A simplified model of the lightning performance of

a driven rod earth electrode in multi-layer soil thatincludes the effect of soil ionisationKenneth J. Nixon, Ian R. Jandrell

School of Electrical & Information EngineeringUniversity of the Witwatersrand, Johannesburg

2050, South AfricaEmail: k.nixon@ ee.wits.ac.za, ijandrell @ee.wits.ac.za

Andrew J. PhillipsElectric Power Research Institute

P.O. Box 217097, CharlotteNorth Carolina 28221, USAEmail: aphillip @epri.com

Abstract- It is proposed that a single apparent resistivity valuecalculated from the steady state resistance equation and themeasured steady state resistance can be used as a simplificationfor lightning current transient performance modelling of a drivenrod earth electrode in multi-layer soil. The proposal is verifiedagainst results obtained using transient analysis of an equivalentcircuit that includes the effect of soil ionisation and full-scaleexperimental results of current impulse tests on a single verticalearth rod in three-layer soil.

I. INTRODUCTIONThe steady state performance of a practical earth electrode is

well understood and detailed in a substantial body of literature[1]-[3]. Typically, an earth electrode can take a variety ofshapes and forms and is installed in ground with wide rangingcharacteristics. A common scenario is an electrode installed insoil consisting of various layers due to geological stratification.This scenario is well documented from both practical andtheoretical perspectives for DC and power frequency condi-tions [4]-[6]. However, to simplify modelling, homogeneoussoil conditions are assumed in models used to describe thenonlinear and time-varying effect of ionisation that occursin the soil surrounding an electrode under lightning currenttransient conditions [7], [8].

This paper proposes a simplified approach to modelling thelightning transient performance of a driven rod earth electrodeburied in multi-layer soil. The theory and principle behindthe simplification are discussed, which is then verified againstsimulations and large-scale experimental results. Simulationresults are obtained using transient analysis of an equivalentcircuit that includes the non-linear effect of soil ionisationbased on the Liew-Darveniza model [7], [9]. The experimentalresults used in the study are from a series of outdoor testswhere high current impulses were applied to a single drivenrod earth electrode [10].

II. THEORYA. Hemispherical earth electrode

Consider a basic hemispherical electrode of radius ro buriedin homogeneous soil with resistivity p as shown in Fig. 1. Thesteady state resistance of this electrode is given by [11]:

p (1)U 2w7r0o ' '

For a current I injected into the electrode, the currentdensity J in the soil at a radius r from the electrode is:

JI

27r2 (2)Jonisation is said to occur where the current density exceeds

a particular value J, or the resulting electric field in the soilexceeds a critical breakdown gradient Eo. Using:

p=

E

p(3)

it can be shown that the radius ri of the so-called soilionisation zone is given by:

p1ri (4

p

Fig. 1. A perfect conducting hemispherical earth electrode of radius roburied in homogeneous soil with resistivity p injected with a current I. Theradius of ionisation zone ri is governed by Eo, J, and pi represents theresistivity of this zone.

The above implicitly assumes ionisation occurs within auniform zone around the earth electrode. Bellaschi [12] andPetropolous [13] proposed that the resistivity of this zone piinstantaneously assumed the same value as that of the earthelectrode. In other words, soil ionisation is modelled by anincrease in the effective radius of the electrode. Given itssimplicity, this model is frequently used in larger studies,despite its lack of accuracy.

8211-4244-0365-0/06/$20.00 (c) 2006 IEEE

(4)

IV. SCENARIO CONSIDERED

Liew and Darveniza improved on the basic model describedabove by introducing a dynamic model that introduced aresistivity profile as shown in Fig. 2 [7]. This model accountedfor the time constants that are clearly involved in the process.Additional improved or alternative models have also beenproposed [14]-[16].

1000i-i~~~~~~oion-isation I

1000-

S) 800-- 600- \\\ionisation

deionisation z400- \

200-

0 100 200 300 400current density, J (A/m2 )

Fig. 2. Illustrative profile of dynamic resistivity model as proposed by Liew-Darveniza [7].

C. Dynamic ImpedanceNote that for steady state conditions, an earth electrode is

described in terms of its resistance to earth, however, undertransient conditions it is important to consider its dynamicimpedance. The dynamic impedance of an earth electrode isthe ratio of the instantaneous value of earth electrode voltageto the instantaneous value of injected current:

Z(t) V(t) (5)1(t)The challenge is to describe this dynamic impedance for

an electrode that is installed in non-homogeneous soil thatconsists of multiple layers with different resistivities.

III. PROPOSED SIMPLIFICATION

Since the current density in the soil surrounding the elec-trode is related to the inverse-square of the distance (2), itcan be concluded that when ionisation occurs, the resistanceof the electrode (1) will be dominated by the resistivityof the ionisation zone. In other words the effect of layersin the soil will be significantly reduced. Provided that themodel used adequately describes the steady state value of theelectrode, complex models of the soil resistivity are thereforenot necessary under transient conditions. It is proposed that asingle apparent bulk value of resistivity be calculated using themeasured low current resistance and the resistance equation -

for a hemisphere (1), for a driven rod:

R n°r+ (6)271 r0

To verify the proposed simplification, a driven rod earthelectrode configuration was investigated as shown in Fig. 3.The soil consists of three distinct layers: an upper layer ofsandy loam, a middle portion of clay and a lower layer belowthe water table. The scenario was implemented at the site of theoutdoor experiments and the measured steady state electroderesistance was 48 Q.

Icurrent impulse

copper-clad5

Esteel rod 115.9mm

00

sand~~~~~~~~~moisture: 11,4%

misture: 22.6%

watertable ~~~~~nottoscale!

Fig. 3. Earth electrode and soil configuration considered. Primary charac-teristics and parameters are summarised.

A. Impulse current waveshapes

The dynamic impedance of the earth electrode for fourdifferent current impulses is considered in this paper. Theseimpulses were selected to represent relatively low and rel-atively high peak magnitudes with different waveshapes assummarised in Table I. The exact impulses used were deter-mined by the capabilities of the impulse generator used forthe large-scale testing and are shown in Fig. 4.

TABLE ICURRENT IMPULSE WAVESHAPES CONSIDERED (DEFINED AS PER IEC

60060-1:1989 [17]).

Peak, kA5.228.66.728.6

Waveshape, ,us3.5 I 9.33.9 I 9.75.5 /14.15.7 / 13.8

For the purposes of this study only the part of the currentimpulse before the zero crossing was considered. Therefore,only measurements up to 10 ,us are considered for I1A andI1B, and up to 15 ,us for 12A and 12B.

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-

B. Improved models

Current (kA) VI. EXPERIMENT

10 15Time (,ts)

Fig. 4. Impulse currents considered in simulation and large-scale experiment.

V. SIMULATION

An overview of the simulations performed is provided inthis section - complete details on the models can be foundelsewhere [9].

A. Circuit model

The electromagnetic transient analysis program, ATP-EMTP[18], was used to implement and study the circuit model in thetime-domain. The change in electrode resistance due to soilionisation was modelled using the Liew-Darveniza model [7].Table II summarises the key parameter values used.

TABLE IIPARAMETER VALUES USED IN CIRCUIT MODEL.

Soil parameters:p resistivity, Qm 139

Eo breakdown gradient, kV/m 300Ti ionisation time constant, ,us 2.0T2 de-ionisation time constant, ,us 4.5Electrode parameters:ro radius of rod, mm 7.95I length of rod, mm 2667

The critical soil ionisation gradient of 300 kV/m suggestedby Liew [7] and Mousa [8] was used. Note that this is contraryto the value of 400 kV/m suggested by CIGRE [11]. In theabsence of known values, the ionisation and de-ionisation timeconstants suggested by Liew and Darveniza were used. Forthe scenario considered, p was calculated using (6) and themeasured value of R of 48.2 Q.

Note that the actual measured current obtained from therelevant experiment was applied to the circuit simulation andthe predicted voltage and dynamic impedance values weredetermined.

The experimental results used are from a series of outdoortests where high current impulses were applied to a singledriven rod earth electrode. A brief summary of the experi-mental setup is provided in this section - full details can befound elsewhere [10], [19].The electrode was installed in soil to meet the scenario

shown in Fig. 3 more than a month before testing commencedand its resistance was monitored during this period to ensurethat it remained stable. Precipitation and the depth of the watertable were monitored throughout testing. The resistance of theelectrode during testing was measured to be 48 Q. This valuewas confirmed before and after the application of every current

20 impulse.

A. Overall test site

A scale plan view of the overall test site is shown in Fig. 5.The impulse generator was used to inject a current impulse,I(t), into the driven rod. The injected current was measuredusing a wide bandwidth current transformer and the voltageat the electrode, V(t), was simultaneously measured usingan outdoor high voltage impulse divider. Both measurementdevices were connected to a digital storage oscilloscope viaa fibre optic link system. Attention was paid to minimisingthe overall inductance of the test configuration as well as tolimiting unwanted noise from coupling into the overall mea-surement system. Special precautions were taken to minimisethe voltage induced in the one turn loop formed by the voltagedivider, ground and connections to the voltage divider.

mO 5 loim impulsegenerator

flmeasurement& control

current & shedtransformer

driven rod

Ndivider fibre optic links

Fig. 5. Plan view of the test site showing key components of the experiment.

B. Measurement post-processing

In order to calculate the dynamic impedance, Z(t), usingthe voltage and current measurements and (5), V(t) and I(t)need to be relatively noise-free. It was therefore necessary tofilter the measurements. Care was exercised not to violate theintegrity of the original signal when applying the filters. Post-processing was also necessary to synchronise the Ve (t) and1(t) measurements, since the voltage divider introduced a 240ns delay relative to the current measurement. This delay was

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due to the long length of cable integral to the functioning ofthe divider.

At the beginning of the current impulse, where the currentand voltages are low, there is typically too much noise toreasonably calculate the dynamic impedance. Hence, graphsinvolving calculated curves only start after 1 ,us.

VII. RESULTS

The simulated and experimental results are summarised inFig. 6 and 7. The curves are labelled consistent with thereferencing system shown in Table I.

Voltage: VIA, V1B (kV)Z(t) ZIA, ZIB (Q)50 _

25-40

20-

15-

; 2010-

4Time (,ts)

300

200

100

10

Fig. 6. Comparison of experimental and simulated dynamic resistance valuesfor current waveshape 1 (approximately 3.7/9.5 ,us). Note that multiple axesare used to plot current, voltage and impedance.

0

Z(t) Z2A, Z2B (Q)50

Voltage: V2A, V2B (kV)

VIII. DISCUSSION

There is strong agreement between the simulated and exper-imental values is as can be seen in Fig. 6 and 7. The only minordiscrepancy occurs towards the end of the large magnitudecurrent impulses where the simulated impedance turns up morethan the experimental impedance. However, this phenomenoncan also be observed in Liew and Darveniza's paper and hasbeen further addressed in recent work [16].

The sag before the current peak for measured values for V2Bcan be attributed to a partial failure in the firing mechanism ofthe impulse generator caused by the high current magnitude.

Fig. 8 shows the simulated Liew-Darveniza resistivity pro-file at a radius of 200 mm from the centre of the rod whencurrent I1B is applied to the driven rod. The times of key pointsare indicated on the curve. It is clear that the resistivity of thesoil in the immediate vicinity of the rod rapidly reaches verylow values in the dynamic model. Consequently, the effectof any local differences in resistivity due to soil layers isminimised.

0 2 4current density, J (kA/in2)

Fig. 8. Resistivity profile at a radius of 200 mm from the centre of the500 driven rod generated by the dynamic impedance model for current impulse

IlB. The time value at specific points of the profile are shown.

400The simplification proposed in this paper was applied by

Sekioka et. al. (without explanation) to a new model thatimproves that of Liew and Darveniza [16]. The structure ofthe soil was not described, however the experimental and

200 simulated results presented were also in agreement.

100

Time (,ts)

Fig. 7. Comparison of experimental and simulated dynamic resistance valuesfor current waveshape 2 (approximately 5.6/14.0 ,us). Note that multiple axesare used to plot current, voltage and impedance, and that the timescale isdifferent to Fig. 6.

IX. CONCLUSION

Rather than having to consider the individual resistivities ofall soil layers, satisfactory results can be obtained by usingonly the apparent bulk resistivity value calculated from thesteady state resistance equation and the measured steady statecurrent resistance. This represents a significant and useful sim-plification to modelling the transient behaviour of an electrodein commonly occurring soil conditions. The proposal has beenverified using simulation and large-scale experimental results.

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ACKNOWLEDGEMENTThe authors would like to thank Eskom for support received

through TESP funding; the NRF for support of the HighVoltage research programme; and the DTI for THRIP funding.Thanks are also extended to the Electric Power ResearchInstitute for providing the resources and for funding the large-scale testing at the EPRI Lenox site; in particular, specialthanks are extended to the late Ken Wormwood for his helpin the construction of the test setup.

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[3] W. Chisholm and J. Anderson, "Guide for transmission line grounding:a roadmap for design, testing and remediation," EPRI, Palo Alto,California, Tech. Rep. 1002021, 2004.

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[7] A. C. Liew and M. Darveniza, "Dynamic model of impulse character-istics of concentrated earths," Proc. of the IEE, vol. 121, no. 2, pp.123-135, Feb. 1974.

[8] A. M. Mousa, "The soil ionization gradient associated with discharge ofhigh currents into concentrated electrodes," IEEE Trans. Power Delivery,vol. 9, no. 3, pp. 1669-1677, July 1994.

[9] K. J. Nixon and I. R. Jandrell, "Quantifying the lightning transientperformance of an earth electrode," Trans. of the SAIEE, vol. 95, no. 1,pp. 18-23, Mar. 2004.

[10] J. Anderson, "High current impulse testing of full-scale ground elec-trodes," EPRI, Palo Alto, California, Tech. Rep. 1006866, 2002.

[11] CIGRE WG 33:01, "Guide to procedures for estimating the lightningperformance of transmission lines," WG 01 (Lightning) of Study Com-mittee 33 (Overvoltages and Insulation Co-ordination), Oct. 1991.

[12] P. L. Bellaschi, R. E. Armington, and A. E. Snowden, "Impulse and 60-cycle characteristics of driven grounds - part II," AIEE Transactions,vol. 61, pp. 349-363, 1942.

[13] G. M. Petropoulos, "The high-voltage characteristics of earth resis-tances," IEE Journal, vol. 95, no. 2, pp. 59-70, 1948.

[14] A. Geri, G. M. Veca, E. Garbagnati, and G. Sartorio, "Non-linearbehaviour of ground electrodes under lightning surge currents: Computermodelling and comparison with experimental results," IEEE Trans. onMagnetics, vol. 28, no. 2, pp. 1442-1445, Mar. 1992.

[15] A. C. L. Junping Wang and M. Darveniza, "Extension of dynamic modelof impulse behaviour of concentrated earths at high currents," IEEETrans. Power Delivery, vol. 20, no. 3, pp. 2160-2165, July 2005.

[16] S. Sekioka, M. I. Lorentzou, M. P. Philippakou, and J. M. Prousalidis,"Current-dependent grounding resistance model based on energy balanceof soil ionisation," IEEE Trans. Power Delivery, vol. 21, no. 1, pp. 194-201, Jan. 2006.

[17] IEC 60060-1, "High-voltage test techniques. Part 1: General definitionsand test requirements," IEC, Geneva, 1989.

[18] W. Meyer and T. Liu, Electromagnetic Transients Program Rule Book.Bonneville Power Administration, 1982.

[19] K. J. Nixon, I. R. Jandrell, and A. J. Phillips, "Measuring the abso-lute transient voltage of a real earth electrode," in j4th InternationalSymposium on High Voltage Engineering, Beijing, China, Aug. 2005.

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