Exposure to Low Frequency Magnetic Fields of a Transformer Station

Abstract—Evaluation of human exposure to nonionizing

electromagnetic radiation in the conditions of standardized

electromagnetic compatibility depends on calculation and measuring

of low-frequency electric and magnetic fields. Calculation of the low-

frequency magnetic field in and around a transformer station will be

presented in this paper. This calculation will be conducted by

modeling transformer station using EFC-400LF software package,

which is capable for two and three-dimensional numerical solving of

magnetic fields distribution.

Keywords—Numerical solving, Experimental measuring, Low-

frequency magnetic fields, Exposure to nonionizing electromagnetic

radiation

I. INTRODUCTION

UNDAMENTAL problems of electromagnetic

compatibility and evaluation of the human exposure to

nonionizing electromagnetic emissions are calculation and

measuring of the low-frequency (LF) electric and magnetic

fields. Various experimental methods and specialized

equipment are used for measuring of electromagnetic fields,

whereas numerical solvers of the non-linear differential

equations are used for the calculation of LF electric and

magnetic fields. Today, there are number of software packages

that calculate distribution of electromagnetic fields in two-

dimensional (2D) and three-dimensional (3D) environment.

Very often they have integrated field optimization methods of

complex power systems. These software packages require

model of the observed object and identification of the field

sources. Field sources can be simplified and dismembered into

smaller peaces. Calculation of LF electromagnetic fields is

performed using the law of superposition. In other words, it is

necessary to summarize the influences of each filed source to

get values of the resulting field.

Izudin Kapetanovic Ph.D., El. Eng. Member IEEE, Faculty of Elec. Eng.,

University of Tuzla; Franjeva ka 2, 75000 Tuzla, Bosnia and Herzegovina

(E-mail: [email protected] ).

Vlado Madžarevi Ph.D., El. Eng., Member IEEE, Faculty of Elec. Eng.,

University of Tuzla; Franjeva ka 2, 75000 Tuzla, Bosnia and Herzegovina


Alija Muharemovic Ph.D., El. Eng., Faculty of Elec. Eng., University of

Sarajevo; Zmaja od Bosne bb, 71000 Sarajevo, Bosnia and Herzegovina


Hidajet Salkic M.Sc. El. Eng. PE Elektroprivreda BiH, ED Tuzla; Rudarska

38, 75000 Tuzla, Bosnia and Herzegovina (Corresponding author

Tel: (+387) 35 304 361, Fax: (+387) 35 304 362,

(E-mail: [email protected]).

When it comes to the protection from electromagnetic field

emissions, two areas with different limitation levels of electric

and magnetic fields are recognized. According to the ICNIRP

policies, European Union (EU) references 1999/519/EC and

EU directive 2004/40/EC, these limitation values refer to the

root mean square (RMS) values of the electric field intensity

(E) and magnetic field density (B) for the constant exposure of

the human body to the electromagnetic field emissions. These

areas are:

The area of the increased sensitivity (E=5 kV/m; B=100

μT), and

The area of the professional exposure (10 kV/m; B=500

μT).

II. CALCULATION OF LOW-FREQUENCY MAGNETIC FIELD

Calculation of low-frequency magnetic field distribution

can be performed using the relation for induction of flat finite-

length streamline and the law of superposition.

According to Biot-Savart law, the element of flat

streamline dleld , shown on Fig. 1, produces magnetic flux

density in arbitrary point of space T equal to:

2

sin

4

1

R

dlidH (1)

Where: i – is a conductor current intensity,

dl – is an element of a flat streamline,

R – is distance between conductor element dl and

point P, and

- is angle between element dl and vector R

(according to Fig. 1 2

).

It should be emphasized that rotation symmetry exists;

therefore resulting magnetic flux density is gained by applying

cylindrical coordinate system. According to Fig. 1, follows:

lR

RldiBd

34 (2)

Where: zereR zr ( eee zr ,, - are unit vectors in

cylindrical coordinate system ),,( zr ),

Vector product from equation (2) is:

edlreedlreredleRld rzzrz )( (3)

Therefore, equation (2) can be written as:

Exposure to Low Frequency Magnetic Fields of

a Transformer Station

Izudin Kapetanovic P.hD, Vlado Madzarevic P.hD, Alija Muharemovic P.hD, Hidajet Salkic* M.Sc.

F

World Academy of Science, Engineering and TechnologyVol:2 2008-10-21

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http://waset.org/publications/8330/Exposure-to-Low-Frequency-Magnetic-Fields-of-a-Transformer-Station

eR

rdli

R

RxldiBd

ll33 44

(4)

Considering that dr , as well as dl

dRcos and

R

dcos , and after integration of contributions from all

elements, follows:

2

1

cos4

cos

cos4

1

cos4

2

2

3

dd

ieBd

dd

dieBd

Rd

dRe

iBd

(5)

Finally, for magnetic flux density of flat finite length

streamline it can be written:

12sinsin

4 r

ieB (6)

Density of magnetic flux in any point of space can be

calculated by superposing contributions of each conductor.

Conductors can be approximated with certain number of flat

finite length streamlines (segments). The number of segments

significantly depends on conductor geometry. Position of

segments, their currents and phase angles represents the input

data for calculation of magnetic flux density in desirable

points of space. As it can be seen from equation (6), direction

of magnetic flux density vector is defined by unit vector e in

cylindrical coordinate system. Since the positions of segments

in space are different, as well as directions of their

corresponding induction vectors, it is necessary to dismember

the resulting magnetic flux density vector on components in

direction of each coordinate axe of global system that is not

bounded for certain segment. Coordinates of start and end

points of segments can be set in rectangular coordinate system.

Fig. 1 The element of flat streamlines

For a given segment AB in rectangular global system, Fig.

2, the expression for magnetic flux density in point C, induced

by current ik of segment k is:

BC

PB

AC

APkk

R

R

R

R

CP

titB

4

(7)

Where: AP, AC, PB i BC – are distances between

individual points.

Fig. 2 Segment in rectangular coordinate system

In order to dismember the magnetic flux density vector on

its components, it is necessary to know its direction in global

system. Direction of magnetic flux density vector is

perpendicular on a plain defined by vectors ABR and

BCR ,

apropos it is equal to a direction of a resulting vector of their

vector product:

zyx

zyx

kji

BCAB

bbb

aaa

eee

RRG (8)

Cosines of angles, created by magnetic flux density vector

and coordinate axes x, y, and z, are equal to the ratios of

individual axes vectors and resulting vector:

F

caca

G

G yzzyxBcos

F

caca

G

Gzxxzy

Bcos (9)

F

caca

G

G xyyxzBcos

Where

222

xyyxzxxzyzzy cacacacacacaF

By knowing cosines of angles it is possible to determine

each component of magnetic flux density in time domain:

)(cos)(,

tBB kBtkx

)(cos)(,

tBB kBtky (10)

)(cos)(,

tBB kBtkz

Total amount of magnetic flux density vectors, produced by

currents of n segments, is gained summarizing the

contributions of all segments:


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2

1

,

2

1

,

2

1

,)()()()(

n

i

iz

n

i

iy

n

i

ix tBtBtBtB (11)

Where )(),(),(,,,

tBtBtB iziyix - are the components of

magnetic flux density of segment i.

For presentation of the magnetic field, effective value of

magnetic flux density is used, according to the following

expression:

T

zyxef tBtBtBT

B

0

222)()()(

1 (12)

Modeling of the transformer station elements

Calculation of LF magnetic fields distribution was

conducted using the EFC-400LF software package. This

software package consists of a part that ministers data input

and presentation and a part that minister numerical calculation

of magnetic fields. These two parts are connected trough the

input and output libraries. Block diagram of EFC-400LF

software package is presented in Fig. 3.

Fig. 3 Block diagram of the EFC-400LF software package

In order to analyze influence of magnetic fields constant

emissions on the human body, it is necessary to calculate the

distribution of the stationary sinusoidal LF magnetic fields.

Electromagnetic field around the transformer station (TS), at

frequency of 50 Hz is a quasistatic field, and consists of a

conservative component of the electric field produced by the

charges and eddy component of the electromagnetic field

produced by currents. Complex geometry of the TS elements

requires 3D calculation. Calculations of magnetic fields in

points that are far a way from filed sources are conducted by

using the thin-wire approximation. This approximation means

that conductors are presented as one-dimensional lines with

disregard of insulators, because their influence has a local

character. Each conductor requires following parameters:

Beginning coordinates (the beginning of a segment) –

Xp, Yp, Zp,

End coordinates (the end of a segment) – Xk, Yk, Zk,

Line or phase voltage – Ul, Uf (depending on settings in

“Options” menu – Technical Power T.L.),

Conductor current,

Phase angle,

Frequency,

Conductor geometry: shape, radius, length, height,

distance between conductors, specific electric resistance,

permittivity, permeability, etc.

Application of the EFC-400LF software package for the

calculation of the electromagnetic field is presented on

example of the typical Compact Concrete Transformer Station

(CCTS) 10(20)/0.4 kV, 630 kVA – “DELING”. Apparatus of

TS consists of:

Overlapping energy transformer; with nominal

transmission ratio 10(20)/0.4 kV; nominal power 630

kVA; nominal frequency 50 Hz; connection type Dyn5;

short circuit voltage Uk=4 %; voltage regulation ±2x2.5

%,

Middle voltage (MV) distribution conjunction block; is a

“Ring Main Unit” (RMU) type CCF 12/24 kV, 400 A,

SAFERING with three field – two conducting fields and

a transformer field – which are SF6 gas insulated,

completely armored and protected from the dangerous

touch voltage. Conducting fields are equipped with three

phase separator with the ground switch – nominal voltage

of 24 kV and nominal current of 400 A – and ancillary

mechanism 2NO+2NC. RMU SAFERING 12/24 kV

conjunction blocks, manufactured by “ABB”, are tested

for 16 kA/sec of thermal and 40 kA of dynamic (impulse)

short circuit current,

Low voltage (LV) conjunction block; consists of three

fields – one supplying and two conducting fields – with

nominal current 1250 A, short circuit enduring current 25

kA, enduring maximal current 52.5 kA, and a level of

protection IP 21. Three phase separator – type OETL

1250, 1250 A, 690 V, “ABB” – is placed inside the

supplying field. Up to eight groups of LV high-pedantic

separators – type XLBM 400 A, 690 V, 50 kA, “ABB” –

are placed inside the conducting field and mounted on

the separator rod to enable three phase disconnection

(noncharged). At the LV side of the 630 kVA power

transformer, short circuit currents of up to 22.06 kA can

appear. Short circuit impulse current at the 0.4 V voltage

level is 48.90 kA. LV conjunction blocks are tested for

25 kA of thermal and 52.5 kA of impulse short circuit

current.

Conjunction conductor between the MV side of a

transformer and MV field of a conjunction block

constructed with three single conductor cables with

polyethylene insulation – type 3x(XHE 49-A 1x50/16

mm2 or 3x(XHE 49-A 1x150/25 mm2) – with nominal

voltage of 20 kV and tolerated current charge of 210 A.

Distance between fixating cable clips is 600 mm

maximum. Cables are taped at the spacing of 1.0 m and

make a fasten bundle.

Conjunction conductor between the LV side of a

transformer and LV conjunction block constructed with

single conductor PVC insulated cable resistant to

temperatures up to 378.15 K (105 C) and with nominal

voltage up to 1 kV. Type label for phase conductors is

3x(2xP/MT 1x240 mm2 1 kV), and for neutral conductor

is 1x(P/MT 1x240 mm2 1 kV).

Since the main electrical equipment (MV and LV

conjunction blocks and power transformer) is tested according

to the IEC standards (IEC439 and IEC298 for LV and MV

conjunction blocks, respectively, and IEC76 for power


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transformer) it can be deduced that above technical parameters

are verified.

The transformer station is connected to the distribution

electrical grid of city of Tuzla with 10/20 kV cables placed

under the ground. Import of the cables into the TS is carried

out through the openings in TS foundation. Transformer

station housing is constructed with pre-manufactured concrete

elements which constitute TS walls with dimensions of

280×186×255 cm. There are three conditionally separated

areas inside the TS; area for mounting of the transformer, and

areas for MV and LV blocks (Fig. 4a and 4b).

Fig. 4a: Intersection of the transformer station

Fig. 4b: Base of the transformer station

Safety standards are fulfilled according to the DIN-

VDE0848-1 norm. Middle voltage distribution conjunction

block is modeled using the EFC-400LF software package,

with maximal current load '

mI =36.4 A, nominal secondary

voltage of 0.4 kV, and maximal current load ''

mI =909 A. The

load of 909 A is very rare, but the calculation is conducted for

the worst possible case so fulfilling of the safety standards for

other cases can be deduced from this case. It can be seen that

maximal current load of the LV transformer side is evenly

distributed at four derivations for 227 A. Main electromagnetic

field sources are MV and LV bus bars and MV transformer

clamps, whereas the influence of MV and LV conjunction

equipment surrounded with grounded cabinets and housings or

cable screens can be disregarded. The calculation of the

magnetic field is conducted for the areas inside and outside the

TS, neglecting the TS housing due to the safety improvement

according to the regulations for protection from

electromagnetic field emissions.

Two (2D) and three-dimensional (3D) disposition of the TS

is presented in Fig. 5a and 5b. The main difference between

the real TS and its model depends on the conductor

subdivision on finite number of segments. Conductors are

divided in 635 segments with resolution of dx=dy=dz=0.1 m.

EFC-400LF software is capable of solving the system of

differential equations for the matrix with 16000×16000

elements (Methods: LU – decomposition or conjugated

gradients). In this case, matrices have 261×261 elements and

will produce the values of electric and magnetic field in 68121

points of observed area of 169 m2, with resolution of

dx=dy=dz=0.05 m, as well as matrix with 261×101 elements

that produce values in 26361 points of observed area of 65 m2

with resolution dx=dy=dz=0.05 m. Visual presentation of

magnetic flux density calculated values is conducted using

MATLAB.

Fig. 5a: 2D presentation of the TS in EFC-400 software

Fig. 5b: 3D presentation of the TS in EFC-400 software


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III. CALCULATION OF MAGNETIC FIELD DISTRIBUTION

Calculation of the magnetic field distribution was

conducted:

In XY plane of a transformer station with limits of -5 m x

8 m and -5 m y 8 m

at the height of z=1.75 m above the ground level, which

represents the level of the human head.

In XZ plane of a transformer station with limits of -5 m x

8 m and 0 m z 5 m

at y=-0.2 m, apropos 0.2 m from the south side of the TS

at y=2.10 m, apropos 0.2 m from the north side of the TS

In YZ plane of a transformer station with limits of -5 m y

8 m and 0 m z 5 m

at x=-0.2 m, apropos 0.2 m from the east side of the TS

at x=3.10 m, apropos 0.2 m from the west side of the TS

A. Calculation of magnetic field distribution in XY plane

surface

Values of the magnetic flux density are observed in the

areas I, II, III, and IV of the XY plane, with distances of 0.2

m, 1.0 m, 1.5 m, and 2 m from the transformer station walls at

the height of z=1.75 m. Fig. 6a, 6b, 7a, and 7b are presenting

2D and 3D distribution of the magnetic flux density.

Maximum values of the magnetic flux density are:

between 10.712 μT and 54.863 μT in the area I,

between 6.918 μT and 32.161 μT in the area II,

between 3.759 μT and 16.579 μT in the area III, and

between 2.246 μT and 10.198 μT in the area IV.

Magnetic flux densities inside the transformer station are

reaching their maximum values at the cross sections of the XY

plane with primary clamps of the power transformer and cable

connections with MV and LV conjunction blocks. These

values are between 0.05 mT and 6.40 mT, whereas outside the

TS these values drop down to the values between 100 μT and

50 μT. According to the results, values of the magnetic flux

density outside the TS at the distance of 0.2 m are below the

value of the 54.863 μT whereas at distances between 0.5 m

and 1.5 m these values dropping down to values between

32.161 μT and 2.246 μT.

Fig. 6a: 2D continual distribution of magnetic flux density in XY

plane surface (z=1.75 m)

Fig. 6b: 3D continual distribution of magnetic flux density through

XY plane surface (z=1.75 m)

Fig. 7a: 3D presentation of the magnetic flux density continual

distribution through XY plane (z=1.75 m)


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Fig. 7b: 3D presentation of the magnetic flux density continual

distribution through XY plane (z=1.75 m)

B. Calculation of magnetic field distribution in XZ plane

surface

For observed XZ plane, at distance of 0.2 m (y=-0.2 m),

values of the magnetic flux density for z=0.50 to 1.75 m

matched with LV conjunction block are between 14.051 μT

and 10.686 μT, whereas matched with the MV conjunction

block it has a value of 8.111 μT. Magnetic flux density values

for z=1.00 to 1.50 m, matched with power transformer, are

between 10.095 μT and 12.539 μT. Fig. 8a and 8b present 2D

and 3D continual distributions of magnetic flux density in this

area of XZ plane surface.

At distance of 0.2 m (y=2.10 m) for observed XZ plane

values of magnetic flux density are between 101.102 μT and

145.202 μT for z=1.00 m matched with LV conjunction block,

between 51.521 μT and 80.082 μT for z=1.00 to 1.75 m

matched with MV conjunction block, and between 35.197 μT

and 74.145 μT matched with power transformer. 2D and 3D

presentations of the results from this area of XZ plane are

shown in Fig. 9a and 9b.

Fig. 8a: 2D continual distribution of magnetic flux density through

XZ plane (y=-0.2 m)


XZ plane (y=-0.2 m)

Fig. 9a: 2D continual presentation of magnetic flux density through

XZ plane (y=2.10 m)

Fig. 9b: 3D continual presentation of magnetic flux density through

XZ plane (y=2.10 m)


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C. Calculation of magnetic field distribution in YZ plane

At distance of 0.2 m (x= -0.2 m) for observed YZ plane,

values of the magnetic flux density are between 96.238 μT and

131.326 μT for z=0.2 to 0.5 m matched with LV distribution

conjunction block, whereas for z=1.00 to 1.75 m it drops down

to 54.843 μT.2D and 3D presentation of continual

distributions of magnetic flux density for this area are shown

in Fig. 10a and 10b.

For observed plane, at distance 0.2 m (x=3.10 m), values of

magnetic flux density are between 40.194 μT and 68.846 μT

for z=0.2 to 1.0 m matched with MV distribution conjunction

block. For z=1.00 to 2.00 m matched with bus bar these values

drop down to 27.954 μT. Fig. 11a and 11b present 2D and 3D

distributions of magnetic flux density for this area of

observation.


YZ plane surface (x=-0.2 m)


YZ plane surface (x=-0.2 m)


YZ plane (x=3.10 m)


YZ plane (x=3.10 m)

IV. CONCLUSION

Calculation and measuring of low-frequency magnetic

fields, as well as their correlation, represent the basic problems

in transmission and distribution of electric power in conditions

of standardized electromagnetic compatibility and exposure of

humans to nonionizing electromagnetic radiation. Resolution

of these problems corresponds to solving nonlinear differential

equations by modeling and applying the numeric methods, as

well as by experimental measuring models of electric and

magnetic fields. Mathematical model of the calculation of

magnetic flux density distribution in and around the

transformer station is presented in this paper, using Biot-

Savart law for flat finite streamline.

Respecting the fact that magnetic flux density is

proportional to the load and that typical load of the

transformer station is around 50% of nominal power, maximal

values of magnetic flux density will not oversee the limits for

increased sensitivity and professional exposure established by

the standards.

Original scientific contribution of conducted research


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represents determination of three dimension (3D) distribution

of low-frequency magnetic field, its interaction in conditions

of complex geometry of transformer station and standardized

electromagnetic compatibility (EMC) in area of biologic

influence of electromagnetic fields. Obtained three-

dimensional (3D) mathematical models are representing very

complex functional dependence of magnetic field distribution,

as a base for objectified physical measurements in order to

create optimal versions for solving electromagnetic

compatibility (EMC) in existing and new power facilities.

Satisfying accuracy of results gained by calculations

comparing to experimental measuring values with EFA-300

Field Analyzers instrument is confirmed, indicating that

initiation and developing such calculations for designing of

constructive solutions for transformer station is reasonable.

From the economic point of view, such way of calculation can

reduce the requirements for expensive experimental

measurements and substation reparations, indicating that

complex theoretical researches are resulting in appropriate

constructive solutions. Introduced mathematical models,

calculations, measuring, and three-dimensional visual

distribution of magnetic field, are representing the real

assumption for researching of interaction between

electromagnetic fields and human body on macroscopic and

static level, revealing optimization criteria in aim to create a

new technological solutions and methods for designing. The

research results are important from scientific point of view, as

well as a possibility for practical implementation.

REFERENCES

[1] D. Poljak, “Human exposure to nonionizing radiation”, Kigen Ltd.,

Zagreb 2006.

[2] D. Poljak, Advanced modeling in computational electromagnetic

compatibility, New Jersey, Wiley-Interscience, 2007

[3] H. Salki , V. Madžarevi , A. Muharemovi , E. Huki : “Numerical

solving and experimental measuring of low frequency electromagnetic

fields in aspect of exposure to nonionizing electromagnetic radiation”,

The 4th International Symposium on Energy, Informatics, and

Cybernetics: EIC 2008 In the Context of The 12th Multi-conference on

Systemics, Cybernetics, and Informatics: WMSCI 2008 June 29th – July

2nd, 2008 – Orlando, Florida, USAB.

[4] V. Madžarevi , A. Nuhanovi , A. Muharemovi , H. Salki : “Numerical

calculation of magnetic dissipation and power transformers”,

ELECTROCOMP 2005, Seventh International Conferences on

Computation and Experimental Methods in Electrical Engineering and

Electromagnetism, 16-18 March 2005 Orlando, Florida, USA

[5] H. Salki , V. Madžarevi , I. Kapetanovi , A. Muharemovi : “Numerical

calculation of magnetic dissipation and forces on coil in power

transformers”, CIRED 2005, 6-9 June 2005, Turin, Italy

[6] A. Muharemovi , S. Hanjali , H. Salki , A. Kamenica ”Electromagnetic

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[7] V. Madžarevi , H. Salki , Z. Salki , D. Ba inovi “Calculation of low

frequency electrical fields of the transformer station respecting the

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Exposure to Low Frequency Magnetic Fields of a Transformer Station

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