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Proc. of 24-th International Conference on Lightning protection(ICLP'98) , Birmingham, U.K., 14-18 Sept. 1998, Vol. 1, pp. 524-529.

COMPARISON BETWEEN SIMULATION AND MEASUREMENT OFFREQUENCY DEPENDENT AND TRANSIENT CHARACTERISTICS

OF POWER TRANSMISSION LINE GROUNDING

Leonid Grcev and Vesna ArnautovskiUniversity "St. Kiril and Metodij"

Republic of Macedonia

Abstract This paper describes application ofthree different theoretical models for high fre-quency and transient analysis of grounding sys-tems depending on their complexity. The first twoare based on transmission line and the third oneon rigorous electromagnetic field theory. The first

one is suitable for the simplest single horizontaland vertical ground electrodes, the second one issuitable for more complex arrangements ofgrounding electrodes, typical for transmissionline grounding, and the third one is suitable forarbitrary complex grounding systems. Paper then presents comparison between rigorous and simpli-fied theoretical and experimental results by EDF.Soil ionization was not considered since only lowcurrents were used in the considered experiments.

1 INTRODUCTION

The operational safety and proper functioning ofelectric power systems is influenced by the properdesign of their earth terminations. The design ofgrounding circuits becomes particularly importantin case of power system abnormal operation orlightning. In such cases the grounding systemsmust be able to discharge impulse currents intothe earth without causing any danger to people ordamage to installations [1].

In contrast to the grounding systems behavior at

low frequencies [2], the high frequency and tran-sient behavior is considerably more complex.This problem has been approached from boththeoretical [3][17] and experimental [19][26] points of view.

Regarding the experimental work, it can be seenthat the most systematic measurements have been performed by the lectr ici t de France (EDF),[21], [23][26]. However, only smaller and sim- pler grounding structures, typical for power linetransmission line grounding, were investigated.

Most of the previous theoretical work is based onsimplified quasi-static approximation and circuittheory [3][12]. More recently, rigorous formula-

tions based on antenna theory, which are derivedfrom the full set of the Maxwells equations, has been used [13][17]. The exact and quasi-stat icmethods, applied to vertical rod electrodes, have been compared in [28], analyzing the limitationsof the validity of quasi-static methods.

The dynamical behavior of grounding systemsdepends on two different physical processes: non-linear behavior of soil due to soil ioniza-

tion in the immediate proximity of thegrounding electrodes, and

propagation of electromagnetic waves alonggrounding electrodes and in soil.

Soil ionization occurs for large enough currentswhen the electric fields at the ground electrodesurface may become greater than the ionizationthreshold of approximately 300 kV/m [30]. As a

result of this phenomenon, when smaller elec-trodes are subjected to high current impulses,their ground impedance may be reduced for a fac-tor of 2 or 3 from their low current value, after ashort period of time (approximately 5s).

The propagation effects are effectively analyzedin frequency domain. Such effects become moredominant in electrically larger and more compli-cated structures. Buried structures are electricallylarger at higher frequencies and in better conduct-ing soil. Therefore, these effects are more impor-tant when steep impulses, with higher frequencycontent, are considered.

This paper firstly describes three different modelsfor high frequency and transient analysis ofgrounding systems depending on their complex-ity. The first one is suitable for the simplest: sin-gle horizontal and vertical ground electrodes. Thesecond one is suitable for more complex arrange-ments of grounding electrodes, typical for trans-mission line grounding. The third one is suitablefor arbitrary complex grounding systems. Paperthen presents comparison between rigorous andsimplified theoretical and experimental results byEDF Soil ionization was not considered sinceonly low currents were used in the consideredexperiments.

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2 SIMULATION OF SINGLEHORIZONTAL AND VERTICALGROUND ELECTRODES

The complex valued, frequency dependent longi-tudinal impedance and transversal admittance perunit length are solved in the well-known refer-ence book by Sunde [3]:

Z j

a

+

( ) ln .

02 22

185

(1)

Y j

ah

+( )

ln .

1112

2

b g (2)

where and a are length and radius of the elec-trode, andh is depth of the electrode. Here, theinternal impedance of the electrode is neglected.Also here describes the propagation of a TEM-wave in homogeneousearth with resistivity, permittivity and perme-ability

b g b g= + j 0 1/ j

0.

The characteristic impedance ZC and the propaga-tion coefficient are given by:

Z Z Y C b g b g b g= / (3)

b g b g b g= Z Y (4)The solution of the nonlinear equation (4) for the propagation coefficient leads to the solution ofthe characteristic impedance (3).

Simple formulas for the characteristic impedanceZC and the propagation coefficient of verticalrod electrodes are [26]:

Z a

j jC

= F H G I

K J +

24 1

10ln

( )

= + j 0 1( / ) j (5)

Corresponding simple formulas for linear hori-zontal electrodes are:

Z ah

j jC

= F H G I

K J +

ln

( )22

12 1

0

= + j j0 1( / ) / 2 (6)

Then, the grounding impedance of the electrode Zwith length is obtained by:

Z Z C = coth (7)

The time domain response is then obtained byapplication of inverse Fourier transform:

v t Z j i t ( ) ( ) ( )= F F 1 m r (8)

Here v(t ) is the response to arbitrary excitationi(t ), Z ( j ) is the impedance to ground (7), andF and F 1 are Fourier and inverse Fourier transform,respectively.

3 SIMULATION OF TRANSMISSIONLINE GROUNDING SYSTEMSWITHIN EMTP

Once the characteristic impedance and the trans-fer function of linear earth conductors are known,more complex arrangements of grounding elec-trodes can be modeled by a network of transmis-sion line segments, provided that coupling be-tween the different grounding electrodes seg-ments can be neglected. At first sight, it is notevident that this assumption is permissible, but ithas been shown [12] that the resulting error iswithin acceptable limits. This approach has greatadvantage in simultaneous modeling of thegrounding system together with live parts of the power electric system components. It is also ca- pable of modeling soil ionization effects. Inter-ested reader may find all details on the model, itsimplementation within widely used ATP versionof Electromagnetic Transien ts Program (EMTP),its validation by comparison with experimentaldata and its application in practical lightning pro-tection studies in [12]. However, application ofthis method for more extended and complex sub-station meshed grounding systems, may lead toerroneous results [18].

4 SIMULATION OF ARBITRARYCOMPLEX GROUNDING SYSTEMS

The computational methodology is based on thegeneral method of moments [33]. This methodol-ogy is first developed for antennas near to and penetrating the earth, and later it is applied togrounding systems [13][15]. More details onmodifications of antenna solutions for groundingsystems can be found in [32].

The grounding system is assumed to be a networkof connected straight cylindrical metallic conduc-tors with arbitrary orientation [15]. The first stepis to compute the current distribution, as a re-sponse to injected current at arbitrary points onthe conductor network. First, the conductor net-work is divided into a number of fictitioussmaller segments. Then axial current distributionin the conductor network I ( ) is approximated bya linear combination of M expansions functions

F k ( ) [15]:

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(9) I I F k k k

M

b g b g==

0

e ( Z )

where I k are unknown current samples. Longitu-dinal current distribution (A1) may be evaluatedfrom the system of equations:

Z I V = (10)

0

45

80

120

150

P h a s

i n d e g

0.001 0.01 0.1 1Frequency (MHz)

0

40 M o d u l e

( Z ) i n

Figure 2: Measurement and simulation of fre-quency dependent impedance of 16 me-ters vertical rod electrode.

Surgegenerator

AuxiliaryelectrodeStudied

electrode(current return)

Auxiliaryelectrode

(potential reference)

Adaptationresistance

Currentmeasurement(coax. shunt)

Resistive divider 60 m

Voltagemeasurement

Figure 1: Measuring set-up (adapted from [ 21 ]).

where the elements of the column matrix [ I ] areunknown current samples, elements of [ Z ] expressall mutual electromagnetic interactions between

parts of the conductor network, and elements of[V ] are related to the excitation. Ref. [15] pro-vides all details on evaluation of the elements of[Z], and [12] give complete derivation of the for-mulas for the electric field.

When current distribution in the conductor net-work is known, it is a simple task to evaluate:

electric field [12], voltage [15] and impedance[14]. Integration of this method with the EMTP isdescribed in [ 17 ].

The advantage of this method in the analysis oflarger and more complex substation groundingsystems has been demonstrated in [ 18 ].

5 FIELD MEASUREMENTS BY EDF

Recordings from extensive field measurements oftransient voltages to remote ground performed by

the Electricite de France (EDF) are used to verifyabove described models. Impulse currents have

been fed into single- and multi-conductor ground-ing arrangements and resulting transient voltageto remote ground has been measured by means ofa 60 m long ohmic divider with measuring band-width of 3 MHz [ 21 ].

Figure 1 provides only a simple illustration of themeasuring set-up. Surge generator with a peakvalue of 20 kV was connected to the investigatedelectrode with a conductor, which was insulatedfrom ground and adapted to the surge generatorscharacteristic impedance ( Z c 500 ). The result-ing current impulses had peak values about 30 Aand rise times adjustable from 0.2 to 3 s. To

avoid stationary waves generated on high fre-quencies, the investigated electrode was con-nected to the potential reference auxiliary elec-trode by a voltage divider with high voltage (HV)arm of sufficient length (60 m). The HV arm wascomposed of a series of ceramic resistances con-nected to very short connectors. By employingthis measuring arrangement a constant transferfunction in the measuring bandwidth could be

realized. Interested reader is referred to numerous publication s by the EDF (fo r example [21], [23] [26]) for more details on the measurements.

6 COMPARISON OF SIMULATION AND

MEASUREMENT RESULTS

Figure 2 illustrate computed and measured fre-quency dependent impedance of a vertical rodelectrode with length 16 m. The studied earthelectrode was constructed of a 50 mm 2 coppercable inserted in holes 62 mm in diameter filledwith a mixture of bentonite and water. The semi-liquid mixture coating of the earth electrodes hada resistivity about 1 m, while the resistivity ofthe surrounding soil was 1300 m. However, anaverage resistivity of equivalent homogeneousmedium is set for the simulations to 450 m tomatch low current low frequency rod resistance toearth. Also, the soil relative permittivity has not

been measured and is set to 10.

The simulations were made using the rigorouselectromagnetic field approach (denoted by EMFin Fig. 2) and using the formulas (5). The resultsshow good agreement with the measurements per-formed by EDF in the whole observed frequencyrange.

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u

i

Figure 3: Measurement and simulation of tran-sient voltages to remote ground at the beginning point of 15m long horizontalwire.

u

i

Figure 4: Measurement and simulation of tran-sient voltages to remote ground at the beginning point of 8m long horizontalwire.

Figure 3 shows the oscillograms of recorded cur-rent impulse injected in the beginning point of 15meters long horizontal ground wire and transientvoltage to remote ground at the same point on thewire. The electrode was constructed of a 116 mm2 copper wire buried at 0.6 m depth. The character-istics of the soil were not separately measured atthe time of the recording of the oscillograms.Therefore, the soil resistivity was set to 70mand the relative permittivity to 15 in [27] and[24], to match low frequency ground resistance.The simulations were made using the rigorouselectromagnetic field approach, and using theSundes approach (eqs. (1)(4) and (8)). The re-sults are compared with the EMTP simulationresults [12] and with the measurements performed by EDF [27] and [24]. The simulation resultsshow good consistency with the measurements.

Figure 4 shows similar comparison between simu-lations and measurement for shorter horizontalgrounding electrode. The electrode was con-structed of a 116 mm2 copper wire, with 8 mlength buried at 0.6 m depth. The characteristicsof the soil were not separately measured. The soilresistivity was set to 65m and the relative permittivity to 15, to match the low frequencyresistance to ground of the electrode. Transientvoltages to remote ground were computed usingthe rigorous electromagnetic field approach, andthe results are compared with the EMTP simula-tion results and with the measurements performed by EDF. Figure 4 shows that there is an agree-ment between the simulation results except duringthe current rise when the measured voltage ishigher than the corresponding values of the com- putation.

Figures 5 illustrate comparison between meas-

urements and simulation of transient voltages toremote ground of a double-loop grounding. Theloops were of 116 mm2 copper wire with dimen-sions 1 1.5 m2. The upper loop was buried at 1

m and the lower loop at 2 m depth. Loops wereconnected with vertical ground conductor at themiddle point of the larger loop side. The charac-teristics of the soil were not separately measured.The soil resistivity was set to 68m and therelative permittivity to 15, to match the low fre-quency resistance to ground. Again, there is anagreement between the simulation results exceptduring the current rise when the measured voltageis higher than the corresponding values of thecomputation.

The higher measured than computed voltages dur-ing the current rise were also observed duringvalidation of the simulation and measurementresults at EDF at Paris, France [27] and [24]. It

Figure 5: Measurement and simulation of tran-sient voltages to remote ground of dou- ble-loop power transmission line towergrounding.

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was concluded in [24] that the measured voltagesare likely to be amplified by some remaining in-ductive voltage drop during the wave front alongthe divider that is added to the actual potentialrise at the clamp of the ground conductors. Itshould be noted that the presented results of thecomputations are only voltages to neutral groundof points at the surface of the buried conductor.The connecting conductors and the measurementcircuit with the 60 m long voltage divider werenot included in the simulation.

7 CONCLUSIONS

The comparison between different theoreticalmethods show that the most adequate for simula-tion of high frequency and transient performanceof power transmission line grounding is method based on transmission line theory. That is espe-cially true for the method that is integrated withinEMTP [12], since it is also capable for simulationof the soil ionization effects.

The rigorous method based on the electromag-netic field theory does not have any advantageover more simplified methods for analysis ofgrounding electrode arrangements typical for power transmission line grounding. This methodhas clear advantage in the analysis of larger andmore complex substation grounding systems [18].

Knowledge of the soil characteristics is criticalfor successful simulation of the high frequencyand transient behavior of grounding systems.However, the necessary soil characteristics arenot always measured and have to be estimated,which introduce uncertainty in the comparison.

In some of the analyzed cases, simulated resultstend to underestimate the peak values of transientvoltages. Further research is necessary to investi-gate the influence of simplified modeling of theequivalent homogeneous soil at higher frequen-cies and the influence of the measuring circuit onthe measured and simulated results.

In spite of uncertainties in the estimation of thesoil parameters, simulations lead to results gener-ally consistent with measured ones.

ACKNOWLEDGMENT

The first author acknowledges helpful and con-structive discussions with Dr. Frank Menter andDr. Marcus Heimbach (both formerly at the Insti-tute of High Voltage Engineering at the TechnicalUniversity of Aachen, Germany) during his visitsto the Institute. Results of comparison betweenmeasurement and simulation based on EMTP are

from the Diploma Thesis by Mrs. Britta Heim- bach (formerly at Technical Universi ty ofAachen). Her help during preparation of the simu-lations is gratefully appreciated.

The work was partially supported by the Ministryof Science of the Republic of Macedonia.

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AddressProf. Leonid GrcevElektrotehnicki fakultetKarpos II bb, P.O. Box 57491000 Skopje, Republic of MacedoniaPhone: +389-2-362224, Fax: +389-2-364262Email: leonid.grcev@ieee.org