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Abstract-- The fault current distribution among various paths,

such as shield wires, neutral wires, cable sheaths, electric line

structure grounds, and substation or power plant grounding

systems, is computed and analyzed for several scenarios. A

parametric analysis of the effects of several key variables on the

fault current distribution is carried out. The variables include:

cross section of power lines, length of power lines, tower footing

resistance, grounding system resistance, type of static wires, and

soil resistivity. In this paper, the fault current distribution andelectromagnetic interference levels have been studied and

evaluated for a typical electrical network with overhead and

underground cable lines. Furthermore, a measure has been

provided to effectively reduce interference to acceptable levels.

Index TermsElectromagnetic interference, fault currents,

grounding, power cables, power distribution lines, transmission

lines

I. INTRODUCTION

LECTRICAL engineers are often faced with the necessity

of having to design grounding systems and

electromagnetic interference mitigation measures to meetspecific criteria concerning personnel safety or integrity of

equipment. In grounding design, during single phase-to-ground

fault conditions, a portion of the fault current will discharge

into the soil through the grounding network and cause a

potential rise in the grounding system and induce voltages in

neighboring conductors. A high potential can result in

dangerous step and touch voltages and transferred potentials at

remote locations as well.

On the other hand, when high voltage transmission and

distribution lines share a common corridor with other utility

lines such as pipelines and rail tracks, electromagnetic

interference caused by the power lines on the non-energized

utility lines during single phase-to-ground faults occurring at

any location along the entire power lines is a serious concern

because it can result in electric shocks and can threaten the

integrity of the neighboring utility lines.

The fault current distribution among various paths, such as

This work was supported by Safe Engineering Services & technologies

ltd.

The authors are with Safe Engineering Services & technologies ltd, 3055

Blvd. Des Oiseaux, Laval, Quebec, Canada H7L 6E8 (e-mail:

[email protected]).

shield wires, neutral wires, cable sheaths, electric line structure

grounds, and substation or power plant grounding systems, is

an important factor that affects the design of the grounding

system, the induced electromagnetic interference levels along

the utility lines, and mitigation measures, if necessary. Several

studies of fault current distribution for various situations have

been analyzed in recent years [1-2].

The fault current distribution is difficult to determine

accurately since it is not easy to account for the large number

of variables such as complex electric line networks and

grounding systems. Detailed computer methods are usually

used to obtain accurate results. IEEE STD 80-2000 [3]

suggests a graphical method for determining the maximum

fault current injected into the grounding system. The method

attempts to correlate the substation zero sequence fault current

obtained from a standard short circuit study to the actual

current flowing between the grounding systems and

surrounding earth. This provides a quick and simple method to

estimate the current division, avoid complex computations and

give acceptable results for a few simple examples compared

with the computer method. However, it is an approximatemethod that focuses on a few typical line configurations that

may not apply in many cases.

This paper presents a parametric analysis in which the fault

current distribution among various paths is accurately

computed during single phase-to-ground fault conditions. The

effects of the following variables on the fault current

distribution are studied: cross section of power lines, length of

power lines, tower footing resistance, grounding system

resistance, type of static wires, and soil resistivity.

Moreover, this paper presents the results of a recent

electromagnetic interference study in a shared corridor

occupied by 345 kV transmission lines, railroad tracks and gas

pipelines which are parallel to the electric lines along the

corridor that consists of a 37 km long underground 345 kV

power cable network and a 74 km long overhead transmission

line network. The fault current distribution and

electromagnetic interference levels are studied and evaluated

for the overhead lines and underground power cables

respectively. Furthermore, a measure to effectively reduce

interference to acceptable levels is presented and discussed in

detail.

Fault Current Distribution in Transmission and

Distribution Systems with Shield Wires, Neutral

Wires and Cable SheathsJ. Liu, F. P. Dawalibi Senior Member, IEEE, J. Ma, Senior Member, IEEE,

and S. Fortin,Member, IEEE

E

The International Conference on Electrical Engineering 2009

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II. COMPUTATION METHOD

A circuit approach and a frequency domain method are

used to carry out the fault current distribution and

electromagnetic interference computations through accurate

simulation of the electric network. The circuit approach used

in this paper accounts for all the key elements necessary to

calculate the fault current distribution accurately during

normal conditions, imbalance conditions, and fault conditions.

The circuit and frequency domain methods together take

induction effects fully into account and the computation results

contain the combined effects of the inductive, conductive, and

capacitive interference. All simulations have been carried out

by using the CDEGS software package [4].

III. COMPUTER MODEL

Fig. 1 shows the parameter settings that are considered in

the computer models for this study.

Fig. 1. Structure of the parametric fault current distribution study

The reference case consists of a 10 km long 230 kV

transmission line with a span length of 250 m. At one end of

the line, a generating station feeds a substation located at the

other end. We assume that a 10 kA single phase-to-ground

fault occurs at the substation. The cross section of the line is

shown in Fig. 2.

Fig. 2. Overhead T/L cross section for the reference case

The phase conductors are 2156 kcmil ACSR (bluebird).

The static wires are Alumoweld 19 No. 7 395.6 kcmil. A

uniform soil with a 100 ohm-m resistivity is used in the model.

The tower footing resistance is 15 ohms. The substation

grounding resistance is 1 ohm and the generating station

grounding resistance is assumed to be 0.1 ohm. The computed

fault current split factor, i.e. the ratio of the fault current

injected into the substation grounding system to the total fault

current is 34.9% for this reference case.

This study is based on the reference computer model, fromwhich many computer simulations of representative

transmission and distribution lines are created by varying one

parameter at a time. It is not possible to present all the results

obtained for each analyzed case. However, a number of typical

cases have been selected and presented here in detail.

IV. COMPUTER RESULTS

A. Length of T/L

The computation results for transmission lines of different

lengths are shown in Fig. 3. Little change in the fault current

split factor is observed when the length of the transmission lineis greater than 2.5 km. This shows that the impact on the fault

current distribution of the transmission line length is small

when the length exceeds 10 spans.

Fault Current Split Factors

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40 45 50

Length of the Transmission Line (km)

FaultCurrentSplitFactor(%)

Fig. 3. Fault current distribution for different T/L lengths

B. Transmission Line Cross Section

Different transmission line cross sections are shown in Fig.

4.

Fig. 4. Different transmission line cross sections

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It can be seen from the computation results shown in Fig. 5

that some transmission line configurations produce higher fault

current split factors than other configurations. Clearly, the

main factor governing the fault current distribution is always

the geometry distance between the faulted phase wire and the

static wires rather than the overall configuration of the

transmission lines. When the faulted phase wire is close to the

static wires, the mutual coupling between the phase and static

wires is stronger. As a result, more current flows along thestatic wires back to its source and less current is injected into

the grounding grid.


10

20

30

40

Horizontal (Fault is on

Phase A)

Wide Horizontal (Fault

is on Phase A)

Vertical (Fault is on

Phase A)

Vertical (Fault is on

Phase C)

Transmission Line Cross Section


Fig. 5. Fault current distribution for different transmission line cross sections

C. Type of Static (Ground) Wire

The computation results for different types of static wires

are shown in Fig. 6. As we can see, the materials of the static

wires can significantly affect the fault current split factor.

More current returns to its source via the static wires when the

static wires are more conductive. As a result, less current is

discharged by the grounding system at the faulted substation.


10

20

30

40

50

60

Steel Aluminum Copper

Type of Static Wire


Fig. 6. Fault current distribution for different types of static wires

D. Tower Resistance

The computation results for different tower resistances

along the transmission line are shown in Fig. 7. The resultsindicate that the fault current split factor is increasing with the

increase of the tower resistance. This can be easily explained

by the fact that less current will come back through the path

consisting of the static wires and tower footings when the

tower resistance is high. However, this effect will be small

when the tower resistance is about 20 ohms or more.

E. Soil Resistivitiy

Four soil resistivities, 10, 100, 1000 and 10000 ohm-m are

used to compute the self impedance of the static wire and the

mutual impedance of the phase conductor and the static wire.

The fault current distribution has been studied as shown in Fig.

8. It has been found that the fault current distribution is slightly

influenced by the soil resistivity. The fault current has a

tendency to go back to the source through the static wires

when the soil resistivity is high and therefore less current is

injected into the grounding grid.

F. Substation Ground Resistance

Fig. 9 shows what happens when the faulted substation ground

resistance changes. As expected, the fault current split factor

decreases when the faulted substation ground resistance is

high. Most of the fault current will return to the source through

the static wires once the faulted substation ground resistance

reaches a high value (on the order of 5 ohms in this case).


0

5

10

15

20

25

30

35

40

45

50

0 20 40 60 80 100

Tower Resistance (ohms)

FaultCurrentSp

litFactor(%)

Fig. 7. Fault current distribution for different tower resistances


0

5

10

15

20

25

30

35

40

1 10 100 1000 10000

Soil Resistivity (ohm-m)

FaultCurrentSplitFac

tor(%)

Fig. 8. Fault current distribution for different soil resistivies


0

10

20

30

40

50

60

0 5 10 15 20

Substation Ground Resistance (ohms)

FaultCurrentSplitFactor(%

)

Fig. 9. Fault current distribution for different faulted substation resistances

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G. Generating Station Ground Resistance

Fig. 10 shows the computation results with respect to

different generating station ground resistances.


20

25

30

35

40

45

50

55

0 1 2 3 4 5 6 7 8 9 10Generating Station Ground Resistance (ohms)


Tower Resistance-5 ohms




Fig. 10. Fault current distribution for different generating station ground

resistances

It is interesting to observe that the fault current split factor

varies by following different patterns when the generating

station ground resistances have different values. The

complexity of the relationship between the fault current split

factor and the generating station ground resistance have been

discovered. When the tower resistance is small, the fault

current split factor will remain practically constant or increase

slightly. On the other hand, the fault current split factor will

gradually decline with the increase of the generating station

ground resistance when the tower resistance is about 100 ohms

or more.

H. Underground Power Cable Configuration

Two typical cables have been modeled to demonstrate the

fault current distribution. The horizontal and mixed

configurations are shown in Fig. 11.

Fig. 11. Different configurations of the underground cable

The length of the underground cables is 3 km. The

underground cables are modeled as a stranded conductor core

surrounded by a lead sheath. The equivalent relative resistivity

and the relative permeability of the sheaths were derived based

on typical values. The cable is a XLPE insulated cable and the

characteristics used to perform the calculation are as follows:

Cable core: 3500 kcmil copper conductor

Cable overall diameter: 12.8 cm

Copper core diameter: 5.2 cm

Lead sheath: extruded lead, inner diameter = 9.4 cm, and

outer diameter: = 10.5 cm

Lead sheath equivalent relative resistivity (with respect to

copper) and permeability(with respect to free space): 12 and 1

Two ground wires are installed with the underground

cables. The radius of the ground wire is 0.8 cm. The

underground cables are divided into sections (from one vault

location to another). Two ground rods are installed per cable

vault (i.e., every 600 m). The ground resistance is 15 ohms.The computed fault current split factors are 1.6% and 2.2%

for the horizontal and vertical configurations, respectively.

Little change is observed when the overall configurations are

different. This is due to the fact that the mutual coupling

between the sheath and cable core is very strong because of the

small distance between the two conductors. In the case of an

underground cable, the mutual coupling plays a very important

role in the current distribution, as expected.

V. TYPICAL AC INTERFERENCE STUDY

A typical AC interference study that involves an electric

network consisting of overhead lines and underground cablesis presented in this section.

A. Network Description and Computer Model

Fig. 12 shows the plan view of the electrical network under

study.

Fig. 12. Plan view of the electrical network under study

The underground power cables between Substation #1 and

Substation #3 consist of two 345-kV circuits utilizing XLPE

insulated cables. The total length of the underground cables is

37 km and a railroad roughly follows the underground cables

for about 21 km. The overhead portion of the 345-kV

transmission lines between Substation #3 and Substation #7 is

approximately 74 km. A gas pipeline and a railroad share the

same corridor with the 345-kV overhead transmission line for

about 6.4 km, respectively.

The 345-kV transmission line can cause AC interference to

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the railway system and pipelines. Especially, the induced

voltages and currents on the railway and pipeline facilities can

result in a shock hazard and threaten the integrity of both

facilities during single phase-to-ground fault conditions.

The complete model consists of the transmission line phase

conductors, static wires, underground cables, rails, rail ballast

resistances, insulating joints, track arresters, rail track circuits,

and railroad equipment house grounds. Various soil structures

have been modeled along the entire common-corridor. In thispaper, the electromagnetic interference under fault conditions

has been analyzed and presented.

The data and characteristics used in the simulations are as

follows:

The overhead line consists of the ACSR phase wires and

Aluminum 7#8 static wires

The underground cable characteristics are the same as in

the previous section

The maximum load current is 1.5 kA per phase for the

new 345 kV line and 1.2 kA per phase for the existing

345 kV line

A 130 lb steel rail was selected and the separationdistance between rails is 1.5 m

The pipeline has a radius of 30 cm and is covered with

coal tar coating

Figs. 13 and 14 show the typical cross sections of the

overhead lines and underground cables.

Fig. 13. Cross section of the underground cable conduit

Fig. 14. Cross section of overhead transmission lines

The touch voltage is one of the important quantities that

should be computed and examined. In this paper, the touch

voltages when a person contacts a rail track or a pipeline when

standing 1 m away on both sides of the rail track or pipeline

are calculated to ensure that safety concerns are addressed.

B. Computation Results

The computation results are summarized here. The worst

rail touch voltage under fault conditions for the underground

cable portion is 94 V only which is below the IEEE Standard

80 safe limit of 519 V based on a 800 ohm-m native soil, as

shown in Fig. 15. The low touch voltage is caused by theproximity of the lead sheath to the underground cable core that

results in a very strong mutual coupling between them. As a

result, most of the fault current is going back to the remote

source through the sheath. As a result, the induced EMF on the

rail is small due to the cancellation effect of the core current

by the sheath current. The induced EMF caused by the ground

conductors paralleling the cable sheath is also small because

little current is flowing into the ground conductors.

Rail Touch Voltages

0

100

200

300

400

500

600

700

0 5000 10000 15000 20000 25000

Distance along Railway in Parallel with the Underground Cable (m)

TouchVoltages(V)

Rail Touch Voltages

Touch Voltage Limit

Fig. 15. Rail touch voltages along the underground cable

The worst rail and pipe touch voltages under fault

conditions for the overhead portion are 2244 V and 1010 V,

respectively. Both of them are above the IEEE Standard 80

safe limit based on various soils along the entire length of the

railway and pipeline. The computation results for the touch

voltages along the rail are shown in Fig. 16. In contrast to the

underground cable situation, a large amount of the fault

current is injected into the tower grounds along the common-

corridor due to the high fault current split factor in the case of

an overhead line with two Aluminum 7#8 static wires.

Maximum Rail Touch Voltages

0

500

1000

1500

2000

2500

0 1000 2000 3000 4000 5000 6000 7000

Distance along Railway in Parallel with the Overhead T/L (m)

TouchVoltages(V)

Rail Touch Voltages

Touch Voltage Limit

Fig. 16. Rail touch voltages along the overhead transmission lines

Therefore, mitigation measures are required on the railway

and pipelines facilities which parallel the overhead

transmission lines.

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C. Mitigation Measure

A mitigation measure consisting of three continuous

mitigation wires along the railway and pipeline is presented.

Two continuous mitigation wires bonded to the railway

through track arresters at regular intervals and buried 1 m

away from the edge of the railway are installed along the

exposed railway zone on both sides of the railway. Similarly, a

zinc mitigation wire along the exposed pipeline located about

1 m away from the edge of the pipeline is installed. Themitigation wire is connected to the pipeline through PCR

(Polarization Cell Replacement) or solid-state decoupler

devices. In case of a fault, the continuous mitigation wires

provide additional grounding for the railway and pipeline and

furthermore, act as screening conductors, thus decreasing the

induced pipe and rail potential rise. This measure reduces

interference levels considerably, as can be seen in Fig. 17 for

the rail touch voltages. As a result, the computed rail and pipe

touch voltages have been reduced to less than 250 V and 300

V, respectively, which satisfy the safety design limits.

Maximum Rail Touch Voltages with Mitigation Wires

0

100

200

300

400

500

0 1000 2000 3000 4000 5000 6000 7000

Distance along Railway in Parallel with the Overhead T/L (m)

TouchVoltages(V)

Rail Touch Voltages

Touch Voltage Limit

Fig. 17. Rail touch voltages along the overhead transmission lines with

mitigation wires

VI. CONCLUSIONS

A parametric analysis of the fault current distribution along

electric power transmission network has been conducted.

Effects of the various parameters which influence the fault

current split factor have been studied. The parameters include

power line cross section, length of power lines, tower footing

resistance, station grounding system resistance, types of static

wires, and soil resistivity. All charts, observations, and

computation results offer useful clues to better understanding

of the fault current distribution. Furthermore, a typical study of

electromagnetic interference on railways and pipelines caused

by electrical overhead transmission lines and undergroundcables under fault conditions has been carried out as an

example. This real case study shows how modern

computational approaches can be used to analyze complex

electromagnetic interference issues and produce accurate

results.

VII. REFERENCES

[1] S. Tee, F. P. Dawalibi, and J. Liu, "Influence of current distribution in

enclosed underground power cables on the overheating of the steel

casing enclosure," The International Conference on Electrical

Engineering (ICEE), Kunming, China, July 10 - 14, 2005.

[2] W. K. Daily and F. P. Dawalibi, "Cost reduction and minimization of

land based on an accurate determination of fault current distribution in

neutral conductors,"IEEE Trans. Power Delivery, vol. 8, no. 1, pp. 97-

103, January 1993.

[3] IEEE Guide for Safety in AC Substation Grounding, IEEE Standard 80-

2000.

[4] CDEGS Software Package, Safe Engineering Services & technologies

ltd., Montreal, Quebec, Canada, 2006.

VIII. BIOGRAPHIES

Ms. J. Liu received the B.Eng. and the M. Eng. degree in Electrical

Engineering in 1985 and 1990, respectively. She is presently serving as

scientific researcher at Safe Engineering Services & technologies ltd. Her

research interests are electrical grounding systems, EMC, and various aspects

of electrical power system analysis, modeling, control, and management.

She is the author of more than 30 papers on electrical power system

safety, power quality, EMC, and computer applications.

Dr. F. P. Dawalibi (M'72, SM'82) was born in Lebanon in November

1947. He received a Bachelor of Engineering degree from St. Joseph's

University, affiliated with the University of Lyon, and the M.Sc. and Ph.D.

degrees from Ecole Polytechnique of the University of Montreal. From 1971

to 1976, he worked as a consulting engineer with the Shawinigan Engineering

Company, in Montreal. He worked on numerous projects involving power

system analysis and design, railway electrification studies and specialized

computer software code development.

In 1976, he joined Montel-Sprecher & Schuh, a manufacturer of high

voltage equipment in Montreal, as Manager of Technical Services and was

involved in power system design, equipment selection and testing for systems

ranging from a few to several hundred kV.

In 1979, he founded Safe Engineering Services & technologies, a

company specializing in soil effects on power networks. Since then he has

been responsible for the engineering activities of the company including the

development of computer software related to power system applications.

He is the author of more than 200 papers on power system grounding,

lightning, inductive interference and electromagnetic field analysis. He has

written several research reports for CEA and EPRI.

Dr. Jinxi Ma (M'91, SM'00) was born in Shandong, P. R. China in

December 1956. He received the B.Sc. degree from Shandong University, P.

R. China, and the M.Sc. degree from Beijing University of Aeronautics and

Astronautics, both in electrical engineering, in 1982 and 1984, respectively.

He received the Ph.D. degree in electrical and computer engineering from theUniversity of Manitoba, Winnipeg, Canada in 1991. From 1984 to 1986, he

was a faculty member with the Department of Electrical Engineering, Beijing

University of Aeronautics and Astronautics. He worked on projects involving

design and analysis of reflector antennas and calculations of radar cross

sections of aircraft.

Since September 1990, he has been with the R & D Dept. of Safe

Engineering Services & technologies in Montreal, where he is presently

serving as manager of the Analytical R & D Department. His research

interests are in transient electromagnetic scattering, EMI and EMC, and

analysis of grounding systems in various soil structures.

Dr. Ma has authored and coauthored more than one hundred papers on

transient electromagnetic scattering, analysis and design of reflector antennas,

power system grounding, lightning and electromagnetic interference analysis.

He is a senior member of the IEEE Power Engineering Society, a member of

the IEEE Standards Association, and a corresponding member of the IEEE

Substations Committee and is active on Working Groups D7 and D9Dr. S. Fortin was born in 1962. He received a B. Sc. degree (1985) in

Physics from Laval University, Quebec and a Ph. D. degree (1991) in Physics

from the University of British Columbia, Vancouver. His area of

specialization was in the theoretical aspects of high-energy particle physics.

In 1992-1993, he was a research assistant with the Nuclear Physics

Department at the University of Montreal, again specializing in particle

physics.

He joined Safe Engineering Services & Technologies Ltd. as a research

scientist in 1994. His research interests include the computation of

electromagnetic fields at various frequencies and transient phenomena. Dr.

Simon Fortin has published about 40 papers on lighting, grounding and

electromagnetic fields compatibility related problems.

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2.07_I9FP0151_E.pdf