Correlation between laboratory and field tests on the impulse impedance of rod-type ground electrodes

Y. Chen and P. Chowdhuri

Abstract: A previous study on laboratory-model ground rods showed that the impulse impedance of these ground electrodes is a function of the injected impulse current and fits the relationship: Z=k$, where k and a are two parameters which depend upon the electrode configuration, soil properties and the impulse waveshape. The power-frequency and impulse impedances of two vertical rods embedded in the soil of a field near the university campus are measured. It is found that the ground electrodes in the field also have the similar relationship with the injected current. In complementary experiments, the same soil is tested in the laboratory with a laboratory model electrode system, consisting of a vertical rod embedded in the axis of a cylindrical soil holder with controlled moisture content in the soil sample. The objective is to correlate the laboratory data on the impulse impedance to estimate the impulse impedance of the ground electrodes tested in the field and compare the results with that of the actual field tests. It is possible to estimate the impulse impedance of the ground electrodes in the field from tests performed on laboratory-model electrodes. In correlating the laboratory data to the field data, the critical electric field of soil ionisation plays a critical role, which depends upon the soil properties, e.g. soil resistivity. Future research should be directed to find a more precise relationship between the critical electric field and the soil properties.

1 Introduction

When lightning strikes the sheld wire or the tower of an overhead power line, impulse current flows along the tower and is dissipated in the earth, raising the transient voltage across the line insulator. The magnitude of this transient voltage is a function of the voltage drop across the tower- footing impedance under transient conditions, with a higher tower-fooling impedance producing a higher insulator voltage. Although this tower-footing impedance is assumed to be equal to the steady state power-frequency resistance in the analysis of lightning performance of overhead lines, in reality it is a function of the impulse current, decreasing with higher currents. This was discussed previously [I].

Soils from different regions in Tennessee were tested in the laboratory in different soil holders and laboratory- model ground rods under different waveshapes of the applied impulse [I]. It was shown that the relationship between the impulse impedance of a ground rod and the applied impulse current can he expressed as

Z = kl; (1)

where Z is the ground-rod impulse impedance (Q), Ip is the peak impulse current (A), and k and c( are two parameters which depend upon the electrode configuration, soil properties and the waveshape of the applied impulse.

Q IEE. 2003 IEE Proceedings online no. 20030246 dot IO. IM9/iiFgld:20030246 Paper fin[ mxived 2lsL August 2002 and in revlied form 191h December 2002 Y . Chen is with the lrnpulse NC. Inc., Mount Olive, NC, 28365, USA P. Chowdhu" i s with the Center for Elctnc Power, Tennessee Tchnolqical University. P . 0 . Box 5032, Cookevillc. TN 38505. USA

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Generally, the ground-electrode impulse impedance is defined as [2]:

where V,, is the peak of the applied impulse voltage and Zp is the peak of the impulse current flowing through the soil. The ground-electrode impulse impedance' has also been defined as [3]:

where Vjp is the magnitude of the applied impulse voltage at the instant of the peak of the impulse current. The difficulty in defining the impulse impedance as Z, or Z, is that the peaks of the voltage and the current do not occur at the same instant because of the nonlinearity of the soil impulse impedance, particularly at high currents when soil ionisa- tion sets in. Moreover, high-frequency oscillations are superimposed on the voltage and current waves caused by corona pulses during soil ionisation. In addition, the grounding system initially appears to he a capacitive impedance, particularly for high-resistivity soil and/or fast- rising applied voltage and current. The instantaneous impedance of a ground rod as a function of time, Z(r) = V(r)/Z(t), is plotted in Fig. 1.

The sharp spikes on the impedance profile are origi- nated by current spikes which, in turn, are produced by high-frequency corona caused by soil ionisation. Therefore, defining the impulse impedance by either Eq. ( 2 4 or Eq. (2b) is impractical. Moreover, the impe- dance is not constant during the application of the impulse. We have proposed a new definition of the impulse

IEE Proe-Gene,. Tmmm Dixrrib.. Vol. 150, No. 4, July ZW3

l o 1

0 5 10 15 20 time, ps

-2 1

Fig. 1 Profile qf'inipdse inipehnce ofground rod

impedance [I]:

(2c) VW, Z& = - 1'I.y

where and are the average voltage and current during the application of the impulse. Vac(, and larg were obtained by measuring the voltage and current at each point on the voltage and current traces and averaging from the total number of points. The computation was performed using microsoft Excel.

Vertical steel rods, embedded in soil_ were impulsed in a field adjoining the campus of Tennessee Technolo_dcal University during the present study to test the validity of (I) . In addition, the same soil was tested in the laboratory in cylindrical soil holders of I O and 2Ocm diameter with laboratory-model ground rods, similar to the previous study.

The primary objective of the present study was to estimate the impulse impedance of ground rods in the field by performing impulse tests in the laboratory on a small- scale model of the ground-rod system. The experiments can be divided broadly into (i) field tests, and (ii) laboratory tests. The purpose of the laboratory tests was to determine if the laboratory test results could be correlated to the field test results.

2 Field tests

During the field tests, the steady-state resistivity of the soil surrounding the test electrodes was measured with a commercial soil resistivity measurement system prior to

Hipotronics model PP50-5 trigatran

the impulse tests. The four-point measurement scheme was used for the steady state resistivity measurements (41. Four vertical rods (electrodes) were buried in soil, equally spaced at A = 7.62 m. Later, measurements were performed with two additional spacings, i.e. A = I.Om and 0.3 m. The three- point measurement scheme was used to measure the power- frequency resistance of the test ground rods (Fig. 2). The

test current rod

reference rod

Fig. 2 method

Mernurement of ground electrode resistmce by three-point

current-retum and reference-potential rods in Fig. 2 were 2.5m long, 1.59cm diameter vertical galvanised steel rods embedded in the soil.

The soil moisture content was estimated by weighing the moist soil from the test site, drying it for 48 h above 100°C in an oven and weighing the dry soil.

Two single galvanised steel rods were tested. The schematic for the impulse tests is shown in Fig. 3 and the dimensions of the two test rods are shown in Table I .

A single-stage, 50 kV, 1.2/50 ps impulse, generator was connected between the test ground rod and the ground- retum electrode. The ground-return electrode consisted of

ic 7.62 m +

1 driven ground rod

42 I

Table 1: Dimensions of the tested ground rods

Length, cm Diameter, cm Burial depth, m

30.48 0.9525 0.2286

45.72 1.5875 0.3048

ten 2.5111 long, 1.59cm diameter copper-clad steel rods. They were buried vertically in the ground around the circumference of a circle of 8 m diameter. The ten rods were connected to a circular copper plate, which was placed on a wooden pole at the centre of the circle. This copper plate was connected to the impulse generator. The output voltage was measured by a 10.8 kO, 430.6:l resistive voltage divider (response time < 80 ns) and the current by a 300 Hz current transformer with a I O load resistor. The signals were recorded by a twochannel, 60MHz digital oscilloscope and the data were stored in a laptop computer.

3 Laboratory tests

All laboratory tests were performed with soil from the field test site. Two different test configurations were used, as shown in Table 2.

Table 2 Dimensions of soil sample holders

Test configuration Sample holder Sample holder height, cm inner diameter,

cm

1

2

10 10

10 20

Rod diameter=0.635cm, burial depth=3cm

The soil sample from the field-test site was dried in an oven at about 120°C for at least 24 h. The dried soil was then cooled to room temperature in a closed container, weighed and mixed with deionised water of the required amount. The moist soil was sieved to remove lumps before fihng the lOcm soil holder with it. The soil was then compacted in the soil holder with a 4 kg weight before the vertical rod was placed in the middle. The rod was held in place by a wooden bridge. The procedure for testing with the'20 cm soil holder was the same, except that exactly four times the weight of moist soil was used and the soil was compacted by a 16kg weight. All laboratory tests were performed with two soil moisture contents by weight: 10% and 15%.

The 60 Hz resistance of the soil sample was measured by applying a variable 60Hz voltage between the rod and the outer shell of the cylindrical soil holder. The voltage was

varied from 25V in steps of 25V up to IOOV, and then back again in 25 V steps to 25 V.

The 1.2/50~s impulse voltage was generated by a four- stage 20 kV Marx generator and applied across the rod and the outer shell of the cylindrical soil holder. Seven impulses were applied with increasing amplitudes. The output voltage was measured with a IOkR, 401:1, 300MHz resistive voltage divider. The current was measured with a 300 MHz current transformer with a 50R load resistor. The signals were recorded by a four-channel 500 MHz digital oscillo- scope and processed and stored in a personal computer.

4 Test results

4.7 Field tests The average power-frequency resistivity of the soil from the earth's surface to the depth A is given by [4]:

p , = 2 n . A . R (Om); (3)

where A is the distance between the electrodes, and R is the meter reading. The power-frequency resistances of the test rods were also measured by the soil resistivity meter. using the three-point measurement scheme (Fig. 2). The compo- site soil resistivity as 'seen' by the test electrode can be evaluated from the equation

(4)

where & is the measured resistance of the test rod (meter reading), t, is the burial depth of the rod and Y is its radius. Table 3 summarises the power-frequency measurements on the test rod.

Table 4 summarises the impulse tests on the two ground- rod configurations. Z,, and Z,,, as defined in Eq. (%) and (2c) are shown in Table 4. Z,, and Z,, were computed from the measured applied voltage and current. These impe- dances are plotted in Figs. 4 and 5 as a function of the peak impulse current. A curve was plotted using the least square technique to match the seven experimental points.

4.2 Laboratory tests The resistivity, ps, of the soil sample was computed from the measured resistance, R, from the following equation:

where V and Z are the voltage across and the current through the soil sample, I , is the depth of the rod in the soil, r, is the inner radius of the cylindrical soil sample holder, and r, is the radius of the rod.

Figs.6 and 7 show the plots of impulse impedance profiles for laboratoly-model ground rods.

Table 3 Summary of power-frequency field tests on ground rods p,. p2, p3 measured with A= 7.62 m. 1 m and 0.3028 m, respectively: pg calculated from measured test-rod resistance, Rd by (4)

~

Test no. Rod dia- Burial Soil Soil resistivity. Clm Measured Soil meter depth IQ, moisture. p, P2 P3 Rd, R resistivity I2rL cm cm % pg.

1 0.9525 22.86 16.17 244.10 148.20 63.40 287 105.9 2 0.9525 22.86 12.91 242.62 344.77 144.04 327 120.4

3 1.5875 30.48 16.17 244.10 148.20 63.40 220 114.6

4 1.5875 30.48 12.91 242.62 344.77 144.04 253 131.7

Table 4 Summary of field impulse tests on ground rods

Rod diameter, Burial depth, Soil moisture, Impulse impedance, k n cm cm % kR

0.9525 22.86 16.97 2,"s 0.2940 -0.1375

ZP 0.2937 -0.1475 1.5875 30.48 12.91 z., 0.2874 -0,1119

ZD 0.2786 -0.1253

0.18-

c 0.16-

$ 0.14- 1

c ; 0.12-

.- E 0.10-

0.18,

. . .

!:Ir,, measured Z

, , , ,

least square fit 002

0 0 50 100 150 200 250 300 350

peakcurrent, A

a

0.18,

3 0.08- - 2 0.06-

0.04 -

0.02 -

.-

0.16-

0.14- r g 0.12-

.E 0.08. %

.- E

c i 0.10- P

0.06 -

0.04-

0.02,

. " g 0.10-

.E 0.08- 0 P

D (I)

2 0.06- E

0.04- .-

least square fit

0 50 100 150 200 250 300 350

peak current, A

b

Fig. 4 Rod diameter= 0.9575cm, burial depth = 22.8hm, soil moist. ure = 16.97% oZ,,,= VJ/,,z; h=0.294, a=-0.1375 b Z,,= Kp/ID: k=0.2937, a= -0,1475

Profiles of qround-rod impulse impedance: field tests

5 Analysis

5.1 Models of electrode systems

5.1.1 Model for laboratory tests: For laboratory tests in a cylindrical soil sample holder and a cylindrical rod with hemispherical tip, the resistance for the ground-rod system is

0.20,

O j 0 50 100 150 200 250 300

peak current. A

a

0.1a1

measured Z

0 50 100 150 200 250 300

peak current, A

b

Fig. 5 Profiles of ground-rod impuhe impedunce: field tests Rod diameter= 1.5875cm. burial deolh= 30.48cm. soil moist- ure= 12.91% U Z m l = V&//& k=0.2874, x=-O.1119 b Zp= l'J/,,: k=0.2786, a=-0.1253

r, is the radius of the rod (m). Under high impulse currents, the soil surrounding the embedded rod will ionise. The extent of ionisation will depend on the level of the injected current, being limited by the critical electric field for ionisation, E,.. It is assumed that the soil resistivity is negligible inside the ionised zone compared to that of the rest of the soil. This is the dynamic model of the electrode system. The electric field at a radial distance, r , from the rod axis is given by

423

7

14 7 -

5 4

I

D ~P .- E 3 -

a 2 -

0 ,

l -

E .-

peakcurrent, A a

7 ,

:I:\* measured2 least square fit D

.- "> I

7 -

6.

cm 4 . 8 .E 3 .

9 E 2 E

a

D

.-

0

l -

. :-5-\ .

. least square lit EzT! least square lit

. . 0 1 2 3 4 5 6 7

peakcurrent, A b

Fig. 6 Profiles of ground-rod impulse impedance: laboratory tests Test COnfigurdtiOn I of Table 2; soil moisture = 15%, soil re- sistivity = 31s Qm U Z,,= VnCv/L,: k=4.3139, a=-0.2215 b Z,= Vq/I,: k=4.2012, a= -0.2343

where i(r) is the current density (Aim') at a radial distance r from the rod axis, and I is the total injected current. Then, at the edge of the ionisation zone (r = r,):

From (S), the quadratic equation of r, is:

and

where a = 2xE,, b = 2xE,I, and c = -pyZ. Replacing r,in (6) by r; will give the impulse impedance, Z,,, of the electrode system consisting of the rod embedded in soil at the axis of the cylindrical soil holder, i.e.

surface to infinity:

If the level of the injected current exceeds a critical value, the soil surrounding the rod will ionise, extending the effective radius of the rod to the edge of the ionised zone (rr + T i ) , similar to the case of the model for laboratory tests in a cylindrical soil holder. If the critical electric field, E, is known, then the radius, r,, of the ionisation zone surrounding the rod, i.e. the effective radius of the rod, can be derived from (10). Knowing r,, the impulse impedance of the system consisting of the rod embedded in semi-infinite earth can be found by replacing r, in (12) by ri:

From (S), ri is a function of the injected current, I. increasing with higher I. From (11) and (13), the impulse impedance, Z,,,,,, is a function of r;, and hence a function of I. Therefore, Z,, decreases with increasing current for both the laboratory setup and the field setup.

5.7.2 Model for field tests: For a single ground rod with hemispherical tip, buried in semi-infinite earth, the ground resistance of the rod can be computed by integrating the resistance of the elemental cylindrical shell from the rod

424 IEE Proc.-Gmer Tramm. Dkrrib.. V d I S U . No. 4, J u b 2003

CHANl 5.000 Vldiv "+!

c 2 t

5 8 - c m

CHAN2 100.0 mVldiv

I f I a

b

Fig. 8 soil holder Soil holder: lOcm high and lOcm diameter Ground rad: diameler=0,635cm. embedded 3 - in soil U soil moisture= 10% (p!,=2OfMh) b soilmoisture=ZO% (p,=71.lQm)

Volraqe and currenf profiles.$). qround rod in cylinrlrical

5.2 Critical electric field The critical electric field, E,, for soil ionisation is the most significant parameter in the nonlinear characteristics of the impulse impedance of gound electrodes. However, no agreement has been found in estimating E,. Oettle suggested a value of 1000 kV/m [5], whereas Mousa suggested a value of 300kV/m for typical soil [6]. However, typical soil is atypical. Originally, Oettle proposed an empirical equation for E,. as a function of soil resistivity, pg, based on tests:

E, = 241pYt5 (kV/m) (14) We believe that a constant value of E, is not justified.

Fig. 8 shows the voltage and current profiles from two tests in the laboratory on the same soil. The two tests were identical, except that in Fig. Xu, the soil moisture was 10% (pe= 2000Qm) and in Fig. 86, the soil moisture was 20% (p,=71.1 Qm). In Fig. 8u, the soil withstood the voltage, whereas in Fig. 86, it sparked over. Therefore, we adopted (14), pending further research.

5.3 Correlation between tests As the electric field is the most important parameter, the criterion for correlation between two sets of tests should be that the electric fields for the two sets of tests be the same. If the parameters for the series 1 tests are put, it and It (soil resistivity, current density and current), and similarly pU2. i2 and I2 for series 2, then

I' 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

peak current. A a

-

s 5 8 : \\+ - - - - - - - - - - - - .-

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 peak ~urreni. A

b

Fig. 9 correlation between two laboratory test confrgurations Laboratory test configuration 2 of Table 2 soil moisture= 15% Correlated with lest configuration 1 of Table 2 and 15% soil moisture (Fig. 6) 01 Z,, = V'/Ioui correlated with test of Fig. 6a (estimated: k = 6.41 IO: a=-0.1825, measured k=6.1910: a=-0.2325) h Z,= V@/I; correlated with test of Fig. 6b (estimated: k=6.2301: a=-0.1953; measured k=6.1272 u=-O.2195)

Estimated and e.rperimenta1 impulse-impedance profiles:

where I t , rrl and 1 2 , rrz are the embedded lengths and radii of the ground rods for the two configurations. Then, the current, I*, of the second setup corresponding to It in the first setup, i.e. Et(rrl) = E2(r,*), is

For correlation between the two test setups in the laboratory, (6) gives:

and

or

For correlation between a laboratory test and a field test, the equation for Zt i s the same as in (17rr). Invoking (13):

425

8 0,051

, , , ,

estimated _ _ _ 0

0 50 100 150 200 250 300 350 peakcurrent. A

a

a 0.10- 3 -

" , 0 50 100 150 200 250 300 350

peakcurrent. A b

Fig. 10 correlation hetwen Iubburarorj' andfield tesrs Field test configuration I of Table I : soil moisture= 16.97% Correlated with test configuration 2 of Table 2 and 15% soil moisture (Fig. 7) U Z,,g = V,,,,/Iou~ correlated with test of Fig. 7u (estimated: k = 0.3440 z=-O.l638; Measured k=0.2940: cr=-O.l375) h Z,= Kp/fp: correlated with test of Fig. 7h (estimated k=0.3312 a=-O.1590; Measured: k=0.2937 0=-0.1475)

kkiimuied und rrperimenral impulse-iiiipedance pnfi1e.s:

or

If the electric field is higher than Ec, the actual radii of the rods should be replaced by their effective radii.

For each point (II, Z J of the laboratory test, the corresponding point (12, Z,) can thus be estimated either for a second laboratory setup or for a setup in the field by applying (16) and (IS) or (20). A curve is then plotted for the estimated points by the least square method, and k and a for Z = k P are estimated. Figs. 9 and I O show the correlations between two laboratory tests, and between laboratory and field tests, respectively.

6 Discussion

The field tests with rod-type ground electrodes confirm our earlier findings from laboratory tests that the impulse impedance of a rod electrode follows (I) . We have defined the impulse impedance in two ways, as given in (2b) and (2c). The values of k and a estimated in either way, do not differ significantly (Tahle4). However, the scatter of the

individual points from the least square plot of 2 is lower when (24 is used.

We have succeeded in correlating the laboratory results with that of the field, i.e. the results of the field tests could be predicted from the laboratory tests in small soil sample holders (Figs. 9 and 10). In the analysis for correlation, we have assumed that the critical electric field in the soil is a function of the soil resistivity, which follows (14). Extensive tests need to he performed on soil samples to amve at a better relationship between the critical electric field and the soil resistivity. The critical electric field may also be a function of other variables, such as the waveshape of the applied impulse. The tests were performed with a 1.2/5Ops applied impulse voltage. For waveshapes with shorter front times, the soil permittivity may become significant. Eventually, the impulse impedance of a ground rod system may be predicted from soil characteristics without perform- ing any small-scale laboratory tests.

The soil resistivity was measured, using (3), with a soil resistivity meter in several ways. The four rod electrodes were spaced equally with separation distance, A = 7.62 m, I m and 30.48m. The power-frequency resistance of the test electrode was measured by the three-electrode method (Fig. 2) and the soil resistivity was computed by (4). A significant difference in the results was noted (Table 3). We believe that the difference was caused by the variation in the resistivity in different layers of soil. The resistivity computed from the measured resistance of the test electrode, i.e._ from (4), was finally used because it is the resistivity which the test electrode 'sees'.

7 Conclusions

1. The impulse impedance of rod type ground electrodes follows the relation, Z = U;, where k and a are two parameters which are functions of the soil properties and the electrode configuration for a given impulse waveshape. This is similar to the relationship found previously in laboratory tests on small soil sample holders. 2. It is possible to estimate the impulse impedance of ground rods in the field from test results in the laboratory. 3. The critical electric field of soil ionisation is a significant parameter in the impulse behavior of ground electrodes. It is expected that the impulse impedance of a ground rod in the field may be estimated without performing any laboratory tests if the relationship between the critical electric field and the soil resistivity were known accurately. Therefore, efforts should be directed to extensive tests on the soil critical electric field.

8 References

Chowdhun. P.L.: ' I m p u k impdance tests on laboratory model ground electrodes'. Suhnzirred lo IEE Pruc., Genrr. Trmsm. Disrrib Bellaschi. P.L.: 'Impulse and 60sycle charactenstics afdnven grounds'. AIEE Tram.. 1941, 60. pp. 12.~128 Liew, A.C.. and Dawenh, M . : 'Dynamic model of impulse charactenstics of concentrated earths'. P w c lmr Elecrr Eng.. 1974, 121. (2). pp. 12?-135 IEEE Guide for measuring earth resistivity. ground Impedance. and carth surface potentials of B ground system (Part I). IEEE Standard 8 I- 1983 Oettle. E.E.: 'A new general estimation cuwe for predicting the impulse impedance of concentrated earth electrodes'. IEEE Trmr. Poircr Ddic.. 1988, 3. (4), pp. 202G2029 Mousa, A.M.: 'The soil ionization gradient associated with discharge of high currents into concentrated elmtrades', IEEE Tram. P o w r Delia, 1994. 9, (3). pp. 16691677

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