1 Slavko Vujević, Petar Sarajčev and Jakov Petrović** *University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture,

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Slavko Vujević*, Petar Sarajčev* and Jakov Petrović**

*University of Split, Faculty of Electrical Engineering, Mechanical Engineering

and Naval Architecture, HR-21000 Split, Croatia

TLM Model for the Lightning Transient Analysis of the GSM Base Station

Workshop 'Impact of Communications Technology to EMC'

**Zagrebinspekt d.o.o. HR 10000, Zagreb, Croatia

Contact: [email protected]

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Transmission line model (TLM) for the GSM base station lightning transient analysis

is presented.

Introduction


TLM model is based on the use of the well-known ATP-EMTP software package.

Direct lightning strike to the GSM base station tower is modelled with the Heidler's

type of surge current source.

The earthing grid and the GSM base station's tower structure are approximated by the circular cross section conductors.

In numerical model, conductors are subdivided into segments (1D finite elements)

and Clark's model with distributed parameters is used.

Because of limitations of ATP-EMTP software package, the leakage resistance of

buried segments is modelled as lumped parameter.

Analytical expressions for distributed and lumped segment parameters are derived

using the average potential method.

Results obtained by the developed TLM model, are compared with the results obtained with more exact electromagnetic model (presented in [3]).

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Transmission Line Model of the GSM base station tower (1)

A Clark's model with distributed constant

parameters is then applied on each tower

segment. Input data for Clark's model are:

a) Resistance per unit length

b) Surge impedance

c) Propagation velocity

d) Segment length.

GSM base station tower conductors are, by applying the finite element technique, subdivided into segments (1D finite elements).

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Ad b) Surge impedance of the GSM tower segment is defined by the following

equation:

sL

Z C


Ad a) Per unit resistance of the tower segment (1D finite element) can be computed

as follows: s

2o

R r

where:

ρs – resistivity of the segment [Ωm],

ro – equivalent radius of the tower segment conductor [m].


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av

QC

where:

Q – electric charge uniformly distributed along the segment [C],

ℓ - length of the segment [m],

av – average potential of the segment.


Per unit capacitance of the tower segment depends on the position of that segment,

relative to the earth surface. It can be computed by means of average potential

method, as follows:

where:

L – per unit inductance of the tower segment [H/m]

C – per unit capacitance of the tower segment [F/m].


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Per unit capacitance of the segment can be computed as follows, [4]:

s

o o

s self mut

'

4 4C

d dd ' d I I r r



The first integral in the expression for the per unit capacitance computation

accounts for the self-capacitance, while the second integral accounts for the

mutual capacitance between the tower segment and it’s image.

where:

ε0 = 8.854∙10-12 [As/Vm] – dielectric constant of the vacuum.

Iself, Imut - double integrals.

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Once the capacitance is computed, one can easily obtain the needed value of the segment's per unit inductance from the following relationship:

where μ0 = 4π∙10-7 [Vs/Am] is relative permeability of the vacuum.

o oLC

Value of the second integral (mutual per unit capacitance between segment and

it’s image) depends on the position of the 1D finite element/segment relative to the

earth surface, as will be explained later.

All these integrals can be computed analytically. This fact contributes to the

numerical stability of the derived method.

Surge impedance of the GSM tower segment can be written as:

o os

LZ

C C

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Ad c) Modal propagation velocity of the surge current through the GSM tower segments is equal to the velocity of light, i.e.:


Ad d) Segment length (in meters) shouldn’t exceed maximum value which is

defined by:

max

8

max 6

103

f

where fmax presents maximal frequency (in Hz) of interest, found in the

lightning surge.

c = 3108 m/s


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Transmission Line Model of the earthing grid (1)

Each conductor of the earthing grid, by applying the finite element technique, can

be subdivided into segments (1D finite elements).


A Clark's model with distributed constant parameters is then applied on each

segment. Input data for Clark's model are:

a) Resistance per unit length

b) Surge impedance

c) Propagation velocity

d) Segment length.

Ad a) Per unit resistance of the earthing grid segment (1D finite element) can be computed as follows:

s2o

R r

Because of limitations of ATP-EMTP software package, the leakage resistance of

buried segments is modelled as an additional lumped parameter.

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Ad b) Surge impedance of the earthing grid segment is defined by the following

equation:


o r o rs

LZ

C C

where:

L – per unit inductance of the earthing grid segment [H/m]

C – per unit capacitance of the earthing grid segment [F/m].

εr – relative dielectric constant of the earth,

ε0 = 8.854∙10-12 [As/Vm] – dielectric constant of the vacuum,

μ0 = 4π∙10-7 [Vs/Am] is permeability of the vacuum,

μr = 1 is relative permeability of the earth.

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Again, per unit capacitance of the buried conductor segment depends on the position

of the segment respective to the earth surface. Following figure shows a buried

segment in arbitrary position, relative to the earth surface.

Per unit capacitance of the segment can be computed by means of average

potential method.



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Similarly to the aforementioned analysis employed for the GSM tower model, per unit capacitance of the segment can be computed as follows, [4], [5]:

s

o r o r

s self mut

'

4 4 C

d dd ' d I I r r


Ad c) Propagation velocity of the lightning surge in the earth can be estimated by

the following relation:8

r r

c 3 10v

where c represents velocity of the light in the air and εr presents the relative

dielectric constant of the earth.


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Ad d) Each of the earthing grid segments should satisfy the following relation

for the maximum length (in meters):

maxmax

3160

6 f

where:

ρ – resistivity of the earth [Ωm],

fmax - maximal frequency of interest found in the lightning surge [Hz].


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Leakage resistance of the buried conductor segments

Leakage conductance of the buried segment is represented in EMTP with the

concentrated resistance on each side of that segment. Double value of the

resistance on each side of the segment is chosen (2RL) in order to obtain value of

RL after the parallel connection.

s

sL self mut self mut2 2

'

d dd ' dR I I R R

r r4 4

- self resistance of the segment in homogeneous and

unbounded medium (earth),

where: selfR

mutR - mutual resistance between segment and its image

in relation to earth surface,

Value of the earthing grid conductor's segment resistance (RL) is composed of

two terms:

ρ – resistivity of the earth [Ωm].

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Analytical solution of double integral Iself

2 2o 2 2

self o oo'

rd ' dI 2 ln r r

r r

The double integration is performed along the segment axis (curve ’ in the Figure

below) and along the curve on segment surface, which is parallel to the segment

axis (curve Γ in the Figure below).

Expressions for distributed and lumped segment parameters include two double

integrals. The first of them is integral:

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Analytical solution of double integral Imut (1)

The second double integral is: s

smut

d dI

r

Analytical solution of integral Imut depends on the position of the segment relative

to the earth surface.

Three different segment arrangements will be examined:

• Segment is parallel to the earth surface

• Segment is perpendicular to the earth surface

• Segment is in aslope position to the earth surface

If segment is buried at depth h parallel to the earth surface, integral solution is

(ro 2h Iself Imut ):

2 22 2

mut

4 hI 2 ln 4 h 2 h

2 h

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If segment is perpendicular to the earth

surface, the first integration is carried out

along the axis of segment image (curve Γs in

the Figure), while the second integration is

carried out along the curve on segment

surface, which is parallel to the segment

axis (curve Γ in the Figure).

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If segment is perpendicular to the earth surface, the integral solution is:

2 2 2 21 2mut 1 1 o 2 2 o

o o

2 233 3 o

o

u uI u Arsh u r u Arsh u r

r r

u 2 u Arsh u r

r

where:

1 1 2u h h

2 1 2u h h

3 1 2u h h

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If segment is in aslope position to the

earth surface, parameters signed in the Figure can be computed as follows:

2 22 1d (h h )

where d represents orthogonal projection

of the segment onto the earth surface.

1 2p p

2 1

min h , hx z

h h

1 2k k

2 1

max h , hx z

h h

2

2

2dcos 1

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If segment is in aslope position to the earth surface, the integral solution can be

written as:

mut p p k k p k k pI 2 B(x ,z ) B(x ,z ) B(x ,z ) B(x ,z )

where for ro << ℓ:

2 2 2oB(x,z) x ln z x cos x z r 2 x z cos

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Lightning surge model

Lightning surge model used for the simulation is based on the Heidler's model of

current source, which can be described with the following expression:

n

t 10

n

1

t

Ii(t) e

t1

where:

Io , η – peak value of the lightning current and it’s correction factor, respectively

n – factor influencing the rate of rise of the function

– the strike duration; interval between t = 0 and the point on the tail where the

function amplitude has fallen to 50 % of its peak value

– duration of the lightning surge front. 1

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Verification of the model (1)

60x60 m earthing grid with 10x10 meter

square meshes, constructed of copper

conductors with diameter 1.4 cm, buried at

0.5 m depth, is considered for the numerical examples.

Concerning the injection of the lightning surge current, two scenarios are considered:

- injection of the current in the corner point of the grid (point 1)

- injection of the current in the middle point (point 25).


Soil is homogenous with resistivity 100 Ωm

and relative permittivity 36, according to [3].

Lightning surge current parameters are: 1.0167 kA amplitude and 1/20 μs shape.

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In ATP‑EMTP simulation all parameters of the earthing grid conductor segments

are computed according to the presented mathematical relations, by means of a

computer program (preprocessor) developed for that purpose.

Compress -> Extract

(grouping feature of the

EMTP) has been

employed.



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(f ile Grounding1.pl4; x-v ar t) v :1 v :9 v :17

0 4 8 12 16 20[us]-1

1

3

5

7

9

11

[kV]

Temporal transient voltage response in nodes 1, 9 and 17.

Scenario 1 - results

Spacial transient voltage distribution (3D graphical form).



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Scenario 2 - results

(f ile Grounding2.pl4; x-v ar t) v :25 v :33 v :49

0 5 10 15 20[us]-500

500

1500

2500

3500

4500

5500

[V]

Temporal transient voltage response in nodes 25, 33 and 49.

Spacial transient voltage distribution (3D graphical form).



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GSM base station numerical example (1)


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Following figures present temporal transient overvoltages: a) In the GSM tower foot

(junction between tower and earthing grid), b) In the middle (point 25) of the earthing grid.

(f ile GSMTow er_Grounging.pl4; x-var t) v:XX0001

0 2 4 6 8 10[us]0

50

100

150

200

250

300

[kV]

(f ile GSMTow er_Grounging.pl4; x-var t) v:XX0290

0 2 4 6 8 10[us]0

2

4

6

8

10

12

[kV]

Direct lightning strike into the top of the GSM tower is considered. Following

lightning current parameters are selected: 80 kA amplitude and 1/20 μs shape.

Resistivity of the soil is 100 Ωm, and relative permittivity 9.

Simulation results

a) b)


GSM base station numerical example (2)

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Conclusion


• Due to the limitations of the transmission line model approach and the

application of the ATP-EMTP software package, the electromagnetic coupling

between segments could not be taken into account.

• By comparing the presented results with those obtained by more exact

electromagnetic model (presented in [3]), good agreement has been obtained, both

in the computed amplitude of the overvoltage, as well as in the temporal and spatial

overvoltage distributions.

• The earth model is limited to the heterogeneous earth.

• The soil ionization effect can be included.

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References


[1] Kizilcay, M.; Høidalen, H. K.: "ATP‑EMTP Beginner’s Guide for EEUG Members", European EMTP‑ATP Users Group e. V., 2000.

[2] Prikler, L.; Høidalen, H. K.: "ATPDRAW Version 3.5 for Windows

9x/NT/2000/XP – Users’ Manual", European EMTP‑ATP Users Group e. V.,

2002.

[3] Grcev, D. L.: "Computer Analysis of Transient Voltages in Large Grounding Systems", EEE Transactions on Power Delivery, Vol. 11, No. 2, pp. 815-823, 1996.

[4] Petrović, J.: "Using the ATP-EMTP Software Package in the LPS Analysis", B. Sc. Thesis, University of Split, FESB Split, Split, 2004, (in Croatian).

[5] Vujević, S., Sarajčev, P. and Sarajčev, I., "EMTP Modelling of Direct Lightning Strikes to the GSM Base Station Tower", SoftCOM 2005, Split, Marina Frapa, 2005.

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THANK YOU !


Documents

1 Slavko Vujević*, Petar Sarajčev* and Jakov Petrović** *University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture,

1 Slavko Vujević, Petar Sarajčev and Jakov Petrović** *University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture,