8/16/2019 Accurate Modelling of Rod Driven Tower Footing

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IEEE Transactions on Pow er Delivery,

Vol.

11,

No. 3

July 1996

ACCURATE MODELLING

OF

ROD DRTVEN

TOWER

FOOTING

M.E. Almeida

M.T.Correia de Bassos

Senior Member,

IEEE

IST-Universidade Tecnica de Lisboa / Instituto

da

EnergmINTERG

1096 Lisboa Codex, Portugal

Abstract For evaluating the lightning performance

of

transmission lines by computer simulation the accurate

modelling

o f

tower footing is very important.Inparticular the

decrease of the earth resistance observed for high values of the

current flowing from the tower to earth has to be considered.

In this paper different modelling approaches allowing to take

into accouut the non-linear behaviour of the tower footing are

overviewed and a uew model to describe the soil ionization

process

is

presented. The proposed model corresponds to

considering the ionized soil region

as

an equifield shell.

In

order to represent the ionization phenomena the values o f the

resistivity on the ionized region are decreased according to the

local current density and the electric field is kept at a critical

value. Deionization o f the soil is also taken into account.

Simulation results are presented and compared to the

published results of experimental tests.

I. INTRODUCTION

On most electric energy systems, lightning is the main

cause of unscheduled supply interruptions. Computer

simulation is an important tool for evaluating the lightning

perforinance of transmission lines, and the adequate

modelling techniques for the different system's components

have to be established. In particular, it has been emphazised

by different authors that the predicted lightning

backflashover rates are very sensitive to the resistances

ascribed to the tower footings. In particular, the soil

resistivity is

a

dominant factor for the evaluation of

grounding system parameters.

If large current densities

flow

from the tower footing into

the soil, the critical field strength of the soil can be

This paper was presented at the 1995 ESMO Conference

held in Colum bus, Ohio, October 29-November 3; 1995.

exceeded, and its partial breakdown occurs. Then, the

conductor is surrounded by a corona-type discharge pattern.

The ionized area occupies a confined space in which the

conductivity becomes much greater than in the rest of the

soil. In this situation, the ground electrodes display a non-

linear transient behaviour and present

a

lower resistance to

ground.

It is considered that the decrease of the tower footing

resistance, under lightning conditions, has to be taken into

account in order to optimize the design of the tower earthing

[l] , and in order to obtain inore accurate results when the

lightning performance of transmission lines is evaluated by

computer simulation [2] 3 ] .

Different models have been developed to describe the soil

ionization process, and simulation results have been

compared to measured values. Basically, the different models

succeed in representing the decrease

of

the earth electrode

resistance by considering either the decrease of the earth

resistivity, or by assuming an increase

of

the earth electrode

effective size. Therefore, the different models can be

classified as following either a variable soil resistivity

approach, or a variable electrode geometry approach. The

most representative soil ionization models are summarized

in the present paper, and the corresponding values

of

the

electric field in the ionized region are investigated. The

viability

of

these values

is

discussed in the light of the

physics of the soil ionization, and an alternative model is

proposed following a variable soil resistivity approach

11. BACKGROUND

For including the soil ionization phenomena 111

modelling an earth electrode, two main approaches have

been followed

i l The

Variable GeometryApproach

Different authors model a gwen electrode embedded in

an ionized soil as an electrode

of

increased dimensions

embedded in

a

non-ionized soil [4-71 Therefore, this

approach corresponds to considering the soil resistivity

unchanged, and a lower resistance to ground is obtained by

0885-8977/96/ 05.00 995 IEEE

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increasing the contact area with the earth electrode, the non-

linear behaviour being given by the dependence of the

equivalent electrode geometry on the current flowing into

soil. The so-called effective Qmensions of the earth electrode

are obtained, for each value of the current, by assuming that

the electric field may not exceed a given critical value E,,

which depends on the nature of the soil. The effective radius

of

a

rod driven electrode (fig.

1)

plotted as

a

function of the

current is presented in fig.

2. 

Results correspond to injecting

a double-exponential current source

3.5

kA/5 pA6.5 nto

a single driven rod with = 0.61 in r = 0.075 n being the

non-ionized soil resistivity po=

50

2m and the critical

electrical field E , = 1.1 kV/cm

If a variable geometry approach is followed, the ionized

region being assimilated to the conductor, the electric field

in that region is therefore considered to be null, as if the

ionized region was short-circuited with the electrode.

This

shows that earth electrode models following this approach,

although allowing to reproduce the decrease of the earth

electrode resistance obtained in experimental tests, are far

from being in accordance with the physics of the soil

ionization phenomena.

ro

E

: : i rcm

.:. I

_ ...-.::.

.30

0.25

0.15

0.05

3 0.20

E 0.10

+

0.00

Fig. 1 Single driven rod.

1000 2000

3000 4000

Current

[A]

Fig.

2

Effective radius versus current intensity.

B.

The Variable esistivity Approach

In this approach, the decrease of the earth electrode

resistance for high values of the current is explained by the

decrease of the soil resistivity in the region surrounding the

electrode, as

a

consequence of soil ionization phenomena,

which are considered to occur

as

far

as

the soil critical

breakdown field E is reached.

Liew and Darveniza [3] have proposed an analytical

model to represent the time-variation and the non-linear

characteristics

of

some basic forms of concentrated

grounding electrodes. In their model, the resistivity of the

ionized zone decays in an exponential manner, being the

rate of decay established in order to fit the experimental

results. The ionization process, although being triggered by

the electrical field, is considered in this model, independent

from the field intensity. Above a critical value of the current

density, the ionization process is governed by its own

dynamics, resulting on the decrease of the soil resistivity as a

function of time, and independent from the local electric

field.

The values of the electrical field in the ionized region

have been obtained according to Liew and Darveniza model

for the same conditions as above (fig. 3 . The variation law

of the soil resistivity, being independent from the electric

field, this cannot be controlled inside the ionization region.

In the results presented in fig. 3 , it can be noticed that the

electric field at the electrode surface shows values much

higher than the critical field.

Fig.

-

2 0

5

9

s 1.0

j

0.5

0.0

0

1000 2000

3000 4000

Current

[A]

3 Electric field at the electrode surface versus current

intensity, obtained with Liew and Daweniza model.

111. THE EQUlFIELD MODEL

Following

a

variable resistivity approach, a new

ionization model was developed. It corresponds to assuming

that the critical value of the electric field is never exceeded,

and therefore considers that, when ionization occurs, the

area surrounding the electrode is an equifield region. This

can be noticed in figure

4 

where the electric field at the

electrode surface is presented, for the same conditions as

above.

Using the methodology developed by Liew and

Darveniza, the region surrounding the earth electrode is

divided into small shells, with uniform thickness dr These

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shells are defined by equipotential surfaces, using cylinder-

hemisphere concept, figure 1.

As

dr

is small compared to the

conductor length, the earth current flowing out from the

shell surface can be assumed to flow radially.

The soil is homogeneous and isotropic and has a constant

resistivity po as long as he electric field around the electrode

remains below the soil critical breakdown fieldE .

As

the surge current I injected into the ground electrode

increases, the electric field E in the vicinity of the electrode

surface eventually exceeds the critical value and soil

breakdown occurs. The resistivity pk of a elemental shell k

inside the ionized region decays, following the equation:

E

pk

= L A k

I

being the equipotential surface area of the shell k .

Beyond ionization zone, the resistivity of the soil remains

at its nominal value po.

As the current decreases from its crest value, the region

where the electric field is below the critical value -

deionization zone - the resistivity

of

each shell recovers to

the nominal value, following the equation:

where z I is the deionization time constant, k is the electric

field related to the shell k and pki is the resistivity of the shell

k at electric field intensity

E

during the decay period.

The total resistance of the electrode is obtained summing

the elemental resistances of the shells, from the surface of

the rod to the in ki ty .

1 2

e 1.0

&

0.8

0 6

2

7

0 4

. 0.2

0.0

0 1000 2000

3000

4000

Current [A]

Fig.

4 Electric field at the electrode surface versus current

intensity, obtained with the proposed new model.

IV.

SIMULATION

RESULTS

To determine the accuracy and applicability of the

proposed soil ionization model, Liew and Darveniza

experimental tests are taken as reference values. To illustrate

the performance of this model the case presented in fig.3 of

their paper was chosen.

In this case a

3.5kA/5 ps116 5 ps

double-exponential

current

was

injected into a single driven rod with 0.61

m

r

= 0.075

m

The electrode is buried in a sand and gravel

mix soil with the characteristics:

po =

5

L2m

E =

1.1

kV/cm

71 =

4 5

ps

In figures 5-7 the simulation results are presented. These

results are in good agreement with the experimental test

refered above and published in [ 3 ] .

30

- 25

G

20

15

.2 10

2 5

I 0 1 I I I

~

0 1000 2000 3000 4000

Current

[A]

Fig. Impulse resistance as a fimction of

the

current, obtained with

the proposed new model.

30 I

0 10 20 30

40

time [ps]

Fig. 6

Impulse resistance

as

a function of time, obtained with the

proposed new model.

80000

I

0 1000 2000 3000 4000

Current

[A]

Fig.

7

Voltage/current curve, obtained with the proposed new

model.

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M T

Correia de Barros was born in

Lisbon, Portugal, in 1951, and received

the Dipl. in Electrical Engineering in

1974 and the Doctor’s Degree in 1985,

both fiom IST - Technical University of

Lisbon. She is currently an Associate

Professor at the same University. Her

main research interests are the fields of

High Voltage Engineering

and

Electromagnetic Transients.

V. CONCLUSIONS

A new soil ionization model was developed using a

variable resistivity approach. The proposed model considers

that, when ionization occurs, the area surroundmg the

electrode is an equifield region. On the ionized regon the

resistivity decrease according to the local current density,

being the electric field kept at the critical value. The

dynamic soil deionization is also taken into account.

The accuracy of the model is fairly good, being the

computed results in accordance to the ones obtained

experimentally.

VI. REFERENCES

[11 EPRl, “Transmission Line Grounding”, EPRI EL-2699,

Vol.1, Project 1494-1, October 1982. Prepared by Safe

Engineering Services Ltd., Montreal, Quebec, Canada.

[2] A.C.Liew, M.Darveniza, “Dynamic Model of Impulse

Characteristics of Concentrated Earths”, Proc. IEE, Vol. 121,

N”2,

February 1974, pp. 123-135.

[31 M.Darveniza, M. A. Sargent,

G .

.Limbourn, A. C.Liew,

R.0 Caldwell, J.R.Currie, B CHolcombe, R.H.Stillman,

R.Frowd, “Modelling for Lightning Performance

Calculations”, IEEE Trans. on Power Apparatus and

Systems, Vo1.98, No 6, NovemberDecember 1979.

[4] R.Velazquez, D.Mukhedkar, “Analytical Modelling of

Grounding Electrodes Transient Behaviour”, IEEE Trans.

on Power Apparatus and Systems, Vol.103, pp.1314-1322,

June 1984.

[ 5 ] C.Mazzetti, G.M.Veca, “Impulse Behaviour of Ground

Electrodes”, IEEE Trans. on Power Apparatus and Systems,

Vo1.102, pp.3148-3156, September 1983.

[6] S.V.Filho, C.M.Portela, “Modelling of Earthing Systems

for Lightning Protection Applications, Including

Propagation Effects”, Ro c. ICLP-92, pp. 129- 132 Berlim,

Germany, September 1992.

[7] F.E.Menter, L.Grcev, “EMTP-Based Model for

Grounding System Analysis”, Paper 94

WM

135-4 PWRD

presented at IEEE Winter Meeting., 1994

M.E.Almeida was born in Mozambique,

in 1962, and received the Msc degree in

Electrical Engineering in 1990, from

IST-Technical University

of

Lisbon. She

is currently a Research Assistant, and

prepares

a

Ph D Thesis under the

supervisionofProf. Correia de Barros.