and at a single frequency, and that the bodies are homogeneous
and with a shape that can be described analytically (as is the case of spheres, spheroids,
etc.). Therefore, they cannot easily take into account the fact that the human body is a nonhomogeneous structure with a complex shape.
Nevertheless, analytical models can be used for simple cases of calculations and/or to
validate numerical calculations.
In the particular case of the homogeneous models developed in this standard, the induced
current density is independent of the conductivity and the permittivity (low frequency
approximation).
5.2
5.2.1

Semi-spheroid
Analytical

In Annex A, the detailed analytical solutions for a spheroid in a uniform electric field are
presented as a function of spheroid's geometrical and electrical parameters and of the
magnitude and direction of the electric field vector (Figure 7). The spheroid representation is
equivalent to the semi-spheroid in the presence of the ground plane as explained in 4. 3.
z
E0 Z
L

R

E0R

y


x
IEC 756/07

Figure 7 – Conductive spheroid exposed to electric field

L is the length of the semi-major (rotational) axis of the spheroid (axis Z),
R is the length of the semi-minor axis of the spheroid ( R is also the radius of the circular cross
section of the spheroid at the symmetry plane (plane XY)).


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

– 16 –

The shape factor for electric field KE is calculated for 2 orientations of the field vector: E0
parallel to Z axis (therefore KE and E0 are called KEZ and E0 Z) and E0 perpendicu lar to Z axis
(therefore KE and E0 are called KER and E0R ).
The results of this anal yti cal calculation are summarised hereu nder in Figures 8 and 9.

F i g u re

9

g i ve s

m a g n i tu d e

N O TE


Th e

co n d u cti v i ty

of

th e

1

i n te rn a l

of

th e

re s u l t

k V /m

at

e l e c t ri c

hu man

of

50


a n a l yti ca l

ca l cu l a ti o n

of

th e

l o ca l

c u rre n t

d e n s i ty

J

s

,

fo r

"

E

ca n

be


ca l cu l a te d

fr o m

th e

c u rre n t

d e n si ty

i

J

as

E

=
i

Jσ
/

,

w h e re

1 0 –7


KEZ
E-field parallel to Z axis
1 0 –8

1 0 –9

KER
E-field perpendicular to Z axis

1 0 –1 0

1

a

fi e l d

H z.

fi e l d

m od el .

th e

KER as a function of

KE (F/M)


!

Figure 8 gives in a graphic form the result of the calculation of KEZ and
the ratio L/R (shape parameter).

10
L /R

1 00
IEC 757/07

! Figu re 8 – Calculation
of the shape factor for electric field KE for a spheroid
exposed to an u nperturbed electric field"

σ

i s

th e


– 17 –

BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

1 04

Jsz

E-Field parallel to Z axis

J (μA/m 2)

1 03

1 02

Jsr
E-Field perpendicular to Z axis
1 01

1 00

1

10

L /R

1 00
IEC 758/07

Figure 9 – Current density JS induced by an unperturbed electric field (1 kV/m, 50 Hz)
in a spheroid versus parameter L / R (values in µA/m²)

Direct application:

Considering the values for the reference man (see 4.3) L /R = 9, 86 and L = 1 ,76 m, exposed
to 50 Hz vertical electric field with a magnitude of 1 kV/m, the curves in Figures 8 and 9 give:


K EZ ≅ 2, 68 × 1 0 −9 A.s/V.m
and

JS Z = K EZ . f. E0 Z ≅ 0,1 34 mA/m ²
5.2.2

Numerical

Different methods can be used to determine the current induced by an external electric field
E0 in a conductive object. I n the following computations, a finite elements method was used.
Physical parameters for the air are [27, 33, 51 ]:
=1
σ = 0 S/m
Characteristics of the semi-spheroid model are:
εr

L = 1 , 76 m
R = 0, 1 78 m

= 1 05
σ = 0,2 S/m
In the example given here, the mesh of the semi-spheroid is composed of 2744 surface
elements (see Figure 1 0).
εr


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017


– 18 –

L = 1 ,76 m

R = 0, 1 78 m

IEC 759/07

Figu re 1 0 – Di mension s an d mesh of the semi-sph eroid
In the computation dom ain, the external 50 H z electric field E0 is generated by a plane
electrode at 1 0 m from the ground plane, with an electrical potential of 1 0 000 V. The dom ain
is assum ed to be axisym m etrical.

Figure 1 1 shows the perturbed electric field in the air, close to the sem i-spheroid. The sem ispheroid distorts the lines of electric field, which becom e perpendicular to the surface of the
spheroid. Without the sem i-spheroid or far from it, these lines of electric field are vertical.
E0 =1 kV/m

IEC 760/07

Figu re 1 1 – Distortion of power frequ en cy el ectric fi eld l in es close
to th e con du ctive semi-sph eroi d


– 19 –

BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

The current density in the centre of the semi-spheroid is very similar to the current density
value from analytical calculation.

The variation is less than 1 % along the vertical axis and the current density should be
considered as constant. As a result, it can be considered that this simple numerical model
gives results identical to those of the analytical calculation.

5.3 Axisymmetrical models
5.3.1 Analytical
Table 3 gives values derived in the course of calculating the current density in the spheroid.
The surface area in the third row was calculated from the height and mass using Equation (3).
In the next row the 0,82 factor was applied (Equation (4)) to remove non-outward facing
surfaces when standing. Using the outward-facing surface area and Equation (7) gives in the
next row the radius R for a half spheroid having the same surface area. The following row
presents the corresponding L/R . It is approximately the same for both reference man and
reference woman.

Table 3 – Derived data using spheroid model at 50 Hz
Reference man
1 ,76
73
1 ,899

Reference woman
1 , 63
60
1 , 662

Reduced surface area of body SB R , m 2

1 , 557

1 ,363


Spheroid radius R , m
Current density JS Z in spheroid per kV/m, mA/m 2

0, 1 78
9,86
0, 1 34

0,1 68
9, 68
0,1 30

Ground current per kV/m, µA

1 3, 4

1 1 ,6

Height L , m
Mass M, kg
Total surface area of body SB T , m 2

L /R

The current density JS Z in the spheroid depends only on the parameter L/R , the electric field
and frequency. For L/R = 9,86 the current density throughout the spheroid is
JS Z = 0,1 34 mA/m 2 per kV/m of electric field at 50 Hz. For 60 Hz, it is 20 % higher.
The vertical current density JS Z is uniform throughout the spheroid. The vertical current flowing
through a horizontal layer of the spheroid therefore increases progressively from zero at the
top to a maximum at the ground. This is because of the displacement current is entering the

spheroid progressively over its whole height.
In practice the human body is not a half spheroid but has an effective horizontal radius that
varies unevenly with vertical position as represented by the axisymmetrical model.
The assumption is made that at a particular height the same overall current flows as in the
spheroid, but it flows in the different cross sectional area of the asymmetrical model at that
height. Thus at a particular height h above ground, the induced current density in the
axisymmetrical model JA is given by:
J A ( h ) = JS ( h ) ×

horizontal area of the spheroid
horizontal area of the human


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

– 20 –

or
r 2 (h)
J A ( h ) = JS ( h ) * S
rA2 ( h )

where rS (h) is the horizontal radius of the spheroid at height h and rA (h) is the horizontal
radius of the axisymmetrical model at height h .
The vertical cross section of a spheroid through its axis is an ellipse and the radius rS (h) at
height h of a semi-spheroid is:
rS ( h ) = R

1 − (h / L ) 2


2,00
2.00

2.00
2,00

11,80
.80

1 .80
,80

11,60
.60

1 .60
,60

11,40
.40

1 .40
,40

11,20
.20

11 .20
,20


Vertical position m

Vertical position m

The variation of current density with height is shown in Figure 1 2 for reference man and
reference woman.

11,00
.00
0,80
0.80

1 .00
,00
0.80
0,80

0,60
0.60

0.60
0,60

0,40
0.40

0.40
0,40


0,20
0.20

0,20
0.20

0,00
0.00
0,0
0.0

0,2
0.2

0,4
0.4

0,6
0.6

0,8
0.8

11 ,0
.0

Currentdensity,
density mA/m
mA/m2 2
Current


1 .2,2

1 ,4
.4

0,00
0.00
0,0
0.0

0,2
0.2

0,4
0.4

0,6
0.6

0,8
0.8

11,0.0

2
Current
Currentdensity
density,mA/m
mA/m 2


11,2.2

1 ,4
1 .4
IEC 761/07

Outlines of the spheroidal model and axisymmetrical models used are also shown. Left: man, right: woman.

Figure 1 2 – Calculated induced current density JA(h) in the body standing in a vertical
50 Hz electric field of 1 kV/m

The current density is maximum in the ankle, and there is a smaller maximum in the neck.
The current density in the neck is slightly greater at the base of the neck than at the top of the
neck even though its diameter is slightly larger at its base. Table 4 gives the maximum current
density in the neck for reference man and reference woman and also gives the corresponding
neck diameter at the point of the maximum.


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

– 21 –

The quantity of interest is the external electric field EBR required to produce a current density
equal to the basic restriction. This is found by dividing the basic restriction ( JBR in mA/m²) by
the current density per kV/m ( JA in mA/m²/(kV/m)).
E BR = J BR J (neck)
A


Values of EBR are given for the two most commonly used basic restrictions JBR : 2 mA/m 2
(public) and 1 0 mA/m 2 (occupational).
These calculations are of average current density in the neck and assume the current is
uniformly distributed across the horizontal cross section of the neck. Allowance for nonuniform conductivity and its effect on current density within the neck and in the central
nervous system tissue is made in 6.4.

the basic restrictions in terms of internal electric fields, i.e. Ei
! For
1 00 mV/m (occupational), the external electric field E required

BR :

20 mV/m (public) and
to produce an internal
electric field equal to the basic restriction Ei BR is found by the following relation:
BR

EBR = σEi BR J (neck)
A

where σ is the conductivity of the human model.
T a b l e 4 – E l e c t ri c fi e l d
b a s i c re s t ri c t i o n s

JBR

EBR
E BR

or


re q u i re d

i

in

mA/m 2

JA ,

current density in neck per kV/m,
Circumference at base of neck, m
EBR , electric field for a 2 mA/m 2 basic restriction in the
neck, kV/m
EBR , electric field for a 1 0 mA/m 2 basic restriction in the
neck, kV/m
EBR , electric field for a 20 mV/m basic restriction in the
neck, kV/m ( σ = 0, 2 S/m assumed)
EBR , electric field for a 1 00 mV/m basic restriction in the
neck, kV/m ( σ = 0, 2 S/m assumed)

5.3.2

t o p ro d u c e

th e n e ck a t 5 0 H z

R e fe re n c e


R e fe re n c e

m an

wo m a n

0, 244
0, 425

0, 286
0, 368

8, 2

7, 0

41

35

1 6, 4

1 4, 0

82

70

Numerical


Numerical calculations are presented for reference man and reference woman for the
axisymmetrical body-model providing confirmation of the validity of the analytic approach.
Numerical results for a reference 1 0-year-old child are given in Annex C.
The computation domain is identical to that used for the calculation for the semi-spheroid
model (see 5.2.2 and Figure 1 3).
The values of the physical parameters are the same as were used previously:
– ε r = 1 and σ = 0 S/m for the air
– ε r = 1 0 5 and σ = 0, 2 S/m for the human body
The dimensions of the axisymmetrical human model are given in table B.4. Its shape is
illustrated in Figure 6.

"


BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

– 22 –

Energised
electrode

Human body
model
Ground plane

IEC 762/07

Figure 1 3 – Computation domain
The results are given hereafter for the reference man and woman.


5.3.2.1

Reference man model

IEC 763/07

Figure 1 4 – Mesh of the man body model and distortion of power frequency electric
field lines close to model
Figure 1 4 shows the perturbed electric field in the air, close to the m odel. I n the sam e way as
previousl y, the human bod y model distorts the lines of electric field, which become
perpendicular to the surface of the bod y. Without the human bod y model or far from it, these
lines of electric field are vertical.
Figure 1 5 gives the distortion of the electric field equipotential lines due to the presence of the
hum an bod y m odel, and the distribution of the electric field m agnitude. The distortion is the
strongest close to the head of the m odel, which also means that the electric field is the
stronger in this area.


– 23 –

BS EN 62226-3-1:2007+A1:2017
IEC 62226-3-1:2007+A1:2017

IEC 764/07

Figure 1 5 – Distribution of potential lines and 50 Hz
electric field magnitude (man model)
The maximum value of the electric field in the air around the head is 1 8 kV/m (without the
human bod y model, the unperturbed external electric field value is E0 = 1 kV/m).

Figure 1 6 gives the result of the computation of induced currents inside the human bod y
model. These values have been calculated along the rotational axis of the model. These
values correspond to an unperturbed 50 Hz electric field E0 = 1 kV/m.
Induced current for E = 1 kV/m

1 200,00
Ankle

Induced current density J (μA/m 2)

1 000,00
800,00
600,00
400,00
Neck
200,00
0,00

0,00

0,20

0,40

0,60

0,80

1 ,00


1 ,20

1 ,40

1 ,60

1 ,80

2,00

Height m
IEC 765/07

Figure 1 6 – Computation of induced currents JA along a vertical axis, and distribution
of induced currents in the man model at 50 Hz