Analysis of Faults in Overhead Transmission Lines

ANALYSIS OF FAULTS IN OVERHEAD TRANSMISSION LINES

Presented to the faculty of the Department of Electrical and Electronic Engineering

Department

California State University, Sacramento

Submitted in partial satisfaction of the requirements for the degree of

MASTER OF SCIENCE

Electrical and Electronic Engineering

William Patrick Davis

FALL 2012

THE ANALYSIS OF FAULTS IN OVERHEAD TRANSMISSION LINES

A Project

William P. Davis

Approved by:

______, Committee Chair Turan Gonen, Ph.D.

______, Second Reader Preetham Kumar, Ph.D.

______Date

Student: William P. Davis

I certify that this student has met the requirements for format contained in the University format manual, and that this project is suitable for shelving in the Library and credit is to be awarded for the project.

______, Graduate Coordinator ______Preetham Kumar, Ph.D. Date

Department of Electrical and Electronic Engineering

iii

Abstract

ANALYSIS OF FAULTS IN OVERHEAD TRANSMISSION LINES

William P. Davis

When designing power transmission systems, electric utility companies are expected to follow a set of standard specifications that are briefly described in this research. The idea to be kept in mind is that during the planning and construction phases of transmission lines, natural elements, such as trees for example, there will be less of a chance of fault occurrences and therefore more power system reliability.

Faults in transmission lines are one of the elements that will affect the reliability of the system. The more fault occurrences, the lesser the system reliability, since this causes outages in the power system that may result in the interruption of service.

The electric utility companies are expected to provide the consumer a continuous and also a high quality of service at a competitive and reasonable cost.

This means that they have to insure the reliability of the system to provide the consumer with a service that is consistent with the safety of personnel and equipment and meet their demands within not only the specifications of voltage and frequency but with a high degree of reliability and within reasonable cost to the consumer.

______, Committee Chair Turan Gonen, Ph.D.

______Date

ACKNOWLEDGEMENTS

Thank you to Professors Gonen and Kumar as this would not have been possible without both their help and guidance. To my family and friends for all the support throughout the years and believing that this would one day be possible.

Also, I would like to thank, via Professor Gonen, the original undergraduate Power

Senior Project Group whose work was the initial basis for the production of this report.

My especial gratitude to my beloved fiancée, Miss Amanda K. (Mandie) Ryan, for without her contributing effort, the completion of this report would not have been possible.

TABLE OF CONTENTS

Page Acknowledgments v

List of Tables vii

List of Figures viii

Chapter 1. INTRODUCTION 1

2. THE LITERATURE SURVEY 2

2.1 Transmission lines 2

2.1.1 Introduction 2

2.1.2 Requirement of Transmission Lines 2

2.1.3 Selection of Voltage for High-Voltage Transmission Lines 3

2.1.4 Choice of Conductors 4

2.2 The Nature and Causes of Faults 5

2.2.1 Lightning 5

2.2.2 Pollution 8

2.2.3 Fires 8

2.3 Types of Faults 9

2.4 Fault Detection 13

2.4.1 Fault Detection Using Composite Fiber-Optic 13

2.4.2 Fault Detection Using Neural Network 15

3. MATHEMATICAL DESIGN 18

3.1 Introduction 18

3.2 Types of Faults 18

3.2.1 Shunt Faults 18

3.2.2 Series Faults 19

3.3 Shunt Fault Computation 20

3.3.1 Single Line-to-Ground Faults 20

3.3.2 Double Line-to-Ground Faults 25

3.3.3 Line-to- Line Faults 29

3.3.4 The Balanced Three-Phase Fault 31

3.4 Series Fault Computations 33

3.4.1 Open Line Open (OLO) 33

3.4.2 Two Line Open (TLO) 35

4. THE APPLICATION OF THE MATHEMATICAL MODEL 37

4.1 Introduction 37

4.2 Calculation of the Network Sequences 38

4.3 Single Line-to-Ground Fault 44

4.4 Double Line-to- Ground Fault 45

4.5 Line-to- Line Fault 50

4.6 The Balanced Three-Phase Fault 52

vii

4.7 Series Fault 52

5. MODEL SIMULATION OF THREE-PHASE COMPENSATED NETWORK..56

6. CONCLUSION 62

References 63

viii

LIST OF TABLES

Tables Page

Table 4.1 System Data 38

LIST OF FIGURES

Figures Page

Figure 2.1 Flashover Faults on Transmission Lines [6] 7

Figure 2.2 Configuration of Lightning Arrester [6] 7

Figure 2.3 Lightning Arrester Unit [6] 7

Figure 2.4 Lightning Arrester with Zinc Oxide [6] 7

Figure 2.5 Single Line-to-Ground Fault 11

Figure 2.6 Line-to-Line Fault 11

Figure 2.7 Double Line-to-Ground Fault 12

Figure 2.8 Three-Phase Fault 12

Figure 2.9 The functional parts of protective relay 17

Figure 3.1 Single Line-to-ground Fault Schematic 23

Figure 3.2 Equivalent Circuit for single Line-to-Ground Fault 23

Figure 3.3 Double Line-to-Ground Fault Circuit 28

Figure 3.4 Sequence Network for Double Line-to-Ground Fault 28

Figure 3.5 Example of Line to Line Fault 30

Figure 3.6 Line-to-Line Equivalent Circuit 30

Figure 3.7 A Balanced Three-Phase Fault 33

Figure 3.8-(a) One line open: general representation [8] 34

Figure 3.8-(b) One line open: connection of sequence networks [8] 34

Figure 3.9-(a) Two lines open: general representation [8] 36

Figure 3.9-(b) Two lines open: interconnection of sequence networks [8] 36

Figure 4.1 System and fault location 39

Figure 4.2 Positive Sequence Network and steps in its reduction 39

Figure 4.3 Negative Sequence Network and its reduction 41

Figure 4.4 Zero Sequence Network and its Reduction 42

Figure 4.5 Sequence Network connection for SLG fault 48

Figure 4.6 Sequence network for DLG fault 48

Figure 4.7 Sequence network For LL fault 51

Figure 4.8 Sequence network for balanced 3Φ fault 51

Figure 4.9 Thevenin equivalent of positive, negative, and zero sequence networks_53

Figure 5.1 Simulink Model of 3-phase compensated network 57

Figure 5.2 Simulink Model output parameter block 58

Figure 5.3 (a) Output of Bus B1 59

Figure 5.3 (b) Output of Bus B2 60

Figure 5.3 (c) Output of Bus B3 61

Chapter One

INTRODUCTION

The Electric Power System is divided into many different sections. One of which is the transmission system, where power is transmitted from generating stations and substations via transmission lines into consumers. Both methods could encounter various types of malfunctions is usually referred to as a “Fault”.

Fault is simply defined as a number of undesirable but unavoidable incidents can temporarily disturb the stable condition of the power system that occurs when the insulation of the system fails at any point. Moreover, if a conducting object comes in contact with a bare power conductor, a short circuit, or fault, is said to have occurred. The causes of faults are many, they include lighting, wind damage, trees falling across transmission lines, vehicles or aircraft colliding with the transmission towers or poles, birds shorting lines or vandalism.

In this study, the causes and effects of faults in the overhead transmission lines were the focus of the research. Some of the many causes of faults, and some detection methods will be discussed in chapter two (2). Chapter three (3) will illustrate the mathematical model, and chapter four (4) will demonstrate the application of this model for some hypothetical situations.

Chapter Two

THE LITERATURE SURVEY

2.1. Transmission lines

2.1.1 Introduction

The electric energy produced at generating stations is transported over high voltage transmission lines to utilization points. In the early days (until 1917), electric systems were operated as isolated systems with only point-to-point transmission at voltages that are considered low by today’s standards.

2.1.2 Requirement of Transmission Lines

Transmission lines should transmit power over the required distance economically and satisfy the electrical and mechanical requirements prescribed in particular cases. It would be necessary to transmit a certain amount of power, as a given power factor, over a given distance and be within the limit of given the regulation, efficiency and losses. The lines should stand the weather conditions of the locality in which they are laid. This would involve wind pressures and temperature variation at the places and the lines should be designed for the corresponding mechanical loading. The regulation would give the voltage drop between the sending-end and the receiving-end. The possibility of a corona formation and corresponding loss would be another consideration. The charging current of the line depends on the capacity of the line and should not exceed the limit. As far as the general requirements of transmission lines are concerned, the lines should have enough capacity to transmit the required power, should maintain

3 continuous supply without failure, and should be mechanically strong so that there are no failures due to mechanical breakdowns also. [2]

2.1.3 Selection of Voltage for High-Voltage Transmission Lines

With increase in the power to be transmitted over long distances, use of high voltages for power transmission has been developed. However, a choice could be made out of the standard voltages that are used in the country. The voltage selected has to be economical and depends on the cost of the lines, cost of apparatus such as transformers, circuit breakers, insulators, etc. This cost increases rapidly for voltages in the range of 230 kV and above. For higher power, it is worthwhile to check whether the required power can be transmitted using lower power voltages, e.g. transmission at 230 kV using capacitors installed on the line instead of higher voltages. The voltages used as standards in many countries 11 kV, 22 kV, and 33 kV for short lines, 66 kV and 110 kV for medium lines and 132 kV, 166 kV, 230 kV and above for long lines.

In the selection of voltage of transmission lines, the existing and future voltage of the other lines in the vicinity should be considered. This is required for the possible interconnection of the grid lines. In such cases, it may be necessary to choose voltages higher than the most economical voltage. Possible developments in the location should also be considered in justifying the choice of voltage. The choice of voltage is also liked with the conductor size, when transmitting the required power.

The power to be transmitted and the distance over which it is to be transmitted together decide the voltage to a certain extent.

As regards to the distance of transmission, 11 kV and 33 kV lines are used for short distances, while the other lines may be used for the appropriate distances.

This is just a very rough guide for preliminary work, to start detailed design of the line required. The choice of conductors, etc. also affects the choice. In designing a transmission line, It would, therefore, be worthwhile to consider two or three possible voltages and two or three conductor sizes to obtain the required characteristics of the line within the given limitations.

2.1.4 Choice of Conductors

The conductors available are hard-drawn copper or stranded conductors, or

ACSR conductors. For short lines with comparatively low voltages up to 33 kV, copper conductors are used if available. For high-voltage lines, the increase in the span and the weight of the conductors to be supported becomes an important consideration. ACSR conductors are commonly used for high-voltage work. In most countries where copper is not available in plenty and needs to be imported, it would be worthwhile to use ACSR conductors wherever possible.

The size of the conductor selected depends on the length of the transmission line, load on the line and the voltage of the line. For a given loss of energy, expressed as percentage of the energy to be transmitted, the cross section of the conductor as well as its weight varies inversely as the square of the voltage of the line. The loss in the transmission line is 3I2r per unit length of the line, where r is the

5 resistance per unit length of the line. The current in the line depends on the voltage and the power factor of the load to be supplied. As the voltage increases, the cross section of the conductors reduces, and up to a certain extent, use of higher voltages reduces the loss. However, for high voltages (above 166 kV) other losses should be considered, i.e. due to leakage over insulators and Corona loss. The value of the charging current also increases for the high voltages and this affects the line current.

The cost of the conductors depends on their weight. The safe current carrying capacity in amperes for bare copper stranded overhead.

2.2 The Nature and Causes of Faults

The nature of a fault is simply defined as any abnormal condition, which causes a reduction in the basic insulation strength between phase conductors, or between phase conductors and earth or any earthed screens surrounding the conductors. In practice, a reduction is not regarded as a fault until is it is detectable, that is until it results either in an excess current or in a reduction of the impedance between conductors, or between conductors and earth, to a value below that of the lowest load impedance normal to the circuit. Thus a higher degree of pollution on an insulator string, although it reduces the insulation strength of the affected phase, does not become a fault until it causes a flashover across the string, which in turn produces excess current or other detectable ab normality, for example abnormal current in an arc-suppression coil. Following are some of the main causes:

2.2.1 Lightning

More than half of the electrical faults occurring on overhead power transmission lines are caused by lightning (see Figure 2.1). The main conventional approaches for reduction of the lightning flashover faults on power lines are lowering of the footing resistance and employing of multiple shielding wires, and differential insulation.

However, these methods have not been sufficient to prevent flashover faults.

In the mean time application of arresters to lines has been a better solution in recent years. This alternate approach is to install an arrester to prevent the flashover of insulator assemblies. It is important that the arrester should be strong enough in order to withstand excessive lightning strikes. A newly developed suspension-type line arrester has been developed by incorporating ZnO elements into the shed of a conventional suspension insulator (Figures 2.3 and 2.4). It has an arrester function along with the normal electrical and mechanical functions of a line insulator. It is a gapless type that has the advantage of reliable surge absorption with no delay in discharge. The new arrester holds promise not only for the prevention of lightning faults, but also as means of achieving economical insulation in the overall transmission systems. [6]

2.2.2 Pollution

Pollution is commonly caused by deposited soot or cement dust in industrial areas, and by salt deposited by wind-borne sea-spray in coastal areas. A high degree of pollution on an insulator string, although it reduces the insulation strength of the affected phase, does not become a fault until it causes a flashover across the string, which in turn reduces excess current or other detectable abnormality, for example abnormal current in an arc-suppression coil.

2.2.3 Fires

The occurrence of fire under transmission lines is responsible for a great number of line outages in many countries. Faults are mainly due to conductor to

9 ground short circuit at mid-span or phase-to-phase short circuit depending on line configuration and voltage level. To reduce these outages to a minimum, the clearance of existing lines must be increased in forests. Clearing and vegetation on the line right of way in such areas is also a consideration. Another problem arising from burning is the contamination of the insulators due to the accumulation of particles (soot, dust) on its surfaces. In this case, the line insulation requirements should be determined in such a way that the outages under fire could be reduced to a minimum. [5]

Other causes of faults on overhead lines are trees, birds, aircraft, fog, ice, snow loading, punctured or broken insulators, open-circuit conductors and abnormal loading.

2.3 Types of faults

Power system faults may be categorized as shunt faults and series faults. The most occurring type of shunt faults is Single Line-to-ground faults (SLG), which one of the four types of shunt faults, which occur along the power lines. This type of fault occurs when one conductor falls to ground or contacts the neutral wire. It could also be the result of falling trees in a winter storm. This type could be represented as in Figure 2.5.

The second most occurring type of shunt faults is the Line-to-Line fault (LL).

It is the result of two conductors being short-circuited. As in the case of a large bird standing on one transmission line and touching the other, or if a tree branch fall on top of the two of the power lines. This type could be represented as in Figure 2.6.

Third type of fault is the Double Line-to-Ground fault (DLG), Figure 2.7.

This can be a result of a tree falling on two of the power lines, or other causes. The fourth and least occurring type of fault is the balanced three phase (Figure 2.8), which can occur by a contact between the three power lines in many different forms.

Series faults can occur along the power lines as the “result of an unbalanced series impedance condition of the lines in the case of one or two broken lines for example. In practice, a series fault is encountered, for example, when lines (or circuits) are controlled by circuit breakers (or fuses) or any device that does not open all three phases; one or two phases of the line (or the circuit) may be open while the other phases or phase is closed.” [8]

2.4 Fault Detection

2.4.1 Fault Detection Using Composite Fiber-Optic

In electric power supply services, power transmission lines are very important and very indispensable. For that, power transmission lines are equipped with various protection systems that are checked varies times periodically because of the unexpected troubles that may destroy the lines. For the purpose of protecting these lines, a new system was invented to discover the Fault Location using

Composite Fiber Optic Overhead Ground Wire (OPGW). This system deals mainly with most causes of fault situations such as lightning, dew, snow, fog, or gales. This new fault location system was developed to find out where electrical fault happened on overhead power transmission lines by detecting the current induced in the ground wire. Any fault situation needs the fastest processing in fixing the fault. For that, the fault location system helps engineers to detect the point or the section where an electrical fault happened in very logic time.

Since the fault information is uncertain, the new fault location deals with the fault information as a current distribution pattern throughout the power line, and

14 applies Fuzzy Theory to realize the human-like manner of fault used by power engineers. Mainly, the fault location method measures the current induced in the

OPGW at many points along the line, these points are various sensors mounted on the tower and transmits the information to the central monitoring station through the optical fiber within the OPGW. So the fault information system is mainly given by sensing and data transmission. Electrical faults occurring on power transmission lines can be classified into two types: grounding and short circuit fault.

The transmission that gets to the central monitor station deals with current characteristic features. In order to locate the fault, engineers must use the features of currents that deal with the phase angle and the amplitude and relate these features to

Fuzzy Theory. The idea arose of using Fuzzy Theory as a fault theory algorithm similar to this kind of human thinking. There were some sets for Fuzzy theory: SdI

(large amplitude change) Sd(large phase angle change) SdIp (large angle change),

SIS2 (amplitude approximately half of saturation current Is) and finally SIn (amplitude larger than normal). For that the possibility of grounding faults occurring can be expressed by:

(2.1)

Maximum Fault grounding is expressed by

(2.2)

The possibility of short circuit fault is expressed

(2.3)

The maximum short circuit fault is expressed

(2.4)

Also, we have to know that the FI sensors divide all faults occurring in a section. In general his system already has been applied to several commercial power transmission lines and successfully located the sections of the faults [9].

2.4.2 Fault Detection Using Neural Network

As indicated before, protecting transmission is very important task in safeguard electric power systems. For that, faults on transmission lines need to be detected, classified, and located accurately. All these actions must be taken in very short time to clear the fault. The new approach of neural network to fault classifications for high speed protective relaying is a good manner in solving any fault classification for high speed protective relaying is a good manner in solving any fault happened to the transmission lines. Mainly this scheme is based on the use of neural architecture and implementation of digital signal processing concepts. Figure

2.9 shows functional parts of protective relay. The protective relay need sampled values of currents and voltages of three lines build inputs of the system. In general, a knowledge control module controls all other parts of the relay and is responsible for sending trip signals. The fault detection module is signals that a fault location classification module uses samples of normalized currents (i) and voltages (v).

A1KHz sample rate is use to ensure that the fault type classification can be done in a timely fashion. This module classifies weather a 1-phase-to-ground, 2-phase-to- ground, phase-to-phase or a 3-phase fault has occurred. In the classification process,

16 arcing and non-arcing must be known in order to obtain a successful automatic reclosing. Generally speaking, neural network classifies the fault into types. The first type (1-phase, 2-phase, 3-phase faults) is fast 5-7 ms and reliable. The second type, arcing and non-arcing faults support a successful automatic reclosing. [1]

Chapter Three

MATHEMATICAL DESIGN

3.1 Introduction

Fault or short-circuit studies are obviously an essential tool for the electric energy systems engineer. The task here is to be able to calculate the fault conditions and to provide protective equipment designed to isolate the faulted zone from the remainder of the system in the appropriate time. The least complex category computationally is the balanced fault. This tempts the engineer to base his decision on its results. The balanced fault could (in some locations) result in currents smaller than that due to any other type of fault. However, the interrupting capacity of breakers should be chosen to accommodate the largest of fault currents.

A fault occurs when two or more conductors that normally operate with a potential difference come in contact with each other. The contact may be a physical

4metallic one, or it may occur through an arc. In the metal-to-metal contact case, the voltage between the two parts is reduced to zero. On the other hand, the voltage through an arc will be of a very small value.

3.2 Types of Faults

3.2.1 Shunt Faults

1. Single line-to-ground faults

2. Line-to-line faults

3. Double line-to-ground faults

4. Balanced or symmetrical three phase faults

Overhead lines are constructed of bare conductors. Wind, sleet, trees, cranes, kites, airplanes, birds, or damage to supporting structure are causes for accidental faults on overhead lines. Contamination of insulators and lightning over voltages will in general result in faults. Deterioration of insulation in underground cables results in short circuits. This is mainly attributed to aging combined with over loading. About

75 percent of the energy system’s faults are due to the shunt fault type and result from insulator flashover during electrical storms. Only one in twenty faults are due to the balanced fault.

3.2.2 Series Faults

1. One line open

2. Two line open

The series types of faults occur due to an unbalanced series impedance condition of the lines. This could occur when fuses or any device, which does not open all three phases, one or two phases, controls circuits. It is also the result of one or two broken lines, or impedance inserted in one or two lines. Such faults could occur as a result of one or two phases of the line open while the other phase or phases are closed.

When the system impedances and admittances are constants the method of symmetrical components can be used to determine fundamental frequency currents and voltages in the system with one or two open conductors. The existing impedance of a transformer is an example of impedance, which is not constant, but varies with the applied voltage.

As a result of a fault, currents of high value will flow through the network to the faulted point. The amount of current will be much greater than the desired thermal ability of the conductors in the power lines or machines feeding the fault.

Which causes temperature to rise which in turn may cause damage by annealing of conductors and insulation charring. In addition to this, the low voltage in the neighborhood of the vault will render the equipment inoperative.

3.3 Shunt Fault Computation

3.3.1 Single Line –to- Ground Faults

Assume that the phase a is shorted to ground at the fault point F as shown in figure 3.1. Phase b and c currents are assumed to be negligible, and we can thus write

The sequence currents are obtained as follows:

To find the positive sequence value we use

(3.1)

This gives

(3.2)

For the negative sequence current, we have

(3.3)

This gives

(3.4)

Likewise for the zero sequence current, we get

(3.5)

We can then conclude then that in the case of a single line-to-ground fault, the sequence currents are equal, and we write

(3.6)

With the generators normally producing balanced three phase voltages, which are positive sequence only, we can write

Let us assume that the sequence impedances to the fault are given by Z1, Z2, Z0. We can write the following expressions for sequence voltages at the fault:

(3.7)

(3.8)

(3.9)

The fact that phase a is shortened to the ground is used. Thus

We also recall that

(3.10)

We conclude

(3.11)

The resulting equivalent circuit is shown in Figure 3.2

We can now state the solution in terms of phase currents:

(3.13)

For phase voltages we have

(3.14)

(3.15) The last two expressions can be derived easily from the basic relations.

For phase b, we have

(3.16)

Using equations 3.7, 3.8, and 3.9, we find that

Which reduces to

(3.19)

And since

(3.20)

We obtain

(3.21)

Similarly we get the result for phase c.

3.3.2 Double Line-to-Ground Faults

In this case, we will consider a general fault condition. We assume that phase b has fault impedance of Zf ; phase c has a fault impedance of Zf ; and the common line-to-ground fault impedance is Zg as shown in Figure 3.3.

The boundary conditions are as follows:

(3.22)

(3.23)

The potential difference between phase b and c is thus

(3.24)

Substituting in terms of sequence currents and voltages, we have

(3.25)

As a result, we get

(3.26)

The sum of the phase voltages is

(3.27)

In terms of sequence quantities this gives

(3.28)

Recall that since Ia = 0, we have

(3.29)

We can thus assert that

(3.30)

Substituting for Va0 from equation 3.26, we get

(3.31)

The above reduces to

(3.32)

Now we have

(3.33)

(3.34)

(3.35)

Consequently,

(3.36)

It is clear from equation (3.36) that the sequence networks are connected in parallel, which could be seen in Figure 3.4. From the equivalent circuit we obtain the positive sequence current

(3.37)

The negative sequence current in

(3.38)

Finally,

(3.39)

3.3.3 Line-to-Line Faults

In the case of line-to-line fault a short circuit occurs between two phases.

Assuming that phase a is the un-faulted phase, Figure 3.5 shows a three-phase system with a line-to-line short circuit between phases b and c. The boundary conditions in this case are

(3.40)

(3.42) The first two conditions yield

(3.43)

(3.44)

The voltage conditions give

(3.45)

which gives

(3.46)

(3.47)

(3.48)

The equivalent circuit will take on the form shown in figure 3.6. Note that the zero sequence network is not included since .

3.3.4 Balanced Three-Phase Vault

Let us now consider the situation with a balanced three-phase fault on phases a, b, and c, all through the same fault impedance Zf. This fault condition is shown in

Figure 3.7. It is clear from inspection of this figure that the phase voltages at the fault are represented by

(3.49)

(3.50)

(3.51)

The positive sequence voltages are obtained using the following

(3.52)

Using equations (3.49; 3.50 and 3.51), it was concluded that

(3.53)

However, for currents we get

(3.54)

The negative sequence voltage is similarly given by

(3.55)

The zero sequence voltage is also

(3.56)

For a balanced source we have

(3.57)

(3.58)

(3.59)

Combining equations (3.54 and 3.57), it was to conclude

(3.60)

As a result,

(3.61)

Combining equations (3.55 and 3.58) gives

Finally equations (3.56 and 3.59) give

3.4 Series Fault Computations

3.4.1 One Line Open (OLO)

From Figure 3.8, it can be observed that the line for one the open line conductor in phase a is infinity, whereas the line impedances for the other two phases have some finite values [8]. Therefore, the positive, negative, and zero sequence currents can be expressed as

(3.62)

And by current division,

(3.64)

Or simply

(3.65)

Where

(3.66)

3.4.2 Two Line Open (TLO)

If two lines are open as shown in Figure 3.9, then the lime impedances for the

OLO in phases b and c are infinity, whereas the line impedance of phase a has some finite [8]. Therefore,

And

(3.67)

By inspection of Figure 3.9, the positive, negative, and zero currents can be expressed as

(3.68)

Chapter Four

THE APPLICATION OF THE MATHEMATICAL MODEL

4.1 Introduction

Fault calculation is the analysis of power system electrical behavior under fault conditions, with particular reference to the effects of these conditions on the power system current and voltage values. Together with other aspects of system analysis, fault calculation forms and indispensable part of the whole function and process of power system design. Correct design depends essentially on a full knowledge and understanding of system behavior and on the ability to predict this behavior for the complete range of possible system conditions. Accurate and comprehensive analysis, and the means and methods of achieving it, are therefore of essential importance in obtaining satisfactory power system performance and in ensuring the continued improvement in performance which results from the development and application of new methods and techniques.

The applications of power system analysis cover the full range of possible system conditions, they being divisible into two main classes, namely conditions in which the power system is operating in a normal healthy state, and others in which it is subjected to one or more of a wide variety of possible fault conditions. The analysis of these conditions and their effects on the power system is of particular relevance to such considerations as:

(a) The choice of suitable power system management, with particular

reference to the configuration of the transmission or distribution network.

(b) The determination point of the required load and short-circuit ratings

of the power system plant.

protection of the power system.

4.2 Calculation of the Network Sequences

Given the following system, in Figure 4.1 in the case of a fault at F. Assume the following data in p.u:

Table 4.1 System Data for figure 4.1

Network component MVA rating Voltage rating (kV) X 1 (pu) X 2 (pu) X 0 (pu) G1 200 20 0.2 0.12 0.06 G2 200 13.2 0.37 0.25 0.08 T1 200 20 / 230 0.2 0.2 0.2 T2 200 13.2 / 230 0.225 0.225 0.225 T3 200 20 / 230 0.27 0.27 0.27 T4 200 13.2 / 230 0.16 0.16 0.16 L1 200 230 0.11 0.11 0.25

L2 200 230 0.33 0.33 0.6

The positive, negative, and zero network sequences, were obtained using sequence impedance reduction. The positive, negative, and zero network sequences are shown in figures 4.2, 4.3, and 4.4 respectively.

4.3 Single Line-to- Ground Fault

Using the data given earlier, assume there is a SLG and find the voltages and currents at the fault point. The interconnection between the sequence networks for a

SLG is illustrated in Figure 4.5. The sequence network is connected in series for

SLG fault.

The sequence currents are given by

Therefore,

The sequence voltages are as follows

The phase voltages are thus

4.4 Double Line-to-Ground Fault

Using the sequence derived from the first example, assume having a DLG fault with Zf = j0.06p.u and Zg = j0.025p.u. Find the voltages and currents at the fault point. The sequence network connection is as shown in Figure 4.6.

Sequence currents are as follows:

Ia1 =

The sequence voltages are calculated as follows

The phase currents are obtained as

Phase Voltages are

4.5 Line-to-Line Fault

For the given network sequences in the first example, assuming a line to line fault. From the sequence network connection in Figure 4.7, we can find sequence currents at the fault point and sequence voltages thereby

The phase currents are thus

The sequence voltages are

The phase voltages are obtained as shown

4.6 The Balanced Three-Phase Fault

Using the calculated sequences in the first example, we can obtain the short circuit current at the fault point for a balanced three-phase fault

4.7 Series Fault

Given the power system, in Figure 4.8, and in the case of a fault at F and Fꞌ, assume the following data in p.u.

The positive, negative and zero network sequence, at fault points F and Fꞌ are shown in Figure 4.9 using Thevenin’s equivalents.

Case 1. Assuming that there is a One Line Fault at phase (C). Positive, negative, and zero sequence currents were calculated as shown.

In the case of fault at Phase (C)

Case 2

Assuming that there is a Two Line fault at phases (C-A). positive, negative, and zero sequence currents were calculated as shown:

In case of fault at phase (C-A)

Chapter Five

MODEL SIMULATION OF THREE-PHASE COMPENSATED NETWORK

This chapter describes the simulation of the three-phase compensated network, using the Simulink© modeling tool. The Simulink model is show below in

Figure 5.1

A three-phase, 60 Hz, 735 kV power system transmitting power from a power plant consisting of six 350 MVA generators to an equivalent network through a 600 km transmission line. The transmission line is split in two 300 km lines connected between buses B1, B2, and B3. In order to increase the transmission capacity, each line is series compensated by capacitors representing 40% of the line reactance. Both lines are also shunt compensated by a 330 Mvar shunt reactance. The shunt and series compensation equipments are located at the B2 substation where a

300 MVA 735/230 kV transformer with a 25 kV tertiary winding feeds a 230 kV,

250 MW load. The series compensation subsystems are identical for the two lines.

For each line, each phase of the series compensation module contains the series capacitor, a metal oxide varistor (MOV) is protecting the capacitor, and a parallel gap protecting the MOV. When the energy dissipated in the MOV exceeds a threshold level of 30 MJ, the gap simulated by a circuit breaker is fired. CB1 and

CB2 are the two line circuit breakers.

The generators are simulated with a Simplified Synchronous Machine block.

Universal transformer blocks (two-windings and three-windings) are used to model the two transformers. Saturation is implemented on the transformer connected at bus

B2. Voltages and currents are measured in B1, B2, and B3 blocks. These blocks are

Three-phase V-I Measurement blocks where voltage and current signals are sent to the Data Acquisition block through Goto blocks.

GEN B1 B2 B3 1 3 .8 e3 V 7 3 5 e3 V 7 3 5 e3 V 7 3 5 e3 V 1 pu 1 .0 1 2 pu 1 .0 3 pu 1 pu -7 .5 5 2 deg. 1 6 .3 9 deg. 7 .3 5 4 deg. 0 deg. Pm m -C- Pm A A a aA A a A a A a aA A a aA A SSM B B b bB B b B b B b bB B b bB B -C- E C C c c C C c C c C c c C C c c C C CB1 Line 1 Series CB2 Series Line 2 E 6*350MVA 6*350 MVA B1 B2 B3 30,000 MVA (300 km) Comp. 1 Compensation (300 km) 13.8 kV 13.8/735 kV 735 kV (unit 2) Machine initialized for

P=1500 MW

A B

A B C A B C

Vt=13.8kV C

A B C 100 MW Fault A a2 330 Mvar (1) Breaker b2 c2 B a3 b3 C c3

300 MVA

735/230 kV

A B C A B C

Scopes 330 Mvar (2) 250 MW

Data Acquisition

Discrete, Ts = 5e-005 s.

? The 'Model initialization function' defined in the Three-Phase Series Compensated Network Model Properties automatically sets the sample time Ts to 50e-6 s

Figure 5.1 Simulink Model of 3-phase compensated network The output parameters of the simulation are shown in Figure 5.2 below, which has three main sections: Bus B1 parameters, Bus B2 parameters, and Bus B3 parameters.

Vabc_B1 Vabc B1 (pu)

Iabc_B1 Iabc B1 (pu/100MVA) BUS B1

Vabc_B2 Vabc B2 (pu)

Iabc_B2 Iabc B2 (pu/100MVA)

Multimeter BUS B2

Va_Cs Va Cs (pu)

Ia_MOV Ia MOV (A)

Wa_MOV Energy MOVa (J)

Sig_Cs1

Figure 5.2 Simulink Model output parameter block The scope outpus for Buses 1, 2, and 3 are shown below in Figures 5.3 (a), (b) and (c) respectively.

Figure 5.3 (a) Output of Bus B1

Figure 5.3 (b) Output of Bus B2

Figure 5.3 (c) Output of Bus B3

Chapter Six

CONCLUSION

The electric utilities companies are expected to provide consumers with a continuous and high quality service at a competitive and reasonable cost. This means that they have to insure the reliability of the system to provide consumers with a service what is consistent with the safety personnel and equipment, and meet their demands within specified voltage and frequency.

Faults in the transmission lines are one of the elements that the reliability of the system is affected by. The more faults that take place, the less reliable the system is, since they could cause outages in the power system, which may result in an interruption of the service.

Therefore, when designing the power transmission systems, electric companies are expected to follow the set of standard specifications that are briefly described in chapter two of this research, keeping in mind that the further away transmission lines are from natural elements, such as trees, the less faults occurrences will be and the more reliable the power system will be.

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