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TRANSIENT IMPEDANCE OF GROUNDING RODS
I. F. Gonos F. V. Topalis I. A. Stathopulos
National Technical University of AthensDepartment of Electrical
and Computer Engineering, High Voltage Laboratory
Abstract: The aim of this paper is thecorrelation of the
transient impedance and itsparameters with the stationary
resistance ofsimple grounding systems. Impulse current testsof the
standard form 8/20 s were performed onseveral types of equilateral
triangles and singledriven rods of different lengths. The
injectedcurrent in the grounding system and thedeveloped potential
were recorded, resulting inthe determination of the time variation
of thetransient impedance. Further mathematicalanalysis of the
experimental results led to simplelinear relations between the
parameter oftransient impedance and the stationaryresistance. The
results provide usefulinformation for the design of a grounding
systemand the measures for the protection ofinstallations from
lightning strokes.
Key words: Grounding system, transientimpedance, stationary
resistance.
1. Introduction
The grounding systems serve multiple purposes.Not only they do
insure a reference potentialpoint for the electric and electronic
devices butalso provide a low resistance path for faultcurrents
into the earth. Such fault currents canarise either from internal
sources or fromexternal ones e.g. by lightning strokes
andindustrially-generated static electricity. Theresistance of
grounding systems has an essentialinfluence on the protection of
the groundedsystem. Grounding systems can consist of one ormore
vertical or horizontal ground rods, three ormore vertical ground
rods connected to eachother and two or three-dimensional grids
frommetal rods and foundation grounding systems.
The behaviour of the grounding system underlightning determines
the degree of protectionprovided. This makes obvious the purpose
ofanalysis procedures predicting the transientresponse of grounding
systems. If an equivalentcircuit approach is adopted these
procedure canbe implemented in a simulation model [1-7].
The specific value of impulse impedance whichis of main interest
is the one corresponding tothe beginning of the steep ascent for
the wave-front. The results reveal its value to be quitehigher than
the stationary value of its groundresistance and reduces to this
latter value [3, 5].
The work presented in this paper refers to theproblem of
transient analysis of practicalgrounding systems consisting of
grounding rodsunder impulse lightning currents.
2. Fundamentals
The driven rod is one of the simplest and mosteconomical form of
electrodes. The stationaryresistance R of a driven rod is given by
thefollowing formula [7]:
R ln8 l
d1=
2 l
(1)
where: is the resistivity of the ground,l is the length of the
rod andd is the radius of the rod.
Fig. 1: Equivalent circuit for a driven rodstressed by an
impulse current
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When the electrode voltage changes with time,there will be a
conductive current in addition toa capacitive current. The
equivalent circuit of adriven rod under impulse current is shown
inFig. 1. The resistance R of the rod is given bythe Eq. (1) and
the inductance L of such a rod isequal to [7, 8]:
L ln4 l
d10 7=
2 l (2)
The capacitance C of the ground rod is [7]:
C
18 ln4 l
d
10 9=
r l (3)
where r is the dielectric constant of the soil.
The impulse impedance of a grounding system isnecessary for
determining its performance whiledischarging impulse currents to
ground, as in thecase of lightning and transient grounds faults.The
impulse impedance is define Z is defined asthe ratio of the impulse
voltage to the impulse:
Z tU ti t
( )( )( )
= (4)
U(t)
i(t)
Z(t)
t2t1
Imax
Umax
Fig. 2: Definition of the parameters of impulseimpedance
Four parameters of impulse impedance (Fig. 2)are defined as
follows [3]:
Z1 = max(Z(t)) (5)
ZU t
i t21
1
=( )
( )(6)
ZU ti t3
1
2
=( )
( )(7)
ZU t
i t42
2
=( )
( )(8)
where:Z1 is the maximum value of the ratio of impulsevoltage to
impulse current, Z2 is the ratio of themaximum value of voltage to
the respectivevalue of current when voltage reaches itsmaximum, Z3
is the ratio of maximum value ofvoltage to the maximum value of
current and Z4is the ratio of voltage when current reaches
itsmaximum to the maximum value of current.
It is obvious:
Z1 > Z2 > Z3 > Z4>R (9)
A lightning discharge affects the resistance of agrounding
system in two ways. The current is upto 100 kA or more and has a
much higherfrequency spectrum than the stationary case.The
transient impedance becomes greater as:
the inductivity of the wire and of theconnection becomes
greater
the high value of current can dry the ground,
the high frequency spectrum shortens theelectrical length of
long grounding wires
the skin effect rises the resistance and theinductivity of wires
due to the value of thefrequency.
The transient impedance becomes smaller as theelectrical field
strength on the surface ofgrounding system can reach values
wherepredischarges in the ground start; thesedischarges can lead to
ground ionisation thatdestroy layers with high resistance [4].
3. Experimental apparatus and testtechniques
The layouts of grounding system (Fig. 3) weretested
experimentally under impulse lightningcurrent of waveshape 8/20 s
The maximumvalue of the current was varying up to 3 kA. Thefirst
grounding layout was a single driven rodand the second one was an
equilateral trianglewith three vertical rods. Cooper rods
withdiameter 20 mm were used. The measured value
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of the earth resistivity was found to be equal to30 m. The
waveforms of the impulse currentand of the potential of grounding
system wererecorded directly by a data acquisition systemcontrolled
by a personal computer, withmeasuring bandwidth of 20 MHz.
Fig. 3: Experimental set-up
4. Test results
The measurements values of peak voltage, peakcurrent and
impedance of ten different groundinglayouts are presented in Table
1.
Table 1: Experimental results.
Electrode l[cm]
R[]
Upeak[kV]
Ipeak[A]
Z3[]
A rod 50 68.2 5.14 13.7 375A rod 75 31.0 5.08 16.5 308A rod 100
22.3 5.03 17.7 284A rod 125 14.6 5.00 18.8 266A rod 150 12.1 4.99
19.3 259
Three rods 50 27.0 4.91 16.7 294Three rods 75 15.6 4.87 18.3
266Three rods 100 10.7 4.83 19.3 250Three rods 125 7.6 4.80 20.0
240Three rods 150 6.9 4.79 20.3 236
0 10 20 30 40 50 60 70 80 90 100-5
0
5
10
15
20
t [sec]
I [A
]
Fig. 4: Waveform of the injected current.
In these figures, the test results for thegrounding system of a
driven rod with diameter20mm and length 75cm are presented.
Thewaveforms of the injected current is shown inFig. 4. The
measured potential with reference tothe ideal earth is shown in Fig
5. The transientimpedance of the grounding system under thisstress
is the one of Fig. 6.
0 10 20 30 40 50 60 70 80 90 1000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
t [sec]
U [V
]
Fig. 5: Waveform of the potential.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000
t [sec]
Z [
]
Fig. 6: Variation of the impulse impedance
5 10 15 20 25 30230
240
250
260
270
280
290
300
R []
Z3
[]
Fig. 7: Variation of the impulse impedance vs.stationary
resistance for driven rod.
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10 20 30 40 50 60 70240
260
280
300
320
340
360
380
R []
Z3
[]
Fig. 8: Variation of the impulse impedance vs.stationary
resistance
The variation of the parameter Z3 of impulseimpedance versus the
stationary resistance ofsingle driven rod is presented in Fig. 7.
Therespective variation of the equilateral triangle ispresented in
Fig 8. Further mathematicalanalysis of the experimental results
leads to thefollowing relation between Z3 and R of thesingle
driven
Z R3 2 053 237 5= +. . (10)
A similar relation for the equilateral triangle,was found to
be:
Z R3 2 847 2187= +. . (11)
5. Conclusions
The performed measurements show that thetransient impedance
reaches its maximum valuevery fast (fraction of microsecond)
andconsecutively is reduced to the value of thestationary
resistance. the one corresponding tothe beginning of the steep
ascent for the wave-front. The results reveal the value of
thetransient impedance to be quite higher than thestationary
resistance. The determined analyticalrelations between the
parameters of the transientimpedance and the stationary resistance
allowthe limitation or even elimination of time andmoney consuming
experiments. It will alsofacilitate the optimisation of any
plannedgrounding system. The computer aidedoptimisation of
grounding systems is veryuseful, since the improvement of them
after theirinstallation is a difficult task and sometimes
notpossible.
References.[1] Suflis, S.A., Gonos, I.F., Topalis, F.V. and
Stathopulos I.A.: Transient behaviour of ahorizontal grounding
rod under impulsecurrent, Recent Advances in Circuits andSystems,
Word Scientific PublishingCompany, Singapore, 1998, pp. 61-64,
[2] Suflis, S.A., Gonos, I. F., Topalis, F. V. andStathopulos I.
A.: Transient behaviour of ahorizontal grounding rod under
impulsecurrent, 2nd International Conference onCircuits, Systems
and Computers (IMACS-CSC98), October 1998, Piraeus, Greece,pp.
289-292.
[3] Gonos, I.F., Antoniou, M.K., Topalis, F.V.and Stathopulos I.
A.: Behaviour of agrounding system under impulse lightningcurrent,
6th International Conference andExhibition on Optimisation of
Electrical andElectronic Equipment (OPTIM 98), May1998, Brasov,
Romania, pp. 171-174.
[4] Bogensperger, H.J., Frei, J. and Pack, S.:Resistance of
grounding systems, stationaryand transient behaviour, 9th
InternationalSymposium on High Voltage Engineering,August 1995,
Graz, Austria, pp. 6715-1-4.
[5] Verma, R. and Mukhedkar D.: Impulseimpedance of buried
ground wire, IEEETrans. on Power Apparatus and Systems,1980, PAS-99
(5) pp. 2003-2007.
[6] Meliopoulos, P.A. and Moharam, G.M.Transient Analysis of
Grounding Systems,IEEE Trans. on Power Apparatus andSystems, 1983,
PAS-102 (2) pp. 389-397.
[7] Kalifa, M.: High Voltage Engineering,Theory and Practice,
Dekker, USA, 1990,pp. 331-356.
[8] Gupta, R.B., and Thapar, B. ImpulseImpedance of Grounding
Grids, IEEETrans. on Power Apparatus and Systems,1980, PAS-99 (6)
pp. 2357-2362.
Address of AuthorsNational Technical University of AthensDept.
of Electrical and Computer Engineering42, Patission Str., GR-10682
Athens, GreeceTel.: +30-1- 7723539, 7723627, 7723582Fax.: +30-1-
7723628, 7723504Email.: [email protected]
[email protected] [email protected]
