Bsi bs en 62226 3 1 2007 + a1 2017

As it wi b s own in 5.3 of this stan ard, the c r ent den ity is u if orm throu hout the spheroid but de en s on the ratio L/R of its semi-major axis an semi-minor axis.. Numerical calc

ICS 1 2 0.2

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

This Bri sh Stan ard was

published u der the authoriy

of the Stan ards Policy an

Strate y Commi e

on 3 Oct ob r 2 0

ISBN 9 8 0 5 0 9 8 4 7

T hi s Br i ti sh Sta n d ar d i s th e U K i mpl emen t at i on of EN 62 26-3-1:20 7+A1:2017

It is id entical to IEC 62 26-3-1:20 7, incorporating amendment 1:2016

The UK p rticip tion in its prep ration was entrusted to Technical Commit e

GEL/ 10 , Human ex osure to low f equency and high fequency

electroma netic ra iation

A lst of org anizations represented on this commit e can be obtained on

request to its sec etary

This publcation do s not purport to include al the neces ary provisions ofa

contract User are responsible for its cor ect a plcation

Compl anc with a British Standard cannot confer im munity f om

It super edes BS EN 62 26-3-1:20 7 which is withdrawn

The start and finish of tex t introduced or altered b amendment is

i ndicated in the text b tag s Tag s indicating chang es to IEC text carr y

the n mber of the IEC amendment Fo ex mple, text altered b IEC

amendment 1 is indicated b !"

NOR ME EUR OPÉENNE

Euro e n Commite for Electrotec nical Stan ardiz ation

Comité Euro pé n de Normalsation Electro te ch iq e

Euro äis hes K omite für Elektro tec nis he No rmu g

Ce ntral Se creta ria t: ru d Sta ss a rt 3 5, B - 10 0 Bru s els

© 2 0 CENELEC - All rig ts of e ploitatio in a y form a d b a y me ns reserv ed worldwid for CENELEC memb rs

R ef No.EN 6 2 6-3- :2 0 E

ICS 17.2 0.2

En ls version

Ex posur e to electric or magnetic fields

in t he low and int ermediate f equency range -

Met hods for calculat ing t he cur ent densit y

and internal elect ric field induced in t he human body -

Part 3-1: Exposure to electric fields -

Analy t ical and 2D numerical models

Exposition aux c amps électriques

ou magnét iques à bas e

et moyenne féquenc -

Mét hodes de c lc l des densit és

de c urant induit et des c amps élect riques

induit s dans le corps humain -

Part ie 3-1: Exposit ion

à des c amps électriques -

Modèles analyt iques et numériques 2D

(CEI 62226-3-1:2007)

Sic erheit in elekt risc en

oder magnet i c en Feldern im niedrigen

und mit tleren Frequenz bereic -

Verahren z ur Berec nung der induz iert en

Körperstromdic t e und des im mensc lc en

Körpers induz ierten elekt risc en Feldes -

Tei 3-1: Ex osition gegenüber

elekt rische Feldern -

Analytisc e Modele

und numerisc e 2D-Modele

(IEC 62226-3-1:2007)

This Euro e n Standard was a pproved b CENELEC o 2 0 -0 -01 CENELEC me mb rs are b und t o c o mply

w it h t he CEN/CENELEC Int ernal Re gulatio s whic h s pulat e the c onditio s fo r giv in this Euro e n Sta dard

the st at us of a n tio al st andard wit hout a y alt eratio n

Up-t o-dat e lst s a d biblo ra phic a l re fe re c es c o nc ernin s c h n t io al st andard ma b o btain d o

a plc atio t o the Ce tral Se retariat o r to a y CENELEC member

This Europe n St andard ex ists in t hree o fficial ve rsio s (En lsh, Fre c h, Germa ) A versio in a y ot her

la gua ge made b t ra slat io under the resp nsibi ty of a CENELEC me mb r int o it s o wn la gua ge a d n tified

to t he Ce tra lSec reta riat h s the sa me st at us as t he oficial versio s

CENELEC memb rs are t he n tio al ele t rotec hnic al c o mmit t ees of Au tria, Belgium, Bulg ria, Cy ru , the

Cze h Republc , De ma rk, Est onia, Finla d, Fra c e , Germa y, Gre c e, Hun a ry, Ic ela d, Irela d, Italy, L t v ia,

Lithua ia, Lux emb urg, Malt a, the Nethe a d , Norwa , Pola d, Portug l, Ro ma ia, Slova k ia, Slo ve ia, Sp in,

Swede , Swit zerla da d the United Kin do m

January 2017

The text of doc ment 10 / 125/ FDIS, future edition 1 of IEC 62 26-3-1, prep red by IEC TC 10 , Method

for the as es ment of electri , mag etic an electromag etic field as ociated with h man exp s re, was

s bmited to the IEC-CENELEC p ralel vote an was a proved by CENELEC as EN 62 26-3-1 on

20 7-0 -01

This Euro e n Stan ard is to b u ed in conju ction with EN 62 26-1:20 5

The folowin dates were fi ed:

– latest date by whic the EN has to b implemented

at national level by publcation of an identical

national stan ard or by en orsement

– latest date by w hic the national stan ard conflctin

with the EN have to b with r awn

(dow) 2010-0 -01

Endorsement notice

The text of the International Stan ard IEC 62 26-3-1:20 7 was a proved by CENELEC as a Euro e n

Stan ard without an modification

– 2 –

Foreword t o amendment A 1

The t ex t of doc ment 10 /37 /FDIS, fut ure IEC 6 2 6-3-1:2 0 /A 1, pre ared by IEC/TC 10

"Met hod for t he as es ment of elect ric, mag etic an elect romag etic field as ociat ed w it h h man

ex pos re" w as s bmit t ed t o t he IEC-CENELEC p ralel v ote an a proved by CENELEC as

EN 6 2 6-3-1:2 0 /A 1:2 17

The folowin dat es are fix ed:

• lat est date by whic the doc ment has t o b

implement ed at nat ional level by

publcation of an ident ical nat ional

st an ard or by en orsement

• lat est date by whic the national

st an ard c onflct in w it h the

doc ment hav e to b with raw n

At t ent ion is drawn to t he p s ibi ty t hat some of t he element s of t his doc ment may b the s bject of

p t ent rig t s CENELEC [an / or CEN] s al not b held resp n ible for ident ifyin an or al s c

p t ent rig t s

Endorsement notice

The t ex t of t he Int ernat ional Stan ard IEC 6 2 6-3-1:2 0 /A1:2 16 was a prov ed by CENELEC as a

Euro e n Stan ard w it hout an modificat ion

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

INTRODUCTION 6

1 Sco e .7

2 Exp s re to electric f ield .7

3 General proced re 10 3.1 Sha e factor 10 3.2 Proced re 10 4 Human b dy models 1

4.1 General 1

4.2 Sur ace are 1

4.3 Semi-spheroidal model .12 4.4 Axis mmetrical b d model 14 5 Calc lation of in u ed c r ent 15 5.1 General 15 5.2 Semi-spheroid 15 5.3 Axis mmetrical models .19 5.4 Comp rison of the analytical an n merical models 2

6 Influen e of electrical p rameters .2

6.1 General 2

6.2 Influen e of p rmitivity .2

6.3 Influen e of con u tivity 2

6.4 Non-homogene u con u tivity .2

7 Me s rement of c r ents in u ed by electric f ield 2

7.1 General .2

7.2 Cur ent f lowin to the grou d 2

An ex A (normative) Analytical solution for a spheroid in a u if orm electric field .2

An ex B (normative) Human b d axis mmetrical model 3

An ex C (informative) Chi d b dy model 3

An ex D (inf ormative) Example of u e of this stan ard .3

An ex E (informative) Numerical calc lation method 4

Bibl ogra h 51

Fig re 1 – Il u tration of the phenomenon of c r ents in u ed by electric f ield in a h man b d stan in on the grou d 9

Fig re 2 – Potential l nes of the electric field generated by an energised wire in the a sen e of an o jects (al distan es in metres) .9

Fig re 3 – A re l stic b d model 1

Fig re 4 – Sc eme of the semi-spheroid simulatin a h man b in stan in on a zero p tential plane .1

2

Fig re 5 – Eq ivalent spheroid radiu , R, vers s heig t, L, an for dif ferent mas , M .14

Fig re 6 – The axis mmetrical b d model f or the ref eren e man (left an woman

(rig t 14

Fig re 7 – Con u tive spheroid exp sed to electric f ield 15

Fig re 8 – Calc lation of the s a e fa tor for ele tric fiel d K

E

f or an spheroid exp sed

to an u p rturbed electric field 16

Fig re 9 – Cur ent den ity J

S

in u ed by an u p rturb d electric f ield (1 kV/m, 5 Hz)

in a spheroid vers s p rameter L/R (values in µA/m²) 17

Fig re 10 – Dimen ion an mes of the semi-spheroid 18

Fig re 11 – Distortion of p wer f req en y electric field lnes close to the con u tive

semi-spheroid 18

Fig re 12 – Calc lated in u ed c r ent den ity J

A (h) in the b d stan in in a vertical

5 Hz electric field of 1 kV/m .2

Fig re 13 – Computation domain 2

Fig re 14 – Mes of the man b d model an distortion of p wer f req en y electric f ield l nes close to model 2

Fig re 15 – Distribution of p tential l nes an 5 Hz electric f ield mag itu e (man model) .2

Fig re 16 – Computation of in u ed c r ents J A alon a vertical axis, an distribution of in u ed c r ents in the man model at 5 Hz 2

Fig re 17 – Mes of the woman b d model an distortion of p wer f req en y electric f ield l nes close to model 2

Fig re 18 – Distribution of p tential l nes an 5 Hz electric f ield mag itu e (woman model) .2

Fig re 19 – Computation of in u ed c r ents J A alon a vertical axis, an distribution of in u ed c r ents in the woman model at 5 Hz 2

Fig re A.1 – Con u tive spheroid exp sed to electric field 2

Fig re B.1 – Normal sed axis mmetrical models L ft: man, Rig t: woman 3

Fig re C.1 – Computation of in u ed c r ents J Z alon a vertical axis, an distribution of in u ed c r ents in the 10 ye rs ref eren e c i d model 3

Fig re E.1 – Spheroid model 4

Fig re E.2 – Sp ce p tential model 4

Fig re E.3 – Exemple of c arge simulation method u in rin s .4

Fig re E.4 – Sup rf i ial c arges integral eq ation method, c tin of the b d into N elements .4

Fig re E.5 – Mes of the b d u in f i ite element method 4

Fig re E.6 – Imp dan e method 4

Fig re E.7 – Ye -method: Electric an mag etic grid f or sp tial dis retization 5

Ta le 1 – Data for referen e man an ref eren e woman 12 Ta le 2 – Values of arc in(e) / e f or dif ferent values of L/R .13 Ta le 3 – Derived data u in spheroid model at 5 Hz 19 Ta le 4 – Electric field E BR req ired to prod ce b sic restriction J BR in the nec at 5 Hz .21

Ta le 5 – Comp rison of values of the s a e f actor f or electric field K E an cor espon in c r ent den ities f or an u p rturb d 5 Hz electric field of 1 kV/m 2

Ta le B.1 – Me s res f rom antro omorphic s rvey u ed to con tru t vertical dimen ion of axis mmetrical model [5 ] 3

– 4 – IEC 62226- 3- 1:2007+A1:2017

Ta le B.2 – Me s res f om antro omorphic s rvey u ed to con tru t the radial

dimen ion of axis mmetrical model [5 ] 3

Ta le B.3 – Normal sed model dimen ion 3

Ta le B.4 – Axis mmetric model dimen ion f or ref eren e man an referen e woman whose mas an heig t are defined by ICRP [3 ] an are given in Ta le 1 3

Ta le C.1 – Referen e values provided by ICRP for male an f emale c i dren .3

Ta le C.2 – Dimen ion of the referen e c i dren (in m ex e ted SB R in m²) 3

Ta le C.3 – Res lts of analytical method for the referen e c i dren 3

Ta le D.1 – Normalsed dimen ion of the women model 4

Ta le D.2 – Calc lation of the dimen ion for a sp cific p rson 41

INTRODUCTION

Publ c interest con ernin h man exp s re to electric an mag etic field has led

international an national organisation to pro ose l mits b sed on recog ised ad erse

ef fects

This stan ard a pl es to the feq en y ran e for whic the exp s re l mits are b sed on the

in u tion of voltages or c r ents in the h man b d , when exp sed to electric an mag etic

f ield This f req en y ran e covers the low an intermediate feq en ies, up to 10 kHz

Some method des rib d in this stan ard can b u ed at hig er f req en ies u der sp cific

con ition

The exp s re l mits b sed on biological an medical exp rimentation a out these

f un amental in u tion phenomena are u ual y cal ed “b sic restriction ” They in lu e safety

f actors

The in u ed electrical q antities are not directly me s ra le, so simplfied derived l mits are

also pro osed These l mits, cal ed “referen e levels” are given in terms of external electric

an mag etic field They are b sed on very simple models of coupl n b twe n external

f ield an the b d These derived l mits are con ervative

So histicated models for calc latin in u ed c r ents in the b d have b en u ed an are the

s bject of a n mb r of s ientif i publ cation These models u e n merical 3D

electromag etic f ield computation codes an detai ed models of the internal stru ture with

sp cific electrical c aracteristic of e c tis ue within the b d However s c models are sti

develo in ; the electrical con u tivity data avai a le at present has con idera le

s ortcomin s; an the sp tial resolution of models is sti progres in Su h models are

therefore sti con idered to b in the f ield of s ientific rese rc an at present it is not

con idered that the res lts o tained fom s c models s ould b fixed in efinitely within

stan ard However it is recog ised that s c models can an do make a u eful contribution

to the stan ardisation proces , sp cial y f or prod ct stan ard where p rtic lar cases of

exp s re are con idered When res lts f om s c models are u ed in stan ard , the res lts

s ould b reviewed f rom time to time to en ure they contin e to reflect the c r ent statu of

the s ien e

– 6 –IEC 62226- 3- 1:2007+A1:2017

EXPOSURE TO ELECTRIC OR MA GNETIC FIELDS

This p rt of IEC 6 2 6 a pl es to the f req en y ran e f or whic exp s re l mits are b sed on

the in u tion of voltages or c r ents in the h man b d when exp sed to electric f ield

This part def i es in detai the coupl n factor K – introd ced by the IEC 6 2 6 series to

ena le exp s re as es ment f or complex exp s re situation , s c as non-u if orm mag etic

f ield or p rturb d electric field – for the case of simple models of the h man b dy, exp sed to

u if orm electric f ield The coupl n factor K has diff erent ph sical interpretation de en in

on whether it relates to electric or mag etic field exp s re It is the so cal ed “s a e f actor f or

electric field”

This p rt of IEC 6 2 6 can b u ed when the electric field can b con idered to b u iform,

f or feq en ies up to at le st 10 kHz

This situation of exp s re to a “u if orm” electric f ield is mostly fou d in the vicinity of hig

voltage overhe d p wer s stems F r this re son, i u tration given in this p rt are given f or

p wer f eq en ies (5 Hz an 6 Hz)

2 Exposure to ele tric field

Alternatin electric f ield are generated by energised con u tors (i.e u der voltage) In the

immediate vicinity of domestic electrical eq ipment, s c as l g ts, switc es, fo d mixers an

iron , local electric- ield stren th a out 10 V/m may b fou d Su h f ield are non-u iform,

but their stren th are f ar b low the levels recommen ed in saf ety g idel nes, so there is no

ne d of calc lation of in u ed c r ents in s c exp s re situation

Hig er electric-ield stren th may b f ou d in the vicinity of hig voltage eq ipment s c as

electric p wer l ne In the f req en y ran e covered by this stan ard, it is con idered that

exp s re f om p wer l nes is the only sig ificant exp s re source for publc regardin saf ety

g idel nes l mits

Guidel nes on h man exp s re to electric field are general y expres ed in terms of in u ed

c r ent den ity or internal electric f ield These q antities can ot b me s red directly an the

purp se of this doc ment is to give g idan e on how to as es these q antities in u ed in the

h man b d by external (en ironmental) electric field E

0

The in u ed c r ent den ity J an the internal electric field E

iare closely l n ed by the simple

relation:

i.Eσ

where σ is the con u tivity of the b d tis ue u der con ideration

Al the calc lation develo ed in this doc ment u e the low f req en y a proximation in whic

displacement c r ents are negl gible, s c that εω/σ is les than 1 in the b d This

a proximation has b en c ec ed u in publ s ed tis ue data [2 ,31]

1

in the low f req en y

ran e an it has b en f ou d to b val d for f req en ies up to at le st 10 kHz an is pro a ly

val d at hig er f req en ies

Computation b sed on so histicated n merical models of the h man b d [2 ] also

demon trate that this as umption is val d at f req en ies up to more than 10 kHz by s owin

that the relation hip b twe n the in u ed c r ent den ity in the b dy an the prod ct of

f req en y an external electric field hardly varies at al b twe n 5 Hz an 1 MHz, an is only

sl g tly altered at 10 MHz

Analytical models can b u ed f or simple cases of calc lation

Electric f ield cau e displacement of electric c arges in con u tive o jects (in lu in l vin

b dies) an , b cau e these field are alternatin , the electric c arges move b c ward an

f orward The res lt is an “in u ed” alternatin c r ent in ide the con u tive o ject This

c r ent de en s only on:

– the s a e an size of the con u tin o ject;

– the c aracteristic (mag itu e, p larisation, degre of non-u if ormity, etc.) of the

u p rturb d f ield (f ield whic is me s red in the a sen e of an con u tin o ject ;

– the f req en y of the f ield

– the variation of con u tivity of the o ject (in homogene u media, the c r ent den ity

in u ed by electric f ield do s not de en on con u tivity)

Fig re 1 i u trates this in u tion phenomenon for the case where the b d is in electrical

contact with the grou d

—————————

– 8 –

Althou h some g idel nes on h man exp s re to electric f ield ado t internal electric f ield as

a lmitin p rameter, f or re son of simpl f i ation, the content of this stan ard is presented

mainly in terms of in u ed c r ent den ities J, f rom whic values of internal electric f ield E

Elec t ric field

In uced c urrents

IEC 70/0

Figure 1 – I lu tration of th phe ome on of c r e ts induc d by a ele tric f ield in a

h ma body sta ding on the groun

The typical case of publc exp s re to an electric field is u der hig voltage p wer

tran mis ion l nes In this case, the distan e b twe n the source of field an the h man b d

is large an the field in the zone close to the grou d, in the a sen e of an con u tive o ject,

can b con idered to b u if orm (se Fig re 2)

3 General proc dure

3.1 Shape fa tor

In the low an intermediate f req en y ran e, the relation b twe n the in u ed c r ent in the

h man b d (J) an a u iform electric f ield (E

0) can b red ced to:

0 fEKJ

is de en ant on the size, the con u tivity, the f orm an the p sition of the model of the

h man b d It is also de en ant on the location within the b d where the in u ed c r ent

den ity is evaluated K

E

is in e en ent of the f req en y f or analytical as es ment of the

in u ed c r ent prod ced by electric field (se An ex A)

or Farad p r metre (F/m), whic relates to the f act that the

exp s re to the electric f ield cor esp n s ph sical y to a ca acitive coupl n b twe n the f ield

source an the con u tive o ject exp sed to the f ield

3.2 Proc dure

The c r ent den ity in ide an in ivid al can b estimated analytical y, f ol owin a thre stage

proces The f irst stage is to compute the c r ent den ity in a semi-spheroid, whose

dimen ion are c osen to b st re resent the p rtic lar b d As it wi b s own in 5.3 of this

stan ard, the c r ent den ity is u if orm throu hout the spheroid but de en s on the ratio L/R

of its semi-major axis an semi-minor axis

The secon stage is to u e a re l stic axis mmetrical model of a h man b d to determine the

c r ent den ity as a fu ction of vertical p sition within the b dy

In u ed c r ents are calc lated f or men an women as wel as c i dren u in ref eren e

values f or their heig t, mas an s rf ace are publ s ed by ICRP [3 ] Suf f icient inf ormation

is given here to a ply the method to p rson of an weig t an heig t

Numerical calc lation are also presented demon tratin the val dity of the analytical

ref er sp cif i al y to c r ent den ity (or internal electric f ield) in the central nervou s stem, so

the p rtic lar are of interest within the b d is the spinal cord in the nec , d e to the smal

cros section of the nec , whic con entrates the c r ent (or internal electric f ield) in that

region

!

"

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

4 Human body models

In s ientif i l terature, man models of dif f erent complexity have b en u ed for the

as es ment of c r ents an internal f ield in u ed by electric or mag etic f ield (Fig re 3)

Examples of s c so histicated calc lation are given in the bibl ogra h It mu t b

emphasised that these computation have b en p r ormed u in dedicated softwares whic

req ire hig ly sp cial sed comp ten es an are not widely avai a le Theref ore, it is

con idered that s c computational tec niq es are not relevant with regard to stan ardisation

o jectives

IEC 72/0

Figure 3 – A re l stic body model

Analytical calc lation are p s ible when u in simple models, s c as the model of a

spheroid in a u iform electric f ield

4.2 Surfa e are

The s r ace are of a b dy (SB) is u ed to s ale b th the spheroidal an the axis mmetrical

b d models f or dif f erent sized b dies It de en s on the heig t an the mas of the b dy

The re ort of the ICRP [3 ] Ba ic An t omic l a d Ph siol ogic l Data for U se in Rad iol ogic l

P rotect ion: Refere c Valu s, provides an algorithm givin the total s rf ace are (SB

T) of a

p rson as a f un tion of its heig t L (in metres) an mas M (in k ):

4

4 2,05

514,0

T

4

16,

In our case, only the outward -f acin s rf ace are of the b d is con idered, whic is

a proximately 8 % of the total s rf ace are SB

T

The 18 % red ction comprises 3 % for

ex lu in the soles of the fe t, 6 % for ex lu ing the tou hin s r ace of the leg , an 8 % f or

ex lu in the in er s r ace of the arms an han s an 1 % for the p rineum The red ced

s rf ace are (SB

R) is theref ore:

TR

8,

Ta le 1 gives the res lts f or the referen e man an the referen e woman whic are

Table 1 – Data for refere c ma a d ref ere c woma

To calc late the in u ed c r ent den ity in ide a h man stan in on a con u tin plane it is

neces ary to model the ref lection of the b dy in the grou d Th s the b d is re resented by

half of the spheroid (Fig re 4) an the reflection by the other half (Fig re 7) The semi-major

axis L of the spheroid is set to the heig t of the p rson b in re resented

The semi-minor axis (i.e the radiu ) R is c osen to give the same total c r ent f lowin into the

grou d throu h the f eet when the b d is grou ded as f or the b d it re resents This is

ac ieved by en urin that the spheroid has the same outward-f acin s rf ace are SB

=

ee

RL

RSB

arc sin

12

S

(5) – 1 –

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

1

LR

where SB

R

is given by eq ation (3) an (4) Th s

π+

22

SB

BB

where

ee

LB

)arc sin(

=

B is a fu ction of R, but as arc in( )/ varies only slowly with L/R, as s own in Ta le 2, B also

varies only slowly with L/R, an therefore B can b determined u in an a proximate value for

π++

−

=

S2

5 5,0

7 8,0

SB

LL

Fig re 5 presents the res lt gra hical y It can be u ed to fin the radiu R f rom the heig t L

an mas M of a p rson For example, the referen e man, whose mas is 7 k an heig t is

1.76 m, the radiu R is 0,17 m an L/R is 9,8

0,10

0,15 0,2

0,20,3

The axis mmetrical b d model re resents the es ential fe tures of the b d : its heig t, total

s race are , nec dimen ion , an a proximate vertical prof ile However it can ot b a

p r ect re resentation of the b d b cau e the b d is not axis mmetrical Fig re 6 i u trates

the radial cros section of the axis mmetrical model f or the ref eren e man an woman

0.00.20.40.60.8

0.20.40.60.81.01.21.41.61.8

An ex B des rib s how data fom an anthro ometric s rvey of 2 2 8 women an 1 17 men,

c osen as a re resentative sample f rom the US Army, were u ed to develo the

axis mmetrical model The model is def i ed by 13 (radiu , heig t co rdinates

5 Calculation of induced cur ent

Analytical models to q antify the relation hip b twe n in u ed c r ents in con u tive b dies

an external electric field are general y b sed up n the most simple as umption that the

external f ield are u iform an at a sin le f eq en y, an that the b dies are homogene u

an with a s a e that can b des rib d analytical y (as is the case of spheres, spheroid ,

etc.) Theref ore, they can ot e si y take into ac ou t the fact that the h man b d is a non

-homogene u stru ture with a complex s a e

Nevertheles , analytical models can b u ed for simple cases of calc lation an /or to

val date n merical calc lation

In the p rtic lar case of the homogene u models develo ed in this stan ard, the in u ed

c r ent den ity is in e en ent of the con u tivity an the p rmit ivity (low f req en y

a proximation)

5.2 Semi-spheroid

5.2.1 Analytic l

In An ex A, the detaied analytical solution f or a spheroid in a u if orm electric field are

presented as a fu ction of spheroid's ge metrical an electrical p rameters an of the

mag itu e an direction of the electric f ield vector (Fig re 7) The spheroid re resentation is

eq ivalent to the semi-spheroid in the presen e of the grou d plane as explained in 4.3

Figure 7 – Conductiv spheroid e pos d to ele tric field

L is the len th of the semi-major (rotational) axis of the spheroid (axis Z),

R is the len th of the semi-minor axis of the spheroid (R is also the radiu of the circ lar cros

section of the spheroid at the s mmetry plane (plane XY)

The s a e factor for electric f ield K

EZ

0Z) an E

ER

0R)

The res lts of this analytical calc lation are s mmarised hereu der in Fig res 8 an 9

Fig re 8 gives in a gra hic f orm the res lt of the calc lation of K

indu e by a unperturbe ele tric field (1 kV/m, 5 Hz)

in a sph roid v rs s parameter L/R (v lu s in µA/m²)

Direct a pl cation:

Con iderin the values for the referen e man (se 4.3) L/R = 9,8 an L = 1,7 m, exp sed

to 5 Hz vertical electric field with a mag itu e of 1 kV/m, the c rves in Fig res 8 an 9 give:

A.s/V m

106,2

9

×

≅

EZK

an

²mA/ m

13,0

0S

≅

=

ZEZZ

EfKJ

5.2.2 Numeric l

Dif ferent method can b u ed to determine the c r ent in u ed by an external electric f ield

E

0

in a con u tive o ject In the fol owin computation , a f i ite elements method was u ed

Ph sical p rameters for the air are [2 ,3 ,51]

R = 0,17 m σ = 0,2 S/m

In the example given here, the mes of the semi-spheroid is comp sed of 2 4 s rf ace

electrode at 10 m f rom the grou d plane, with an electrical p tential of 10 0 0 V The domain

is as umed to b axis mmetrical

Fig re 1 s ows the p rturb d electric f ield in the air, close to the semi-spheroid The semi

-spheroid distorts the l nes of electric f ield, whic b come p rp n ic lar to the s rf ace of the

spheroid Without the semi-spheroid or f ar f rom it, these l nes of electric field are vertical

The c r ent den ity in the centre of the semi-spheroid is very simi ar to the c r ent den ity

value f rom analytical calc lation

The variation is les than 1 % alon the vertical axis an the c r ent den ity s ould b

con idered as con tant As a res lt, it can b con idered that this simple n merical model

gives res lts identical to those of the analytical calc lation

5.3 Axis mmetric l models

5.3.1 Analytic l

Ta le 3 gives values derived in the course of calc latin the c r ent den ity in the spheroid

The s rf ace are in the third row was calc lated f om the heig t an mas u in Eq ation (3)

In the next row the 0,8 f actor was a pl ed (Eq ation (4) to remove non-outward facin

s rf aces when stan in Usin the outward-f acin s rf ace are an Eq ation (7) gives in the

next row the radiu R f or a half spheroid havin the same s r ace are The f ol owin row

presents the cor esp n in L/R It is a proximately the same for b th referen e man an

referen e woman

Table 3 – Deriv d data usin sph roid model at 5 Hz

Referenc man Referenc woman

Re u e s ra e are of b d S B

R, m2

in the spheroid de en s only on the p rameter L/R, the electric field

an f req en y For L/R = 9,8 the c r ent den ity throu hout the spheroid is

is u if orm throu hout the spheroid The vertical c r ent f lowin

throu h a horizontal layer of the spheroid therefore in re ses progres ively f rom zero at the

to to a maximum at the grou d This is b cau e of the displacement c r ent is enterin the

spheroid progres ively over its whole heig t

In practice the h man b d is not a half spheroid but has an ef f ective horizontal radiu that

varies u evenly with vertical p sition as re resented by the axis mmetrical model

The as umption is made that at a p rtic lar heig t the same overal c r ent flows as in the

spheroid, but it flows in the dif ferent cros sectional are of the asy mmetrical model at that

heig t Th s at a p rtic lar heig t h a ove grou d, the in u ed c r ent den ity in the

axis mmetrical model J is given by:

t heofare

horizont al

spheroid

t heofarehorizont al

)()(

SA

×

hJ

or

)(

)(

*)()(

hr

hr

hJh

radiu of the axis mmetrical model at heig t h

The vertical cros section of a spheroid throu h its axis is an el pse an the radiu r

The variation of c r ent den ity with heig t is s own in Fig re 12 f or ref eren e man an

ref eren e woman

0.00.20.40.60.81.01.21.41.61.82.0

Current d n ity,mA /m

20.0

Outln s of th s h roid l mo el a d a is mmetric lmo els u e are als s own L f t: ma , rig t: woma

Fig re 12 – Calc late ind c d c r e t de sity J (h) in th bod sta ding in a v rtic l

5 Hz ele tric f ield of 1 kV/m

The c r ent den ity is maximum in the an le, an there is a smal er maximum in the nec

The c r ent den ity in the nec is sl g tly gre ter at the b se of the nec than at the to of the

nec even thou h its diameter is sl g tly larger at its b se Ta le 4 gives the maximum c r ent

den ity in the nec f or ref eren e man an ref eren e woman an also gives the cor esp n in

– 20 –IEC 62226- 3- 1:2007+A1:2017

The q antity of interest is the external electric field E

Breq ired to prod ce a c r ent den ity

eq al to the b sic restriction This is f ou d by dividin the b sic restriction (J

B: 2 mA/m

2

(publ c) an 10 mA/m

2

(oc up tional)

These calc lation are of average c r ent den ity in the nec an as ume the c r ent is

u iformly distributed acros the horizontal cros section of the nec Alowan e f or non

-u iform con u tivity an its eff ect on c r ent den ity within the nec an in the central

nervou s stem tis ue is made in 6.4

5.3.2 Numeric l

Numerical calc lation are presented f or referen e man an ref eren e woman f or the

axis mmetrical b dy-model providin con rmation of the val dity of the analytic a pro c

Numerical res lts f or a ref eren e 10-ye r old c i d are given in An ex C

The computation domain is identical to that u ed for the calc lation f or the semi-spheroid

an σ = 0,2 S/m for the h man b d

The dimen ion of the axis mmetrical h man model are given in ta le B.4 Its s a e is

For the b sic restriction in terms of internal electric f ield , i.e E

iB: 2 mV/m (publ c) an

10 mV/m (oc up tional), the external electric f ield E

Breq ired to prod ce an internal

electric f ield eq al to the b sic restriction E

iB

is f ou d by the f ol owin relation:

(nec k )

Ai

JE

E

B

Bσ

=

where σ is the con u tivity of the h man model

Table 4 – Ele tric f ield E

Figure 13 – Computation domain

The res lts are given here f ter f or the referen e man an woman

5.3.2.1 Refere c ma model

IEC 73/0

Figure 14 – Me h of the ma b dy model a d distortion of p wer fre ue c ele tric

f ield l ne clos to model

Fig re 14 s ows the p rturb d electric f ield in the air, close to the model In the same way as

previou ly, the h man b d model distorts the l nes of electric f ield, whic b come

p rp n ic lar to the s rf ace of the b dy Without the h man b d model or f ar f rom it, these

l nes of electric field are vertical

Fig re 15 gives the distortion of the electric f ield eq ip tential l nes d e to the presen e of the

h man b d model, an the distribution of the electric f ield mag itu e The distortion is the

stron est close to the he d of the model, whic also me n that the electric f ield is the

– 2 –IEC 62226- 3- 1:2007+A1:2017

IEC 74/0

Figure 15 – Distribution of pote tial l ne a d 5 Hz

ele tric field ma nitude (ma model)

The maximum value of the electric f ield in the air arou d the he d is 18 kV/m (without the

h man b d model, the u p rturb d external electric field value is E

0

= 1 kV/m)

Fig re 16 gives the res lt of the computation of in u ed c r ents in ide the h man b d

model These values have b en calc lated alon the rotational axis of the model These

values cor esp n to an u p rturb d 5 Hz electric f ield E

The value of the in u ed c r ent den ity J is given in mA/m

2

The in u ed c r ent den ity is

hig er where the cros section of the model is smal (nec or an le)

5.3.2.2 Refere ce woma model

IEC 76/0

Figure 17 – Me h of the woma body model a d distortion of p wer

f re u nc ele tric f ield l ne clos to model

Fig re 17 s ows the p rturb d electric f ield in the air, close to the model In the same way as

previou ly, the h man b d model distorts the l nes of electric f ield, whic b come

p rp n ic lar to the s rf ace of the b d Without the h man b d model or f ar f rom it, these

l nes of electric field are vertical

Fig re 18 gives the distortion of the electric f ield eq ip tential l nes d e to the presen e of the

h man b d model, an the distribution of the electric f ield mag itu e The distortion is the

stron est close to the he d of the model, what also me n that the electric f ield is the

stron er in this are

– 24 –IEC 62226- 3- 1:2007+A1:2017

IEC 77/0

Fig re 18 – Distribution of pote tial l ne a d 5 Hz electric field ma nitude

(woma mod l)

The maximum value of the electric f ield in the air arou d the he d is 18 kV/m (without the

h man b d model, the u p rturb d external electric field value is E

0

= 1 kV/m)

Fig re 19 gives the res lt of the computation of in u ed c r ents in ide the h man b d

model These values have b en calc lated alon the rotational axis of the model These

values cor esp n to an u p rturb d electric f ield E

The value of the in u ed c r ent den ity J is given in mA/m

2

The in u ed c r ent den ity is

hig er where the cros section of the model is smal (nec or an le)

5.4 Comparison of the a alytic l a d numeric l models

With the re l stic s a e model presented in 4.4 an develo ed in An ex B, the hig est c r ent

den ities are fou d in are s with smal section l ke the nec or the an les, where s with

semi-spheroid models, the in u ed c r ent den ity is con tant alon the vertical axis

Ta le 5 comp res the res lts in the nec f or the n merical an the analytical re l stic model

f or 3 dif f erent h man s a es (man, woman an c id) For comp rison purp ses, the values

u ed by ICNIRP are also given in Ta le 5

There is a go d agre ment b twe n the res lts f or the analytical an the n merical model n

of the axis mmetrical b d model

F r example, an electric f ield of 8 kV/m at 5 Hz is calc lated to give an averaged in u ed

c r ent in the nec of ref eren e man of 1,8 mA/m² with the n merical method an of

1,9 mA/m² with the analytical method As explained in 6.4, the c r ent den ity in the spinal

cord s ould b lower

6 Inf luenc of electrical parameters

6.1 Ge eral

This clau e stu ies the in uen e of electrical c aracteristic of l vin tis ues on the res lts of

the computation of in u ed c r ents Two p rameters are stu ied: relative electrical

p rmit ivity an electrical con u tivity

The computation con ition an domain are simi ar to those u ed in the previou clau e

6.2 Inf lue c of permit ivity

A series of computation have b en p rormed u in a con tant electrical con u tivity of the

sphere (σ = 0,2 S/m), an dif f erent values of relative electrical p rmit ivity: ε

r

= 10 , 10

3

,105

,

10

7

Detai ed res lts are not given, but the computation res lts have proved to b in e en ent of

the value of the relative electrical p rmitivity in this ran e of p rmit ivity

1,6× 10-8

) an dif f erent values of electrical con u tivity: σ = 0,1; 0,2; 0,4 an 0,8 S/m.

Res lts of computation have s own that the mag itu e of the in u ed c r ent is in e en ent

of the con u tivity

As a con lu ion, the in u ed c r ent den ity is de en ent only on the ge metry of the h man

b d when the electrical p rameters are homogene u in the b d However, when the

electrical p rameters are non-homogene u in the b d , the c r ent den ity is hig ly

de en ant of the variation of electrical p rameters b twe n adjacent organ

6.4 Non-homoge eous cond ctivity

Guidel nes s c as those of ICNIRP sp cify the b sic restriction in terms of the c r ent

den ity in the central nervou s stem rather than in the nec as a whole Becau e the

con u tivity of the spinal cord is lower than the average con u tivity of the nec , the c r ent

den ity in the spinal cord is lower than the average in the nec The data f or con u tivity

presently avai a le are not go d enou h to determine the red ction f actor with an

confiden e More exp rimental work is in progres to provide more rel a le con u tivity

inf ormation an wi b publ s ed as Part 4 of this stan ard These data wi b u ed to

recommen in Part 4 an a pro riate red ction f actor

7 Me surement of cur ents induc d by ele tric f ields

7.1 Ge eral

Internal b dy c r ents are in u ed in a b d when p rtial or whole-b dy exp s res to f ield

oc ur Sp cial me s rement tec niq es are u ed to evaluate the in u ed c r ents A

compl cation as ociated with evaluatin the mag itu e of in u ed c r ent relates to p thway

throu h whic these c r ents f low in the b d With electric f ield exp s re, the in u ed

c r ents f low throu h the b d , or p rts of the b d , commonly throu h the leg an the f eet

to the grou d or flo r (whic ever is the lowest p tential s rf ace in contact with the b d ) In

this case, u e of in trumentation, whic is in ef f ect placed in series with the b d an grou d,

can provide a me s re of these electric- ield in u ed c r ents

Bod c r ents are general y taken to b the in u ed c r ent as ociated with exp s re of the

b dy to radio f req en y f ield , but without an direct contact with o jects other than the

grou d up n whic the s bject may b stan in Several common tec niq es are u ed f or

me s rin b d c r ents in lu in clamp-on “lo p“ typ c r ent tran f ormers f or me s rin

c r ent throu h the an le or calf , an p ral el plate “stan -on-meters“ f or me s rin c r ents

that f low to grou d throu h the f eet

7.2 Cur e t f lowin to the ground

2

Sg

RJ

This c r ent can b me s red [14,2 ,4 ,4 ]

The cor esp n in c r ent to grou d p r kV/m f or ref eren e man is 13,2 µA an f or referen e

The c r ent f lowin into the grou d can b f ou d from the prod ct of the c r ent den ity J