2D Computation and Measurement of Electric and Magnetic

Slavko Vujević, Dino Lovrić and Tonći Modrić

University of Split,

Faculty of Electrical Engineering, Mechanical Engineering and Naval

Architecture,

Croatia

2D Computation and Measurement of Electric

and Magnetic Fields of Overhead Electric

Power Lines

INDS’11 & ISTET’11 – S. Vujević, D. Lovrić, T. Modrić

Introduction


the problem of computing the power frequency electromagnetic field can be

considered as quasistatic → electric and magnetic field computed separately

computation of electric and magnetic field accomplished using a 2D

approximation of a power line

short power line is considered, conductor charge density is approximated by a

constant

results will be compared to measurements underneath a 400 kV overhead power

line

Mathematical model of overhead electric power line

2D numerical algorithm → short conductors

→ conductor sag neglected


thin-wire approximation

conductors treated as line sources parallel to

earth surface

homogeneous earth

conductors positioned along x-axis

field distribution will be computed along y-z

plane in the middle of the section

Scalar electric and vector magnetic potentials

solutions of Helmholtz differential equations reduce to solutions of Poisson

differential equations (quasistatic approximation)


scalar electric potential for n conductors:

n

i

BiBi

iAi

Ai

i

BiAi

dR

FdR104

1

vector magnetic potential for n conductors:

n

i

AiAi

i

Ai

dR

IiA1

1

4

0

2D computation of power line magnetic field

numerical algorithm is based on Biot-Savart law


conductor current flows along the axis and generates the magnetic field

components of magnetic flux density in y-z plane for x = 0:

iI

0xB

n

iii

i I

dd

zzB

1i2

22

0y

44

n

iii

i I

dd

yyB

1i2

22

0z

44

zy BBB

Total effective (rms value:)

2D computation of power line electric field

conductor charge density approximated by a constant →


electric field intensity is computed from

i

zyx EEEAjE ,,

the components of the electric field intensity are computed from:

00 xxxxx AjAjEE

y

zy

y

zyxEE xxyy

,,0,,00

z

zy

z

zyxEE xxzz

,,0,,00

i

i

Q

zyx EEEE

rms value:


vector magnetic potential for x = 0 needed in:


0

xx AjE

n

i i

i

ix d

d

nIA1

22

0

0

24

2

is computed from:

22iii zzyyd

Ai

AiAi

dR

1


scalar electric potential for x = 0 needed in equations


y

zyEy

,,0

can be obtained from:

z

zyEz

,,0

i

n

i ii

QD

Fd

zy

1

11

0 2sinh

2sinh

2

1,,0

phasors of the ith conductor charges are unknown


phasors of the ith conductor charges are computed using the point collocation

method:


njQDZFdZn

i

jiji ...,,2,1;)()(1

ji

v

v

vZ22

n2

1)(

22

0

v is replaced by:

iii rd 0

iii zD 2

jizzyyd jijiij ;22

jizzyyD jijiij ;22

Input data of the overhead power line


(kV)i (A)iIi y (m) zs (m)

L11 -10.7 12.58 234.40º 228-4.2º

2 -10.4 12.58 234.40º 228-4.2º

L23 -0.15 12.58 234.4240º 228235.8º

4 0.15 12.58 234.4240º 228235.8º

L35 10.4 12.58 234.4120º 228115.8º

6 10.7 12.58 234.4120º 228115.8º

SW1 7 -7.44 19.09 00º 00º

SW2 8 7.44 19.09 00º 00º

6 phase conductors (AlFe 490/65) and 2 shield

wires (Alumweld 19/9)

376 m long power line section

The sag of the conductors was

taken into account by:


szzs 3

2

Other input data:

Hzf

mS

r

50

/1.0

10

measurements taken on a clear

winter day (10 °C)

terrain mostly clear except sporadic

bushes

measurements along y directed

observation profile at z = 1 m

Input data of the overhead power line

Measuring equipment and procedure


electric field meter Monroe Electronics Model 238A-1

AC Fieldmeter

measurer has influence on electric field distribution →

measuring probe must be used

Measuring equipment and procedure


magnetic field meter Sypris Triaxial ELF Magnetic Field

Meter Model 4090

measurer does not have influence on the magnetic field

distribution

Comparison of results – magnetic field


Comparison of results – electric field


Summary


2D algorithms for computation of electric and magnetic fields of overhead power

lines

good agreement was found between the computed results and measurements

more advanced models are needed for more complicated structures such as

electric power substations

better results can be achieved by taking the sag into account (3D algorithm)

Thank you!


Documents

2D Computation and Measurement of Electric and Magnetic