G20535

A Study on High Voltage AC PowerTransmission Line Electric and

Magnetic Field Coupling with NearbyMetallic Pipelines

A Thesis Submitted for the Degree of

Master of Science (Engineering)

in the Faculty of Engineering

By

Abhishek Gupta

Department of Electrical Engineering

Indian Institute of Science

Bangalore-560012, INDIA

August 2006

Dedicated to

my beloved parents

Abstract

In the recent years, there has been a trend to run metallic pipelines carrying petroleum products

and high voltage AC power lines parallel to each other in a relatively narrow strip of land. The

case of electromagnetic interference between high voltage transmission lines and metallic pipelines

has been a topic of major concern since the early 60’s. The main reasons for that are:

• The ever increasing cost of right-of-ways, suitable for power lines and pipelines, along with

recent environmental regulations, aiming to protect nature and wildlife, has forced various

utilities to share common corridors for both high voltage power lines and pipelines. There-

fore, situations where a pipeline is laid at close distance from a transmission line for several

kilometers have become very frequent.

• The rapid increase in energy consumption, which has led to the adoption of higher load and

short circuit current levels, thus making the problem more acute.

Due to this sharing of the right-of-way, overhead AC power line field may induce voltages on the

metallic pipelines running in close vicinity leading to serious adverse effects. This electromagnetic

interference is present both during normal operating conditions as well as during faults. The

coupling of the field with the pipeline takes place either through the capacitive path or through

the inductive or conductive paths.

In the present work, the induced voltages due to capacitive and inductive coupling on metallic

pipelines running in close vicinity of high voltage power transmission lines have been computed.

The conductor surface field gradients calculated for the various phase configurations have been

presented in the thesis. Also the electric fields under transmission lines, for both single circuit and

double circuit (various phase arrangements) have been analysed. Based on the above results, an

optimum configuration giving the lowest field under the power line as well as the lowest conductor

surface gradient has been arrived at and for this configuration induced voltage on the pipeline has

been computed using the Charge Simulation Method (CSM). For comparison, induced voltages on

the pipeline have been computed for the various other phase configurations also. A very interesting

iii

iv

result is that the induced voltage on the pipeline becomes almost negligible at a critical lateral

distance from the center of the powerline and beyond which the induced voltage again increases.

This critical distance depends on the conductor configuration. Hence it is suggested that the

pipeline be located close to the critical distance so that the induced voltage would be close to

zero.

For calculating the induced voltage due to the inductive coupling, electromotive force (EMF),

induced along the pipeline due to the magnetic field created by the transmission line has been

calculated. The potential difference between the pipeline and the earth, due to the above in-

duced EMFs, is then calculated. As the zones of influence are generally formed by parallelism,

approaches, crossings as well as removals, the computation involves subdividing the zone into

several sections corresponding to these zones. The calculation of voltages is carried out at both

the ends of the sections. Each section is represented by an equivalent π electrical network, which

is influenced by the induced EMF. The induced EMF is calculated during faulted conditions as

well as during steady state conditions. Inductive coupling calculations have been carried out for

the following cases:

• Perfect parallelism between powerline and pipeline.

• Zone of influences formed by parallelism, approaches, crossings and removals.

It has been observed that when the pipeline is approaching the HV transmission line at an

angle, then running parallel for certain distance and finally deviating away, the induced voltage is

maximum at the point of approach or removal of the pipeline from the transmission line corridor.

The induced voltage is almost negligible near to the midpoint of the zone of influence. The profile

of the induced voltage also depend on whether the pipeline is grounded or left open circuited

at the extremities of the zone of influence. Effect of earth resistivity and anti-corrosive coatings

on induced voltage has also been studied. For mitigating the induced voltage on the pipeline,

numerous low resistive earthings have been suggested. Results show that significant reduction in

induced voltage can be achieved as the number of earth points is increased.

Declaration

I hereby declare that the work reported in this thesis is entirely original. It was carried out by

me in the Department of Electrical Engineering, Indian Institute of Science, Bangalore, India. I

further declare that it has not formed the basis for the award of any degree, diploma, membership,

associateship or any similar title of any University or Institution.

August 2006 Abhishek Gupta

v

Acknowledgments

I would like to express my profound gratitude to my research adviser and mentor Dr. Joy

Thomas M., for introducing me to the exciting field of Electromagnetic Coupling. He has

always shown keen interest in discussions. He was ready to help whenever I approached him.

He has given me ample freedom during the entire M.Sc.(Engg.) tenure and it helped me in

developing independent thinking ability. I gratefully acknowledge Dr. Joy Thomas M. for constant

encouragement (especially at bad times). I have thoroughly enjoyed my tenure at Indian Institute

of Science under his guidance. Words are not just enough to thank him.

I thank prof. Lawrence Jankinse, chairman, Department of Electrical Engineering for his co-

operation and support during my M.Sc. (Engg.) tenure. I thank the staff of electrical department

office for all their cooperation and instant help. I thank all the people who are directly or indirectly

helped me in my research work.

I am happy to get friends like Raghvendra Pandey, Rahul Rahulanker, Dhirendra Kumar

Tiwari, Pradeep Gupta, Sumit Vashishtha, Amit Sultaniya, Shaleen Mohan, Sanjeev Sharma,

Amit Singh, Jyothirmayi, Bhupendra Karma, Vibhor, Ankit, Paromita, Sankalp, Sushil, Shashank

and many others, who made my life memorable at Indian Institute of Science.

Special thanks to Sisir Kumar Nayak, for all the useful and fruitful discussions I had with him

at difficult phases of my M.Sc.(Engg.) tenure. Special thanks to Satanu who helped me during

my tenure both academically and morally. I have enjoyed discussions with both of them.

I thank my present lab mates Venkatesulu, Senthil, Sudalaimuthu for making the lab environ-

ment happy and cheerful.

I am deeply indebted to my parents for all the support, especially to my mother Smt. Krishna

Gupta who has worked hard to put me at a position from where I can make a good career, father

Shri. I. C. Gupta for constant encouragement and my sisters and brothers for support.

Abhishek Gupta

vi

Contents

Abstract ii

Declaration iv

Acknowledgments vi

1. Introduction 1

1.1 Description of Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Capacitive Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Capacitive Coupling Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Inductive Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3.1 Effects of Inductive Coupling . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Conductive Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4.1 Conductive Coupling Mechanisms . . . . . . . . . . . . . . . . . . . . . . . 6

1.4.2 Effects of Conductive Coupling . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Mitigation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5.1 Pipeline Powerline Separation . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5.2 Measures Applied to Transmission Line . . . . . . . . . . . . . . . . . . . . 8

1.5.3 Measures Applied to Pipelines . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2. Review of the Previous Work 11

2.1 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Scope of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

vii

Contents viii

3. Computational Methods 19

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Fields Under Transmission Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.1 Electrostatic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.2 Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Capacitive Coupling Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.4 Inductive Coupling Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4.1 Perfect Parallelism Between Powerline and Pipeline . . . . . . . . . . . . . 29

3.4.2 Zone of influences formed by parallelism, approaches, crossings and removals 34

4. Results and Discussions 36

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Electrostatic Field Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2.1 Conductor Surface Gradient Computation . . . . . . . . . . . . . . . . . . 41

4.3 Magnetic Field Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.4 Induced Voltage due to Capacitive Coupling . . . . . . . . . . . . . . . . . . . . . 43

4.5 Inductive Coupling Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.5.1 Perfect Parallelism Between Powerline and Pipeline . . . . . . . . . . . . . 47

4.5.2 General Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.6 Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5. Conclusions 58

5.1 Capacitive Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.2 Inductive Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Bibliography 60

List of Figures

1.1 Electric and magnetic field produced by transmission line. . . . . . . . . . . . 2

1.2 Capacitive coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Inductive coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Conductive coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.1 Two of the phase conductors with their images . . . . . . . . . . . . . . . . . . 20

3.2 Components of electrostatic field due to HV line . . . . . . . . . . . . . . . . . 22

3.3 Transmission line conductor with its image . . . . . . . . . . . . . . . . . . . . 23

3.4 Discrete line charges used in the CSM. Cross-section of the conductor and

pipeline are not to scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.5 Representation of the circuit formed by the pipeline and the earth. . . . . . . 26

3.6 Zone of influence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.7 Voltage along a pipeline extending beyond the zone of influence. . . . . . . . 31

3.8 Voltage along a pipeline when it extends beyond the zone of influence only in

one direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.9 Voltage along a pipeline when it is earthed at one extremity. . . . . . . . . . 33

3.10 π model representation of the pipeline-earth equivalent circuit. . . . . . . . . 35

4.1 Single circuit horizontal configuration with ground wire. . . . . . . . . . . . . 37

4.2 Comparison of electric fields under single circuit horizontal transmission line

with and without the ground wires, VLL = 275 kV. . . . . . . . . . . . . . . . 38

4.3 Single circuit horizontal configuration, VLL = 400 kV. . . . . . . . . . . . . . . 38

4.4 Electric fields under horizontal transmission line, VLL = 400 kV. . . . . . . . 39

4.5 Double circuit vertical configuration chosen for the study. . . . . . . . . . . . 39

ix

List of Figures x

4.6 Electric field profile for various phase configuration of a double circuit HV

transmission line rated 275 kV. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.7 Double circuit delta configuration. . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.8 Electric field profile for various double circuit delta configurations, VLL =

275 kV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.9 Single circuit horizontal configuration VLL = 500 kV. . . . . . . . . . . . . . . 44

4.10 Single circuit vertical configuration VLL = 500 kV. . . . . . . . . . . . . . . . . 44

4.11 Magnetic field profile under single circuit horizontal and vertical transmission

line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.12 Induced voltage on the pipeline for various phase configurations. . . . . . . . 46

4.13 Comparison of induced voltages due to horizontal and vertical configurations

VLL = 500 kV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.14 Induced voltage along the pipeline (Case (a)). . . . . . . . . . . . . . . . . . . 48

4.15 Current along the pipeline (Case (a)). . . . . . . . . . . . . . . . . . . . . . . . 48

4.16 Induced voltage along the pipeline (Case (b)). . . . . . . . . . . . . . . . . . . 49

4.17 Induced voltage along the pipeline (Case (c)). . . . . . . . . . . . . . . . . . . 50

4.18 Current along the pipeline (Case (c)). . . . . . . . . . . . . . . . . . . . . . . . 50

4.19 Induced voltage on pipeline during normal operation (bituminous coating). . 52

4.20 Induced voltage on pipeline during normal operation (polyethylene coating). 52

4.21 Effect of soil resistivity on induced voltage on pipeline having bituminous

coating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.22 Effect of soil resistivity on induced voltage on pipeline having polyethylene

coating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.23 Induced voltage on pipeline during fault at one extremity of the zone of in-

fluence (bituminous coating). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.24 Induced voltage on pipeline during fault at one extremity of the zone of in-

fluence (polyethylene coating). . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.25 Fault inside the zone of influence. . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.26 Induced voltage on the pipeline for a fault inside zone of influence (bituminous

coating). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

List of Figures xi

4.27 Induced voltage on pipeline for a fault inside the zone of influence (polyethy-

lene coating). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.28 Effect of earthing resistance on induced voltage on pipeline having polyethy-

lene coating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

List of Tables

1.1 Currents likely to produce ventricular fibrillation . . . . . . . . . . . . . . . . 7

4.1 Conductor surface gradients for double circuit vertical configurations, VLL =

275 kV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2 Conductor surface gradients for double circuit delta configurations, VLL =

275 kV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

xii

Chapter 1

Introduction

1.1 Description of Problem

In the recent years, there has been a trend to run metallic pipelines and electric power lines

parallel to each other in a relatively narrow strip of land. This trend is mainly due to the

numerous restraints imposed by private and governmental agencies concerning the routing and

the environmental impact the construction of such facilities have on a given area.

In addition, the tendency of government regulatory agencies to restrict or deny public utilities

access to new right-of-way and the several court rulings to that effect are establishing what has

been described as the “principle of non-proliferation” of utility corridors. Thus, the proximity

of electric power lines and metallic pipelines have become more and more frequent. Due to this

sharing of the right-of-way, electric power line field may induce voltages on the metallic pipelines

running in close vicinity to the HV transmission lines leading to serious adverse effects. These are

becoming more and more of a concern, particularly in view of the increased fault current for which

the newer electric networks are being designed and commissioned. Typical electric and magnetic

field of a HV transmission line, which are the sources of induced voltages, are shown in fig. 1.1.

Generally speaking, the electric and magnetic fields created by a transmission line cause induced

charges and currents in neighboring metallic objects. At the same time, under certain conditions,

an individual that comes in contact with the metallic object near a transmission line can suffer

electric shock.

The electrical influence depends on the electrical characteristics and the geometry of the indi-

vidual system. The severity of the effect is directly related to the electrically continuous length

of the pipeline that runs parallel to the power line and how well the pipeline is insulated from

1

1.1. Description of Problem 2

Figure 1.1: Electric and magnetic field produced by transmission line.

ground. Possible hazards due to the sharing of Rights-of-Way are:

1. Risk of electric shock to working personnel making contact with the pipeline.

2. Risk of damage to the pipeline coating and to the metal.

3. Risks of damage to the flange used to insulate different sections of pipeline.

4. Risks of damage to the equipment connected to the pipeline.

5. Threat to integrity of the pipeline.

Voltage can be induced on a pipeline from overhead power lines in close proximity by the

following ways:

1. Capacitive Coupling

2. Inductive Coupling and

3. Conductive Coupling

These coupling processes are described in the following sections.

1.2. Capacitive Coupling 3

Figure 1.2: Capacitive coupling

1.2 Capacitive Coupling

The capacitive coupling results from the electric field of the high voltage transmission line and

it induces electric charges in the neighboring metallic pipelines. This is a form of capacitive

coupling operating across the capacitance between the AC transmission lines and the pipeline, in

series with the capacitance between the pipeline and the adjacent earth as shown in figure 1.2.

Such a potential is not normally induced on a buried pipeline since the capacitance between the

pipeline and earth is negligible, even when dielectric bonded coatings are used. However, during

installation, a voltage can be produced by the influence of a strong electrical field on an insulated

pipe when being lifted up from the ground and carried around using a crane.

In some cases, the voltage can be above the maximum safe voltage limit for a pipe. However,

in normal situations, contacting the pipe will only result in a slight electrical shock and the pipe

voltage is immediately reduced to zero.

1.2.1 Capacitive Coupling Mechanism

Parameters that affect the capacitive coupling are given below.

• Capacitive influence varies with the transmission line voltage. Higher the voltage level of

1.3. Inductive Coupling 4

transmission line, higher will be the capacitive coupling.

• The capacitive influence decreases with increase in lateral distance between the transmission

line and the pipeline.

• For transmission lines having more than one circuit, the phase arrangement of circuits has

an important influence.

1.3 Inductive Coupling

The inductive effect is, perhaps, the most important of all the three couplings. The inductive

interference is the result of the magnetic field (see fig. 1.3) generated by the power line. Aerial

and underground pipelines that run parallel to or in close proximity to transmission lines or

cables are subjected to induced voltages caused by the time-varying magnetic fields produced by

the transmission line currents. In case of a three phase system, if all the three phase wires are at

equal distances from the axis of the pipeline, voltage induced on the pipeline will be zero. However,

this case is seldom met, as most of the time, the asymmetry between the three phase conductors

and the pipeline causes the induction of non-zero voltage in the pipeline. The inductive influence

problem is severest in the case of faults. The induced electromotive forces (EMF) cause currents

circulation on the pipeline and voltages between the pipeline and the surrounding earth.

In the normal operating conditions, the balance of the three phase currents causes no substan-

tial effect. In this case, voltage induced is low, due to the geometrical asymmetry of the pipeline

from powerline. However under faulted conditions, high voltages and currents may be induced in

the nearby pipeline, which may result in shock hazards to people or working personnel touching

the pipeline or other metallic structures connected to it.

1.3.1 Effects of Inductive Coupling

Inductive coupling may pose threat to the security of people working in the vicinity of pipeline

running in proximity of the transmission line. When induced voltage under steady state exceeds

50-65 V, then it becomes necessary to take safety measures. During fault to earth, higher voltages

are admissible, due to the short duration of the fault and low probability that somebody will touch

the pipeline during fault.

1.4. Conductive Coupling 5

Figure 1.3: Inductive coupling

In addition, during fault, induced voltage may become more than the withstand capacity of

insulating flange and can damage the insulating flange.

Equipments (especially cathodic protection facility) connected to the pipeline can also be damaged

during a faulted condition. In addition, there is a high risk of damage to the pipeline coating during

fault.

1.4 Conductive Coupling

When a ground fault occurs in an installation (substation, power plant, tower etc.) the current

flowing through the earthing electrode produces a potential rise of the electrode and the neigh-

boring soil with respect to a remote earth.

Conductive coupling occurs between the electrical installation and a nearby pipeline if the pipeline

is directly connected to the ground electrode of the HV system (i.e. inside a power station) or if

the pipeline enters the “Zone of influence” of electrical installation. A high difference of potential

can then appear across the coating of the pipeline due to the local earth potential rise.

In practice, conductive coupling most often results from the second case.


Figure 1.4: Conductive coupling

1.4.1 Conductive Coupling Mechanisms

Pipeline Entering the Zone of Influence

If a pipeline is not influenced by capacitive or inductive coupling, its normal potential can be

assumed to remain very close to the reference potential of the remote earth. Therefore, any Earth

Potential Rise (EPR) at the pipeline location due to fault in a nearby electrical installation is

applied directly to the insulating coating of the pipeline. Problems may appear when the EPR

exceeds the dielectric strength of the coating. In such cases, permanent, but usually very local,

puncturing of the pipeline coating can occur. Melting of the pipeline steel may even occur when

the pipeline is very close to a tower earth electrode.

A fraction of the EPR is then applied to the metallic pipeline (see fig. 1.4). This potential can

be transferred by the pipeline to a remote point such as an insulating flange, pipeline access

point, or cathodic protection system. Depending upon its amplitude, the transferred potential

may generate dielectric stresses at insulating flanges in cathodic protection systems. It may also

create touch and step voltages which may be applied to workers touching the pipeline at access


Table 1.1: Currents likely to produce ventricular fibrillation

Current (mA)Shock Duration (s) Probability of Fibrilation

0.5% 5%0.1 550 7500.2 440 6000.35 300 4000.5 110 2001 60 70

points or standing nearby such points.

Pipelines Bonded to the Earth Electrode

A similar situation appears when a pipeline section is directly bonded to the earth electrode of a

power station(i.e. inside an oil fired power station) or inside the zone of influence of an electrical

installation. When an earth fault in the power network causes a rise of potential of the station

grounding grid, this potential is transferred to the pipeline. Thus, touch voltages (between the

pipeline and the earth) can appear within and outside the station. If safety precautions are not

taken, such voltages might represent a risk for workers (in the station) and for the public (outside

the station). In addition, the ground potential rise of the station is transmitted along the pipeline

and, before decreasing to a safe value, can be applied to the nearest insulating flange.

1.4.2 Effects of Conductive Coupling

Danger to Working Personnel

When a high difference of potential appears between the pipeline and the local earth, workers

touching the pipeline may get a shock. That may cause death and/or ventricular fibrillation.

Currents likely to produce ventricular fibrillation are given in Table 1.1.

Damage to Pipeline

A high-intensity current passing through a small-size coating puncture would heat up the pipeline

steel and, in theory, could make it melt. It can happen only if the pipeline is very close to a

1.5. Mitigation Techniques 8

HV tower footing (or substation grounding grid) that an electric arc appears in the soil and, by

establishing a very low resistance path between the electrode and the pipeline, makes it possible

for a large current to flow directly into the pipeline.

Risk of Damage to Coating

Potential difference between the metallic pipeline and the neighboring soil appears across the

insulating coating. It is shown [1] that glow and arc discharges occur on the whole surface area

of bitumen coated pipelines for relatively low voltages(1000 - 1200 V). During such phenomena,

coating becomes more conductive. Damage to polyethylene coatings will be usually more localized.

Damage to Cathodic Protection Systems

High voltages resulting from transferred potential may damage active cathodic protection system

if proper protection mechanism is not there.

1.5 Mitigation Techniques

Some safety measures, to be taken to keep the induced voltage within safe limits, are given below.

1.5.1 Pipeline Powerline Separation

Moving pipeline line away from the center of the right-of-way reduces the effect of capacitive,

inductive and conductive coupling. Increasing separation is especially effective in case of conduc-

tive coupling. It is not preferred for mitigating the effects of capacitive coupling because pipeline

earthing measures are easy and cost-effective.

1.5.2 Measures Applied to Transmission Line

Earth Wire

Earth wires helps in reducing the ground potential rise in the vicinity of towers and the voltage

due to inductive coupling during earth fault.

1.5. Mitigation Techniques 9

Transposition

Changing the phase sequence of transmission line conductors at regular intervals helps in reducing

the voltage induced on aerial pipelines. Transposition is least effective for underground pipelines.

For double circuit configurations, selecting suitable phase sequence for both the circuits also help

in reducing the influence of capacitive and inductive coupling remarkably.

1.5.3 Measures Applied to Pipelines

Connecting Pipeline to Earth

A very common method, to reduce the induced voltages due to capacitive and inductive coupling,

is to connect the pipeline to the earth. This method works well for capacitive coupling, but to get

effective mitigation for inductive influences, several low resistances at strategic locations (usually

potential peaks) should be connected to the earth. The pipeline must never be connected to the

earthing of a tower [2]. Effective mitigation may be obtained by grounding of the pipeline near

voltage maxima if the grounding impedance is significantly less than the pipeline characteristic

impedance [3].

Insulating Flanges

Insulating flanges are used to subdivide the pipeline into sections inside a long zone of influence

and reduce the inductive influence. It should be placed at regular intervals shorter than the

characteristic impedance of the pipeline.

Insulating Coating

Pipeline insulating coating can be improved to avoid the effect of conductive influence in the

vicinity of a tower. It is done by either increasing the coating thickness or using coating material

having higher resistivity.

Parallel Mitigation Wires

The current that is induced in a bare conductor laid along a pipeline in the whole zone of influence

produces in the pipeline an e.m.f. that partially compensates the e.m.f. produced by the H.V.

1.6. Thesis Outline 10

line. Reduction by a factor 2 is possible with a copper conductor having a cross section of about

50 mm2 [2].

1.6 Thesis Outline

The next chapter gives a brief overview of the literature pertaining to the coupling of power line

fields with the metallic pipeline running in close vicinity.

Chapter 3 gives the theory used for calculating the electric field, the magnetic field and the

conductor surface gradient. Charge simulation method used to calculate the voltage induced

on the pipeline due to capacitive coupling and method used to compute voltage induced on the

pipeline due to inductive coupling has also been explained.

Chapter 4 presents the results and analysis. Various results have been discussed and anal-

ysed to demonstrate the effect of capacitive and inductive coupling on the pipeline. Optimum

configuration has also been suggested using the various computational results.

Last chapter gives the important and useful conclusion drawn from the present study.

Chapter 2

Review of the Previous Work

2.1 Literature Survey

This chapter gives a summary of the previous work done by researchers on the influence of high

voltage AC power line fields on metallic pipelines.

The widely known Carson’s formulae [4] were the basis for the initial attempts to study this

type of interference. The classic papers by Carson and Pollaczek [5] delineate the basic theory of

inductive coupling between parallel conductors in the presence of a half space conductive medium

(earth). Later, Sunde [6] expanded Carson’s and Pollaczek’s work to include layered earth and

conductors near point sources of current.

Later on, J.Pohl [1] came out with the electrical characteristics of the pipelines. Investigations

on determining the earthing resistance of a pipeline surface coated bitumen are described. He

reported that the earthing resistance reduces drastically with increasing voltage. It is also shown

that glow and arc discharges occur on the whole surface area of bitumen coated pipelines for

relatively low voltages(1000 - 1200 V).

Favez et. al. [7] have studied the use of buried mitigation wires using electrical models. Authors

suggested that bonding the mitigation wire to the pipeline via spark gaps provides increased

efficiency in the mitigation.

Allen Taflove and John Dabkowski [8] have predicted the induced voltages on gas transmission

pipelines by a 60 Hz AC power transmission line sharing a joint right-of-way using electrical

transmission line theory. The same authors have also presented field tests on a buried, 34-inch

diameter gas pipeline adjacent to a 525 kV AC power transmission line for 54 miles [9]. Comparison

is made between measured inductive coupling and predictions obtained using the theory developed

11

2.1. Literature Survey 12

by them earlier and presented in [8].

Later on, Taflove and Dabkowski, had come out with some very useful mitigation techniques for

reducing the induced voltage. In one of these papers [10], they describe how a joint pipeline/power

line corridor can be designed to minimize inductive coupling and a second paper authored by

them [11] describes how pipeline grounding methods can be implemented to reduce pipeline voltage

peaks after installation of the utilities on the joint right-of-way.

The problem of induced voltage on buried irrigation pipeline was first examined by Jaffa

and Stewart [12], who used the theory reported in the EPRI report [3] to the specific case of a

buried irrigation pipeline running parallel to a distribution circuit. Authors, also conducted field

measurements that showed that under unbalanced operating conditions, dangerous voltages may

be observed at one end of the pipeline. The case of unbalanced loading may be more dangerous

than a single phase-to-earth fault case, in spite of the lower voltages observed, as it may go

unnoticed even for some days.

Frazier et. al. [13] have presented the results of a study of a utility common corridor in southern

Arizona. A detailed analysis of voltage and currents induced into the pipeline and rail facilities

was performed using the computer program developed during the study.

Dawalibi et. al. [14] have described the computerized analysis which was conducted to ensure

personnel safety and pipeline integrity during power system faults occurring near the Trans Quebec

and Maritimes gas pipeline. In this paper engineering studies were conducted based on methods

reported in the EPRI report [3] to determine the location and magnitude of induced AC voltage

peaks. The maximum coating stress voltage reported, which occurs during fault, is in the order

of 2500 volts.

P. Kouteynikoff [15] presented an international survey, which compared the different national

regulations governing exposure between metal pipelines and HV power structures (overhead or

underground lines, substations etc.). The survey underlined the fact that not all countries attach

equal importance to this type of exposure. Twelve countries reported official rules or “rules of

good practice”.

Jacquet et. al. [16] presented the possible effects of earth potential rise of towers during faults

as well as corrosion problems that may be caused by induced voltage resulting from the normal

operation of high voltage transmission lines.

Brandes et. al. [17] in their paper have examined how steel pipes and their corrosion protection


are affected by the interference from electrical system.

Dawalibi and Southey [18] developed a computational tool software package, ECCAPP (Elec-

tromagnetic and Conductive Coupling Analysis from Powerlines to Pipelines), which resulted from

the EPRI/A.G.A. research program [19]. This paper discusses the fundamental concepts and theo-

ries which are required to predict these coupling effects accurately. The method presented is quite

comprehensive, because it can solve all possible cases of inductive as well as conductive coupling

to multiple buried pipelines. However, the number of segments required to model the pipeline is

usually very large and that imposes unnecessary burden on the computational resources. That

becomes more apparent, and even prohibitive, if that approach is used for transient analysis.

Dawalibi and Southey have presented [20] a set of design curves which illustrate the effects of

various parameters upon conductive and inductive interactions between transmission lines and

pipelines. The parametric analysis indicates that buried mitigation wires can be very effective,

resulting in up to 65% reductions in peak pipeline potentials during fault. Effects on interference

levels due to various factors and effectiveness of certain mitigation have also been discussed.

Jacquet and Kouteynikoff published a report [21], which examined the problems of the influence

of electrical lines on metal pipelines. It also gives different possible mitigation techniques.

Sanz et. al. [22] have presented a summary of the results of the study conducted by a binational

task force on induced effects on metallic structures close to overhead transmission lines.

In a paper by Sobral et. al. [23] it has been shown that the calculation of the interferences

affecting a single communication circuit or a single pipeline, caused by a short - circuit occurring

along a single nearby transmission line can be greatly simplified using the Decoupled Method

[24, 25]. It is also shown that this method allows the representation of both the magnetic and

the resistive couplings existing between the transmission lines and the communication circuit or

pipeline.

Southey et al. [2] presented a new mitigation design approach, which not only reduces AC

voltages effectively and economically, but also provides cathodic protection for the protected

pipeline.

Abdel-Salam et al. [26] developed a method based on Charge Simulation Method (CSM) for

calculating the induced voltages on fence wires/pipelines underneath AC power transmission lines.

The calculated induced voltages compare favorably with those measured experimentally.

Based on computer simulations performed using the software described in References [18,20,27],


as a part of a several major AC interference studies, the performance of a new highly effective

AC interference mitigation method has been demonstrated by Southey et al. [28]. This method,

which combines the effectiveness of grounding conductors and gradient control wires, mitigates

both inductive and conductive interference and provides cathodic protection as well. It has been

shown that the proposed mitigation effectively reduces pipeline potentials with respect to remote

earth to levels below 70 volts throughout the right-of-way and below 44 volts along approximately

98% of the right-of-way, due to the grounding afforded by the gradient control wires.

CIGRE working group 36.02 based on the available literature published a general guide [29]

on the influence of high voltage AC power systems on metallic pipelines.

Yang and Xu [30] studied the change of the magnetic field produced by buried cables, due to

an additional steel pipe nearby. A Fourier series technique was used to calculate the magnetic

field. An iterative procedure is employed to handle the non-linear characteristics of the steel pipe

and to determine the varying permeability in it.

Satsios et al. [31] investigated the two dimensional, quasi stationary, electromagnetic field of a

faulted power transmission line in the presence of a buried pipeline, of mitigation wires and of a

multi-layer ground. The related diffusion equation has been numerically solved by using the Finite

Element Method (FEM). Using FEM results and Faraday’s law, magnetic vector potential, as well

as the voltages induced across the buried pipeline and remote earth, are calculated. Parametric

analysis has shown that there is a significant influence of the depth and resistivity of the first

ground layer, of the resistivities of the different ground layers and of the configuration of mitigation

wires on the electromagnetic field and on the voltages induced across the buried pipeline and

remote earth.

Djogo and Salama [32] proposed a method for calculation of currents and voltages in the system

of parallel pipelines and buried conductors. The method is based on the lossy transmission line

model for buried conductors and the previous methods based on the same approach were modified

by abandoning the Thevenin circuit representation of pipeline sections and by deriving a 4-pole

equivalent π circuit of a pipeline section. A generalized matrix 4-pole equivalent circuit is derived

for a system of parallel buried conductors as well, by using the modal method. A general case of

buried conductors not parallel to the power line is also derived.

Satsios et al. [33] addressed the influence of nonhomogeneous earth on the electromagnetic

field and on the eddy currents induced in all conductive parts, i.e. in overhead ground wires,


mitigation wires, buried pipeline and earth layers. The electromagnetic field diffusion equation

has been numerically solved, using finite element method (FEM). Using FEM results, magnetic

vector potential distribution in the cross-section of the parallel exposure, as well as eddy currents

induced in all conductive parts, are calculated for various nonhomogeneous earth models.

Richard W. Bonds from the ductile iron pipeline research association presented a technical

report [34], which gives some basic theory about the effect of overhead ac power lines paralleling

ductile iron pipelines.

Dawalibi et. al. [35] and Y. Li et. al. [36] in their work examined the mechanism of electro-

magnetic interference caused by a power system substation, including a portion of its incoming

and outgoing transmission lines on a neighboring pipeline. Two approaches, a circuit approach

and field approach, are used to carry out the study. The maximum difference between the two

approaches is less than 15% for the cases studied which involve a parallel pipeline exposure.

Dawalibi et. al. [37] discussed the levels of the touch and step voltages for a few typical right-

of-way system under loaded and faulted conditions. The effects of a typical mitigation system on

the inductive interference levels are also studied.

Christoforidis et. al. [38] presented an improved hybrid method, employing finite-element

method along with Faraday′s law and standard circuit analysis, in order to predict the induced

voltages and currents on a pipeline with defects on its coating, running parallel to a faulted line

and remote earth.

Collet et. al. [39] have shown how observations (1993-1999) and experiments carried out on

site and in the laboratory(1993-1996) have made it possible to define certain relevent parameters

concerning AC corrosion risks. These are from the evaluation and prevention of AC corrosion

risks as practised by Gaz de France. This article presents, in summary form, the measurements

taken into account in the evaluation of AC corrosion risks. They are given with due recognition

to the limits of current knowledge of the phenomena in question.

Southey et. al. [40] had addressed the question of estimating mitigation requirements for

pipelines installed in the high voltage AC corridors. Later in 2003 [41] more difficult problem of

estimating what mitigation is required to maintain pipeline coating stress voltage within acceptable

limits during fault conditions on power systems has been addressed.

Kouloumbi et. al. [42] checked the effectiveness of cathodic protection through in situ long

term monitoring and analysis of pipeline electrical parameters. The results gave an insight into


the cathodic protection system operation, caused by AC interference.

Shwehdi et. al. [43] presented the essential procedures, guidelines, needed data and cautions

for the pipeline running parallel to HV transmission line. The results of a case study of a 380

kV transmission line in the eastern region of Saudi Arabia have been discussed. A mathematical

model is given for the computation of the electrostatic effect of the power line on the pipelines.

Two indexes are used to assess this effect: the maximum electrostatic field and the electric charge

per unit length of the pipe. The impact of the pipeline on the potential and field distributions

around the power line is also discussed. For a 750-kV, three-phase power line, and a pipeline of a

radius 0.5 m, it is seen that the electric field on the pipe can reach 0.175 kV/cm, for a horizontal

separation of about 16 m between them. Both the field and the charge on the pipe will decrease

to almost zero if the pipeline is 100 m from the power line.

Elhirbawy et. al. have presented a paper [44] whose objectives were to undertake a scheme

based on the Finite Difference Method (FDM) for the calculation and analysis of the electromag-

netic fields established by currents in power transmission lines, particularly by those in single-

phase-to-earth fault condition. This paper introduces a physical example for evaluation of the

electromagnetic field coupling between a power transmission line and a pipeline buried in the

body of the earth. This work focuses on developing FDM procedures to solve for the electromag-

netic field derived from Maxwell’s equations applicable to the region in the air, on the earth plane,

and in the body of the earth.

In 2003, Christoforidis [45] discussed a hybrid method employing finite element calculations

along with Faradays law and standard circuit analysis. The method is used in order to calculate the

induced voltages and currents on a pipeline with defects, running in parallel to a faulted line and

remote earth. Non-parallel exposures are converted to parallel ones and dealt with similarly. The

defects are modeled as resistances, called leakage resistances. The fault is assumed to be outside

the zone of influence as well as a single line to ground one such that conductive interference is

negligible. A sample case is analyzed and discussed. The results show that although the pipeline

defects act in a way as to reduce the levels of induced voltages and currents, large currents can

flow to earth through the defects that may damage the pipeline.

Christoforidis et. al. [46] investigated the inductive interference between power lines and

parallel buried irrigation pipelines, using a hybrid method [38,50] employing finite element formu-

lation and circuit analysis. In this work, a case of power line irrigation pipeline geometry, taken


from [12], is analyzed under unbalanced conditions. Moreover, another case of a distribution power

line, which is commonly encountered in the Greek network, interfering with a buried irrigation

pipeline is examined by performing various parametric analysis.

Shwehdi [47] presented complete case study of a 230 KV transmission line EMI effect on a

buried oil pipeline.

Mohamed M. Saied [48] pointed out the problem of the mutual capacitive coupling between

EHV power lines and nearby pipelines sharing the same corridor.

Hyun-Goo Lee et. al. [49] analyzed the induced voltage on the buried gas pipelines using nodal

network analysis. The induced voltage on the 71.3 km long gas pipeline running parallel to the

22.9 kV power line is analyzed, and the maximum induced voltage is 4.78 V at the starting point

of the longest parallel segment.

Christoforidis et. al. [50] has discussed a new hybrid method employing finite element calcu-

lations and standard circuit analysis that may be used in order to calculate the induced voltages

and currents on a pipeline running parallel to a faulted line. Nonparallel exposures are converted

to parallel ones and dealt with similarly.

In the same year, Christoforidis et al. published another paper [51]. In this study, the influence of

a soil structure composed of layers with different resistivities, both horizontally and vertically, on

the inductive part of this interference is investigated. The method used to determine the inductive

interference comprises finite-element calculations and standard circuit analysis. The results show

that good knowledge of the soil structure is necessary in order to estimate the above interference

with minimum error.

Al-Alawi et. al. [52] presented a technique based on the development of an artificial neural

network (ANN) model for predicting the electromagnetic interference effects on gas pipelines

shared right-of-way (ROW) with high voltage transmission lines. It had been demonstrated that

the ANN-based model developed can predict the induced voltage with high accuracy. The accuracy

of the predicted induced voltage is very important for designing mitigation systems that will

increase overall pipeline integrity and make the pipeline and equipments connected to pipeline

safe for operating personnel.

CIGRE/CIRED Joint Working group C4.2.02 [53], provided background information regarding

the AC corrosion phenomenon with reference to important parameters and conditions. It has been

mentioned that, the AC voltage between the pipeline and a reference electrode placed above the

2.2. Scope of the Thesis 18

pipeline should not exceed:

1) 10 Vrms if soil resistivity is higher than 25 ohm-m.

2) 4 Vrms if soil resistivity is equal to or lower than 25 ohm-m.

at any point of the pipeline under normal operating conditions of AC power system.

Bortels et. al. [54] presented a recently developed simulation software tool for predictive

and mitigation techniques for pipeline networks influenced by high-voltage (HV) power lines. The

software can deal with any configuration (no limitation on the number of pipes, transmission lines,

bonds, groundings, coating, and soil resistivity) and is very user friendly and robust since a general

applicable algorithm is used to calculate the induced electromagnetic force (EMF), eliminating

the need for a subdivision of the pipelines in sections parallel or not to the transmission line(s).

With the calculated values for the EMF, the induced voltages and currents are then obtained by

solving the well-known transmissionline model using a numerical technique that allows to specify

the pipeline parameters (diameter, coating, soil resistivity, etc.) for each individual section of the

pipeline.

2.2 Scope of the Thesis

It is evident from the literature survey that due to the sharing of the right of way, electric power line

field may induce voltages on the metallic pipelines running in close vicinity to the HV transmission

lines leading to serious adverse effects. Thus in the present work, computational techniques have

been developed to estimate the induced voltages due to both capacitive and inductive coupling

on metallic pipelines running in close vicinity of high voltage power transmission lines. This work

attempts to suggest an optimum configuration giving the lowest field under the power line as well

as the lowest conductor surface gradient and for this configuration induced voltage on the pipeline

has been computed.

It is also seen from the literature survey that there is a lack of comprehensive study on the

effect of various parameters such as earth resistivity, pipeline coating resistivity etc. on the induced

voltages on pipeline. So this work is also an attempt to provide precise knowledge about the effect

of aforementioned parameters on induced voltages on pipeline.

The next chapter discusses the various computational methods used in the present work.

Chapter 3

Computational Methods

3.1 Introduction

The present thesis aims at computing the induced voltages due to capacitive and inductive coupling

on metallic pipelines running in close vicinity of high voltage power transmission lines. Before

computing the induced voltages, an optimum configuration of the phase conductors based on the

lowest conductor surface gradient as well as field under transmission line needs to be arrived at.

Before installing the pipeline, one has to consider the following so as to arrive at a suitable location

of the pipeline based on the optimum phase configuration of the transmission line giving the lowest

field at the ground.

1. Fields under the transmission line for various phase configurations so that the configuration

giving the lowest field at the ground could be arrived at.

2. Field profile in the right-of-way so that the pipeline could be located suitably in the lower

field region.

3. Conductor surface gradient for different phase configurations so that one can ascertain that

the chosen configuration also gives the lower conductor surface gradient such that the Elec-

tromagnetic Interference (EMI) or the Radio Interference(RI) performance of the power line

is within acceptable limits.

These have been studied for various single and double circuit HV power transmission lines and

finally for the optimum configuration as well the various other configurations considered, induced

voltages on the pipeline have been computed.

19

3.2. Fields Under Transmission Line 20

Figure 3.1: Two of the phase conductors with their images

The following section discusses the methodology of computation of the fields under transmission

line as well as the conductor surface gradient.

3.2 Fields Under Transmission Line

3.2.1 Electrostatic Field

For the calculation of the field under the power line, phase conductors are considered as infinite

line charges. To determine the electric field under transmission line, Maxwell’s potential coefficient

matrix ‘[P ]’ is calculated based on the coordinates of the phase conductors and the ground wires,

using equations (3.1) and (3.2) given below. The distances between the phase conductors and

their images are shown in fig. 3.1. Elements of Maxwell’s potential coefficient matrix ‘[P ]’ are,

Pii = ln

(2Hi

req

)(3.1)


Pij = Pji = ln

(Ii,j

Aij

), i 6= j (3.2)

Where,

H i is the height of ith conductor above ground

I ij is the distance between ith conductor and image of jth conductor

Aij is the distance between ith and jth conductor

req = R(N.r/N)1/N (3.3)

req is the equivalent radius of the conductor bundle.

Where,

r is the radius of the sub-conductor in the bundle

R is the bundle Radius or the radius of the pitch circle on which the sub-conductors of the bundle

are located

N is the number of sub-conductors in a bundle

Further, the inverse of Maxwell’s potential coefficient matrix is pre-multiplied with column

vector ‘[V ]’ as shown in equation (3.4), where column vector ‘[V ]’ contains line to ground voltages

of all the phase conductors and the ground wires. This gives the line charge densities, ‘[Q ]’ of the

phase conductors as well as the ground wires.

[Q] = [P ]−1[V ] (3.4)

Then the horizontal and vertical components of the field due to the three phase conductors at

the desired locations are calculated separately using equation (3.5) and (3.6) given below [56].

Fig. 3.2 shows the component of the electric field at the observation point A(x,y) due to one

phase conductor and its image. The horizontal component of the electric field Ehi of the ith phase

conductor is given by the following equation.

Ehi =

(qi

2πεor

)(x− xi)

[1

D2i

− 1

D′2i

](3.5)


Figure 3.2: Components of electrostatic field due to HV line

Similarly, vertical component of the electric field Evi is as follows.

Evi =

(qi

2πεor

)[(y − yi)

D2i

− (y + yi)

D′2i

](3.6)

Resultant of the horizontal and vertical components of the field gives the total electric field at

the desired locations as shown in eqn. 3.7.

Etn =(E2

hn + E2vn

)1/2(3.7)

Where,

Ehn =n∑

i=1

Ehi and Evn =n∑

i=1

Evi

In order to know which configuration gives the lowest field under the transmission line, electric

fields at one meter height above the ground for various configurations have been calculated using

the above equations.


Figure 3.3: Transmission line conductor with its image

Conductor Surface Gradient

Conductor surface gradients [55–57] have been computed for the various conductor configurations

so that one can ascertain that the chosen configuration gives the lowest conductor surface gradient

such that the Electromagnetic Interference (EMI) or the Radio Interference (RI) performance of

the power line is within acceptable limits. Using equation (3.8), conductor surface gradient for

an N- conductor bundle is calculated. Effect of earth has been taken in to account by considering

the image of phase conductors and the ground wires.

Es =q

2πεor

[1 +

(N − 1)r

R

](3.8)

Elements of the column vector ‘[Q ]’ in equation (3.4) give line charge density of phase conduc-

tor/ground wire. The charge on each sub conductor ‘q ’ is obtained by dividing line charge density

of the phase conductor by the number of sub-conductors in the bundle.

3.2.2 Magnetic Field

The components of magnetic flux density due to a overhead conductor at (hn,dn) which carries a

phase current In (see fig. 3.3) are given in eqn.(3.9) and eqn.(3.10) [58].


Bxn = −2× 10−3In

[(y − dn)

r2cn

− (y + dn + α)

r2in

]Gauss (3.9)

Byn = 2× 10−3In

[(x− hn)

r2cn

− (x− hn)

r2in

]Gauss (3.10)

Where,

rcn =((x− hn)2 + (y − dn)2

)1/2

rin =((x− hn)2 + (y + dn + α)2

)1/2

α =√

2δe−jπ/4, δ = 503 (ρg/f)1/2

ρg = Earth resistivity, f = Frequency, δ = Skin depth of the earth

Equations (3.9), (3.10) are valid as long as the distance from the field point to the conductor

is smaller than λ/20 where λ is the free space wavelength (λ = 3 × 108/f meters). In addition,

they are valid for field points above or near the earth’s surface.

Powerlines generally consists of several phase conductors and shield wires. By superposition, the

magnetic field of a transmission line can be written by adding the field components given by

eqn.(3.9) and (3.10) for each conductor. The resultant field for N conductors are:

Bx =N∑

n=1

Bxn (3.11)

By =N∑

n=1

Byn (3.12)

3.3. Capacitive Coupling Calculation 25

Figure 3.4: Discrete line charges used in the CSM. Cross-section of the conductor andpipeline are not to scale.

3.3 Capacitive Coupling Calculation

Charge Simulation Method (CSM) [26, 59] has been used for the computation of the induced

voltage, due to capacitive coupling, on a metallic pipeline running below the transmission line.

The metallic pipeline is assumed to be at a height of 1 meter above the ground. To simulate the

surface charge on the phase conductors and the pipeline, they are modeled as infinite line charges.

Each transmission line phase conductor is modeled by four infinite line charges kept slightly inside

the periphery of the conductor/wire. Pipeline is modeled by sixteen infinite line charges also kept

slightly inside the periphery of the pipeline as shown in fig. 3.4. Images of the simulation charges

are also considered with respect to the ground plane in this study. The potential φ at any point

P(xp, yp) due to the simulation charge ‘q ’ located at (xj, yj) is calculated using equation (3.13)

given below.

φ =qi

2πεorln

(√(xp − xj)2 + (yp + yj)2

√(xp − xj)2 + (yp − yj)2

)(3.13)

Potentials have been computed at various boundary points which are located at the periphery

of the phase conductors, ground wires and the pipeline. Dirichlet boundary condition is applied

at the surface of the phase conductors. Potential applied is VLG at phase A, −VLG/2 at phase B

and phase C, where VLG is the line to ground system voltage. The second boundary condition

3.4. Inductive Coupling Calculation 26

Figure 3.5: Representation of the circuit formed by the pipeline and the earth.

dictates that sum of the charges simulating the pipeline is equal to zero.

With the help of the boundary conditions mentioned above and the known potentials, as many

linearly independent equations as the number of unknown line charges (used for simulation) have

been obtained. Solving these equations, charge densities of the line charges can be obtained.

Further, using the line charge densities thus computed, induced voltage on the pipeline can be

arrived at.

For various transmission line configurations, induced voltages on the pipeline located at differ-

ent distances from the mid point of the line have been calculated using CSM. Results are discussed

in the next chapter.

3.4 Inductive Coupling Calculation

For calculating the induced voltage due to inductive coupling, first Electro Motive Force (EMF),

induced along the pipeline due to the magnetic field created by the transmission line is calculated

and then potential difference between the pipeline and the earth, due to these induced EMF’s, is

calculated.

There is a clear difference between induced EMF’s and voltage appearing on the pipeline. EMF’s

are distributed voltage source inside the pipeline/earth circuit because of inductive coupling.

These EMF’s produce voltages on the pipeline, and only those voltages U represent the actual

stresses on pipeline and its equipment (see fig. 3.5).


0 2000 4000 6000 8000 10000 12000−2500

−2000

−1500

−1000

−500

0

500

1000

1500

2000

Zone of Influence (m)

Rig

ht of w

ay

(m)

Pipeline

HV Line

Approach

Parallelism

Crossing

Removal

Figure 3.6: Zone of influence.

As the zones of influence are generally formed by parallelism, approaches, crossings as well as

removals (shown in fig. 3.6), the computation involves subdividing the zone into several sections

corresponding to these zones. The calculation of voltages is carried out at both the ends of the

sections. Each section is represented by an equivalent π electrical network, which is influenced by

the induced EMF.

The induced EMF is calculated, using eqn.(3.14) during a fault and eqn.(3.15) in steady state

condition, with the following representations [21].

dik = distance in meter between conductor i and k

i = 1, 2, 3 for the phase conductor, 4 for earth wire, x for the pipeline

ρ = soil resistivity in Ωm

L = length of the section in meter

kg = reduction factor of the earth wire

ri = radius of the ith conductor in meter

Ri = resistance per unit length of the ith conductor in Ω/m

Rg = resistance per unit length of earth wire


µr = relative permeability of the steel

εr = relative permittivity of the insulating covering of the pipeline

e = thickness of the insulating covering of the pipeline in meter

Ru = specific coating resistance

Id = fault current

Ir = balanced current in steady state

p = parameter equal to 658√

ρ/f

ωMii = reactance per unit length in Ω/m of the circuit i (conductor i/earth)

ωMik = mutual reactance per unit length in Ω/m between the circuits i (conductor i/earth) and

k (conductor k/earth)

ed = jω.M1x.L.Id.kg = j1.25× 10−6.f.L.Id.kg. ln(p/d1x) (3.14)

er = j1.25× 10−6.f.L.Ir(A− bB), with (3.15)

A = ln(√

d2xd3x/d1x) + j(√

3/2) ln(d3x/d2x)

B = ln(√

d24d34/d14) + j(√

3/2) ln(d34/d24)

b = 1.25× 10−6.f. ln(p/d4x)/(Rg + 1.25× 10−6.f. ln(p/r4))

To solve the equivalent circuit shown in fig. 3.5, pipeline longitudinal impedance and admit-

tance has to be calculated which are given in equations 3.16 and 3.17.

Z ′ = Rx + jωMxx (3.16)

Where, for steel pipeline

Rx ' (0.12√

µrf/rx + 0.98f)× 10−6 Ω/m

ωMxx ' (0.12√

µrf/rx + 1.25f ln(p/rx))× 10−6 Ω/m

Y ′ = G + jωC (3.17)


Where, G = Conductance per unit length and C = Capacitance per unit length between pipeline

and earth.

G ' 2πrx/Ru

C ' 55.6× 10−12εrrx/e

The following sections deals with concerns the calculation of the response of the pipeline-earth

electrical circuit to the induced EMFs for various pipeline-powerline alignments.

3.4.1 Perfect Parallelism Between Powerline and Pipeline

The calculation presented hereafter is based on the following assumptions:

• The pipeline is parallel to the power line

• The leakage admittance of the pipeline is constant

• Soil resistivity along the parallel route is constant

In case of perfect parallelism, pipeline-earth equivalent circuit is drawn as shown in fig.( 3.5).

The equations for this equivalent circuit can be written as follows.

dU

dx= E − IZ ′ (3.18)

dI

dx= −Y ′U (3.19)

Where,

E = EMF induced on the pipeline per unit length

E = jfµ0I

2

[ln

d2xd3x

d21x

+ j√

3 lnd2x

d3x

]V/m (3.20)

From eqn. (3.18) and (3.19),d2U

dx2= γ2U (3.21)


where, γ2 = Z ′Y ′

d2I

dx2− γ2I + Y ′E = 0 (3.22)

On solving the above equations,

U(x) = −Z[Aeγx −Be−γx

](3.23)

I(x) = Aeγx + Be−γx +E

Z ′ (3.24)

where, characteristics impedance Z = Z ′/γ =√

Z ′/Y ′

For x = 0, eqns. 3.23 and 3.24 can be written as

U(0) = −Z [A−B] (3.25)

I(0) = A + B +E

Z ′ (3.26)

Terminating impedance at x = 0 is Z1 (see fig. 3.5).

U(0)

I(0)= −Z1 (3.27)

Putting the value of U(0) and I(0) from eqn. 3.25 and 3.26 in eqn. 3.27,

(Z1 − Z)A + (Z1 + Z)B = −Z1E

Z ′ (3.28)

For x = L, eqns. 3.23 and 3.24 can be written as

U(L) = −Z[AeγL −Be−γL

](3.29)

I(L) = AeγL + Be−γL +E

Z ′ (3.30)

Terminating impedance at x = L is Z2 (see fig. 3.5).

U(L)

I(L)= Z2 (3.31)


Figure 3.7: Voltage along a pipeline extending beyond the zone of influence.

Putting the value of U(L) and I(L) from eqn. 3.29 and 3.30 in eqn. 3.31,

AeγL(Z2 + Z) + Be−γL(Z2 − Z) +Z2E

Z ′ = 0 (3.32)

On solving eqn. 3.28 and 3.32 value of A and B is obtained as given below,

A =E

2Z ′(1 + r1)r2 − (1 + r2)e

γL

e−2γL − r1r2

B =E

2Z ′(1 + r2)r1 − (1 + r1)e

γL

e−2γL − r1r2

eγL

The reflection factors r1 and r2 at the beginning and at the end of the parallel stretch are given

below,

r1,2 =Z1,2 − Z

Z1,2 + Z

Few particular cases are worth examining.

a) The pipeline continues for several kilometers after the end of the parallel routing

with the powerline

For this case (refer to fig.(3.7)),

Z1 = Z2 = Z


Figure 3.8: Voltage along a pipeline when it extends beyond the zone of influence only inone direction.

it gives r1 = r2 = 0

U =E

2γ

[eγ(x−L) − eγx

](3.33)

I =E

Z ′

[1− eγ(x−L) − eγx

2

](3.34)

Highest pipeline potential is at the ends ( x = 0 and x = L)

Umax =E

2γ

[1− eγL

]

At the mid point of parallelism, i.e. at x = L/2, U = 0

b) The pipeline continues at x ≤ 0 and is isolated at x = L with an insulating flange

For this case (refer to fig.(3.8)),

Z1 = Z, Z2 = ∞it gives r1 = 0, r2 = 1

U =E

2γ

[eγx

(2e−γL − e−2γL

)− eγx]

(3.35)


Figure 3.9: Voltage along a pipeline when it is earthed at one extremity.

and

U(L) = Umax =E

γ

(1− eγL

)(3.36)

U(0) =−E

γ

[1 + e−2γL + 2e−γL

](3.37)

c) The pipeline is grounded at x = 0 and continues beyond x ≥ L

For this case (refer to fig.(3.9),

Z1 = 0, Z2 = Z

this gives, r1 = -1, r2 = 0

U =E

2γ

[eγx − e−γx

]− eγL (3.38)

at x = 0, U = 0 and at x = L,

U(L) = Umax =E

2γ

[1− e−2γL

](3.39)


d) The pipeline is isolated at both ends of the close proximity region with insulating

flanges

For this case,

Z1 = Z2 = ∞,

this gives r1 = r2 = 1

U =E

γ

eγx − eγ(L−x)

eγL + 1(3.40)

at x = 0 and x = L,

Umax =E

γ

eγL − 1

eγL + 1(3.41)

and at the mid point of parallelism (x = L/2), U = 0.

3.4.2 Zone of influences formed by parallelism, approaches, crossings

and removals

For the zones of influence which are generally formed by parallelism, approaches, crossings as well

as removals, the computation involves subdividing the zone into several sections corresponding

to these zones. The calculation of voltages is carried out at both the ends of the sections. Each

section is represented by an equivalent π electrical network, which is influenced by the induced

EMF. In order to validly assimilate a section to a parallelism an oblique approach with distances

d1 and d2 at the ends can be approximated to a parallelism with a separation equal to√

d1.d2 on

condition that the ratio between maximum and minimum distances is lower than 3. Equation of

cell i (fig. (3.10)) is given by the expression,

−Zi−1,iIi−1 + (Zi−1,i + Zin + Zi,i+1)Ii − Zi,i+1Ii+1 = ei = Ei.Li (3.42)

Where,

Zi−1,i = 2/(Yi−1 + Yi) and Zi,i+1 = 2/(Yi + Yi+1)

Li = length of the section i

ei = EMF induced in the section i


Figure 3.10: π model representation of the pipeline-earth equivalent circuit.

System of equations for the entire zone of influence having n sections can be written as,

(Z0,1 + Z11 + Z1,2)I1 − Z1,2I2 = e1

−Z1,2I1 + (Z1,2 + Z12 + Z2,3)I2 − Z2,3I3 = e2

.

.

.

−Zn−2,n−1In−2 + (Zn−2,n−1 + Z1n−1 + Zn−1,n)In−1 − Zn−1,nIn = en−1

−Zn−1,nIn−1 + (Zn−1,n + Znn + Zn,n+1)In = en

The voltage between pipeline earth at the frontier between sections i and i+1 is equal to,

Ui,i+1 = Zi,i+1 (Ii − Ii+1) (3.43)

The next chapter presents the results obtained and the discussions on the results.

Chapter 4

Results and Discussions

4.1 Introduction

This chapter presents the computational results obtained based on the various methods discussed

in the previous chapter. In this chapter results of induced voltage due to capacitive and inductive

coupling on metallic pipelines running in close vicinity of high voltage power transmission lines

have been discussed. In addition to induced voltages, an optimum configuration of the phase

conductors based on the lowest conductor surface gradient and field under transmission line has

been arrived at. This chapter also reports the conductor surface field gradients calculated for

the various configurations. Electric and magnetic field profile under transmission line, for single

circuit and double circuit (various phase arrangements) have also been analyzed.

4.2 Electrostatic Field Computations

In order to know which configuration gives the lowest field under the transmission line, electric

fields at one meter height above the ground for various configurations have been calculated. To

calculate the electric field under the power line, phase conductors are considered as infinite line

charges. The line charge densities of the phase conductors are calculated using eqn. 3.4. Then the

horizontal and vertical components of the field due to the three phase conductors at the desired

locations are calculated separately using equation (3.5) and (3.6) [56].

Initially a 275 kV single circuit horizontal transmission line as shown in fig. 4.1 has been

considered for the study. Equivalent radius of each of the phase conductors is 0.429 m and radius

36

4.2. Electrostatic Field Computations 37

Figure 4.1: Single circuit horizontal configuration with ground wire.

of the ground wire is 0.06 m. Electric fields with and without the ground wires have been computed

and are shown in fig. 4.2. As can be seen from fig. 4.2, effect of ground wire is negligible and hence

they can be neglected for calculating fields under transmission lines.

To study the effect of transmission line height on electric field in the right-of-way, a 400 kV

single circuit horizontal configuration as shown in fig. 4.3 has been taken. Electric field at the

ground level is calculated for different heights of the phase conductors. The results are shown in

fig. 4.4.

Now electric fields under transmission line for 275 kV double circuit vertical configuration as

shown in fig. 4.5 with different phase configurations as given in Table 4.1 have been computed.

The results are shown in fig. 4.6. As can be seen, the field profiles are different for different

configurations. For configuration ]1 and ]2 electrostatic field is maximum at the center of the

right-of-way and decreases to negligible value at about 30 meters from the center of the right-of-

way. For other configurations, field is having lower value at the center of the right-of-way and

increases to a maximum value and then gets progressively reduced as one moves away from the

center of the transmission line corridor. Right-of-way of transmission line can be arrived at and a

suitable location for the pipeline can be chosen with the help of fig. 4.6, where the electric field is

at a relatively low value.

Similarly fields under transmission line for 275 kV double circuit delta configuration as shown


Figure 4.2: Comparison of electric fields under single circuit horizontal transmission linewith and without the ground wires, VLL = 275 kV.

Figure 4.3: Single circuit horizontal configuration, VLL = 400 kV.


−40 −30 −20 −10 0 10 20 30 400

1

2

3

4

5

6

7

E.S

. F

ield

kV

/m

Distance (m)

11 m

13 m

15 m

Powerline Height

Figure 4.4: Electric fields under horizontal transmission line, VLL = 400 kV.

−10 −5 0 5 100

5

10

15

20

25

30

35

Horizontal Distance (m)

Ve

rtic

al H

eig

ht

(m)

A

C’

B’

A’

C

B

Ground Wire Ground Wire

Figure 4.5: Double circuit vertical configuration chosen for the study.


−50 −40 −30 −20 −10 0 10 20 30 40 500

0.5

1

1.5

2

2.5

3

3.5

4

E.S

. F

ield

kV

/m

Distance in meter from the center of right of way

#1

#2

#3

#4

#5

Phase Configurations

Figure 4.6: Electric field profile for various phase configuration of a double circuit HVtransmission line rated 275 kV.

Figure 4.7: Double circuit delta configuration.


−60 −40 −20 0 20 40 600

0.5

1

1.5

2

2.5

3

3.5

4

4.5

E.S

. Fie

ld k

V/m

Distance in meter from the center of right of way

#1

#2

#3

#4

#5

Phase configutaions

Figure 4.8: Electric field profile for various double circuit delta configurations, VLL = 275 kV.

in fig. 4.7 with different phase configuration have also been computed. Full system voltage is

assumed to be applied to A, A’, whereas phase conductors B, B’, C, C’ are assumed to be at

half the system voltage. The results are shown in fig. 4.8. Configuration ]1 and ]2 give almost

identical field profile and the maximum value of electric field is at the center of right of way.

Electric field profile produced by configuration ]4 is not identical at the both halves of right of way.

Configuration ]5 gives lowest value of electric field just below the transmission line conductors.

All configurations produce similar electric field profile for the distances more than 20 meters from

the center of right of way i.e. electric field gets progressively reduced.

4.2.1 Conductor Surface Gradient Computation

Based on the method discussed in section 3.2.1, conductor surface gradients for five different

phase configurations for a double circuit 275 kV line have been computed and the results are

given in Table 4.1. The dimensional details are given in fig. 4.5. Radii of the phase conductors

and the ground wire are 1.265 cm and 0.75 cm respectively. Different phase configurations are

obtained by changing the position of the phase conductors A’, B’ and C’ with respect to the


Table 4.1: Conductor surface gradients for double circuit vertical configurations, VLL =275 kV

Configuration No. Phase Configuration Conductor Surface Gradient (kV/cm)A B C A’ B’ C’

A A’]1 B B’ 12.923 14.991 14.020 12.923 14.991 14.020

C C’A B’

]2 B A’ 14.134 14.819 13.993 14.819 14.134 13.993C C’A A’

]3 B C’ 12.878 15.007 14.578 12.878 14.578 15.007C B’A B’

]4 B C’ 14.501 14.820 14.489 14.778 13.978 15.011C A’A C’

]5 B B’ 14.388 14.995 14.713 14.713 14.995 13.976C A’

phase conductors A, B and C. Full system voltage is assumed to be applied to A, A’, whereas

phase conductors B, B’, C, C’ are assumed to be at half the system voltage. For configuration ]1,

the computed values are compared with the results given in Ref. [60]∗ and they are found to be

matching. In configuration ] 2, the highest surface gradient on any of the conductors is lower

than the highest surface gradient in any of the other configurations. Hence this would be the

preferred configuration, as long as surface gradient is the only criterion for choosing a particular

phase configuration. Similarly configuration ] 5 is the second preferred configuration based on the

same criterion.

* Transmission Line data from Ref. [60] is given as Appendix - A on page 59-A

Similarly for double circuit delta configuration (fig. 4.7) transmission line conductor surface

gradients have been computed and the results are given in Table 4.2. In configuration ]2, the

highest surface gradient on any of the conductors is lower than the highest surface gradient in any

of the other configurations.

4.3. Magnetic Field Computation 43

Table 4.2: Conductor surface gradients for double circuit delta configurations, VLL = 275 kV

Configuration No. Phase Configuration Conductor Surface Gradient (kV/cm)A B C A’ B’ C’

A A’]1 13.01 13.084 14.118 13.01 13.084 14.118

C B B’ C’A C’

]2 13.810 13.086 13.882 13.883 13.086 13.810C B B’ A’

A A’]3 13.018 14.936 13.733 13.018 13.733 14.936

C B C’ B’A C’

]4 13.219 14.932 13.886 14.503 13.731 13.807C B A’ B’

A B’]5 13.208 14.496 14.120 14.496 13.208 14.120

C B A’ C’

4.3 Magnetic Field Computation

Magnetic fields are the source of inductive coupling. In this section comparison between magnetic

field produced by horizontal and vertical configuration of the transmission line phase conductors

has been made. Magnetic field profiles for horizontal(see fig. 4.9) and vertical(see fig. 4.10) config-

uration have been computed using theory given in section 3.2.2. Magnetic field profile for single

circuit horizontal and vertical configuration have been shown in fig. 4.11. As can be seen horizon-

tal configuration gives higher magnetic field than vertical configuration at the center of the right

of way. At a distance of 40 meter from the center of the right of way, vertical configuration gives

lower magnetic field than horizontal configuration.

4.4 Induced Voltage due to Capacitive Coupling

Using CSM (refer to section 3.3), for all the five possible configurations (Table 4.1), induced

voltages on the pipeline (see fig. 3.4) located at different distances from the mid point of the line

have been calculated. It has been found that different configurations have significant difference

in induced voltage as shown in fig. 4.12. It can be seen from fig. 4.12 that the induced voltage

4.4. Induced Voltage due to Capacitive Coupling 44

Figure 4.9: Single circuit horizontal configuration VLL = 500 kV.

Figure 4.10: Single circuit vertical configuration VLL = 500 kV.


−80 −60 −40 −20 0 20 40 60 800

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Distance from Center of Right of Way (m)

Mag

netic

Fie

ld (

Gau

ss)

Horizontal ConfigurationVertical Configuration

Figure 4.11: Magnetic field profile under single circuit horizontal and vertical transmissionline.

gets progressively reduced as one moves away from the center of the transmission line corridor.

One can also observe that the induced voltage becomes almost negligible at a critical distance and

beyond which the induced voltage again increases. This critical distance depends on the conductor

configuration. For configuration ]2, the critical distance is close to 15 m, whereas for all other

configurations, the critical distance lies between 26 to 32 m. So depending on the right of way

available one can also think of choosing an appropriate phase configuration and hence the location

of the pipeline. It is suggested that the pipeline could be located close to the critical distance so

that the induced voltage would be close to zero.

A comparison of induced voltages due to single circuit horizontal (fig. 4.9) and vertical (fig. 4.10)

configurations has been done and is shown in fig. 4.13. One can observe that the induced voltage

on the pipeline is higher for the vertical configuration when the pipeline is laid close to the mid

point of the right of way. However, as the position of the pipeline is moved away from the center of

the right of way, the vertical configuration gives a much lower induced voltage than the horizontal

configuration. Hence a vertical configuration of the phase conductors is always preferred whenever

a metallic pipeline is to be run in the same corridor as that of the power transmission line.


0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

3

3.5

Pipeline position w.r.t. the mid point of transmission line (m)

Indu

ced

Vol

tage

(kV

)

#1

#2

#3

#4

#5

Phase Configurations

Figure 4.12: Induced voltage on the pipeline for various phase configurations.

0 5 10 15 20 25 30 35 40 450

2000

4000

6000

8000

10000

12000

Position of Pipeline w.r.t Mid Point of Transmission Line (m)

Induce

d V

olta

ge (

V)

Vertical ComfigurationHorizontal Configuration

Figure 4.13: Comparison of induced voltages due to horizontal and vertical configurationsVLL = 500 kV.

4.5. Inductive Coupling Computations 47

4.5 Inductive Coupling Computations

Results of inductive coupling computations have been discussed in this section.

4.5.1 Perfect Parallelism Between Powerline and Pipeline

In case of perfect parallelism between the powerline and the pipeline, calculation method given

in section 3.4.1 have been used. For the calculation, horizontal configuration having a height of

18.288 meters and a separation of 7.62 meters between phase conductors have been considered.

Pipeline of 0.5 meter diameter is kept at 25 m from the middle phase conductor and buried 5

meters below the ground level. Value of other parameters are given as, soil resistivity ρ = 100

Ωm, Resistivity of steel pipeline ρp = 0.17×10−6 Ωm, L = 10000 m, µr = 300, εr = 5, e = 4×10−3

m, Ru = 104 Ωm2, Ir = 500 A, D = Diameter of pipeline, Resistivity of pipeline coating ρc = Ru/e

Longitudinal impedance per unit length of the pipeline,

z =

√ρpµoµrω

πD√

2+

µoω

8+ j

(√ρpµoµrω

πD√

2+

µoω

2πln

3.7√

ρω−1µ−1o

D

)(4.1)

Admittance per unit length of the pipeline,

y =πD

ρce+ jω

εoεrπD

e(4.2)

Calculation of induced voltages and current for different cases as discussed in section 3.4.1 have

been done.

Results are shown in fig. 4.14 and fig. 4.15 for the case where the pipeline continues to run

for several kilometers after the end of the parallel routing with the powerline (see section 3.4.1

Case (a)). As can be seen in fig. 4.14 induced voltage is almost negligible at the mid point of the

zone of influence and is maximum at both the extremities where pipeline deviates away from the

right of way. An exponential decrease in induced voltage is seen in the pipeline sections which are

running perpendicular to the powerline after deviating away from the common corridor.

Result is shown in fig. 4.16 for the pipeline which continues at x ≤ 0 and is isolated at x =

L with an insulating flange (see section 3.4.1 Case (b)). One can observe that induced voltage

is maximum at the end where pipeline is isolated with an insulating flange. Minimum induced


0 2 4 6 8 10 12 14 16 18 200

5

10

15

Distance Along Pipeline (km)

Ind

uced

Vo

ltag

e (

V)

Figure 4.14: Induced voltage along the pipeline (Case (a)).

0 2 4 6 8 10 12 14 16 18 202

4

6

8

10

12

14


Cu

rren

t (A

)

Figure 4.15: Current along the pipeline (Case (a)).


5 10 150

5

10

15

20

25

30


Ind

uced

Vo

ltag

e (

V)

Figure 4.16: Induced voltage along the pipeline (Case (b)).

voltage is obtained at distance of 9 km along the pipeline.

Results are shown in fig. 4.17 and fig. 4.18 for the pipeline which is grounded at x = 0 and

continues beyond x ≥ L (see section 3.4.1 Case (c)). One can observe that induced voltage is

maximum at the point where pipeline approaches the powerline and induced voltage is zero at the

end where pipeline is grounded.

4.5.2 General Situation

For the zone of influences, which are generally formed by parallelism, approaches, crossings and

removals, calculation method given in section 3.4.2 have been used. Zone of influence given in

fig. 3.6 is taken for calculation. Single phase vertical configuration has been chosen for the study.

Lowest conductor is at a the height of 15 m and separation distance between conductors is 9 m.

Ground wire is located at 45 m above ground. Pipeline is buried at a depth of 1 m for the

entire zone of influence. Value of other parameters are given as ρ = 100 Ωm, µr = 300, εr = 5,

e = 4× 10−3 m, Ru = 103 Ωm2 for Bituminous coating and 105 Ωm2 for Polyethylene coating, D

= 0.3 m, Rg = 1.089×10−4 Ω/m, r4 = 7×10−3 m, Resistivity of pipeline coating ρc = Ru/e


5 10 150

5

10

15


Ind

uced

Vo

ltag

e (

V)

Figure 4.17: Induced voltage along the pipeline (Case (c)).

5 10 152

4

6

8

10

12

14

16


Cu

rren

t (A

)

Figure 4.18: Current along the pipeline (Case (c)).


Calculation of induced voltage is carried out for the following conditions.

Normal Operation

For normal operation, the value of the phase current (Ir) is taken as 1000 (A). Induced voltage

along the pipeline in the zone of influence is shown in fig. 4.19 for the pipeline coated with

bituminous coating and in fig. 4.20 for polyethylene coated pipeline for the normal operation case.

As can be seen, induced voltage is negligible near to the mid point of zone of influence. Maximum

induced voltage is obtained at the point of approaches, crossings and removal.

Effect of different soil resistivities on induced voltages for bituminous and polyethylene coated

pipeline is shown in fig. 4.21 and fig 4.22 respectively. It can be seen in fig. 4.21, for bituminous

coating change in soil resistivity does not effect the induced voltage in the section of zone of

influence where pipeline is running parallel to powerline. But for the sections where pipeline is

approaching or deviating away from powerline, induced voltage increases on increasing the soil

resistivity. Also in fig. 4.22, for the polyethylene coating, change in soil resistivity have only

marginal effect on the induced voltage in the section where pipeline running parallel to powerline.

However, for the sections where pipeline is approaching or deviating away from powerline, induced

voltage increases on increasing the soil resistivity.

Fault at one extremity of the zone of influence

Value of fault current is assumed to be equal to 14 kA. Induced voltage along the pipeline in the

zone of influence during fault at one extremity of the zone of influence is shown in fig. 4.23 for

pipeline coated with bituminous coating and in fig. 4.24 for polyethylene coated pipeline. One can

observe that induced voltage are much higher as compared with normal operation (see fig. 4.19

and fig. 4.20). Maximum induced voltage is obtained at the point of approaches, crossings and

removals.

Fault inside the zone of influence

In case of fault occurring inside the zone of influence as shown in fig. 4.25 value of fault currents

are taken as IA = 18 kA and IB = 7 kA. Induced voltage along the pipeline during fault inside the

zone of influence is shown in fig. 4.26 for pipeline coated with bituminous coating and in fig. 4.27


0 2000 4000 6000 8000 10000 120000

2

4

6

8

10

12

14

16

18

20

Distance Along Powerline (m)

Ind

uced

Vo

ltag

e (

V)

Bituminous Coating R

u = 103

Figure 4.19: Induced voltage on pipeline during normal operation (bituminous coating).

0 2000 4000 6000 8000 10000 120000

5

10

15

20

25

30

35


Ind

uced

Vo

ltag

e (

V)

Polyethylene Coating

Ru = 105

Figure 4.20: Induced voltage on pipeline during normal operation (polyethylene coating).


0 2000 4000 6000 8000 10000 120000

2

4

6

8

10

12

14

16

18

20


Ind

uce

d V

olta

ge

(V

)

30

100

1000

10000

Soil Resistivity ( Ω−m)

Bituminous Coating

Ru = 103

Figure 4.21: Effect of soil resistivity on induced voltage on pipeline having bituminouscoating.

0 2000 4000 6000 8000 10000 120000

10

20

30

40

50

60

70

80


Ind

uce

d V

olta

ge

(V

)

30100100010000

Soil Resistivity ( Ω−m)Polyethylene Coating

Ru = 105

Figure 4.22: Effect of soil resistivity on induced voltage on pipeline having polyethylenecoating.


0 2000 4000 6000 8000 10000 120000

500

1000

1500


Ind

uced

Vo

ltag

e (

V)

Bituminous Coating

Ru = 103

Figure 4.23: Induced voltage on pipeline during fault at one extremity of the zone of influence(bituminous coating).

0 2000 4000 6000 8000 10000 120000

500

1000

1500

2000

2500

3000


Ind

uced

vo

ltag

e (

V)


Ru = 105

Figure 4.24: Induced voltage on pipeline during fault at one extremity of the zone of influence(polyethylene coating).

4.6. Mitigation 55

A B

IA I

B

Figure 4.25: Fault inside the zone of influence.

for polyethylene coated pipeline. As can be seen, induced voltage is negligible at the location of

the fault and that the induced voltage is higher for the polyethylene coated pipeline.

Maximum induced voltage is obtained at the mid point of the zone of influence. Bituminous

and polyethylene coated pipeline give different value of induced voltage. For bituminous coated

pipeline induced voltage decreases rapidly up to 8 km after a maximum value at 6 km. From 8

km to 12 km induced voltage decreases very slowly.

For polyethylene coated pipeline, there is a dip in the induced voltage profile at 9 km and beyond

that induced voltage again increases.

4.6 Mitigation

For mitigating the induced voltage due to magnetic coupling several earthing resistances are

connected at various nodes along the pipeline. Results are shown in fig. 4.28. It can be seen that

the induced voltage reduces on increasing the number of earthing points.

Next chapter gives important conclusions drawn from the present work.

4.6. Mitigation 56

0 2000 4000 6000 8000 10000 120000

200

400

600

800

1000

1200

1400

1600

1800


Ind

uced

Vo

ltag

e (

V)

Bituminous Coating

Ru = 103

Figure 4.26: Induced voltage on the pipeline for a fault inside zone of influence (bituminouscoating).

0 2000 4000 6000 8000 10000 120000

500

1000

1500

2000

2500

Distance along Powerline (m)

Ind

uced

Vo

ltag

e (

V)


Ru = 105

Figure 4.27: Induced voltage on pipeline for a fault inside the zone of influence (polyethylenecoating).

4.6. Mitigation 57

0 2000 4000 6000 8000 10000 120000

5

10

15

20

25


Ind

uc

ed

Vo

latg

e (

V)

One Section

Two Section

Four Section

Eight Section

Grounding wire is connected after every

Figure 4.28: Effect of earthing resistance on induced voltage on pipeline having polyethylenecoating.

Chapter 5

Conclusions

5.1 Capacitive Coupling

Primary objective of this work is to compute the induced voltages due to capacitive and inductive

coupling on metallic pipelines running in close vicinity of high voltage power transmission lines.

The electric fields under transmission lines, for both single circuit and double circuit (various phase

arrangements) transmission lines have been analysed. It is observed that the effect of ground wire

is negligible and hence they can be neglected for calculating the fields under transmission lines.

In addition the conductor surface field gradients calculated for the various phase configurations

have been presented in the thesis. Based on the above results, an optimum configuration giving

the lowest field under the power line as well as the lowest conductor surface gradient has been

arrived at and for this configuration induced voltage on the pipeline has been computed using

the Charge Simulation Method (CSM). It is observed that the induced voltage gets progressively

reduced as one moves away from the center of the transmission line corridor. Induced voltage

on the pipeline becomes almost negligible at a critical lateral distance from the center of the

powerline and beyond which the induced voltage again increases. This critical distance depends

on the conductor configuration. Hence it is suggested that the pipeline be located close to the

critical distance so that the induced voltage would be close to zero.

A comparison of the induced voltages due to single circuit horizontal and vertical configurations

of the transmission lines has also been carried out. It is seen that the induced voltage on the

pipeline is higher for the vertical configuration when it is close to the mid point of the right of

way. However, as the position of the pipeline is moved away from the center of the right of way,

58

5.2. Inductive Coupling 59

the vertical configuration gives a much lower induced voltage than the horizontal configuration.

Hence it can be stated that the vertical configuration of the phase conductors is to be preferred

whenever a metallic pipeline is to be run in the same corridor as that of the power transmission

line as one usually place the pipeline towards the edge of the right of way.

5.2 Inductive Coupling

Magnetic fields are the source of inductive coupling. Hence the comparison between magnetic

field produced by horizontal and vertical configuration of the transmission line phase conductors

has been made. It is seen that the horizontal configuration gives a higher magnetic field than the

vertical configuration.

Inductive coupling calculations have been carried out for the perfect parallelism between the

powerline and the pipeline and for the zones of influence formed by parallelisms, approaches,

crossings and removals. Results show that the terminating impedances used at the extremities of

the zone of influence have very significant effect on the induced voltage along the pipeline. It has

been observed that when the pipeline is approaching the HV transmission line at an angle, then

running parallel for certain distance and finally deviating away, the induced voltage is maximum

at the point of approach or removal of the pipeline from the transmission line corridor. The

induced voltage is almost negligible near to the midpoint of the zone of influence. It is seen that

for bituminous coated pipeline, change in soil resistivity does not effect the induced voltage in

the section of the zone of influence where pipeline is running parallel to powerline. But for the

sections where pipeline is approaching or deviating away from the powerline, the induced voltage

increases as the soil resistivity increases. Similarly for the polyethylene coated pipeline, change

in soil resistivity has only marginal effect on the induced voltage in the section where pipeline

is running parallel to the powerline. However, for the sections where pipeline is approaching or

deviating away from the powerline, induced voltage increases on increasing the soil resistivity.

The profile of the induced voltage also depend on whether the pipeline is grounded or left open

circuited at the extremities of the zone of influence. Effect of earth resistivity and anti-corrosive

coatings on induced voltage has also been studied. For mitigating the induced voltage on the

pipeline, numerous low resistive earthings have been suggested. Results show that significant

reduction in induced voltage can be achieved as the number of earth points are increased.

APPENDIX -A 59-A

Data for Transmission line

Arrow indicates the line configuration compared with the present work

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