Lightning response of transmission lines and impulse behavior of concentrated grounds

In order to minimize the losses, two particular issues associated with the lightning phenomenon have been studied and presented in detail in this thesis: 1 multiple flashovers in multiph

ACKNOWLEDGEMENTS

First and foremost, I would like to express my sincere appreciation and utmost gratitude to

my supervisor, Professor A C Liew, for his invaluable advice, guidance and assistance Thanks him for offering me his insight whenever I needed it and giving me the opportunity to learn from him

I would also like to thank my fellow lab-mates for their encouragement and friendship Sincere thanks and gratitude are also due to Mr Seow Hung Cheng of Power Systems Laboratory for providing various supports for my research

Finally, I thank my husband and parents for their understanding and encouragement during my candidature period

TABLE OF LIST ACKNOWLEDGEMENTS I

TABLE OF LIST II

LIST OF PAPERS ARISING FROM WORK IN THIS THESIS IV

LIST OF FIGURES V

LIST OF TABLES VIII

SUMMARY IX

CHAPTER 1 INTRODUCTION 1

1.1 BACKGROUND 1

1.1.1 Overview on Lightning 3

1.1.2 Review of previous work on calculating the lightning performance of distribution lines 7

1.1.3 Review of Liew’s work on dynamic model of impulse characteristics of concentrated earths 8 1.2 OBJECTIVE 9

1.3 ORGANIZATION OF THIS THESIS 11

CHAPTER 2 MULTIPLE FLASHOVERS ACROSS THE SAME PHASE IN DIFFERENT TOWERS 13

2.1 INTRODUCTION OF LIGHTNING STROKES AND THEIR INFLUENCE TO POWER SYSTEMS 13

2.2 OVERVOLTAGE PROTECTIVE DEVICES 15

2.2.1 Insulators 16

2.2.2 Surge arresters 17

2.3 MULTIPLE FLASHOVERS ACROSS THE SAME PHASE IN DIFFERENT TOWERS 19

CHAPTER 3 PROGRAM MFASP 22

3.1 DEVELOPMENT OF MFASP PROGRAM 22

3.2 FEATURES OF MFASP PROGRAM 23

3.3 FORMULATION OF PROGRAM MFASP 24

3.4 PROGRAM DESCRIPTION 30

CHAPTER 4 CASE STUDY 33

4.1 CASE A—LINE WITH ALL FLASHOVERS SUPPRESSED 35

4.2 CASE B—LINE WITH FLASHOVERS ACROSS THE INSULATORS CONSIDERED 38

4.3 CASE C—LINE WITH FLASHOVERS ACROSS THE INSULATORS AND SURGE ARRESTER CONSIDERED 46

4.4 DISCUSSION AND CONCLUSION 53

CHAPTER 5 DEVELOPMENT OF DYNAMIC MODEL OF IMPULSE BEHAVIOR OF CONCENTRATED GROUNDS 55

5.1 INTRODUCTION 56

5.2 PHYSICAL MECHANISM OF BREAKDOWN 57

5.3 INTRODUCTION OF LIEW’S EXPERIMENT 58

5.3.1 Experiment Equipment and Preliminary Tests [26] 58

5.3.2 Experimental results on soil C—wet loamy sand 62

5.4 INTRODUCTION OF LIEW’S DYNAMIC MODEL [26] 65

5.4.1 Basic Assumptions 65

5.4.2 Liew’s dynamic model 67

5.5 INTRODUCTION OF EXPERIMENT IN CALIFORNIA AND ALABAMA 70

CHAPTER 6 DYNAMIC MODEL OF IMPULSE BEHAVIOR OF CONCENTRATED GROUNDS AT HIGH CURRENTS 72

6.1 INTRODUCTION 72

6.1.1 Breakdown Process 74

6.1.2 Impulse Resistance 77

6.2 PROGRAM 79

6.3 VERIFICATION OF THE NEW MODEL 82

6.3.1 Use of proposed dynamic model to reproduce the triggered-lightning experimental results 82 6.3.2 Use of Proposed Model to Reproduce Liew’s Experimental Results on wet loamy sand (Soil C) 86 6.3.3 Reproduction of Liew’s oscillogram No 4910 89

6.4 DISCUSSION AND CONCLUSION 92

CHAPTER 7 CONCLUSIONS 94

APPENDIX 97

APPENDIX A-TOWER CONFIGURATION 97

LIST OF PAPERS ARISING FROM WORK IN THIS

THESIS

1 Wang Junping and A.C Liew, “Multiple flashovers across same phase in different towers”, manuscript submitted for publication in IEEE Power Engineering Society

Transactions on Power Delivery, IEEE, USA

2 Wang Junping, A.C Liew and M Darveniza, “Extension of Dynamic Model of Impulse Behavior of Concentrated Grounds at High Currents”, accepted for

publication in IEEE Power Engineering Society Transactions on Power Delivery, IEEE, USA

LIST OF FIGURES

Fig 1.1 Diagram showing lightning mechanism and ground current [12] 6

Fig 2.1 Voltage-current characteristics of an ideal overvoltage protection device [15] 15

Fig 2.2 Characteristics of insulators and gaps, all values are based on 11/2×40 positive waves and corrected to standard atmospheric conditions [12] 17

Fig 2.3 Thevenin equivalent circuit to calculate the surge arrester current [13] 18

Fig 2.4 Typical voltage and current waveshapes of the surge arrester during a surge discharge operation [13] 18

Fig 3.1 Voltage waves at a grounded pole node before flashover 25

Fig 3.2 Voltage waves at a grounded pole node after flashover across the insulators 28

Fig 3.3 Flowchart of program MFASP 32

Fig 4.1 220 kV transmission line model 33

Fig 4.2 Waveshape of the injected lightning surge 35

Fig 4.3 Overall voltages on towers 1 and 2 for case A—Line with all flashovers suppressed 37

Fig 4.4 Voltages on nodes involved in the flashovers for case B— Line with flashovers across the insulators considered 40

Fig 4.5 Voltages on nodes of tower 1 for case B— Line with flashovers across the insulators considered 41

Fig 4.6 Voltages on nodes of tower 2 for case B— Line with flashovers across the insulators considered 42

Fig 4.7 Current waveform for case B— Line with flashovers across the insulators considered 43

Fig 4.8 Voltages on all nodes of interest for case C— Line with flashovers across the insulators and surge arrester considered 48

Fig 4.9 Voltages on nodes of tower 1 for case C— Line with flashovers across the insulators and

surge arrester considered 49

Fig 4.10 Voltages on nodes of tower 2 for case C— Line with flashovers across the insulators and surge arrester considered 50

Fig 4.11 Currents waveforms for case C— Line with flashovers across the insulators and surge arrester considered 51

Fig 5.1 Equivalent Circuit of Surge Current Tests 58

Fig 5.2 Measurement of Earth Resistance 61

Fig 5.3 Oscillogram and corresponding photograph of surface sparkovers caused by a sparking connection on wet loamy sand (soil C) in the presence of rain sprays [26] 63

Fig 5.4 Oscillogram and corresponding photograph of surface sparkovers from the top of a driven rod when impulsed in wet loamy sand (soil C) in the presence of rain sprays [26] 64

Fig 5.5 Resistivity profiles in Liew’s dynamic-impulse resistance model 66

Fig 5.6 Hemispherical model for direct sparking connection in Liew’s model [26] 68

Fig 5.7 Percentages of return strokes producing detectable filamentary arcing from the base of the strike point as a function of peak stroke current [21] 70

Fig 6.1 Hemispherical model for direct sparking connection in the new model 73

Fig 6.2 Profiles of α as current rises and decays 76

Fig 6.3 Flowchart of the program to compute the earth resistivity 81

Fig 6.4 Sparking radius and the percentage of return strokes producing optically detectable surface arcing versus current peak Numbers above each histogram column indicate the number of strokes producing optically detectable arcing (numerator) and the total number of strokes in that return stroke current range (denominator) [22] 84

Fig 6.5 Coefficient α with current peak ranging from 1kA to 30kA 86

Fig 6.6 Comparison of experimental and calculated voltage and current against time for a sparking connection on wet loamy sand 87

Fig 6.7 Comparison of experimental and calculated resistance against current for a sparking

connection on wet loamy sand 88 Fig 6.8 Comparison of experimental and calculated voltage and current against time for a driven

rod connection on wet loamy sand 90 Fig 6.9 Comparison of experimental and calculated resistance against current for a driven rod

connection on wet loamy sand 91 Fig A.1 220kV transmission line, tower top configuration……… 97

LIST OF TABLES

Table 4.1 Flashovers in Case B Line with flashovers across the insulators considered 44

Table 4.2 Flashovers in case C— Line with flashovers across the insulators and surge arrester considered 52

Table 5.1 Parameters of surge-current generator 58

Table 5.2 Resistivity of soils tested 59

Table 6.1 Input Data for Triggered-Lightning Experiments Simulation 83

Table 6.2 Sparking Radius at Different Current Peaks 85

Table 6.3 Comparison of calculated and experimental results for a sparking connection on wet loamy sand 88

Table 6.4 Comparison of calculated and experimental results for a driven rod connection on wet loamy sand 91

Table 6.5 Input data for calculations to reproduce Liew’s experimental results on soil C 92

SUMMARY

Lightning poses serious hazards to people, buildings, electrical power systems, telecommunication systems and radar stations etc Each year, the devastating effects of lightning cause considerable damage to human beings and properties The understanding

of lightning phenomenon and its subsequent impacts are therefore of great importance In order to minimize the losses, two particular issues associated with the lightning phenomenon have been studied and presented in detail in this thesis: (1) multiple flashovers in multiphase systems including flashovers across the insulation of the same phase in different towers and (2) the dynamic model of impulse behavior of concentrated grounds at high currents

First of all, the phenomenon of multiple flashovers in the multi-circuit and multi-phase line following a lightning strike to it is investigated This leads to the identification of the possible effect of multiple flashovers across the same phase in different towers In previous research, it is commonly thought that a flashover across insulators or through a lightning arrester on a tower can not lead to flashovers across the insulation of the same phase on adjacent towers or that it is of little consequence After the flashover, the earthwire, tower crossarm and the flashed-over phase conductor are connected together with the same voltage Hence, the flashed-over phase conductor comes in parallel with the earthwire Consequently, the voltages of the flashed-over phase conductor and the earthwire remain the same and therefore no voltage difference exists between them This

is, however, true only until the waves arrive at the adjacent tower When the waves arrive

at the adjacent tower, the voltage of the earthwire decreases as a large portion of lightning surge flows along the tower body down to the ground As a result, great voltage differences appear across the insulator strings on adjacent towers, which may lead to more flashovers In this project, a simulation program has been developed to demonstrate this effect of multiple flashovers across the same phase in different towers The simulation program may help to gain a deep understanding of this phenomenon The results obtained are important to the lightning protection of power systems

Second, a dynamic model which describes the impulse behavior of concentrated grounds

at high currents is presented in this thesis This model is an extension of previous models which can successfully account for the surge behavior of concentrated grounds over a much wider range of current densities It is able to describe the well-known effect of ionization of soil as well as the observed effect of discrete breakdowns and filamentary arc paths at much higher currents This model has been verified against the results from experiments on wet loamy sand [26] and also the triggered-lightning experiments in Florida and Alabama [21] The calculated and experimental results are in good agreement

It is hence concluded that the newly developed model can be successfully applied to describe the impulse behavior of concentrated grounds at high currents

CHAPTER 1 INTRODUCTION

Lightning is an awesome occurrence of nature and has been marveled and feared by people since the remotest times Every year lightning strikes to power systems cause serious disturbances, leading to considerable damage and death With the development of large-scale power systems, electric energy is transferred to different loads over long distances via overhead transmission lines Power systems become more susceptible to the damage caused by lightning Therefore, an understanding of the lightning response of power systems is of vital importance

Chapter 1 Introduction

experiment to prove that lightning was electrical in nature and also proposed to use a metallic rod as a lightning interceptor He also was able to infer that the lower part of the thunderstorm was generally negatively charged, a correct observation that was not verified until the early twentieth century[3]

Following Benjamin Franklin there was no significant progress in understanding lightning until the late nineteenth century when photography and spectroscopy became available as diagnostic tools in lightning research The early history of lightning spectroscopy was reviewed by Uman [3] The invention of the double-lens streak camera by Boys in 1900 in England made possible the major advances in our understanding of lightning The first lightning current measurements were made by Pockels [3] in Germany He analyzed the residual magnetic field induced in basalt by nearby lightning currents and by doing so was able to estimate the values of those currents

Modern lightning research can probably best be dated to Wilson in England He was the first to use electric field measurements to estimate the charge structure in the thunderstorm and the charges involved in the lightning discharge[3] After the 1960s, lightning research has become a worldwide activity with increasing interest in lightning and its effects Now

it is possible for people to understand lightning better due to the development of new techniques of data acquisition and recording and new methods of analyses

Generally, lightning can be defined as a transient, high-current electrical discharge between a thunderstorm cloud and earth or from cloud to cloud [3]-[5] The discharge path

is generally measured in kilometers Lightning discharge can be classified as intra-cloud

discharge, inter-cloud discharge, cloud-to-air discharge and cloud-to-ground discharge Among these, cloud-to-ground discharge has gained maximum attention because of its effects on property and people, and also because it can be easily photographed and studied with optical instruments

1.1.1 Overview on Lightning

Generally speaking, the upper part of the cloud carries a positive charge, and the main and lower parts carry a predominately negative charge of roughly equal magnitude At the base of the cloud there exists a small region of positive charge

Due to the lower barometric pressure at high altitudes, an electric field of about 10kV/cm

is required for the initial breakdown Following the initial breakdown, a downward discharge, known as the leader stroke, begins to descend With the descent of the leader stroke, an ionized channel appears between its advancing tip and the charge center in the cloud As the leader approaches the ground, a strong electric field develops between its tip and the ground Usually, the field becomes very intense and can cause a streamer discharge to move upward from the ground to meet the descending leader As a result, electrical continuity is established between the ground and the cloud charge center, leading to the neutralization of the charge on the leader channel This process is manifested by a very bright luminosity traveling along the channel from the ground upwards, known as the return stroke

Chapter 1 Introduction

1.1.1.1 The Stepped Leader

A cloud to ground discharge is initiated by a negative streamer which develops downwards in a series of steps, called stepped leader Schonland and his co-workers determined stepped leaders in the 1930s by using streak-photographic measurements On the basis of measured step length and average earthward speed obtained from streak photograph, stepped leaders were divided into two categories, α and β [3] Type α stepped leaders exhibit a low and relatively uniform average earthward velocity through their trip from cloud base to earth Compared to the β steps, the α steps are generally shorter and do not vary appreciably in length and brightness Type α leaders are less luminous compared

to type β leaders [27]

The stepped leader is thought to start with a local electrical breakdown The breakdown makes mobile the electric charges which previously were attached to ice and water particles The resulting strong concentration of negative charge within the cloud base would produce electric fields, which could then cause a negatively charged column to be propelled downward toward the earth This column is called the stepped leader because it appears to move downward in luminous steps [27]

The lengths of the steps vary between 10 and 200 meters with a median value of 50 meters The time between steps is from 40 to 100 microseconds The overall velocity of advance

of the initial leader is close to 1.0×107cm/sec and remains reasonably constant during most

of its path [26]

1.1.1.2 The Return Stroke

When the stepped leader approaches to within 10-200m of the ground, a streamer from some point on the ground comes up to meet it, and then there commences the return stroke which travels up the previously ionized channel Negative charge is effectively lowered from the cloud to ground even though the luminosity is propagated upwards The return stroke carries the main current of the discharge, ranging from 1kA to 200kA with a median value of 30kA The return-stroke wavefront propagates at a velocity of one-third

to one-tenth the speed of light [27]

1.1.1.3 Subsequent and Multiple Strokes

The potential of the cloud charge center is lowered considerably with the development of

a high conducting arc path between the charge center and ground This process may result

in higher potential differences between this region and another charge center within the cloud, leading to the continued progress of streamers into the cloud and the formation and attraction of streamers from other charge centers When two approaching streamers meet,

a new negative discharge proceeds into the somewhat decayed conducting channel at the cloud base left by the stepped leader and its return stroke A bright band of luminosity called a dart leader then merges from the cloud base and sweeps down the old pre-ionized channel in a continuous fashion without branching The dart leader traverses the return-stroke channel, increasing its degree of ionization, depositing charge along the channel

Chapter 1 Introduction

and carrying the cloud potential earthward once more It thus sets the stage for the subsequent return stroke [27]

The lightning mechanism and ground current is shown in Fig 1.1

Fig 1.1 Diagram showing lightning mechanism and ground current [12]

1.1.2 Review of previous work on calculating the lightning performance

of distribution lines

Since 1920, several methods have been developed to calculate the lightning performance

of transmission lines, including field calculations, traveling wave calculations, geometric models, Monte Carlo techniques, and so on

In 1954, Clayton and Hileman developed generalized curve methods which were based on analogue computer results [6] In 1967, Sargent and Darveniza developed a program that combined the traveling wave calculation and the Monte Carlo technique to predict the outage rates of transmission lines In this technique, the lattice diagram method is used to keep track of the traveling waves The magnitude, time to crest, power frequency voltage and all the other needed parameters of lightning stroke current can be selected in this method Liew [7]-[8] developed a comprehensive Monte Carlo/dynamic traveling wave program WPTL for the calculation of the lightning performance of unshielded wood pole transmission lines In WPTL, the flashed-over conductor is modeled by lumping into a single equivalent conductor when a flashover occurs, and the surge arresters are modeled

by lumping an equivalent resistance into the footing resistance This approach gave results

in good agreement with the observed outage rates and the proportion of fault types for a variety of unshielded transmission line designs Around 1980, Frowd [9] developed an analytical program TWCALC to calculate the response to lightning of a single-phase unshielded distribution line consisting of one phase conductor and an earthed neutral wire

In addition to including all the features of WPTL, TWCALC was developed specially to

Chapter 1 Introduction

include the presence of an earthed neutral wire that is predominant in lines of U.S In 1991, Liew [1]-[2] developed another program 3PHASE, which used a new implementation of a multiconductor traveling wave technique so that voltage and current waves on all phase conductors and the neutral can be calculated This program is an improvement over pervious methods not only because the voltage and current waves on all phase conductors and neutral can be calculated, but also because many features important to the accurate simulation are considered, including the tower types, non-linear effects of corona, dynamic footing resistance, surge-arrester behavior and so on

In this thesis, a new program MFASP (Multiple Flashover Across Same Phase) is

developed In addition to including some features of 3PHASE, MFASP is developed specially to study the phenomenon of multiple flashovers in multiphase systems including flashovers across the same phase in different towers

1.1.3 Review of Liew’s work on dynamic model of impulse

characteristics of concentrated earths

In 1974, Liew and Darveniza developed a dynamic model of impulse characteristics of concentrated earths [16] This model successfully describes the nonlinear and time-iterative behavior of earths with resistivities ranging from 5000Ωcm to 31000Ωcm on a time-to-time basis A series of experiments were conducted at the University of Queensland High-Voltage Laboratory These experiments were used to provide reliable data for the development and verification of the dynamic model The simulation results

proved the success of this model This model can significantly improve the accuracy of lightning-performance calculations based on the Monte-Carlo dynamic traveling-wave approach Furthermore, a convenient and accurate representation of a direct sparking connection to earth was developed in this model

Liew’s model was very successful in cases with diffuse growth of increasing ionization However, it did not attempt to describe the surge behavior of earths at high lightning currents that resulted in discrete breakdown paths In one of his experiments, the discrete breakdown paths were observed with the high-resistivity wet loamy sand (soil C) in the presence of rain sprays [26] In this thesis, a new model capable of describing the characteristics of concentrated grounds at high currents is developed It is an improvement over previous models for the description of the surge behavior of concentrated grounds

1.2 Objective

In this thesis, two aspects will be discussed in detail as follows:

(i) Multiple flashovers in multiphase systems including flashovers across the

insulation of the same phase in different towers

concentrated grounds at high currents

The purpose of the first aspect is to study and simulate multiple flashovers across the insulation of all phases including the same phase in different towers Through computer

Chapter 1 Introduction

simulations, multiple flashovers across the insulation of the same phase in different towers are identified and demonstrated In all, three case studies are performed The aim of these case studies is to investigate the occurrence of multiple flashovers across the same phase

in different towers under different situations, therefore to get a better understanding of it

The phenomenon of multiple flashovers in the multi-circuit and multi-phase line after a lightning stroke to it have been discussed by many researchers, and captured by photographs in [28] and [29] However, until now the possibility of multiple flashovers across the same phase in different towers has not been discussed Therefore, a detailed analysis is very helpful and necessary to the understanding of the lightning response of transmission lines In addition, some problems, such as the use of surge arresters on hill tops to prevent flashovers on adjacent towers, are brought out and discussed They are very important to the lightning protection of power systems

The purpose of the second aspect of this thesis is to develop a new dynamic model to describe the impulse behavior of concentrated grounds at high currents which lead to discrete breakdowns and filamentary arc paths This kind of discrete breakdowns and resulting filamentary arc paths have been reported in several experiments [21-23] [26] However, a suitable concentrated ground model to accurately describe this phenomenon has not been fount yet Thus, to develop a new model is necessary and important to the understanding of the behavior of concentrated grounds subjected to high currents, such as lightning currents

The new model was developed on the basis of Liew’s dynamic model [16] Results from experiments on wet loamy sand [26] and triggered-lightning experiments in California and Alabama [21]-[22] are used to verify the proposed model A computer program is developed to perform the simulations The agreement between the simulation and experimental results is good, which can further prove the accuracy of the proposed model Comparing to Liew’s model, the new model is able to describe the well known effect of ionization of soil as well as the observed effect of discrete breakdowns and filamentary arc paths at much higher currents

1.3 Organization of this thesis

This thesis is organized into seven chapters Following this introduction, Chapter 2 provides a general description of multiple flashovers across all phases including the same phase in different towers

In Chapter 3 the computer program MFASP is explained in detail The explanation includes its formulation, flowchart and features

Three case studies are reported in Chapter 4 The first is where line insulation flashover is suppressed In the second case, flashovers across tower insulators mounted on all towers are allowed to occur as in normal operation; Surge arresters are installed on the tower which is struck by lightning in the final case The simulation results of these case studies are explained in detail in this chapter

Chapter 1 Introduction

Chapter 5 reviews Liew’ experiment on wet loamy sand (soil C) and his dynamic model

of impulse characteristics of concentrated earths Also, triggered-lightning experiments in California and Alabama are briefly introduced in this chapter

A new dynamic model of the impulse behavior of concentrated grounds at high currents is developed in Chapter 6 The computer program to simulate the impulse behavior of concentrated grounds at high currents is also developed and introduced in this chapter Using the new dynamic model and the computer program, results from Liew’s experiment

on wet loamy sand and triggered-lightning experiments in Florida and Alabama are reproduced The agreement between the simulation and experimental results proves the success of the new model

Finally, Chapter 7 concludes this thesis The scope for further work is also briefly presented

CHAPTER 2 MULTIPLE FLASHOVERS ACROSS THE SAME PHASE IN

In the past, with the limited knowledge available, it was believed that it was practically impossible to design transmission lines to overcome direct lightning strikes Therefore, lines were designed on the basis of induced strokes According to the induced-stroke theory, the charged cloud (covering the vicinity of the line) with its accompanying

Chapter 2 Multiple Flashovers Across the Same Phase in Different Towers

gradient of voltage to ground bind a charge on the line The discharge of the cloud to a location other than the line itself released this bound charge, which was then free to travel along the line Tests have shown that actual gradients appearing on the line during near-by discharges are too low to account for the damages frequently seen Now it has been proven that for lines up to the highest voltage now in use, lightning disturbances resulting from direct strokes are usually a principal factor The direct-stroke theory attributes the severe lightning disturbances on any transmission line to direct contact of the discharge with the line [12]

Following a direct lightning stroke on a transmission line tower, part of the lightning surge flows to ground through the tower body and pairs of traveling waves propagate along the overhead earthwire The traveling waves on the overhead earthwire and tower system can generate overvoltages on them These overvoltages depend on several factors, namely, the line characteristic impedance, the level of the lightning current wave, and the tower characteristics as well as the resistance at its footing Basically the voltage waveform and amplitude can be calculated by multiplying the surge current at any instant by the effective surge impedance Overvoltages caused by direct lightning strikes often lead to the insulation flashovers and subsequent fault Therefore, it is of pivotal importance to protect power systems from the effects of direct strokes

Protection against direct strokes requires adequate drainage facilities and adequate insulation structures so that the discharge can drain to ground without affecting the conductors The protection can be achieved in many ways Insulators and surge arresters are two protective devices which are commonly used in power systems

2.2 Overvoltage protective devices

As known, power systems must be protected against overvoltages to avoid insulation flashovers and subsequent fault Protection can be achieved in any time region in which the protective characteristic lies below the withstand characteristic of the insulation Ideally, a protection device must have a voltage-current characteristic as indicated in Fig 2.1

Fig 2.1 Voltage-current characteristics of an ideal overvoltage protection device [15]

The ideal requirements for shunt-connected protective devices can be summarized as follows [13]:

Chapter 2 Multiple Flashovers Across the Same Phase in Different Towers

(1) They must not spark over under temporary voltages under any but the most exceptional circumstances

(2) Their volt/time curve must lie below the withstand level of the protected insulation in any time region in which protection is needed The margin between the two curves must be adequate to allow for the effects of distance, polarity, variations in relative air density, humidity, ageing of the insulation and likely changes in the characteristics of the protective device

(3) They must be able to discharge high-energy surges without changes in their protective level or damage to themselves or adjacent equipment

(4) After discharging a surge, they should reseal in the presence of temporary overvoltages

2.2.1 Insulators

Insulator flashover is determined by comparing the voltage stressing the insulator with its volt-time characteristic If the voltage across the insulator crosses its volt-time curve at any time instant, a flashover is deemed to occur Following the flashover across the insulator, the flashed-over path would be bridged by a short-circuit arc with assumed zero arc voltage [12] The flashover characteristics of standard insulators can be determined by the curves in Fig 2.2, which are based on laboratory tests

Fig 2.2 Characteristics of insulators and gaps, all values are based on 11/2×40 positive

waves and corrected to standard atmospheric conditions [12]

2.2.2 Surge arresters

Surge arresters are installed near the equipment being protected, connecting from the phase conductor to ground The basic elements of a surge arrester are the sparkgap, which works as a fast switch, and the non-linear resistor [13] In normal conditions, the surge arrester acts as an open-circuit, thus preventing the power frequency current from flowing through it When fault occurs, surge arresters change to a relatively good conductor

Chapter 2 Multiple Flashovers Across the Same Phase in Different Towers

capable of discharging the high surge current with a voltage drop lower than the withstand voltage of the protected equipment [14] The equivalent circuit used to calculate the surge arrester current is shown in Fig 2.3

Fig 2.3 Thevenin equivalent circuit to calculate the surge arrester current [13]

The typical voltage and current waveshapes of a surge arrester during a surge discharge operation are:

Fig 2.4 Typical voltage and current waveshapes of the surge arrester during a surge

discharge operation [13]

Following a lightning stroke to a transmission line tower, part of the lightning surge flows

to ground through the tower body and pairs of traveling waves propagate along the overhead earthwire [11] The traveling waves on the overhead earthwire and tower system can generate overvoltages on them With the increase of the injected lightning surge, voltage across the insulation mounted between the tower and phase conductor may rise above its insulation level and leads to multi-phase and multi-circuit flashovers

It was commonly thought that after the flashover of the insulators between the tower and phase conductor, the eathwire, tower crossarm and the flashed-over phase conductor are connected together with equal voltages Hence, previous methods seem to consider the flashed-over phase conductor to be brought in parallel to the earthwire Consequently, the voltages of the earthwire and flashed-over phase conductor remain the same and therefore

no voltage difference exists between them This is, however, true only until the waves travel up to the adjacent tower When the waves reach the adjacent tower, the voltage of

Chapter 2 Multiple Flashovers Across the Same Phase in Different Towers

the earthwire decreases as a large portion of the lightning surge flows along the tower body down to the ground As a result, great voltage differences appear across the insulator string mounted between the adjacent tower and the flashed-over phase conductor, which may lead to more flashovers That is the development of multiple flashovers across the same phase in adjacent towers

The above described formation of multiple flashovers across the same phase in adjacent towers has not been evident in previous research and is different from the formation of frequently mentioned multiple flashovers The former occurs after the initial flashover happens on the stricken tower and the injected lightning surges reach the adjacent towers Since a large portion of the lightning surge flows along the adjacent tower body down to the ground, a great voltage drop appears on the earthwire This may lead to the voltage difference across the insulator string on adjacent tower above its insulation level and subsequent flashovers occur as a result The latter happens because the injected lightning surge flowing on the transmission lines is so large that it can generate overvoltage on them, thereby causing multiple flashovers

The possibility of multiple flashovers across the same phase in different towers has not been discussed before Therefore, a detailed analysis is very helpful to the understanding

of the lightning response of transmission lines In this thesis, a computer program MFASP

is developed which is able to simulate the multiple flashovers across all phases including

on the same phase in different towers Its various features are mentioned later in this thesis

A simple transmission line model is used in the program to illustrate the occurrence of

multiple flashovers across the same phase in different towers under different situations Several results were obtained from the simulations and discussed in depth

Chapter 3 Program MFASP

CHAPTER 3 PROGRAM MFASP

3.1 Development of MFASP program

Many computer programs have been developed by different researchers in order to understand the lightning performance of transmission lines Liew [7]-[8] developed a comprehensive Monte Carlo/dynamic traveling wave program called WPTL This program is used to calculate the lightning performance of unshielded wood pole transmission lines, and it includes the effect of weak links and non-linearities such as corona, wavefront distortion and the voltage-time behavior of the insulation Later Frowd [9] developed an analytical program called TWCALC to calculate the response to lightning of a single-phase unshielded distribution line consisting of one phase conductor and an earthed neutral wire In 1991, Liew [1]-[2] developed another program called 3PHASE This program used a new implementation of a multi-conductor traveling wave technique The voltage and current waves at every point on all phase conductors and the neutral can be calculated This program is very useful to assess the insulation behavior and performance of lines during lightning strikes Based on program 3PHASE, a new computer program MFASP is developed in this thesis Some features of 3PHASE are

included in MFASP Compared to 3PHASE, in MFASP the traveling surges on the flashed-over phase conductor are considered Thus MFASP can be specially used to simulate multiple flashovers on the same phase in different towers It also can be used to simulate the multiple flashovers across all phases, which is almost same to 3PHASE

3.2 Features of MFASP program

Program MFASP has the following features:

1 All node types commonly found in transmission systems are considered They are: (1) Midspan node

(2) Ungrounded pole node

(3) Grounded pole node

(4) Surge-arrester pole node

(5) Pole-footing node

2 Options are provided for power frequency voltage to be considered The exact location

of the lightning stroke can also be chosen

3 A lightning stroke is considered as an ideal current source

4 Insulation flashover is determined by comparing the voltage stressing the insulation with its volt-time characteristic If the voltage across the insulators crosses the volt-time curve at any time instant, a flashover is deemed to occur Following a flashover across the insulators, the flashed-over path is bridged by the short-circuit arc with assumed zero arc voltage [12]

Chapter 3 Program MFASP

5 Surge arresters, with a discharge voltage lower than the voltage which the protected equipment can withstand, are usually installed beside the tower insulators in order to protect them and to provide quenching of the power follow arcs Once the voltage across the surge arrester is above its sparkover voltage, it can change to a relatively good conductor capable of discharging the current surge At the moment of the flashover, the surge arrester installed between the phase conductor and the overhead earthwire is modeled by a current source equal to the surge-arrester current The equivalent resistance

of a surge arrester is determined by its voltage-current characteristics [13]

6 A Bewley lattice [11] is used to store the values of the traveling current waves

7 The behavior of traveling waves on the overhead earthwire and all phase conductors can be fully simulated The successive reflections up and down the towers are also fully represented

3.3 Formulation of program MFASP

In MFASP, the distribution system is considered to be made up of a series of nodes These nodes are classified differently according to their respective mode of earthing and function

In general, five main classes of nodes are identified They are grounded pole node, ungrounded pole node, midspan node, surge-arrester pole node and pole-footing node

The transmission line model in Fig.3.1 is used here to introduce the formulation used in program MFASP It illustrates the set of incident and reflected waves at a junction of a

grounded pole node The lightning stroke is injected into tower 1 Towers 2 and 3 stand on different sides of tower 1, and are equidistant from it

e2

Is=injected lightning surge

overhead earthwirephase A

phase Cphase B

abc

Tower 1

t

Fig 3.1 Voltage waves at a grounded pole node before flashover

ytt = surge admittance of the overhead earthwire

Is = injected lightning current surge

yt = surge admittance of the downlead/tower

ya, yb, yc = surge admittance of phase conductor A, B, C respectively

e1, e4, e5 = incident voltage waves

e2, e3, e6 = reflected voltage waves

Cta, Ctb, Ctc, Cab, Cac, Cbc= coupling factors between conductors

After the lightning strikes a transmission line tower 1, in addition to the surge flowing down to the ground through the tower body, pairs of traveling waves propagate along the

Chapter 3 Program MFASP

overhead earthwire These traveling waves on the overhead earthwire and tower system can generate overvoltages on them Simultaneously, voltages are induced on the parallel phase conductors The traveling waves on the overhead earthwire are reflected at system discontinuities Relations between the incident and reflected waves for each node on overhead earthwire and induced voltages for each node on phase conductors are derived from [1] and [11]

A set of voltage and current equations can be obtained for each conductor before flashover occurs

The voltage equations for node t are as follow:

1 2 3 4 5 6

e +e =e +e =e +e =V t (3.1) Total current into node t is:

(1 2) ( 4 3) ( 5 6) 0

I s+y tt e −e +y tt e −e +y e t −e = (3.2) Solving (3.1) and (3.2) results

Accompanied with the traveling waves on the overhead earthwire are voltages induced on the phase conductors, which can be described and calculated by the following equations

of wires in parallel with the overhead earthwire, and part of the lightning surge will then

be diverted to it

Assume that a flashover happens across the insulator string between phase conductor C and tower 1, as shown in Fig 3.2

Chapter 3 Program MFASP

e2

overhead earthwirephase A

phase Cphase B

e5 e6

VaVbVc

Tower 1 Tower 2Tower 3

e7

e8 e10 e9

e4

VtIs=injected lightning surge

Fig 3.2 Voltage waves at a grounded pole node after flashover across the insulators

After the flashover across the insulators mounted between the overhead earthwire and phase conductor C on tower 1, part of the lightning surge is diverted to phase conductor C Another set of voltage and current equations can be obtained for each conductor as follows:

The voltage equations for node t are:

t V e e e e e e e

e

e

10 9 8 7 6 5 4

c y e e c

y (3.10)

Solving (3.9) and (3.10), we have

V a =C ta× +V t C ab×V b+C ac×V c (3.16)

V b=C tb× +V t C ab×V a+C bc×V c (3.17)

V c =V t (3.18)

Chapter 3 Program MFASP

3.4 Program description

The flowchart of program MFASP is given in Fig.3.3 The program begins with the input

of the following data

1 The stroke data

The user not only has the choice of selecting the stroke termination point, but also the current waveshape and magnitude;

2 Tower configuration

It includes the height of phase conductors and overhead earthwire above the ground plane, spacings between conductors, average span length, and phase conductor radius;

3 Power frequency voltage

Selecting the value of power frequency voltage for including or suppressing its effects;

4 System parameters

Total number of spans to be considered and the travel time of each span;

5 Protection equipment parameters

Sparkover voltage and voltage-current characteristic of surge arresters

Flashover voltage and volt-time characteristic of tower insulators

6 Basic time increment as step size and the maximum number of time that are to be considered

The program proceeds with the computations of self and mutual impedances, admittances, and coupling factors The computation routine at each time instant proceeds as follows: