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Acknowledgements
All praises and thanks to The Almighty Allah, the most merciful and beneficent,
for giving me strength and courage to complete this PhD dissertation. My humblest
gratitude to the Holy Prophet Muhammad (Peace Be upon Him), whose life has been a
continuous source of inspiration and guidance for me.
I would like to express my deepest gratitude to my research supervisor Prof. Matti
Lehtonen for his continuous guidance, support and encouragement. I learned a lot
from his observations and comments to establish the overall direction of the research.
He believed in my capabilities, and provided me with all the support that I needed
during my doctoral studies. Prof. Lehtonen, it was my pleasure and a great honour to
work with you!
I am extremely indebted to Dr. Nagy I. Elkalashy and Dr. Nehmdoh A. Sabiha for
their research cooperation and bearing my long Skype calls for discussions from the
start to the end. It would have been difficult to complete this work without their valuable advice, guidance and the continuous support. I also express my gratitude to Mr.
Mohammad E. M. Rizk for his valuable discussions and contributions to this work. I
thank Dr. G. Murtaza Hashmi, Dr. Kashif Javed and Dr. Muhammad Humayun for
always being extremely helpful during my stay in Finland.
I am grateful to the pre-examiners, Prof. Akihiro Ametani and Dr. Paul Taklaja, for
their valuable feedback on my doctoral thesis.
Special thanks goes to the staff of high voltage laboratory at Aalto University especially Dr. Petri Hyvönen, Dr. Joni Klüss and Jouni Mäkinen for their kind help in carrying out my laboratory work from time and time despite their busy schedule. Many
thanks to Ari Haavisto for taking care of IT related issues.
I would like to express my sincere gratitude to the Department of Electrical Engineering and Automation at Aalto University for the financial support provided by
RIMA and SAGA-EE projects. I would like to offer my special thanks to all the other
members of our research group for providing me a pleasant and encouraging working
environment.
v
My sincere appreciations for my family, my parents, wife, brother, brother-in-law,
sister and niece Maham for their support and prayers during this time. At the end, I
would express appreciation to my beloved daughter, Sarah, whom I missed the most
during my stay in Finland. She bore the pain of living thousands miles apart at an age
and time when she really needed my attention. I dedicate this thesis to my family, the
most important people in my world.
Espoo, December 1, 2015
Farhan Mahmood
vi
Contents
1.
Introduction ............................................................................................1
1.1
Problem Description ...........................................................................2
1.1.1 Fault Statistics in Finland ...................................................................2
1.1.2 Lightning Observations in Finland .....................................................3
1.1.3 Overvoltage Protection of Finnish Medium Voltage Lines ................4
1.1.4 Lightning-Initiated Flashover Arc ......................................................5
1.1.5 Dielectric Strength of Medium Voltage Insulation .............................5
1.1.6 Risk of Insulator Flashovers ...............................................................6
1.1.7 Consideration of Lossy Ground Effect ...............................................6
1.1.8
Mitigation of Lightning-Initiated Flashover Faults ........................7
1.2
Research Contribution ........................................................................7
1.3
Dissertation Outline ............................................................................9
2.
Modelling of Lightning-Initiated Flashover Arc in Medium Voltage Lines
11
2.1
Experimental Set-up .........................................................................12
2.2
Experimental Results ........................................................................14
2.2.1
Recorded Waveforms ...................................................................14
2.2.2
Path of Flashover Arc ...................................................................17
2.2.3
Total CFO and Volt-time Curves..................................................18
2.3
Arc Modelling...................................................................................19
2.3.1
Experimental Arc Characteristics .................................................19
2.3.2
Mathematical Modelling of the Arc..............................................21
2.3.3
Flashover Arc Representations .....................................................23
2.4
Component Modelling in ATP-EMTP .............................................25
2.4.1
Modelling of Impulse Generator...................................................25
2.4.2
Modelling of MV Distribution Line .............................................25
2.4.3
Modelling of Insulator ..................................................................25
2.4.4
Modelling of Wood Pole and Cross arm ......................................26
2.5
Comparison of Experimental and Simulated Results .......................27
vii
2.5.1
Grounded Cross-arm Configuration ............................................. 27
2.5.2
Ungrounded Cross-arm Configuration ......................................... 27
3.
Performance Evaluation of Lightning Overvoltage Protection Schemes for
Pole-Mounted Distribution Transformers ........................................................ 31
3.1
Description of the Modelled Power System ..................................... 32
3.2
Overvoltage Generation Mechanism ................................................ 34
3.3
Results and Discussions ................................................................... 35
3.3.1
Case I: No Protection Installed in the System .............................. 35
3.3.2
Case II: Spark Gaps Installed at the Transformer Terminals without and
with Filtering Element .................................................................................. 37
3.3.3
Case III: Surge Arresters Installed at the Transformer Terminals 39
3.3.4
Case IV: Series Combination of Surge Arresters and Spark Gaps Installed
at the Transformer Terminals ....................................................................... 40
4.
Flashover Characteristics of Medium Voltage Line Insulation ............ 43
4.1
Experimental Work .......................................................................... 44
4.1.1 Test Specimen .................................................................................. 44
4.1.2
Experimental Set-up ..................................................................... 45
4.1.3
Test Method.................................................................................. 46
4.2
Test Results ...................................................................................... 46
4.2.1
Volt-time Characteristics .............................................................. 46
4.2.2
Mean and Standard Deviation of Flashover Probability Distributions
48
4.3
Flashover Characteristics of Test Samples Under Impulse Voltages49
4.3.1
Mathematical Formulation ........................................................... 49
4.3.2
Flashover Probability Distributions for Impulse Voltages ........... 49
4.4
Flashover Characteristics of Insulation for Combined Voltages ...... 50
4.4.1
Modified Probabilistic Model ...................................................... 50
4.4.2
Flashover Probability Distribution for Combined Voltage Test .. 51
5.
Probabilistic Risk Assessment of Medium Voltage Insulation Flashover55
5.1
Experimental Work .......................................................................... 56
5.1.1 Experimental Set up ......................................................................... 56
5.1.2
5.2
Test Results .................................................................................. 57
Probabilistic Model of Multi-phase Insulator Flashovers ................ 58
5.2.1
Mathematical Formulation ........................................................... 58
5.2.2
Results .......................................................................................... 58
5.3
Experimental Verification with Three-Phase Arrangement ............. 59
5.4
Probabilistic Model of Peak Lightning-Induced Overvoltages ........ 62
5.4.1
viii
Effect of Perfectly Conducting and Lossy Ground ...................... 62
5.4.2
Rusck’s Model for Perfectly Conducting Ground ........................62
5.4.3
Darveniza’s Model for Lossy Ground ..........................................63
5.4.4
Methodology for Monte Carlo Simulation Method ......................63
5.4.5
PDF of Peak Lightning-Induced Overvoltages .............................64
5.5
6.
Results and Discussions ....................................................................67
Mitigating the Risk of Medium Voltage Insulation Flashover .............71
6.1
Risk-based Insulation Coordination Method ....................................72
6.2
Upgrading the Line Insulation Level ................................................73
6.2.1
Cost-Benefit Planning Method .....................................................73
6.2.2
General Economic Cost Model .....................................................73
6.2.3
Results and Discussion .................................................................75
6.3
Installation of Surge Arresters ..........................................................76
6.3.1
Configuration of the Overhead Line .............................................77
6.3.2
Profile of the Peak Lightning-Induced Overvoltages ...................77
6.3.3
Risk Assessment ...........................................................................79
6.4
Effect of Combined Surge Arresters and Shield Wire ......................80
6.5
Application Example ........................................................................83
7.
Conclusions and Future Research Work ...............................................85
7.1
Conclusions ......................................................................................85
7.2
Future Research Work ......................................................................87
ix
List of Abbreviations and Symbols
AC
Alternating current/voltage
ATP
Alternative transients program
BCTRAN Standard transformer model in ATP-EMTP
BIL
Basic Impulse Insulation Level
CDF
Cumulative distribution function
CFO
Critical flashover
CIGRE
Conference internationale des grandes reseaux electriques
DC
Direct current/voltage
EMTP
Electromagnetic transients program
FDTD
Finite difference time domain
FMI
Finnish meteorological institute
GFD
Ground flash density
GPR
Ground potential rise
IEEE
Institute of electrical and electronics engineers
IS
Insulator
LDM
Leader development model
Log. std.
Logarithmic standard deviation of soil resistivity
LV
Low voltage
MODELS User-built models in ATP-EMTP
MOV
Metal-oxide varister
MV
Medium voltage
NORDLIS
x
Nordic lightning information system
P
Absolute pressure
PDF
Probability density function
RH
Relative humidity
RMS
Root mean square
R-P
Rod-plane
R-R
Rod-rod
SA
Surge arrester
SG
Spark gap
SI
Standard Impulse
STLI
Short tail lightning impulse
T
Temperature
TACS
Transient analysis control system
VBP
Value-based planning
2-D
Two dimensional
di/dt
Rate of change of current (kA/μs)
dU/dt
Steepness of the overvoltage waveform (MV/μs)
f
Total outage rate (1/100 km-year)
fp
Number of line permanent failures (1/100 km-year)
ft
Number of line temporary failures (1/100 km-year)
fUm (U)
PDF of the lightning overvoltages
g
Instantaneous arc conductance (Siemens)
h
Height of overhead line (m)
hx-arm
Height of cross arm above ground (m)
i
Instantaneous arc current (A)
ir
Interest rate (%)
k
Empirical constant
l
Leader length (m)
n
Economic life of overhead line (years)
q
Customer participation factor
rx-arm
Radius of cross arm (m)
t
Elapsed time (μs)
tc
Corona inception time (μs)
xi
td30/90
Front time (μs)
tf
Time to flashover (μs)
th
Tail time (μs)
tp
Mean duration of line permanent failure (h)
tR
Leader propagation time (μs)
ts
Streamer propagation time (μs)
tt
Mean duration of line temporary failure (h)
x
Distance along the length of overhead line (m)
y
Distance of stroke location from the line (m)
Cb
Load capacitance (pF)
CC
Annual line outage customer cost (€/100 km-year)
CFR
Mean cost of one permanent failure repair (€/fault)
CINV
CLOSS
CMAINT
xii
Equivalent annual line investment cost (€/100 km-year)
Annual cost of losses (€/100 km-year)
Annual maintenance cost of line (€/100 km-year)
COUT
Annual outage cost of the line (€/100 km-year)
Cp
Capacitance of wood pole (pF)
Cs
Discharge resistance (nF)
CTI
Present value of total investment cost (€/100 km)
CTOTAL
Total annual cost of energy distribution (€)
CU
Annual line outage utility cost (€/100 km-year)
CUEC
mean annual customer cost of undelivered energy (€/kWh)
CUEU
Mean annual cost of undelivered energy (€/kWh)
CUPC
Mean annual customer cost of undelivered power (€/kW)
D
Diameter of reactor (m)
E0
Critical field strength (kV/m)
G
Stationary arc conductance (Siemens)
H
Height of the reactor (m)
II, Initial
Crest current (kA)
Im
Peak value of load current in the overhead line (A)
Imed
Median value of peak lightning current (kA)
Ip
Peak lightning current (kA)
Kv
Simplification constant in Rusck’s and Darveniza model
Kw
Winding factor
L
Insulator length (m)
Ls
Self inductance of the series reactor (μH)
Lx-arm
Cross arm inductance (μH)
N
Number of turns of reactor
N1-FO
Number of single-phase flashovers
N2-FO
Number of two-phase flashovers
N3-FO
Number of three-phase flashovers
NFO
Number of flashovers
NT
Number of impulse shots applied at each voltage level
P0
Power outage caused by line trip-out (kW)
Px-FO
Probability of 1-phase, 2-phase and 3-phase flashover for x = 1, 2 and 3
PFO
CDF of insulation flashover voltages
P (U)
Probability of flashover at voltage U
R
Resistance of the overhead line (Ÿ)
Ravg
Average risk of flashover over a distance
Rd
Damping or front resistance (Ÿ)
Re
Discharge resistance (Ÿ)
RFO
Risk of insulation flashover
Rp
Resistance of wood pole (Ÿ)
Sm
Front steepness (kA/μs)
U
Test voltage level (kV)
Uarc
Stationary arc voltage (kV)
Um
Median value of peak lightning-induced overvoltages (kV)
Umax
Peak value of AC voltage (kV)
U50%
Critical flashover voltage (kV)
UPC
Peak induced overvoltage over a perfectly conducting ground (kV)
xiii
ULG
Peak induced overvoltage over a lossy ground (kV)
Z0
Characteristic impedance (Ÿ
ș
Phase angle of the AC voltage
șa
Phase angle of phase a
șb
Phase angle of phase b
șc
Phase angle of phase c
μ0
Permeability of vacuum = 4ʌ×10-7 H/m
ʌ
Constant equal to 3.14159265
ȡ
Soil resistivity (Ÿm)
ȡavg
Average value of soil resistivity (Ÿm)
ı
Standard deviation of U50%
ıi
Logarithmic standard deviation of peak lightning current
ılnUm
Logarithmic standard deviation of peak lightning-induced overvoltages
IJ
Arc time constant (s)
ǻt
Sampling period
ǻ-Y
Delta-wye
xiv
List of Publications
This doctoral dissertation consists of a summary and of the following publications
which are referred to in the text by their numerals
1. F. Mahmood and M. Lehtonen “Experimental Investigation of Lightning-Inititaed
Flashover Faults in Medium Voltage Lines,” International Conference on High Voltage Engineering and Applications (ICHVE’14), Poznan, Poland, Sept. 8-11, 2014.
2. F. Mahmood, N. I. Elkalashy and M. Lehtonen “Modelling of Flashover Arcs in
Medium Voltage Networks Due to Direct Lightning Strikes,” International Journal of
Electrical Power and Energy Systems (JEPE), vol. 65, 2015, pp. 59-69.
3. F. Mahmood, M. E. M. Rizk and M. Lehtonen “Evaluation of Lightning Overvoltage Protection Schemes for Pole-Mounted Distribution Transformers,” International
Review of Electrical Engineering (IREE), vol. 10, no. 5, Sep./Oct. 2015, pp. 616-624.
4. F. Mahmood, M. E. M. Rizk, N. A. Sabiha and M. Lehtonen “Flashover Probability
Distribution and Volt-time Curves of Medium Voltage Overhead line Insulation under
Combined AC and Lightning Impulse Voltages,” International Review of Electrical
Engineering (IREE), vol. 10, no. 5, Sep./Oct. 2015, pp. 625-632.
5. F. Mahmood, N. A. Sabiha and M. Lehtonen “Probabilistic Risk Assessment of MV
Insulator Flashover under Combined AC and Lightning-Induced Overvoltages,” IEEE
Transactions on Power Delivery, vol. 30, no. 4, Aug. 2015, pp. 1880-1888.
xv
6. F. Mahmood, N. A. Sabiha and M. Lehtonen “Effect of Combined AC and Lightning-Induced Overvoltages on the Risk of MV Insulator Flashovers above Lossy
Ground” Electric Power Systems Research, vol. 127, 2015, pp. 101-108.
7. F. Mahmood, M. Humayun and M. Lehtonen “Risk-Based Design Methodology for
the Selection of Insulation Level Against Lightning-Induced Overvoltages in Medium
Voltage Lines,” 19th International symposium on High Voltage Engineering (ISH’15),
Pilsen, Czech Republic, Aug. 23-28, 2015.
8. F. Mahmood, M. E. M. Rizk, N. I. Elkalashy and M. Lehtonen “Application of
Risk-Based Insulation Coordination Method for the Protection of Medium Voltage
Overhead Lines against AC and Lightning-Induced Superimposed Voltages,” submitted to Electric Power Systems Research, 2016.
xvi
Author’s Contribution
Publication 1: Experimental investigation of lightning-initiated flashover faults in
medium voltage lines.
The author Farhan Mahmood had developed the main idea of the paper and was responsible for the interpretation of results, writing and the presentation of the paper
under the supervision of Prof. Matti Lehtonen. The experimental work was carried out
with the assistance of Tatu Nieminen and Jouni Makinen.
Publication 2: Modelling of flashover arcs in medium voltage networks due to direct
lightning strikes.
The main idea of the paper was developed by the author Farhan Mahmood under the
supervision of Prof. Matti Lehtonen. N. I. Elkalashy strongly contributed through
comments and discussions on arc modelling. The experimental work was carried out
with the assistance of Tatu Nieminen and Jouni Makinen.
Publication 3: Evaluation of lightning overvoltage protection schemes for polemounted distribution transformers.
The main idea was initiated by Farhan Mahmood under the supervision of Prof. Matti
Lehtonen. The author Farhan Mahmood was responsible for planning the work, interpretation of the results and writing the publication. Mohammad E. M. Rizk has contributed through discussions and comments.
Publication 4: Flashover probability distribution and volt-time curves of medium
voltage overhead line insulation under combined AC and lightning impulse voltages.
The main idea of the paper was developed by the author Farhan Mahmood under the
supervision of Prof. Matti Lehtonen. Nehmdoh A. Sabiha and Mohammad E. M. Rizk
have contributed through discussions and comments.
xvii
Publication 5: Probabilistic risk assessment of MV insulator flashover under combined AC and lightning-induced overvoltages.
The main idea of the paper was developed by the author Farhan Mahmood under the
supervision of Prof. Matti Lehtonen. N. A. Sabiha has contributed through comments
and discussions on probabilistic modelling and improved the organization of the paper
.The experimental work was carried out with the assistance of Jouni Makinen.
Publication 6: Effect of combined AC and lightning-induced overvoltages on the risk
of MV insulator flashovers above lossy ground.
This paper is an extension of the work done presented in [Publication V]. The main
idea was developed by author Farhan Mahmood under the supervision of Prof. Matti
Lehtonen. N. A. Sabiha has contributed through comments and discussions.
Publication 7: Risk-based design methodology for the selection of insulation level
against lightning-induced overvoltages in medium voltage lines.
The main idea of the paper was developed by the author Farhan Mahmood under the
supervision of Prof. Matti Lehtonen. M. Humayun contributed through comments and
discussions on developing economic cost model.
Publication 8: Application of risk-based insulation coordination method for the protection of medium voltage overhead lines against AC and lightning-induced superimposed voltages.
This paper is an extension of the work done presented in [Publications V]. The main
idea of the paper was developed by the author Farhan Mahmood under the supervision
of Prof. Matti Lehtonen. M. E. M. Rizk strongly contributed in the development of
FDTD code. N. I. Elkalashy has contributed through comments and discussions.
xviii
1. Introduction
Lightning has been identified as one of the major threats to the security and service
continuity of the power supply. The lightning activity in Finland is expected to be
modest due to its high-latitude position (about 60-70 N). However, severe lightning
events occur during summer season, typically from May to September, every year. For
instance, more than 22,000 lightning events had been recorded in Finland on June 27,
2013 [1]. These thunderstorms cause electrical blackouts in the power networks. From
power quality point of view, the momentary and the permanent interruptions caused
by lightning strikes result in the damage to the customer equipment and loss of revenue to both power utilities and customers. Hence, there is a need for further research
to study the lightning overvoltage mechanism that produces the faults in distribution
networks so that the optimum surge protection methods could be designed for the
mitigation of lightning-related faults.
Lightning can produce transient overvoltages by either directly striking the phase
conductor (direct stroke) or the ground in the vicinity of power line (indirect stroke)
[2]. Direct lightning stroke can produce overvoltages up to million volts whereas the
overvoltages induced by a nearby lightning strike are typically in few hundreds of
kilovolts. As the indirect lightning occurs more frequently than the direct ones, the
limited height and the low insulation level of the medium voltage (MV) overhead lines
makes them highly sensitive to induced overvoltages compared to the transmission
lines. The overvoltages resulting from both direct and indirect lightning strikes are
sufficiently high to cause flashover of line insulation [3], [4]. The flashover is a type
of short-circuit fault predominantly caused by a lightning overvoltage when the voltage stress exceeds the withstand voltage of the insulator. Consequently, the air surrounding the insulator becomes fully conductive and loses its dielectric properties.
Thus, a luminous discharge of current appears in the form of an arc over the surface of
insulator through the air between phase and ground [5]. For the accurate evaluation of
lightning overvoltages, better and accurate models are needed that can suitably reproduce the flashover phenomenon across the insulators [6].
1
The selection of insulation strength in relation to the expected overvoltages is a
fundamental requirement for insulation coordination studies [3]. Thus, the reliability
of power systems can be improved by properly coordinating the dielectric strength of
the line insulation with the expected overvoltage stress. In this regard, the statistical
methods are generally preferred over the conventional methods of insulation coordination studies [7]. Accordingly, the performance of distribution lines due to indirect
lightning should be evaluated using statistical methods. In the literature, numerous
statistical studies have been conducted to compute the expected number of flashovers
experienced by a distribution line due to the lightning-induced overvoltages, defined
as flashover rate. The calculation of the flashover rate is based on the assumption that
any lightning event producing induced overvoltage higher than 1.5 times the line critical flashover (CFO) voltage will always result in insulation flashover; also known as
1.5×CFO flashover criterion [2], [8]. As a matter of fact, the flashover of line insulation due to the application of voltage stress is also statistical in nature. In this regard,
only few investigations have been carried out to consider the statistical behaviour of
line insulator flashovers due to combined AC and impulse voltages [9]-[13]. It is revealed in this study that the statistical behaviour of lightning-induced overvoltages and
the insulator flashover voltages could be combined for the assessment of lightning
performance of overhead distribution lines.
1.1
Problem Description
Both direct and indirect lightning strikes usually lead to flashover faults in MV
lines causing outages and damages to the power equipment. Since the occurrence of
lightning cannot be avoided, it is necessary to mitigate the lightning overvoltages by
suitable protection measures to reduce the risk factor associated with flashovers [2],
[14]. Thus, the problem description and the motivation behind this research are briefly
described in the following subsections.
1.1.1
Fault Statistics in Finland
The fault statistics of the Finnish MV network protected by spark gaps are presented in Table 1.1 [16]. The annual fault statistics of Finland reveal that approximately 90% of the total faults in MV networks are transient in nature. Although the
lightning season in Finland is short, considerably high percentage of faults, around
50% occur due to lightning. It can be observed that direct lightning always results in
short circuits and the percentage of such faults is only 10%. On the other hand, the
indirect lightning contributes to around 40% of the total faults. The percentage of earth
faults and multi-phase short circuits due to indirect lightning strikes is 13% and 27%
2
respectively. On the other hand, it is worth-mentioning here that 83% of the total MV
faults occurring on the distribution transformer due to lightning and external influences have been cleared by replacing the spark gaps with surge arresters.
1.1.2
Lightning Observations in Finland
The lightning activity in Finland is recorded by NORDLIS lightning detection network operated by Finnish Meteorological Institute (FMI) covering Finland, Sweden,
Norway and Estonia. The number of NORDLIS sensors typically varies from 30 to 34
and mainly detects cloud-to-ground lightning based on the emitted low frequency
electromagnetic radiation [15]. Figure 1.1 shows the average ground flash density
(GFD) per 100 km2 in Finland for the year 2013 [1]. As depicted in Figure 1.1, high
lightning activity has been detected in the western part of Finland. The average GFD
per 100 km2 in Finland has been estimated to be 0.729 strokes/km2/year. The mean
peak current of the negative and positive lightning flash (i.e. first strokes) are -16.9 kA
and 13.8 kA respectively. The percentage of negative polarity strokes is around 80%
with multiplicity of 2.1 whereas the approximately 20% of the lightning strokes are of
positive polarity with multiplicity of 1.2.
Table 1.1 Distribution of different fault types in Finnish MV network protected by spark gaps
[16].
(a) Total fault statistics
Permanent Faults
10%
Faults in MV Network
Temporary Faults
MV faults occurring on spark gapped distribution transformers
External influences
Lightning
(tree branches, animals)
50%
33%
Faults along the
feeder length
7%
(b) Lightning fault statistics in MV network.
Earth-fault
13%
Lightning
Indirect
Short circuit (two-phase and
three-phase)
27%
Direct
Short circuits
10%
3
Figure 1.1 Average ground flash density (GFD) per 100 km2 of year 2013 in Finland [1].
1.1.3
Overvoltage Protection of Finnish Medium Voltage Lines
In Finland, the MV distribution lines are typically operated at 20-kV in radial configuration and installed on wood poles having metallic or wood cross arm. The power
lines mainly include bare conductors but covered conductors and underground cables
are also used in some areas. Due to the high resistivity of soil, the wood poles are usually ungrounded [16]. Such an overhead line has very high impulse withstand voltage
strength in the range of 2-3 MV and the faults due to induced overvoltages usually do
not occur except at the poles where the distribution transformers are located. However,
the lines are still prone to flashovers due to direct lightning strikes. The distribution
transformers are typically mounted on the poles and the overvoltage protection devices are placed either across the terminals or next to the disconnector switches of the
distribution transformer. Traditionally, the practice is to protect the small distribution
transformers (200 kVA and less) with spark gaps and the larger ones with surge arresters on all the three phases [16], [17]. The distribution lines are exposed to severe
weather effects, such as thunderstorms, rainstorms and windstorms causing faults and
outages in the power networks. For this reason, the lightning performance of the overhead distribution lines subjected to both direct and indirect lightning is investigated in
this work.
4
1.1.4
Lightning-Initiated Flashover Arc
In power networks, electric arcs are produced in different circumstances. For instance, overstressing of line insulation by lightning overvoltages can result in flashovers leading to a short circuit. The short circuit current will then flow in the form of
arc posing a fault in the power system. Therefore, a detailed understanding of the arc
characteristics is very important for the accurate modelling of lightning overvoltages
and the related phenomena.
The mathematical modelling of electric arcs is extremely complex due to the nonlinear nature of its parameters. Several arc models are available in the literature to
represent circuit breaker arcs, long arcs and high impedance arcing faults based on the
theory of arc thermal equilibrium [18]-[25]. These arc models have proved to be quite
useful to model long arcs on the overhead transmission lines as well as short arcs. For
instance, the dynamic arc model in combination with the static arc model has been
employed to model the arc that is formed between a power line and a nearby tree
stroked by lightning impulse voltage [5], [18]. Furthermore, a lot of research has been
made to model the partial-arc and flashover of polluted insulators under different types
of voltage stresses (AC, DC or impulse). Generally, the resistance representing the
arcing phenomenon across the insulators is either neglected or modelled by a constant
linear resistance [26]. Thus, more reliable and accurate models are still needed to represent the arcing phenomenon across the insulators produced by lightning overvoltages. On the other hand, the 1.5×CFO flashover criterion recommended by IEEE standard 1410-2010 as a threshold level for the occurrence of flashover is also quite convenient for reducing the complexity and the simulation time of the model [2], [6].
However, such approximations can lead to erroneous results in the computation of
lightning overvoltages.
1.1.5
Dielectric Strength of Medium Voltage Insulation
The insulation strength against lightning overvoltages is verified by the standard
impulse (SI) voltage test in which the voltage waveform is defined by 1.2/50 μs [7].
However, a number of field observations and simulation studies have shown that the
overvoltages produced by both direct and indirect lightning have much shorter tail
compared to the SI voltage. Furthermore, the overvoltages stressing the line insulation
are always superimposed on power frequency AC voltage. For this reason, the insulation characteristics under both SI and short tail lightning impulse (STLI) voltages
combined with power frequency AC voltage should be investigated for the statistical
insulation coordination studies [9]-[13].
5
1.1.6
Risk of Insulator Flashovers
In conventional method of insulation coordination, the minimum strength of insulation is determined according to the maximum overvoltage stress. Due to the random
nature of overvoltage stress and the flashover of line insulation, the probability of
simultaneous occurrence of both events is very low [7]. Thus, the conventional
method of insulation coordination may underestimate the required insulation level. In
contrast to this, it is more realistic to use statistical methods for the evaluation of
lightning performance of overhead distribution lines.
In the recent years, risk-based insulation coordination methods have been widely
accepted by the researchers [27]-[31]. This is typically the case for lightning protection studies where the occurrence of lightning overvoltages and the consequent flashover of line insulation are both probabilistic in nature. Therefore, the risk of failure for
any power system component can be determined from the probability distributions of
the insulator flashover voltages (component strength) and the peak lightning overvoltages (stress experienced by the component). By definition, risk of flashover represents
the probability that the overvoltage induced by a lightning stroke exceeds the withstand voltage of the insulators resulting in a flashover. The statistical data of overvoltages are obtained from computer simulations using analytical or numerical methods
whereas the insulation characteristics are determined from either laboratory testing or
manufacturer’s data sheet. The overvoltage and the insulation flashover probability
distributions are then optimized using suitable protection measures to obtain an acceptable risk factor within the range of 10-1 to 10-4 per lightning event [7], [32].
1.1.7
Consideration of Lossy Ground Effect
In the past, the lightning performance of overhead distribution lines was determined assuming ground with soil resistivity ȡ = 0, that is, a perfectly conducting
ground. Accordingly, Rusck proposed a simplified analytical model to calculate the
peak lightning-induced overvoltages for a perfectly conducting ground [33]. In practice, the grounds are lossy with finite soil resistivity which can significantly enhance
the peak lightning-induced overvoltages compared to the case of perfectly conducting
ground. In this regard, several analytical and numerical formulations have been proposed by the researchers to incorporate the effect of lossy ground on the resulting electromagnetic fields illuminating the line and the surge propagation along the overhead
line [34]-[40].
6
1.1.8
Mitigation of Lightning-Initiated Flashover Faults
Since the MV lines are more vulnerable to indirect lightning strikes causing flashovers and insulation failures, the lightning protection of MV networks should be appropriately designed by balancing the cost of protection against the benefits achieved
from the relevant mitigation of the consequences of lightning [14]. In this way, the
frequent service interruptions could be avoided and good quality of power supply will
be ensured to the customers. In particular, there are three methods to mitigate the
lightning-induced overvoltages in MV lines: i) upgrading the line insulation level; ii)
addition of shield wire; iii) application of surge arresters [2]-[4], [14].
Increasing the insulation level of the line has a beneficial effect in reducing the
flashovers due to induced overvoltages. However, this method of protection is not
practical against direct lightning [8]. Similarly, the application of shield wire and
surge arresters has proved to be quite beneficial in reducing the number of faults due
to induced overvoltages but they have a minor effect on the number of faults due to
direct lightning in MV lines. The mitigation effect of shield wire depends on the value
of grounding resistance, the distance between shield wire and phase conductor and the
spacing between two consecutive grounding points. On the other hand, the effectiveness of surge arresters to reduce the number of induced overvoltage flashover faults is
also governed by several factors like the value of grounding resistance and the spacing
between two adjacent surge arresters [14], [41]. The installation of surge arresters on
every phase of all the poles can be beneficial against both direct as well as indirect
lightning [42]. The spacing between surge arresters could be increased but the insulation level at the unprotected poles should be well coordinated with the grounding resistance at the protected poles to avoid flashovers at the unprotected poles due to
ground potential rise (GPR) at the protected poles.
1.2
Research Contribution
In this work, the response of a typical Finnish MV unshielded overhead line against
direct lightning is investigated [Publication I]. The experiments were carried out using
full-scale laboratory set up to determine the characteristics of lightning-initiated flashover faults. The total CFO of the line is calculated using up and down test method
with different types (metallic/wood) and configurations (grounded/ungrounded) of the
cross arm. The experiments were repeated with both positive and negative polarities of
the impulse voltages for dry and wet air conditions.
A direct lightning stroke to one phase of a MV overhead line causes flashover in
one or more phases depending on the line properties. The occurrence of flashover is
determined by the actual volt-time curve of the line insulation and once the flashover
7
occurs, the arcing phenomenon is represented by a linear variable resistance to determine the lightning overvoltages [Publication II]. At first, the full-scale laboratory experiments were carried out to determine the actual arc and volt–time characteristics of
the line insulators from the measured overvoltages and currents. Next, the dynamic arc
model has been used to model the experimental arc characteristics and its parameters
are estimated using the closed form of least-square error method. The simple volt-time
model has been fitted to the experimental volt–time characteristics of the line insulators. Finally, the experimental set-up is modelled in Alternative Transients Program–
Electromagnetic Transients Program (ATP-EMTP) and the experimental results are
then reproduced with reasonable accuracy.
In [Publication III], the performance of a typical MV unearthed network in response to both first and subsequent direct lightning strokes is evaluated. ATP-EMTP
simulations were performed to analyze the transient overvoltages at the MV terminals
of distribution transformer. It has been revealed that the effect of subsequent stroke in
terms of overvoltage stress at the low voltage (LV) side of the distribution transformer
is more compared to the first stroke. Next, the effectiveness of various lightning protection schemes consisting of spark gaps and surge arresters is also assessed. It has
been revealed that a properly designed filtering element can be used to reduce the
steep-front overvoltages caused by the breakdown of spark gap. Furthermore, a series
combination of spark gap and low rating surge arrester can be employed to reduce the
cost associated with the installation of surge arresters.
The strength of line insulation against lightning impulse voltages is investigated in
[Publication IV]. In this regard, the volt-time curves and the flashover probability
distributions of the different types of insulation gaps were determined under positive
and negative SI and STLI voltages. The study was further extended by modifying the
probabilistic model of insulation flashover to incorporate the effect of AC voltage.
The modified probabilistic model of insulation flashover for combined AC and lightning impulse voltages is also experimentally validated.
The performance of MV lines due to nearby lightning stroke based on probabilistic
risk assessment has been also introduced in this dissertation [Publication V and VI].
The main contribution of this work is to introduce the combined effect of AC and impulse voltage on the flashover characteristics of a MV pin-type insulator and distinguish the contribution of single-phase and multi-phase flashover faults. Accordingly, a
probabilistic method to compute the risk of insulator flashovers in MV overhead lines
due to combined AC and lightning-induced overvoltages is proposed. The probability
of single-phase, two-phase, and three-phase flashover of insulators has been predicted
using the modified Gaussian probability function by incorporating the effect of AC
8
voltage and has been experimentally validated for the first time. On the other hand, the
peak values of lightning-induced overvoltages on the MV lines are strongly influenced
by the soil resistivity values. For this reason, a comparison of the risk of insulation
flashovers for both perfectly conducting and lossy grounds is also made.
The application of risk-based insulation coordination method to mitigate the lightning-induced overvoltages is also evaluated [Publication VII and VIII]. In this regard,
an optimum insulation level is determined by balancing the total investment cost
against the outage cost associated with the risk of three-phase flashovers. Next, the
proposed methodology is further extended to investigate the effectiveness of surge
arresters and shield wire to mitigate the lightning-induced overvoltages using twodimensional (2-D) finite difference time-domain (FDTD) method. Accordingly, the
risk of insulation flashover is determined along the length of a MV line section by
changing the spacing between the surge arresters. Finally, the application of shield
wire in combination with surge arresters for the mitigation of lightning-induced overvoltages is also proposed in this work. Thus, the work presented in this dissertation
provides strong evidence regarding the lightning-initiated flashover faults, the expected overvoltages on the power lines and proposes suitable protection schemes to
mitigate these lightning overvoltages.
1.3
Dissertation Outline
The contents of this dissertation consist of a summary and Publications I-VIII. The
dissertation is organized as follows:
x
Chapter 2 presents the results of total CFO voltage of a typical Finnish MV
line subjected to direct lightning. The application of the dynamic arc model in
combination with the actual volt-time curves of the line insulation to represent
the flashover phenomenon in MV lines is also illustrated.
x
Chapter 3 investigates the lightning performance of different surge protection
schemes at the MV side of the distribution transformer subjected to both first
and subsequent stroke currents.
x
Chapter 4 reports the experimental evaluation of the insulation strength of different types of test objects in terms of their flashover probability distributions
and the volt-time curves.
x
Chapter 5 summarizes the computational results of the risk of insulation
flashovers due to combined AC and lightning-induced overvoltages for both
perfectly conducting and lossy ground. The experimental validation of the
9
modified probabilistic model of insulation flashover for combined AC and
impulse voltages is also presented.
x
In Chapter 6, the application of risk-based insulation coordination method to
mitigate the lightning-induced overvoltages is illustrated. This involves the selection of optimum insulation level, suitable spacing between the surge arresters and the combined protection provided by the surge arresters and shield
wire.
x
10
Conclusions and future research recommendations follow in Chapter 7.
2. Modelling of Lightning-Initiated
Flashover Arc in Medium Voltage
Lines
Overvoltages in the power system can be caused by both direct and indirect lightning strokes. As most of the overhead distribution lines are not equipped with shield
wire, direct lightning stroke to a phase conductor produces a flashover arc across the
line insulators causing a fault on the power system [43]-[46]. The nature of lightninginitiated flashover mainly depends on the peak value of the applied impulse voltage
and the grounding configuration of the cross arm. For instance, a MV overhead line
with grounded cross arm experiences an earth fault whereas a multi-phase (two-phase
or three-phase) fault is likely to occur when the cross arm is ungrounded in the event
of direct lightning strike.
The lightning performance of overhead distribution lines is evaluated using
1.5×CFO flashover criterion in which the constant 1.5 takes into account the turn-up
in the volt-time curve of line insulation. Furthermore, the occurrence of flashover results into arcing across the insulators that is traditionally being modelled by a constant
linear resistance accounting for the residual arc voltage [47]. On the other hand, the
strength of insulators is defined in terms of the voltage at which the flashover occurs
when subjected to the lightning impulse voltages. However, the flashover voltage of
line insulation is random in nature and should be defined in statistical terms. Therefore, the CFO voltage is defined as the peak value of standard impulse voltage at
which there is 50% probability of insulation flashover under specified conditions [3],
[7]. For insulation coordination studies, the strength of insulators subjected to lightning impulse voltages is generally expressed in terms of CFO voltage. Thus, it is important to accurately determine the CFO voltage by laboratory testing for the prediction of lightning overvoltages.
This chapter presents the experimental results of the CFO voltage for an unshielded
MV overhead line with different types (metallic and wood) and configurations
(grounded and ungrounded) of cross arm. The dynamic interaction between the fault
arc and the power line conductor is also analyzed in this work. The actual volt-time
curves of the line insulators are used to determine the instant at which the flashover
11
occurs and the arcing across the insulators is represented by a variable resistance controlled by the dynamic arc model. Consequently, the influence of considering the actual volt-time curves of the line insulation and the arc model is emphasized to accurately predict the lightning overvoltages using computer simulations.
2.1
Experimental Set-up
The laboratory tests were carried out on a 20-kV overhead line built on a 7 m high
wood pole. The full scale experimental set-up is shown in Figure 2.1 (a). The power
conductors having a diameter of 6 mm, DC resistance of 0.509 Ÿ/km and length of 22
m were placed over 24-kV pin-type insulators for all the three phases. The power conductors were separated by a distance of 1 m on a cross arm of length 2.2 m and brace
of 0.5 m. The power conductors were terminated at the far ends through matching
resistances to avoid reflections so that the line can be regarded as an infinitely long
line to some extent.
Firstly, the experiments were performed by directly grounding the insulator pin
through a lead wire as shown in Figure 2.1 (b). In this case, the flashover occurs
across a single insulator 1and the configuration is known as grounded cross arm configuration. Next, the experiments were repeated by removing the lead wire so that the
multi-phase flashover is observed. This configuration is known as ungrounded cross
arm configuration. Both metallic and wood cross arms were employed in the experiments to compare the flashover characteristics of the test overhead line.
(a) Full-scale experimental set-up
1
In case of a real power system, the voltage of cross-arm depends on the quality of the grounding and the amplitude of lightning current. If this voltage is sufficiently high, there will be
back-flashover to the neighbouring phase, and consequently a multi-phase flashover.
12
(b) Dimensions of the overhead line built on wood a pole with (1) cross arm grounded with lead
wire (2) cross arm ungrounded by removing lead wire
Figure 2.1 Experimental set-up consisting of a test overhead line with measurement system
and impulse generator.
Standard lightning impulse voltages (1.2/50 μs) were applied to one (side-phase
conductor) of the three-phase conductors of the overhead line from an impulse generator (800 kV, 20 kJ). The transient voltages and currents were measured by a Digital
Impulse Analyzer with four measurement channels:
Channel-1: Applied impulse voltage was measured through a resistive voltage divider.
Channel-2: Voltage build-up in the nearest phase (central phase conductor) was
captured through RCT 2000 damped capacitive voltage divider.
Channel-3 and 4: Current flowing into ground through terminating resistances at
the far ends of the centre phase conductor was recorded by a set of Pearson current
transformers. However, in grounded cross arm configuration, the current flowing into
ground through the lead wire was measured by Channel 4.
Since lightning mostly occurs in rainy weather, the laboratory experiments were
performed under both wet-air conditions (artificial raining condition) and dry air
(laboratory weather conditions). The weather conditions for the dry-air and wet-air
conditions were recorded as: T = 22°C, RH = 55.7%, P = 1007.4 hPa and T = 22°C,
RH = 61.5% and P = 1019 hPa respectively. Distilled water having conductivity of
0.01 S/m was employed for the wet tests. Artificial raining was produced in the laboratory at a precipitation rate of 1 mm/min by water spraying equipment placed at a
height of 2 m and 3 m away from the experimental set-up. Finally, the flashover phenomenon was also visually captured by a digital camera.
13
2.2
Experimental Results
The experimental findings, the computed CFO voltages and the volt-time curves
are reported in this section.
2.2.1
Recorded Waveforms
In MV networks with grounded cross arms (metallic and wood), the application of
impulse voltage to one phase of a three-phase overhead line produced flashover across
the surface of single insulator causing a single-phase fault in the system. The insulation strength between the struck phase and ground is provided by only one insulator
i.e. 136-kV in case of 24-kV insulator. The experimental waveforms of the applied
impulse voltage and the voltage build-up in the nearest phase under wet-air conditions
are shown in Figure 2.2. On the other hand, multi-phase flashover is observed in case
of impulse voltage applied to the overhead line with ungrounded cross arm. The occurrence of two-phase or three-phase flashover mainly depends on the magnitude of
applied impulse voltage. Furthermore, the flashover arc utilizes the cross arm as a part
of short-circuit path. This is attributed to the fact that the insulation strength of wood
(350-550 kV per meter [2]) is much higher than the combined strength of two insulators supported on the same metallic cross arm. Thus, the weakest path for the flashover arc is always between two phase conductors through cross arm [48]. The corresponding waveforms of the experimental applied impulse voltage and the voltage
build-up in the nearest phase under wet-air conditions are shown in Figures 2.3 and
2.4. The general features of the observed waveforms can be explained by dividing
them into four periods as: induction period, pre-arc period, flashover period and arcing
period. For ungrounded cross arm configuration, pre-arc and flashover periods are
separated by a pre-strike period as shown in Figures 2.2-2.5. Brief discussion on these
periods is given as follows,
(a) Induction Period: During the induction period, the applied impulse voltage
rises to its peak value and induces a voltage of 5-12 kV in the nearest
phase for both cross arm configurations as shown in Figure 2.4. The magnitude of the voltage build-up in the nearest phase depends on the peak
value of applied impulse voltage, rising time of the impulse voltage and the
distance between the two phase conductors.
(b) Pre-arc (or pre-strike) Period: Meanwhile, the applied voltage starts to drop
after reaching its peak value. Consequently, the induced voltage also drops
to zero. This period is known as the pre-arc (or pre-discharge) period [49].
During this period, the arc does not completely shunts the surface of the insulator and hence, multiple pre-strikes of the partial-arc discharges are ex14
pected to occur over the surface of insulator in case of an overhead line operated with ungrounded cross arm configuration.
(c) Flashover Period: Over the course of time, when the voltage stress be-
comes sufficiently high to exceed the withstand voltage of the insulator;
the arc extends across the surface of insulator causing a flashover. In case
of grounded cross arm configuration, the flashover arc extends over the
surface of insulator under stress so that the flashover current flows into the
ground through the lead wire. On the other hand, the flashover arc appears
over the surface of insulator under stress to the cross arm, and then from
cross arm to the insulator of nearest phase for ungrounded cross arm configuration. Now, the path of flashover current is completed through the
terminating resistances. The voltage stress required to flash two insulators
is higher than the single insulator and therefore, relatively high voltage appears across the insulator of nearest phase at the time of flashover. Due to
the interaction of stray inductance with the stray capacitance of insulator
and measurement system, the voltage gradually collapses to zero through
some oscillations as depicted in Figures 2.4 and 2.5. This period is called
as the flashover period.
(d) Arcing Period: Finally, the applied voltage eventually drops to zero after
the flashover period. This period is called as arcing period.
Figure 2.2 Experimental lightning impulse voltage applied to one phase of a three-phase distribution line for grounded cross arm configuration under wet air-condition.
15
Figure 2.3 Experimental lightning impulse voltage injected to one phase of a three-phase distribution line under wet air-condition for ungrounded cross arm configuration.
Figure 2.4 Experimental lightning-induced voltage on the neighboring phase for grounded
cross arm configuration under wet air-condition.
Figure 2.5 Experimental lightning-induced voltage on the neighboring phase for ungrounded
cross arm configuration under wet air-condition (a) complete waveform (b) pre-arc period (c)
flashover period.
16
2.2.2
Path of Flashover Arc
Experimental studies have indicated that the intensity and the path taken by the
flashover arc mainly govern the extent of damage to the insulation [50]-[52]. Figure
2.6 (a) and (b) shows the path of single-phase and two-phase flashover fault along
with the luminous discharge arc channel over a single and two insulators supported on
a metallic cross arm. However, in case of ungrounded wood cross arm, the path taken
by the flashover arc is always irregular especially under wet conditions. The different
paths taken by the flashover arcs in case of ungrounded wood cross arm are shown in
Figure 2.6 (c) and (d). It was observed that the accessories of the wood pole like cross
arm braces, nuts and bolts combination, helical ties, clamps and the insulator pin significantly affect the path taken by the flashover arc. For instance, the flashover arc
jumps over the insulator of struck phase to nearest phase through the nut-bolt combination of cross arm brace and the wood cross arm. In some cases, the flashover arc
progresses down the pole though the cross arm brace and then jumps up to the nearest
phase through the surface of wet wood due to the conducting layer formed by water on
the surface of the wood.
(a)
(b)
(c)
(d)
Figure 2.6 Lightning Flashover observed with (a) grounded (single-phase flashover) (b) ungrounded (two-phase flashover) metallic cross arm; (c) and (d) wood ungrounded configuration
during artificial rainfall.
17
2.2.3
Total CFO and Volt-time Curves
Using up-and-down test method, the total CFO voltage of the overhead line was
determined for positive and negative polarity impulse voltages under wet and dry air
conditions considering both grounded and ungrounded cross arm configurations. The
results are presented in Table 2.1 after the application of atmospheric correction factor. Following observations can be made from Table 2.1:
x
The CFO voltage for an ungrounded cross arm configuration is higher than
the grounded cross arm configuration.
x
The positive CFO voltages are in the range of 70-95% of the corresponding
negative CFO voltage values.
x
The CFO voltages under dry conditions are higher compared with the wet
conditions. The positive CFO voltage under wet condition is in the range
of 85-95% of the CFO voltage under dry condition whereas the negative
CFO voltage under wet condition is in the range of 75-85% of the CFO
voltage under dry condition.
x
In case of grounded cross arm configuration, the type of cross arm (metallic or wood) does not significantly affect the CFO voltage. On the other
hand, the total CFO voltage of the overhead line significantly changes in
case of ungrounded cross arm configuration.
The relationship between the electric strength of an insulator and the time to flashover is typically represented by volt-time curves. The volt-time curves are established
experimentally by applying a number of standard impulse voltages with different peak
values at each voltage level and then, measuring the flashover time. From the data of
peak applied impulse voltage and the mean flashover time, the volt-time curve can be
constructed. Figure 2.7 shows the simulated volt-time curves in dashed lines where the
dots represent the experimental data points for the positive impulse voltages under
wet-air conditions. It is to be noted that the flashover of single insulator occurs in
grounded cross arm configuration, so the volt-time curve represents the dielectric
strength of one insulator. On the other hand, the volt-time curve for ungrounded cross
arm configuration represents the combined dielectric strength of two insulators as the
flashover occurs over two insulators. Accordingly, the experimental volt-time curves
in combination with the arc model will be employed to predict the lightning overvoltages in the tested overhead distribution line as illustrated in the next sections.
18
Table 2.1 Total CFO Voltage of wood pole line (kV)
Type of
Cross
Arm
CFO voltage for grounded cross arm
configuration causing 1-ph fault (kV)
Dry
Metallic
Wood
+ve
136.6
142.1
-ve
195.8
192.5
Wet
+ve
-ve
129.4
168.2
132.3
171.6
CFO voltage for ungrounded cross
arm configuration causing 2-ph fault
(kV)
Dry
Wet
+ve
-ve
+ve
-ve
217.2
279.9
195.3
215.8
> 500
> 500
339.5
349.6
Figure 2.7 Volt-time characteristics of the line insulators for grounded and ungrounded cross
arm configuration for the positive impulse voltages under wet-air conditions. 2.3
Arc Modelling
The computation of flashover voltage of insulators using theoretical models is important for comprehensive understanding of the flashover phenomenon. Moreover, if
the predicted results are in reasonable agreement with the experimental measurements,
the theoretical model could be used to predict the flashover voltages for insulation
coordination studies; thus reducing the efforts required to conduct laboratory experiments. Accordingly, this section presents the experimental arc characteristics, the proposed mathematical model of the arc and the algorithm for the implementation of the
arc model.
2.3.1
Experimental Arc Characteristics
The voltage drop across the arc channel, Uarc, and the arc current, Iarc, in case of
grounded cross arm configuration are given by,
Uarc ( t ) Uin ( t )
I arc ( t ) I p ( t )
(2.1)
(2.2)
where Uin (t) is the applied impulse voltage (kV) and Ip(t) is the current flowing into
ground through the down conductor (A). On the other hand, Uarc(t) and Iarc(t) for an
ungrounded cross arm configuration can be expressed as,
19
Uarc ( t ) Uin ( t ) U2 ( t )
I arc ( t ) I1( t ) I2 ( t )
(2.3)
(2.4)
where U2(t) is the induced voltage in the neighbouring phase (kV), I1(t) and I2(t) are
the currents flowing into ground through the terminating resistances R1 and R2 respectively.
The electric arc is resistive in nature and is accompanied by the flow of current.
The arc conductance g is defined by the ratio of arc voltage and arc current as,
g( t )
g
I arc( t )
U arc ( t )
(2.5)
Using the equations for Uarc and Iarc for both grounded and ungrounded cross arm
configurations, the corresponding V-I waveforms of the arc in time domain can be
plotted as shown in Figures 2.8 and 2.9. Thus, it can be inferred that the physical behaviour of lightning-initiated arcs is governed by the applied impulse voltage Uin, induced voltage U2 and the currents I1, I2.
Figure 2.8 Experimental (a) arc voltage and (b) arc current for grounded cross arm configuration under wet air conditions.
20
Figure 2.9 Experimental (a) arc voltage and (b) arc current for ungrounded cross arm configuration under wet air conditions.
2.3.2
Mathematical Modelling of the Arc
In this work, the dynamic arc model proposed by Mayr is employed to represent
the arcing phenomenon across the insulators [53]. Accordingly, the general form of
the dynamic arc model is given by,
dg 1
(2.6)
G g dt W
where g is the instantaneous arc conductance, G =ŇiŇ/Uarc is the stationary arc conductance, ŇiŇ is the absolute value of instantaneous arc current, Uarc is the stationary
arc voltage and IJ is the arc time constant.
The two unknown parameters in (2.6), namely, Uarc and IJ are determined from the
experimental V-I characteristics of the arc shown in Figure 2.10. Thus, (2.6) can be rewritten as,
dg
dt
iarc
U arcW
-
g
W
(2.7)
21
dg
C1 iarc - C2 g
(2.8)
dt
where C1 = 1/(Uarc IJ) and C2 = 1/IJ. The two unknowns, C1 and C2, are calculated using
the closed form of the least square error method as follows:
For the kth sample, the discrete formulation of the dynamic arc model can be expressed as,
g k 1 g k
C1 iarc k - C2 g k
(2.9)
't
In matrix form, the discretized dynamic arc model for a certain number of nsamples taken at a sampling period ǻt can be represented as,
ª g k 1 g k
º
«
»
't
«
»
« g k 2 g k 1 »
«
»
't
«
»
#
«
»
« g k n g k n 1 »
«
»
't
¬
¼
ª| i |k
«
«| i |k 1
«#
«
¬| i |k n
gk
º
»
g k 1 » ª C1 º
# » «¬ C 2 »¼
»
gk n ¼
(2.10)
Figure 2.10 Experimental V-I characteristics of the arc for a lightning struck wood pole distribution line for wet air conditions (a) grounded cross arm (b) ungrounded cross arm.
22
The column vector on the left hand side of (2.10) represents the rate of change of
the arc conductance and is determined by substituting the experimental arc conductance obtained from (2.5) at the each sample of the measurement. The right hand side
contains the measurement matrix of the absolute arc current and arc conductance and a
column vector of two unknowns C1 and C2. The column vector of C1 and C2 can be
determined by applying left pseudo-inversion on the measurement matrix. Consequently, Uarc and IJ can be evaluated with the solved C1 and C2 using least square error
estimation. In this way, the arc parameters (Uarc and IJ) are determined from the experimental arc conductance.
Using the proposed methodology, the arc parameters (Uarc and IJ) were calculated
for the flashover and arcing periods for both cross arm configurations. The calculations indicated that the different values of arc parameters (Uarc and IJ) were obtained
for the flashover and arcing periods. Thus, it was decided to sequentially implement
the dynamic arc model during the flashover and arcing periods in such a way that the
arc conductance calculated at the end of flashover period is fed as an initial value at
the start of arcing period. As an example, the arc parameters (Uarc and IJ) as a function
of arc conductance during flashover period for ungrounded cross arm configuration
are presented in Figure 2.11. The values of arc parameters (Uarc and IJ) during flashover and arcing periods for both cross arm configurations are also reported in Table
2.2.
2.3.3
Flashover Arc Representations
The arcing phenomenon across the insulators is represented by the closing of a parallel switch that is in series with a variable resistance controlled by the dynamic arc
model. The switch closes when the voltage across it exceeds the withstand voltage of
the insulator. The arc conductance is computed by sequentially executing the dynamic
arc model during flashover and arcing periods based on universal arc representation
[25].
Figure 2.12 presents the proposed algorithm for the sequential execution of dynamic arc model implemented using Transient Analysis Control System (TACS) feature of ATP-EMTP software [54]. The dynamic arc model during flashover and arcing
periods is solved using two controlled Integrators Type 58 as shown in Figure 2.12.
The closing of the parallel switch across the insulator under stress is synchronized
with the control signal of the controlled Integrator-I to model the flashover. The occurrence of flashover makes the control signal of controlled Integrator-I high whereas the
control signal of controlled Integrator-II is still low. Thus, the arc conductance is calculated by solving the dynamic arc model during the flashover period. The arc con-
23
ductance is then inverted to compute the arc resistance and directly fed to the TACS
controlled variable resistance by the controlled Integrator-II through its reset signal. At
the start of arcing period, the control signal of controlled Integrator-II becomes high.
Now, the dynamic arc model is solved by the controlled Integrator-II for the arcing
period and again fed to TACS controlled variable resistance through its reset signal
after inverting the arc conductance.
Figure 2.11 Arc parameters as a function of arc conductance during flashover period for ungrounded cross arm configuration (a) arc time constant IJ and (b) arc stationary voltage Uarc.
Table 2.2 Arc Model Parameters, Uarc and IJ, during flashover and arcing period for both cross
arm configurations
Cross arm Configuration
Grounded
Ungrounded
24
Uarc (V)
Flashover
Arcing
Period
Period
2000
10000
7000
21000
IJ (sec)
Flashover
Period
1×10-9
1×10-8
Arcing
Period
50×10-3
1×10-8
Figure 2.12 Block diagram for the sequential implementation of dynamic arc model during
flashover and arcing period.
2.4
Component Modelling in ATP-EMTP
The experimental set-up shown in Figure 2.1 is modelled in ATP-EMTP software.
The details of the component modelling are given in the following subsections [55].
2.4.1
Modelling of Impulse Generator
A standard lightning impulse voltage (1.2/50 μs) was produced in the laboratory
using the component values as: Rd = 320Ÿ, Re = 1120 Ÿ, Cs = 62.5 nF and Cb = 800
pF. Using the above component values, the applied impulse voltage was represented
by the exact equivalent circuit of a single-stage impulse generator to accurately reproduce the experimental conditions [7].
2.4.2
Modelling of MV Distribution Line
The parameters of the overhead line exhibit a large variation under a transient
overvoltage compared to the power frequency voltage. As the frequencies of lightning
surge span a large bandwidth (typically 100 kHz to 3 MHz), J. Marti’s frequency dependent line model (Line/Cable Constants subroutine) is used in this study. The reason
is that J. Marti’s model calculates the changing line impedance corresponding to a
wide range of frequencies associated with lightning surge [54]-[56].
2.4.3
Modelling of Insulator
The line insulators are represented by a parallel resistance-capacitance (RC) circuit
connected between the phase conductor and cross arm of the wood pole. The stray
capacitance has an appreciable effect during the induction and pre-arc periods and has
25
been slightly tuned to 80 pF for the insulators considering the wet air conditions
whereas the resistance is assumed to be 25 MŸ [55]. For simulation, the volt-time
curves are generated using the simple volt-time model [57]-[60] as,
U
f
K1 K2
t 0.75
(2.11)
where K1 = 400×L, K2 = 710×L, L is the insulator length (cm) and t is the elapsed time
after lightning stroke (μs). For the tested 24-kV pin-type insulator, L = 18 cm and the
parameters K1 and K2 have been tuned to match the experimental and simulated volttime curves. The flashover of insulator is represented by the closing of parallel switch
when the voltage across the line insulation exceeds the flashover voltage (Uf) of the
insulator determined by the envelope of volt-time curve.
2.4.4
Modelling of Wood Pole and Cross arm
The inductance of steel cross-arm is determined using the formula [47],
§ 2h
·
2 u 10 7 ln ¨ x arm ¸
(2.12)
© rx arm ¹
is the height of the cross-arm above earth and rx-arm is the equivalent raLx arm
where hx-arm
dius of the cross-arm with oblong cross-section.
Figure 2.13 shows the ATP-EMTP model of the experimental set-up for ungrounded cross arm configuration. The equivalent component models are labelled and
shown inside the dashed line boxes. The network events are sequentially executed by
controlling the switches S1, S2, S3, S4 and S5. During the induction period, the switches
S1, S3 and S4 are turned-on while S2 and S5 are turned-off. The closing of the switch S5
is delayed keeping S2 closed and S3 opened during the pre-arc period. The transition
from pre-arc period to the flashover period occurs as soon as the voltage stress exceeds the dielectric strength of the insulator governed by the volt-time curve. Accordingly, the switches S1, S3, S4 are opened while the switches S2 and S5 are closed during
the flashover and arcing periods. Finally, the dynamic arc model is solved sequentially
for the flashover and arcing periods to control the variable arc resistance.
26
Figure 2.13 ATP-EMTP network of the experimental set-up for ungrounded cross arm configuration.
2.5
Comparison of Experimental and Simulated Results
In this section, the comparison of experimental and simulated results is presented
as follows.
2.5.1
Grounded Cross-arm Configuration
The comparison of the experimental and simulated waveforms of the arc voltage
(or the applied impulse voltage) and the arc current for the grounded cross arm configuration is presented in Figure 2.14. It can be deduced that the experimental and
simulated arc voltage and arc current are in close agreement till the end of flashover
period especially in terms of their peak values. However, the simulated waveform
deviates from the experimental waveform during the arcing period till 30 μs. This
deviation could be attributed to the interaction of the stray capacitances of the experimental set-up with the measurement system.
2.5.2
Ungrounded Cross-arm Configuration
Figure 2.15 shows the experimental and simulated applied impulse voltage and the
induced voltage across the nearest phase. It can be noticed that the experimental and
simulated waveforms agree quite well during the flashover period which confirms the
accuracy of the proposed model. Moreover, the experimental and simulated waveforms of the arc voltage (or applied impulse voltage) and arc current are also shown in
Figure 2.16. Although, a good match is obtained between the experimental and simulated arc voltage, the only disagreement in the experimental and simulated arc currents
can be observed. This could possibly be due to the modelling of terminating resis27
tances and grounding system. Although, the proposed method has been applied only
for single-phase and two-phase flashover, but it can also be utilized to model threephase flashovers.
It can be concluded that the models of important phenomena associated with flashover, namely, arc model and the volt-time curves, should be considered to estimate the
lightning performance of overhead distribution lines. The assumption of simplified
1.5×CFO flashover criterion and the constant arc resistance may result in erroneous
results. Finally, the methodology presented in this work is also beneficial for the thorough understanding of flashover phenomena over insulators and the design of protection schemes to mitigate the lightning overvoltages in distribution networks.
Figure 2.14 Comparison between experimental and simulated (a) arc voltage (b) arc current for
grounded cross arm configuration.
28
Figure 2.15 Comparison between experimental and simulated (a) applied impulse voltage (b)
induced voltage across neighboring phase for ungrounded cross arm configuration.
29
Figure 2.16 Comparison between experimental and simulated (a) arc voltage (b) arc current
for ungrounded cross arm configuration.
30
3. Performance Evaluation of Lightning
Overvoltage Protection Schemes for
Pole-Mounted Distribution Transformers
Despite significant improvements in the overvoltage protection, lightning has continued to cause considerable damages to the distribution transformers. In Finland, the
feeders of MV networks are typically designed in radial configuration with ungrounded poles supplying a large number of distribution transformers. As a result, the
single-phase flashover fault due to lightning has self-extinction capability in many
cases [16]. Thus, the lightning overvoltages in MV networks often result in multiphase flashover faults that severely stress the system insulation.
In Finland, the distribution transformers are protected against transient overvoltages using either spark gaps or surge arresters [16]. In case of spark gap protected
transformers, the formation of electric arc between the spark gap terminals practically
collapses the voltage to zero producing an earth fault in the power network. The voltage collapse due to the spark gap breakdown produces steep-fronted overvoltages
causing additional stresses on the transformer windings. The magnitude and steepness
of the steep-fronted overvoltages can be reduced by installing a properly designed
filtering element. In contrast to this, the installation of surge arresters is considered as
the best method of lightning protection due to its fast and smooth operation compared
to the spark gaps. The surge arrester protects the distribution transformer by diverting
the high voltage surges to ground. Since the surge arresters are more costly than spark
gaps, a protection scheme based on series combination of spark gap and low rating
surge arrester is also employed in some regions. Furthermore, the lightning performance of overhead distribution lines is generally evaluated from the overvoltages produced by the first stroke currents. The reason is that the median value of the peak first
stroke current is approximately two to three times higher compared to the subsequent
strokes. However, the subsequent stroke currents have shorter rise time and therefore,
the effect of high di/dt in terms of overvoltage stress should be also investigated [61][63].
31
In this work, the overvoltages caused by both first and subsequent lightning strikes
at the MV terminals of a typical 20/0.4 kV pole-mounted distribution transformer are
investigated. The simulations were performed on a section of a typical MV overhead
line consisting of wood poles, distribution transformer and 24-kV pin-type insulators
using ATP-EMTP software. Accordingly, the performance of different transformer
protection schemes based on surge arresters and spark gaps is evaluated. Finally,
modifications to the conventional lightning protection schemes are also proposed to
reduce the steepness of the overvoltages and the rating of the surge arresters.
3.1
Description of the Modelled Power System
To perform the transient analysis of a 20-kV distribution line as shown in Figure
3.1, various components were modelled as follows:
x
A 3-phase overhead line is simulated by J. Marti’s multi-conductor model
with frequency dependent parameters based on the physical configuration
of a typical Finnish MV line. The overhead line consists of eleven spans of
60 m. One end of the overhead line is connected to a 3-phase, 20-kV, 50
Hz AC voltage source with internal impedance whereas the other end of
the line is terminated by the characteristic impedance to avoid reflections.
x
The distribution transformer was located at a distance of 420 m from the
AC voltage source. BCTRAN model of ATP-EMTP has been used to represent a 400 kVA, 20/0.4 kV distribution transformer [54]. The LV side of
the transformer is loaded with an equivalent impedance of 380 kW, 120
kVAR.
x
The intermediate wood poles of the spans were considered as ungrounded
and modelled by a parallel resistor-capacitor branch with Rp = 4.8 MŸ, Cp
= 5.47 pF for a 8 m high wood pole. The steel cross arm is represented by
an inductance Lx-arm = 1.2 μH [47]. The flashover down the wooden pole is
modelled by a voltage-controlled switch that closes through an arcing resistance of 80 Ÿ when the voltage stress across the pole exceeds 350 kV
peak/m [64].
x
The line insulators and the manually operated disconnector switches are
modelled by stray capacitances of 100 pF/unit. However, the flashover
across insulators is represented by the closing of a switch in parallel with
the stray capacitance of the insulator. The closing of the switch is controlled by leader progression model (LPM) implemented in MODELS fea-
32
ture of ATP-EMTP software [55]. According to LPM, the time to flashover
of an insulator gap can be expressed by,
t f tc t s tl
(3.1)
where tc is the corona inception time and is usually negligible, ts and tl are the
streamer and leader propagation times respectively.
For ts, if the average field strength in the insulator gap exceeds the critical
field strength E0, it is considered that the streamers have crossed the gap. Consequently, the leader starts to propagate and as soon as the leader bridges the
gap, the flashover takes place. Thus, for tl, the leader propagation velocity can
be calculated by [65],
§U(t )
·
(3.2)
kU ( t ) ¨
E0 ¸
© Ll
¹
where U (t) is the instantaneous voltage across the insulator gap (kV), l is the
dL
dt
leader length (m), L is the insulator gap length = 18 cm, E0 is the critical field
strength = 600 kV/m, k is a constant = 1.3 m2.kV-2.s-1. On the other hand, if
the average field strength in the insulator gap is less than the threshold value
E0, the leader propagation stops and the flashover does not occurs.
x
The breakdown of spark gaps is represented by simple voltage-controlled
switches with the breakdown voltage of 100 kV [66].
x
MOV-Type 92 model has been employed to represent the surge arresters.
The parameters of the surge arresters are presented in Table 3.1 and their
V-I characteristics have been obtained from [67], [68] as shown in Figure
3.2. It is to be noted that 6.6 kV surge arrester is used to study the protection scheme consisting of series combination of spark gaps and surge arresters.
x
Based on the data published by CIGRE, the lightning flash was represented
by both first and subsequent stroke currents of negative polarity [69], [70].
The parameters of the first and subsequent stroke currents are reported in
Table 3.2 whereas the waveforms are shown in Figure 3.3.
Figure 3.1 Layout of the analyzed 20-kV MV line.
33
Table 3.1 Surge arresters characteristics
Parameters
Rated Voltage (kV)
Nominal Discharge Current (kA)
Residual Voltage at Nominal Discharge Current (kV)
Maximum Thermal Limit (kJ)
SA-1
22.5
10
35
75
SA-2
6.6
2.5
15
15
Table 3.2 Parameters of first and subsequent lightning [69], [70]
Parameters
Crest Current
Front Time
Front Steepness
Tail
Symbol
II, Initial
td30/90
Sm
th
First Stroke
27.7 kA
3.83 μs
23.3 kA/μs
77.5 μs
Subsequent Stroke
11.8 kA
0.67 μs
39.9 kA/μs
30.2 μs
Figure 3.2 V-I characteristics of the (a) 22.5 kV and (b) 6.6 kV surge arresters.
Figure 3.3 Lightning current waveform for the first and subsequent strokes adopted from [12].
3.2
Overvoltage Generation Mechanism
The section of the modelled distribution line fundamentally consists of wood poles
with ungrounded cross arms except at the disconnector and transformer locations. As a
result, the single-phase flashover faults have self-extinction capability. On the other
34
hand, multi-phase flashover faults produce highest overvoltages in the distribution
network [71], [72].
It has been observed that a direct lightning strike to one phase of a 3-phase distribution line at a distance of 120 m from the transformer produces high voltage surges
that propagate in both directions along the line. During their propagation, these high
voltage surges are attenuated, distorted and caused multi-phase flashovers even on
wood poles with unearthed cross arms provided the resulting overvoltage stress exceeds the dielectric strength of the insulators. For the investigated distribution network
configuration, the peak lightning current less than 1.7 kA results in a naturally recovering single-phase fault. When the peak lightning current is in the range of 1.7-2 kA,
the flashover of two insulators occurs through the metallic cross arm and the remaining poles may or may not experience flashovers. For the peak lightning current greater
than 2 kA, all the three insulators simultaneously flashover whereas the insulators of
intermediate wood poles may experience two-phase or three-phase flashovers depending on the magnitude of stroke current. In case of multi-phase flashover, the flashover
current then finally flows to the nearest distribution transformer. The worst case is
when the peak lightning current greater than 25 kA causes three-phase flashover down
the wood pole.
3.3
Results and Discussions
The effectiveness of different overvoltage protection schemes of the distribution
transformer is assessed by assuming that lightning hits phase A of the overhead line.
No surge protection was considered on the LV side of the distribution transformer.
The analysis was performed for the following four cases as shown in Figure 3.4:
x
Without any protection
x
Spark gaps (without and with filtering element) were connected at the
transformer terminals
x
Surge arresters were connected at the transformer terminals
x
Series combination of surge arrester and spark gap were connected at the
transformer terminals
3.3.1
Case I: No Protection Installed in the System
In case of an unprotected system, lightning surge is applied to the phase conductor
A of the overhead line at a distance of 120 m from the distribution transformer. Figure
3.5 shows the simulated overvoltages produced by the first and subsequent strokes at
the MV and LV terminal of the distribution transformer on the phase where lightning
35
is applied. It can be noticed that the overvoltage produced by the first stroke is approximately doubled compared to the subsequent stroke on the MV side. However,
higher overvoltage is transferred from the MV to LV side of the distribution transformer through the stray capacitances due to higher steepness and short rise time of
the subsequent return stroke current compared to the first stroke.
In Figure 3.6, the effect of the distance of lightning stroke on the overvoltage profile across the distribution transformer is presented. As expected, the lightning current
applied to the nearest pole from the transformer produces highest overvoltage far
above the basic impulse insulation level (BIL), around 150 kV, of the distribution
transformer. For the case of large distances of the lightning stroke, the overvoltage
magnitude is attenuated due to the line parameters. This attenuation can be prominently observed for stroke location greater than 180 m. Furthermore, the difference
between the overvoltage produced by the first and subsequent stroke currents on both
MV and LV sides can be also observed from Figure 3.6. Hence, it can be inferred that
the effect of subsequent stroke is more severe from consumer point of view in terms of
insulation stress compared to the first stroke.
Figure 3.4 Lightning protection schemes for pole-mounted distribution transformers (a) unprotected (b) spark gap with filtering element (c) surge arrester (d) spark gap with surge arrester.
36
(a)
(b)
Figure 3.5 Voltage waveforms at the struck phase of distribution transformer (a) MV (b) LV
terminals for an unprotected network due to first and subsequent strokes at a distance of 120 m.
(a)
(b)
Figure 3.6 Peak voltages at the struck phase of distribution transformer (a) MV (b) LV terminals for an unprotected network due to first and subsequent strokes over a distance from 60 m to
360 m.
3.3.2
Case II: Spark Gaps Installed at the Transformer Terminals without and with Filtering Element
Next, the distribution transformer is protected by a set of three spark gaps on all the
three phases. Figure 3.7 depicts the 3-phase, overvoltage waveforms at the MV terminals of the distribution transformer due to the breakdown of spark gaps. Firstly, the
breakdown of the spark gap of phase A limits the overvoltage to 100 kV. Due to the
mutual coupling between the phases, the voltage of the other two phases oscillates
causing a slight delay in the breakdown of other two spark gaps. In this regard, the
subsequent stroke current results in faster breakdown of the three spark gaps compared
to the first stroke current. As a result, the breakdown of spark gaps due to subsequent
stroke generates more steep-front impulse voltages at the MV side of the transformer.
Thus, the breakdown of spark gaps not only results in earth fault but also severely
stresses the transformer insulation by steep voltage collapse. Furthermore, the breakdown of spark gap causes an increase in the overvoltages transferred to the LV side of
the distribution transformer.
37
(a)
(b)
Figure 3.7 Overvoltages at the MV side of distribution under the operation of spark gaps due
to (a) first and (b) subsequent stroke currents.
The steepness of the overvoltage waveform (dU/dt) at the transformer terminals
due to voltage chopping as a result of spark gap breakdown should be less than 2
MV/μs as per Finnish standard SFS 2646 [73]. To limit the high dU/dt of steep front
overvoltage at the transformer terminals, a series filtering element (choke or reactor)
consisting of inductor and resistor combination can be connected with the distribution
transformer as shown in Figure 3.4 (b) [74], [75]. The series reactor should be designed in such a way that it attenuates high frequency signals associated with lightning
transients and offers no suppression to the low frequency signals (50/60 Hz). The
proper selection of the resistive element is an important aspect in the design of series
reactor to damp the oscillations produced by the L-C circuit. The self inductance of
the series reactor can be calculated by [76],
P 0 N 2S D 2 K w
(3.3)
4H
where ȝ0 is the permeability of free space equal to 4ʌ×10-7H/m, D is the diameter of
Ls
reactor, H is the height of the reactor, N is the number of turns and Kw is a factor that
can be assumed in the range 0.4-0.6 [77]. As an example, 1 μH series reactor with H =
0.25 m, D = 1.5 m and Kw = 0.539, the required number of turns can be calculated as
20.
Some additional simulations were performed by changing the inductance of the series reactor from 1 μH to 10 μH. In this case, a ramp type voltage with a slope of 2
MV/μs was applied to the distribution transformer. For 2 MV/μs steep front overvoltage, the flashover voltage of the double spark gap (2×40 mm) was supposed to be 250
kV [78]. Figure 3.8 illustrates the effect of series filtering element at the MV side of
the distribution transformer to reduce the steepness of the overvoltage waveform. The
full voltage wave is shown in dotted red line whereas the chopped voltage wave due to
spark gap breakdown without any series reactor is represented with solid red line. The
38
limiting effect of 1μH, 2.5 μH, 5 μH and 10 μH series reactor is demonstrated in solid
blue, black, magenta and cyan lines respectively. The results show that the increase of
series reactor inductance from 1 μH to 10 μH limits the steepness of the overvoltage
waveforms from 1.85 MV/μs to 0.85 MV/μs, that is, within the tolerable limits. Thus,
it can be concluded that a properly designed the series filtering element can limit high
dU/dt associated with the steep front overvoltages below 2 MV/μs at the terminals of
the distribution transformer produced by the spark gap breakdown [74], [75].
3.3.3
Case III: Surge Arresters Installed at the Transformer Terminals
In this case, a set of three surge arresters is connected at the MV terminals of the
distribution transformers to limit the transient overvoltages as shown in Figure 3.4 (c)
[79]. The mitigation effect of surge arrester in case of both first and subsequent stroke
currents can be observed from the wave shape of overvoltages at the MV and LV terminals of the distribution transformer as presented in Figures 3.9 and 3.10. The installation of surge arrester limits the overvoltage at the MV terminals of the distribution
transformer around the reference voltage. Overvoltages on the LV side of the distribution transformer have been also limited to around 0.5 kV. As mentioned earlier, the
subsequent stroke current produces slightly higher overvoltages on the LV side of the
distribution transformer compared to the first stroke current.
Figure 3.8 Filtering effect of series reactor limiting steepness of the overvoltage at the MV
terminal of the distribution transformer.
39
(a)
(b)
Figure 3.9 3-phase, overvoltage waveforms at the (a) MV (b) LV side of the distribution transformer protected by surge arresters due to first stroke current.
(a)
(b)
Figure 3.10 3-phase, overvoltage waveforms at the (a) MV (b) LV side of the distribution
transformer protected by surge arresters due to subsequent stroke current.
3.3.4
Case IV: Series Combination of Surge Arresters and Spark Gaps
Installed at the Transformer Terminals
Since the cost associated with the installation of surge arresters is very high, a costeffective method for the protection of distribution transformer is to install a low rating
surge arrester in combination with spark gap as illustrated in Figure 3.4 (d). For instance, 2 × 40 mm double spark gap in conjunction with 6.6 kV surge arrester can be
used for the protection of distribution transformer. In this case, the breakdown voltage
of spark gap is selected according to the lightning protection level whereas the surge
arrester limits the overvoltage to the reference value after the spark gap breakdown to
avoid the problem of voltage collapse to zero. Thus, the breakdown of spark gap occurs at first followed by the surge arrester operation in the event of transient overvoltages. The waveforms of overvoltages due to both first and subsequent current strokes
at the MV and LV terminals of the distribution transformer protected by spark gaps in
conjunction with surge arresters are presented in Figures 3.11 and 3.12. It can be no40
ticed that the breakdown of spark gaps occurs when the magnitude of transient overvoltage exceeds 100 kV and then, 6.6 kV surge arrester limits the voltage to the reference voltage level of around 10 kV. However, the overvoltage at the LV terminals of
the distribution transformers is slightly higher that can be mitigated by LV surge protective devices.
Finally, the energy absorbed by both 22.5 kV and 6.6 kV surge arrester due to first
and subsequent strokes is also measured. For this simulation, lightning flash is applied
at a distance of 60 m from the distribution transformer with an inter-stroke interval of
30 ms. Figure 3.13 depicts the energy absorbed by both protection schemes shown in
Figure 3.3 (c) and (d). As noted, the maximum energy dissipated by 22.5 kV surge
arrester is 49.25 kJ and is below the maximum thermal limit of 75 kJ. In case of transformer protected by series combination of spark gap and surge arrester, the maximum
energy dissipated by 6.6 kV surge arrester is 21.10 kJ that is above the maximum
thermal limit of 15kJ. Therefore, it is recommended to install surge arresters with
higher energy class when the transformer is to be protected by series combination of
spark gap and surge arrester.
(a)
(b)
Figure 3.11 3-phase, overvoltage waveforms at the (a) MV (b) LV side of the distribution
transformer protected by spark gaps and surge arresters due to first stroke current.
41
(a)
(b)
Figure 3.12 3-phase, overvoltage waveforms at the (a) MV (b) LV side of the distribution
transformer protected by spark gaps and surge arresters due to subsequent stroke current.
Figure 3.13 Energy absorbed by surge arresters due to both first and subsequent stroke current.
42
4. Flashover Characteristics of Medium
Voltage Line Insulation
The purpose of insulation coordination is to limit the probability of insulation
flashover below the acceptable value. Thus, the dielectric strength of the line insulation should be selected in accordance with the transient overvoltages for the reliable
design of insulation systems. In statistical insulation coordination, the probability distribution of lightning overvoltages is related with the probability distribution of insulator flashover voltages to obtain the risk of insulation flashover. Therefore, the evaluation of insulation strength is of great importance for the risk-based insulation coordination studies.
Flashover probability distributions and the volt-time curves statistically relate the
occurrence of flashover with the applied voltage stress and the time to flashover respectively. In this regard, several experimental and theoretical studies have been carried out to investigate the breakdown characteristics of different insulation systems
[80]-[84]. On the other hand, field observations have indicated that the lightning overvoltages stressing the line insulation have shorter tail time compared to the SI voltages. Therefore, it is necessary to study the effect of shape, polarity and the peak amplitude of the applied voltage stress on the flashover probability distribution and the
volt-time curve of the insulation gaps. Furthermore, the insulation testing is generally
carried out by applying either AC or SI voltages. As a matter of fact, the overvoltages
produced by lightning are superimposed over the power frequency AC voltage. Therefore, it is important to clarify the insulation characteristics under combined AC and
impulse voltages for the purpose of risk-based insulation coordination studies.
In this work, the flashover probability distributions and the volt-time curves of different types of MV insulation gaps subjected to the lightning impulse voltages are
presented. At first, experiments were performed in the laboratory to determine the
CFO voltage, denoted by U50%, the associated standard deviation ı and the volt-time
curves of the test samples. The measurements have been carried out with both positive
and negative polarity SI and STLI voltages. Next, the Gaussian probability distribution has been employed to represent the flashover characteristics of the test samples
subjected to the impulse voltages. Finally, the flashover characteristics of the test
43
samples under combined AC and lightning impulse voltages are also presented and
validated with the experimental measurements.
4.1
Experimental Work
This section presents brief description of the test samples, experimental set-up and
the test method.
4.1.1
Test Specimen
The test samples consist of one rod-plane, rod-rod spark-gap arrangement and two
porcelain insulators as shown in Figure 4.1. The details of the test samples are given
as:
x
Rod-plane R-P spark-gap arrangement, with electrode length of 15 cm and
gap distance of 10 cm.
x
Rod-rod R-R double spark-gap arrangement, with a gap distance of 2 × 40
mm.
x
Insulator IS-1, generally used with bare or covered conductors having rated
voltage of 24-kV for MV lines. The height of the insulator is 18 cm.
x
Insulator IS-2, having rated voltage of 10-kV and a height of 12 cm, also
used in the MV lines.
Figure 4.1 Test objects (a) rod-plane R-P spark gap (b) rod-rod R-R spark gap (c) insulator IS1 (d) insulator IS-2.
44
4.1.2
Experimental Set-up
The insulation samples have been tested with both SI (1.2/50 ȝs) and STLI (1/10
ȝs) voltages of positive and negative polarity using an impulse generator (800 kV, 20
kJ). The configuration of the experimental set-up for the impulse and combined voltage test is shown in Figure 4.2. In case of impulse voltage test, the impulse voltage
was applied to the top electrode of test samples (groove in case of insulators and rod
for rod-plane arrangement) whereas the lower electrode (pin in case of insulators and
plane for rod-plane arrangement) was grounded. For the combined voltage test, the
test samples were pre-excited by 11 kV (RMS), 50 Hz AC voltage produced by a 200
kVA, 20/0.4 kV, ǻ-Y distribution transformer. A resistance of 50 kŸ, 125 W was
connected between the two voltage sources to limit the current at the instant of flashover. A digital storage oscilloscope (100 MHz, 500 Ms/s) was used to record the voltage across the test samples through capacitive voltage divider (500 pF, 100 kV rms,
400 kV impulse, response time < 100 ns). The experiments were carried out under the
laboratory weather conditions at an atmospheric pressure of 1002.86 hPa, temperature
of 23.2°C and humidity of 35.3%; and the results were then corrected to standard atmospheric conditions.
(a)
(b)
Figure 4.2 Configuration of the experimental set-up for the (a) impulse voltage and (b) combined voltage test.
45
4.1.3
Test Method
The insulation samples were tested using the multi-level method [7]. In this
method, a pre-specified number of shots (at least 20) are applied to the test sample at a
progressively increasing test voltage levels. At each test voltage level, the probability
of flashover P (U) is calculated by the ratio of number of flashovers recorded (NFO)
and the total number of shots (NT) applied at each voltage level. Next, the probability
of flashover P (U) is plotted against test voltage levels U on a probability plot paper
based on normal distribution. Using linear regression, the data points are fitted to the
line of best fit [85]. Accordingly, U50% was determined from the line corresponding to
P (U) = 0.5 and ı from U50%± U16%.
The volt-time curves were established by applying at least 5 impulse shots of same
type, polarity and peak value to the test samples. If all the shots produced flashover,
the mean value of the voltage collapse times and the corresponding peak value give
one point for the volt-time curve [80].
4.2
Test Results
In this section, the experimental volt-time curves, the mean and the associated
standard deviation of the flashover voltages of the test samples subjected to both SI
and STLI voltages are reported.
4.2.1
Volt-time Characteristics
The flashover voltage of the insulation is statistically related with the time to flashover represented by the volt-time curves [86]-[88]. The experimental (dotted points)
and the fitted (solid line) volt-time curves of the test samples are presented in Figures
4.3-4.6. In general, the following observations are made from the volt-time curves of
the test samples,
x
The volt-time curves for both positive and negative polarity SI and STLI voltages are approximately coincident with each other up to around 1.5 μs. This is
due to the small difference in the rise times of the SI and STLI voltages.
x
Due to the different tail times of the SI and STLI voltages, the volt-time
curves deviate from each other in case of both positive and negative polarity
impulse voltages for the flashover times greater than 1.5 μs. The volt-time
curve for STLI voltage lie higher than the SI voltage due to the higher stress
associated with the longer tail of the SI voltage compared to the STLI voltage.
For instance, flashover voltages of 138 kV and 145 kV are observed corre-
46
sponding to the flashover time of 3 μs when positive SI and STLI voltages are
applied to the insulator IS-1 respectively.
Figure 4.3 Experimental and fitted volt-time characteristics of the rod plane R-P air gap for
positive (blue line) and negative (red line) under (a) SI (b) STLI voltage test.
Figure 4.4 Experimental and fitted volt-time characteristics of the rod-rod R-R spark gap for
positive (blue line) and negative (red line) under (a) SI (b) STLI voltage test.
Figure 4.5 Experimental and fitted volt-time characteristics of the insulator IS-1 for positive
(blue line) and negative (red line) under (a) SI (b) STLI voltage test.
47
Figure 4.6 Experimental and fitted volt-time characteristics of the insulator IS-2 for positive
(blue line) and negative (red line) under (a) SI (b) STLI voltage test.
4.2.2
x
Mean and Standard Deviation of Flashover Probability Distributions
Table 4.1 presents the comparison of experimental U50% and ı of the test samples for both SI and STLI voltages. Following observations are made from
Table 4.1:
x
Negative U50% is higher than positive U50% for both SI and STLI voltages.
x
In case of tested air gap, the ratio of negative to positive U50% is approximately
2.4 for both SI and STLI voltages due to higher non-uniformity of the electric
field associated with the rod-plane gap compared to the insulators.
x
Negative U50% is around 5-6% higher than the positive U50% in case of double
rod-rod gap.
x
The ratio of the negative to positive U50% for the tested insulators is in the
range of 1.3-1.4 for both SI and STLI voltages.
x
Due to the lower stress caused by shorter tail time of the STLI voltages, U50%
for STLI voltages is around 4-8% higher compared to the SI voltages for both
positive and negative polarities.
x
The values of ı lie within the range of 1-3% of U50%.
Table 4.1 Experimental flashover characteristics of test objects
Test Sample
R-P
R-R
IS-1
IS-2
48
SI Voltages
Positive
Negative
U50%
ı
U50%
ı
77
2
185
2.5
97.5
2.8
104
2.2
136
3.6
180.5
2.8
94
2
137
2.5
STLI Voltages
Negative
ı
U50%
ı
3
195
3.5
2.5
121
3
3.8
200
4.8
2
150
4
Positive
U50%
82
115
144
99
4.3
Flashover Characteristics of Test Samples Under Impulse
Voltages
This section presents the flashover probability distributions of the test samples subjected to the impulse voltages.
4.3.1
Mathematical Formulation
The probability of insulation flashover P (U) subjected to impulse voltages can be
approximated by normal cumulative distribution function (CDF) as [7],
ª (U U 50% )2 º
exp
«
³ ¬ 2V 2 »¼ dU (4.1)
f
In its simplest form, (4.1) can be reduced in terms of Q-function as [9],
P(U )
1
V 2S
U
§ U U 50%
P(U ) 1 Q ¨
V
©
where Q-function represents the integral of
·
(4.2)
¸
¹
the tail of standard Gaussian distribution
expressed by,
Q
4.3.2
f
§ u2 ·
1
exp ¨ - ¸ du
³
2S x
© 2 ¹
(4.3)
Flashover Probability Distributions for Impulse Voltages
The flashover probability distribution of the test objects under impulse voltage is
determined by inserting the previously evaluated U50% and ı presented in Table 4.1.
Figures 4.7-4.10 show the comparison of the experimental (red dots) and theoretical
(solid lines) flashover probability distributions of the test samples. It can be noticed
that the results predicted by the statistical model are in close agreement with the experimental results.
Figure 4.7 Experimental and statistical flashover characteristics of rod plane R-P air gap for
positive and negative impulse voltages test.
49
Figure 4.8 Experimental and statistical flashover characteristics of rod-rod R-R spark gap for
positive and negative impulse voltages test.
Figure 4.9 Experimental and statistical flashover characteristics of insulator IS-1 for positive
and negative impulse voltages test.
Figure 4.10 Experimental and statistical flashover characteristics of insulator IS-2 for positive
and negative impulse voltages test.
4.4
Flashover Characteristics of Insulation for Combined AC and
Impulse Voltages
In this section, the modified model of insulation flashover and the flashover characteristics for combined AC and impulse voltages are presented.
4.4.1
Modified Probabilistic Model
The flashover characteristics of the test samples subjected to impulse voltages were
analyzed in the preceding section. However, in reality, the induced overvoltage stress50
ing the line insulation is superimposed on the power frequency AC voltage randomly
at a phase angle ș. Therefore, it is important to investigate the overall insulation performance of the test samples subjected to combined AC and impulse voltages. Accordingly, the effect of AC voltage on the flashover probability distribution of the test
samples is taken into account by introducing an additional sinusoidal term Umax sin ș
in (4.2) where Umax and ș are the peak value and the phase angle of the sinusoidal AC
voltage respectively. Thus, (4.2) can be modified as,
§ U U max sin T U 50% ·
(4.4)
P(U ) 1 Q ¨
¸
V
©
¹
Due to the random nature of lightning, the superimposition of impulse voltage on
the AC voltage occurs at an arbitrary phase angle ș. So, the time of the application of
impulse voltage was assumed to be randomly distributed and not synchronized with
the phase angle of AC voltage. Hence, the average probability of insulator flashover
can be calculated by integrating (4.4) from 0 to 2ʌ with respect to ș as in [9],
P(U) 1 4.4.2
1
2ʌ
2ʌ
§ U U max sinT U 50% ·
¸ dT (4.5)
V
¹
³ Q ¨©
0
Flashover Probability Distribution for Combined Voltage Test
Using the same experimental U50% and ı, the flashover probability distributions of
the test samples for the combined voltage test were generated. The results are presented in Figures 4.11-4.14 in which the solid and dashed line indicates the flashover
characteristics of the test samples subjected to the impulse and combined voltages
obtained from (4.2) and (4.5) respectively. Furthermore, the experimental set-up
shown in Figure 4.2 (b) has been employed to compare the experimental flashover
probability distribution of the test samples shown in red dots with the theoretical results for the combined voltage test.
From theoretical point of view, the impulse voltage superimposed on AC voltage
has an average value that is equal to zero, so principally the experimental and theoretical U50% should be approximately same. However, the results shown in Figures 4.114.14 indicate slight shift in the median value of the experimental flashover probability
distribution relative to the theoretical results in the combined voltage test. This shift in
the flashover characteristics could be attributed to the limiting resistance added to the
circuit for protection reasons. On the other hand, the shape of flashover probabilityvoltage curve is also changed due to the superimposition of the impulse voltage on the
AC voltage. For the risk-based insulation coordination studies, the lightning overvoltages and the insulation flashover voltages are represented by suitable probability distributions as,
51
f
RFO
³P
FO
(U ) fU m (U )dU
(4.6)
0
where RFO is the risk of insulation flashover, fUm (U) is the probability density function
(PDF) of the lightning overvoltages and PFO (U) is the CDF of insulation flashover
voltage. From (4.6), it can be inferred that the shape of flashover probability-voltage
curve has a considerable effect on the risk of insulation flashover. To illustrate this,
Figure 4.15 shows the scaled PDF of the lightning overvoltages, the CDF of insulation
flashover voltage and the corresponding risk of flashover with lightning impulse (LI)
and combined AC and lightning impulse voltage (LI+AC). It can be noticed that the
risk of insulation flashover represented by the shaded area is more for combined voltages compared to the impulse voltage alone. This effect of AC voltage is generally not
considered in insulation coordination studies and can underestimate the required insulation level. Therefore, it can be concluded that the effect of AC voltage should be
considered for risk-based insulation coordination studies.
Figure 4.11 Experimental and statistical flashover characteristics of rod-plane R-P air gap for
positive and negative impulse and combined voltage test.
Figure 4.12 Experimental and statistical flashover characteristics of rod-rod spark gap R-R for
positive and negative impulse and combined voltage test.
52
Figure 4.13 Experimental and statistical flashover characteristics of insulator IS-1 for positive
and negative impulse and combined voltage test.
Figure 4.14 Experimental and statistical flashover characteristics of insulator IS-2 for positive
and negative impulse and combined voltage test.
t
RLI+AC
RLI
Figure 4.15 Risk of insulation flashover with lightning impulse (LI) alone and combined LI
and AC voltage.
53
54
5. Probabilistic Risk Assessment of
Medium Voltage Insulation Flashover
Field observations reveal that the majority of insulation flashovers in MV lines are
due to induced overvoltages resulting from nearby lightning strikes. It is important to
investigate the interaction of lightning-induced overvoltages with MV networks so
that the possible improvement in the lightning performance of distribution lines can be
proposed [89]-[91]. In IEEE standard 1410-2010, the flashover rate due to induced
overvoltages is determined using electrogeometric model in combination with Rusck’s
or Darveniza’s model [2]. During the computation of flashover rate, it is assumed that
the flashover of insulation occurs according to 1.5×CFO criterion. Accordingly, a
number of statistical studies have been performed by the researchers to select the required insulation level, decide about the installation of shield wire and/or the proper
spacing between surge arresters to obtain an acceptable flashover rate. On the other
hand, the risk-based insulation coordination method has been widely accepted by the
researchers in the recent years in which the probabilistic nature of both the applied
voltage stress and the component strength is considered [91]-[95]. Accordingly, the
risk-based insulation coordination method has been introduced in this work to evaluate
the lightning performance of overhead distribution lines.
The research on the insulation characteristics has been progressing using either AC
voltage or SI voltage alone and the dielectric strength of the insulations is not tested
for the combined voltages [87], [96]-[99]. In Chapter 4, it has been established that the
effect of combined AC and impulse voltage should be considered for the risk assessment of insulation flashover. Furthermore, the field measurements indicate that the
overvoltages induced by nearby lightning strikes are practically short tailed impulse
voltages compared to the standard lightning impulse (SI) voltage. Therefore, a positive
polarity short-tail lightning impulse (STLI) voltage of 0.97/9.5 μs is applied to the
insulators to model the lightning-induced overvoltages [80], [91].
This chapter presents a probabilistic method to determine the risk of MV insulator
flashovers due to combined AC and lightning-induced overvoltages considering both
perfectly conducting and lossy ground conditions. The flashover characteristics of a
24-kV pin-type insulator are experimentally determined. The modified probabilistic
55
model of insulation flashover is then employed to predict the probability of singlephase, two-phase and three-phase insulator flashover under combined AC and lightning-induced overvoltages. The proposed probabilistic model has been experimentally
validated for the first time using a three-phase AC and an impulse voltage source.
Next, the probability distribution of the peak lightning-induced overvoltages is estimated by applying Monte Carlo simulations on the simplified Rusck’s and Darveniza’s model considering both perfectly conducting and lossy ground respectively.
The risk of insulator flashover is then determined using the probability distributions of
lightning-induced overvoltages and insulator flashover voltages. This study is a first
attempt to illustrate the effect of combined AC and impulse voltages on the occurrence
probability of single-phase and multi-phase flashovers above a perfectly conducting
and lossy ground.
5.1
Experimental Work
The experimental set-up and the test results predicted by the probabilistic model of
insulation flashover are reported in this section.
5.1.1
Experimental Set up
The configuration of the test set-up for the combined voltage test is shown in Figure 5.1. The insulator was vertically mounted on a metallic cross arm. STLI voltages
(0.97/9.5 ȝs) of positive polarity with different amplitudes were applied to the insulator top by an impulse generator (800 kV, 20 kJ). On the other side, the insulator was
energized by an AC voltage of 11.5 kV (RMS), 50 Hz generated by a 200 kVA, 20/0.4
kV, ǻ-Y distribution transformer. In this way, the impulse voltage is superimposed on
the power frequency AC voltage randomly at a phase angle ș and applied to the insulator at the instant of flashover. The flashover current in the circuit is limited by a resistor of 50 kŸ, 125 W. The combined AC and impulse voltage applied to the insulator was measured by a digital storage oscilloscope through a capacitive voltage divider. The flashover phenomenon across the insulators was visually inspected with
high definition camera during the tests. During the measurements, the laboratory
weather conditions were recorded as: atmospheric pressure P = 1002.86 hPa, temperature T = 23.2°C and humidity RH = 35.3%; and then corrected to the standard temperature and pressure conditions. No corrections were made for humidity. As an example, the waveforms of the applied impulse voltage superimposed on the AC voltage
are shown in Figure 5.2.
56
Figure 5.1 Configuration of the experimental set up for combined AC and impulse voltage test.
Figure 5.2 Experimental combined AC and impulse voltage waveforms; impulse voltage superimposed on (a) positive (b) negative half cycle of the AC voltage.
5.1.2
Test Results
The flashover characteristics of the tested insulator were determined using the
multi-level method [7], [85]. For the test 24-kV pin-type insulator with the combined
AC and peak STLI voltage (0.97/9.5 ȝs), U50% = 155 kV and ı = 1.63 kV was obtained
and employed for the estimation of the risk of insulator flashovers.
Figure 5.3 Flashover characteristics of the tested insulator predicted by the probabilistic model
under combined voltages (U50% = 155 kV, ı = 1.63 kV).
57
5.2
Probabilistic Model of Multi-phase Insulator Flashovers
In this section, the probabilistic model of insulation flashover under combined AC
and impulse voltage presented in Chapter 4 is extended to predict the multi-phase
flashovers as well.
5.2.1
Mathematical Formulation
The average probability of insulator flashovers subjected to combined AC and impulse voltages is given by (4.5). The occurrence probability of single-phase and multiphase flashovers is then obtained by assuming that the overvoltage induced on the line
due to nearby lightning strike is approximately same in all the three phases. If P (U) is
the flashover probability of single insulator, the binomial probability distribution can
be used to obtain the probability of exactly x simultaneous flashovers (one, two and
three) in n insulators as,
Px FO (U )
n!
P(U)x ¬ª1-P U ¼º
n x ! x!
n- x
(5.1)
.
where Px-FO (U) is the probability of single-phase, two-phase and three-phase insulator
flashovers. Thus, the probability of single-phase, two-phase and three-phase flashover
of insulators is given by (5.2), (5.3) and (5.4) respectively as,
3
2S
P1 FO (U )
P2 FO (U )
P3 FO (U )
3
2S
2S
1
2S
2S
2S
³ 1 Q u Q
a
b
u Qc dT . (5.2)
0
³ 1 Q u 1 Q u Q dT . a
b
c
(5.3)
0
³ 1 Q u 1 Q u 1 Q dT . a
b
c
(5.4)
0
where
Qi
§ U U m sin Ti U 50% ·
Q¨
¸
V
©
¹
5.2.2
for i = a, b, c and șa = ș, șb = ș-120° and șc = ș+120°
Results
The probability of single-phase, two-phase and three-phase flashover predicted by
the modified probabilistic model given by (5.2)-(5.4) is shown in Figure 5.4. From
Figure 5.4, it can be observed that the probability of single-phase flashover is highest
for the applied voltage within the range of 143 kV to 155 kV. When the applied voltage is increased above 155 kV, the probability of single-phase flashover decreases and
concurrently, the probability of two-phase flashover increases such that it has the
highest probability of occurrence at 163 kV. With further increase in the applied im58
pulse voltage, the probabilities of two-phase and three-phase flashover become equal
at 168.75 kV. Eventually, the probability of three-phase flashover increases to 1 and
the probability of two-phase flashover drop to zero at an applied voltage of 175 kV.
Therefore, it can be deduced that the induced overvoltage of peak amplitude greater
than 175 kV will always result in a three-phase flashover.
It is important to mention that the flashover of the insulator of first phase causes
ground potential rise (GPR) in case of lossy ground. This GPR can significantly affect
the flashover voltages for the insulators of second and third phase depending on the
value of ground resistance. Thus, the probabilistic model presented by (5.2)-(5.4) is
only valid for the very low ground resistance (close to zero) and the effect of GPR is
not considered in this study.
5.3
Experimental Verification with Three-Phase Arrangement
The experimental validation of the proposed probabilistic model of insulator flashover has been carried out for the first time with the combined three-phase AC and
impulse voltages. The modified experimental set up consists of three 24-kV insulators
vertically mounted on the cross arm and simultaneously stressed by an impulse voltage and combined three-phase, 11.5 kV (RMS), 50 Hz, AC voltage source. The current at the instant of flashover was limited by three resistances of 50 kŸ, 125 W as
shown in Figure 5.5. The insulators of the nearest phases were separated by 1 m.
Figure 5.4 Comparison of experimental and fitted flashover (single-phase and multi-phase)
characteristics predicted by the proposed probabilistic model under combined AC and impulse
voltages.
59
Figure 5.5 Configuration of experimental set up for the verification of proposed probabilistic
flashover model of insulator under combined AC and impulse voltage.
The experiment was performed using multi-level test method in which 50 impulse
voltage shots at continuously increasing test voltage levels U were applied to the insulators. It was observed that a flashover of a particular nature (single- and/or multiphase) was produced relative to each shot applied at a particular voltage level. The
probability of single-phase P1-FO (U), two-phase P2-FO (U) and three-phase P3-FO (U)
flashover is then determined by the ratio of the number of single-phase (N1-FO), twophase (N2-FO) and three-phase flashovers (N3-FO) to the total number of applied shots
(NT) respectively at each test voltage level. The results of this test are reported in Table
5.1. It can be noticed that single-phase flashovers is observed only for the magnitude
of the impulse voltages within the impulse voltage range of 130-140 kV. For impulse
voltages greater than 140 kV, both single-phase and two-phase flashovers are spotted.
With further increase in the magnitude of impulse voltages from 145 kV to155 kV, the
frequency of two-phase flashover increases whereas the frequency of single-phase
flashover decreases concurrently. Moreover, all the three types of flashovers were
observed when the voltage was raised from 160 kV to 165 kV. Next, both two and
three-phase flashovers were perceived for impulse voltages between 170 to 175 kV.
Further increase in the applied voltage beyond 180 kV eventually results in only threephase flashovers. Figure 5.6 shows the three types of flashovers recorded using a digital camera during the experiment. The comparison of experimental and theoretical
flashover (single-phase, two-phase and three-phase) probability is also shown in Figure 5.4. The experimental results are represented by dots and found to be in reasonable
agreement with the theoretical results predicted by the probabilistic model. This confirms the validity of the proposed model to predict the probability of insulation flashover under combined AC and impulse voltages.
The results obtained from the probabilistic model of insulation flashover do not
present the complete scenario. Therefore, the probabilistic nature of lightning-induced
60
overvoltages is also evaluated so that the probability of likelihood of lightninginduced overvoltages and how likely they result in insulation flashover can be evaluated.
Table 5.1 Flashover probability for combined AC and impulse voltage (0.97/9.5 μs) test on
three insulators
U (kV)
NT
N1-FO
N2-FO
N3-FO
130
135
140
145
150
155
160
165
170
175
180
50
50
50
50
50
50
50
50
50
50
50
0
1
10
35
39
27
10
2
0
0
0
0
0
0
3
9
23
38
42
15
5
0
0
0
0
0
0
0
2
5
33
42
50
P1-FO (U) =
N1-FO/NT
0
0.02
0.2
0.7
0.78
0.54
0.2
0.04
0
0
0
P2-FO (U) =
N2-FO/NT
0
0
0
0.06
0.18
0.46
0.76
0.84
0.3
0.1
0
P3-FO (U) =
N3-FO/NT
0
0
0
0
0
0
0.04
0.1
0.66
0.84
1
Single-phase Flashover
(a)
Two-phase Flashover
(b)
Three-phase Flashover
(c)
Figure 5.6 Flashover of insulators under combined AC and impulse voltage (a) one insulator
(left) (b) two insulator units (left and middle) (c) two insulator units.
61
5.4
Probabilistic Model of Peak Lightning-Induced Overvoltages
Due to the random nature of lightning parameters, the overvoltages induced by a
nearby lightning strike should be also statistically quantified. The randomness in the
behaviour of lightning parameters is taken into account using Monte Carlo simulation
method [100], [101]. Monte Carlo simulation method is a statistical procedure in
which a large number of random numbers are applied on a mathematical model to
generate the probability distribution of the desired output parameter.
5.4.1
Effect of Perfectly Conducting and Lossy Ground
From an electromagnetic point of view, the electromagnetic fields generated by a
nearby ground strike induce voltages and currents due to electromagnetic coupling.
The induced voltage and current, in turn, generate electromagnetic fields that propagate through the air and interact with the ground. If the ground is assumed to be perfectly conducting (ȡ = 0), the electromagnetic fields do not penetrate the surface of the
ground. Therefore, the ground can be considered as a zero potential surface and consequently, the induced current flows on the surface of the ground. In this case, the
depth of equivalent return conductor is equal to zero and the method of images can be
applied to calculate the induced voltage on the overhead line.
In practice, the grounds are lossy with finite soil resistivity ȡ  0 and can significantly enhance the peak lightning-induced overvoltages compared to the case of perfectly conducting ground. If the ground is assumed to be lossy, the electromagnetic
fields generated by induced voltage and current penetrate from air into the ground and
the zero potential surface lies below the ground. Thus, the depth of equivalent return
conductor will be more causing an increase in the longitudinal impedance of the overhead line. This, in turn, increases the magnitude of lightning-induced overvoltages and
consequently, can lead to higher probability of insulation flashover [102]-[107].
5.4.2
Rusck’s Model for Perfectly Conducting Ground
Rusck presented a simplified formula based on the method of images to calculate
the peak value of overvoltage induced on an overhead line UPC at a nearest point to the
stroke location as [33],
U PC
Z0 ˜ I p ˜ K v
h
y
(5.5)
where Z0 = (1/4ʌ)×¥μ0/İ0 = 30 Ÿ, Ip is the peak lightning current (kA), Kv = 1+(v/c)
/¥[2-(v/c)2] where v is the return-stroke velocity and c is the velocity of light = 3×108
m/s, h is the height of line (m) = 10 m and y is the distance of stroke location from the
line (m).
62
The primary advantage of the Rusck’s model is its simplicity and it can be easily
employed to estimate the peak induced voltage due to indirect lightning. However, it is
based on the assumption of an infinitely long line above a perfectly conducting ground
and may lead to erroneous results when the observation point is not close to the
grounding point. Rusck’s formulation also presumes step current as source of excitation with a constant velocity v that does not represent a realistic scenario. For realistic
line configurations, the line transverse discontinuities such as the grounded shield
wires and the surge arresters cannot be treated using Rusck’s formula.
5.4.3
Darveniza’s Model for Lossy Ground
As mentioned, the assumption of perfectly conducting ground does not represents
the actual situation. Accordingly, a number of analytical and numerical formulations
have been proposed by the researchers to incorporate the effect of lossy ground in the
computation of lightning-induced overvoltages [35]-[40]. In this regard, Darveniza
proposed a semi-empirical extension to the Rusck’s formula by replacing the actual
height of the line with the effective height that accounts for the effect of finite ground
resistivity as [34],
U LG
Z 0 .I p .K v
h 0.15 U y
(5.6)
where v is assumed to be 1.2 × 108 m/s and ȡ is the soil resistivity (Ÿm) [108], [109].
It is worth-mentioning here that Darveniza’s analytical formulation has been widely
accepted to account for finite soil resistivity in the calculation of peak induced voltage
on the overhead line due to its simplicity and ease of computation.
5.4.4
Methodology for Monte Carlo Simulation Method
In this study, Monte Carlo simulation method has been applied on the simplified
Rusck’s and Darveniza’s model to obtain the PDF of peak lightning-induced overvoltages. The procedure for the implementation of Monte Carlo simulation method can be
outlined as follows:
1) Generation of random lightning parameters (e.g. Ip, y, ȡ) for each stroke:
Ip: The statistical distribution of peak return stroke current is assumed to
follow log normal distribution with median value Imed = 16 kA and logarithmic standard deviation ıi = 0.43 kA [1].
y: As there is an equal probability of lightning hitting at some distance
from the line, the distance y is supposed to be uniformly distributed from
50 to 500 m in steps of 50 m.
63
ȡ: Soil resistivity has been also approximated by a log-normal distribution
[110]. Three types of soils (moraines, mires and clays) are considered for
this study. The average and logarithmic standard deviation (log Std) of the
soil resistivity for each type of considered soils in Finland are presented in
Table 5.2. Due to the wide variation of the soil resistivity values measured
at different locations, the logarithmic standard deviation has been selected
in such a way that the generated histogram of soil resistivity spans the entire range as specified in Table 5.2. More information on the values of soil
resistivity for different soil types can be found in [111], [112].
2) Application of Rusck’s and Darveniza’s model for the computation of peak
induced overvoltage generated by each random stroke.
3) Fitting the histogram of peak induced overvoltage with a suitable probability distribution and estimating the corresponding PDF.
5.4.5
PDF of Peak Lightning-Induced Overvoltages
The PDF of peak lightning-induced overvoltages is obtained using 1,000,000 randomly generated lightning events defined by Ip, y and ȡ. Figures 5.7 and 5.8 show the
histogram of the input and output parameters obtained from Monte Carlo simulations.
The histogram of the peak lightning-induced overvoltages is then fitted by a lognormal
probability distribution using MATLAB statistics toolbox [113]. Mathematically, the
PDF of lognormal distribution fUm is represented by,
ª (lnU lnU m )2 º
. exp «
» (5.7)
2V lnUm 2
2SV U
¬
¼
where Um is the median value of peak lightning-induced overvoltage and ılnUm is the
fU m (U )
1
logarithmic standard deviation.
Table 5.2 Soil resistivity values in different regions of Finland
No.
Soil Type
Typical Range (Ÿm)
Average (Ÿm)
1.
2.
Clays
Peat, marsh soil and
cultivated soil
Moraine
25-70
50-250
40
150
Log Std
(Ÿm)
0.24
0.20
1000-10000
3000
0.45
3.
64
(a)
(b)
Figure 5.7 Log-normally distributed histogram of (a) peak lightning current and (b) soil resistivity for the case for the case: ȡavg = 40 Ÿm.
(a)
65
(b)
Figure 5.8 Fitting of randomly generated peak lightning-induced overvoltage with the theoretical lognormal distribution for the case: y = 50 m and (a) ȡavg = 40 Ÿm. (b) ȡavg = 3000 Ÿm.
The median value of the lognormally distributed peak induced voltage for different
distances of the stroke location as a function of soil resistivity is presented in Figure
5.9. It can be inferred that the higher average and logarithmic standard deviation of
soil resistivity results in larger mean and more spread in the PDF of the peak lightning-induced overvoltages. For instance, the distribution of peak lightning-induced
overvoltage has a mean of 114 kV for y = 50 m in case of perfectly conducting ground.
This value increases to 124 kV, 134 kV and becomes almost doubled, around, 205 kV
for ȡavg = 40, 150 and 3000 Ÿm respectively. This clearly demonstrates the importance
of considering the effect of finite soil resistivity for the calculation of peak lightninginduced overvoltages. With the increase in the distance from the stroke location, the
median value of peak induced overvoltage decreases. However, the median value of
peak lightning-induced overvoltage is significantly higher for ȡavg = 3000 Ÿm compared to the cases of other soil types. For instance, the median value of peak lightninginduced overvoltage for ȡavg = 3000 Ÿm is approximately 35% higher compared to the
case of ȡavg = 150 Ÿm for y = 50 m. As the distance between the stroke location and
overhead line is further increased beyond 100 m, the difference between the median
values of the peak induced overvoltages decreases rapidly but still a relatively higher
median values of the peak induced overvoltages is observed at y = 350 m for ȡavg =
3000 Ÿm compared to other soil types. On the other hand, the logarithmic standard
deviation is in the range from 0.4409-0.4305 kV and is dependent on the standard
deviation of the considered soil types.
66
Figure 5.9 Calculated median value of lognormally distributed peak lightning-induced overvoltages Um for different values of soil resistivity.
5.5
Results and Discussions
Risk of flashover is area under the curve given by the product of probability distributions of insulation flashover voltages and the peak lightning-induced overvoltages.
The risk integral for the flashover of insulator for all values of U can be formulated as,
f
Rx FO
³P
x FO
U fU U dU m
(5.8)
0
where fUm is the PDF of lightning-induced overvoltage and Rx-FO, is the risk of singlephase, two-phase and three-phase insulator flashover corresponding to x = 1, 2 and 3
respectively.
Figure 5.10 shows the PDF of peak induced overvoltage (magenta line) and the
probability of single-phase (black line), two-phase (blue line) and three-phase (red
line) flashovers. It can be noticed that as the distance between the stroke location and
the overhead line y increases, the magnitude of the peak induced overvoltage also
decreases and shifts the PDF of induced overvoltage to left. This will reduce the area
under the risk integral and accordingly the risk of insulation flashover will be lower.
Conversely, the risk of insulation flashover will be higher for lightning stroke terminating close to the overhead line. This is attributed to the fact that the intensity of the
electromagnetic fields resulting from a lightning stroke at a distance of 50 m from the
overhead line i.e. y = 50 m will be sufficiently high to cause a three-phase flashover.
Therefore, the risk of three-phase flashover has the highest probability of occurrence
due to the larger overlapping area under the probability distributions of induced overvoltages (fUm) and three-phase flashover voltages (P3-FO).
The computational results for the risk of single-phase, two-phase and three-phase
insulator flashover for seven uniformly distributed stroke locations and four different
67
values of soil resistivity are reported in Table 5.3. The results clearly demonstrate that
the risk of insulator flashover increases in the presence of lossy ground. For instance,
the risk of three-phase flashover is around 31% higher in case of ȡavg = 40 Ÿm for y =
50 m compared to the perfectly conducting ground. One of the most notable effects of
lossy ground is that the risk integrals further increase with higher soil resistivity values. This effect can be predominantly observed for y = 100 m and ȡavg = 3000 Ÿm,
where the risk of three-phase flashover still remains higher than the risk of singlephase and two-phase flashover. This behaviour is attributed to the high potential rise
between the phase conductors and ground caused by the strong electromagnetic coupling in the presence of lossy ground. Thus, it can be observed that the risk of threephase flashover is 1.3270 indicating the occurrence of this event is quite sure for y =
50 m and ȡavg = 3000 Ÿm.
The risk of single-phase flashover exhibits highest value for y > 50 m in case of
low resistivity soils, ȡ = 0 and ȡavg = 40 Ÿm. However, considering highly resistive
soils with ȡavg = 150 Ÿm and ȡavg = 3000 Ÿm, the risk of single-phase flashover dominates over the risk of two-phase and three-phase flashover for y = 100 and 200 m respectively. The risk of two-phase flashover always lies between the risk of singlephase and three-phase flashover.
(a)
(b)
Figure 5.10 Statistical distributions of lightning-induced overvoltage and the insulator flashover voltages for (a) y = 50 m (b) y = 150 m.
68
The average risk of single-phase, two-phase and three-phase flashover over a distance from 50 to 350 m for ȡavg = 3000 Ÿm are 23.1%, 48.9% and 53.9% higher compared to the case of perfectly conducting ground. Furthermore, the risk indices of insulator flashovers are distributed in a specific ratio for the cases of low resistive grounds
i.e. ȡavg = 40 and 150 Ÿm. However, as mentioned before, that the risk of three-phase
flashover is 1.3270 in case of ȡavg = 3000 Ÿm and y = 50 m meaning that this event is
sure to occur and consequently, the occurrence probability of single-phase and twophase flashovers is reduced. When y = 100 m, the risk of three-phase flashover radically drops to 0.2514 with the three risk indices again distributed in a specific ratio.
It can be concluded that the induced overvoltage resulting from a nearby lightning
strike to a highly resistive soil is high enough to cause simultaneous flashover of three
insulators even for longer distances to stroke location [114]. The presence of highly
resistive soils with ȡavg • 3000 Ÿm would further worsen the situation by increasing
the risk of three-phase flashover. Therefore, the assumption of perfectly conducting
ground could underestimate the risk of insulator flashover in an overhead line due to a
nearby lightning strike.
69
0.1389
0.0142
0.0011
1.1144e-04
1.3370e-05
1.9370e-06
3.2303e-07
0.1543
100
150
200
250
300
350
Ravg
R1-FO
50
y
(m)
0.12173
1.1292e-07
7.2463e-07
5.4116e-06
4.9721e-05
5.7394e-04
0.0085
0.1126
R2-FO
Ideal Ground
ȡ=0
0.37557
5.3930e-08
3.8818e-07
3.3261e-06
3.6518e-05
5.3645e-04
0.0116
0.3634
R3-FO
0.17756
8.9815e-07
4.8956e-06
3.0021e-05
2.3303e-04
0.0021
0.0215
0.1537
R1-FO
0.14382
3.2648e-07
1.9010e-06
1.2584e-05
1.0791e-04
0.0011
0.0134
0.1292
R2-FO
ȡavg = 40 Ÿm
0.49749
1.6656e-07
1.0863e-06
8.2346e-06
8.5050e-05
0.0011
0.0201
0.4762
R3-FO
0.19761
2.2110e-06
1.0919e-05
6.3940e-05
4.4096e-04
0.0035
0.0306
0.1630
R1-FO
0.16354
8.3289e-07
4.3833e-06
2.7767e-05
2.1118e-04
0.0019
0.0197
0.1417
R2-FO
Lossy Ground
ȡavg = 150 Ÿm
0.6288
4.5167e-07
2.6553e-06
1.9389e-05
1.7771e-04
0.0020
0.0321
0.5945
R3-FO
0.28610
1.8297e-04
6.2469e-04
0.0023
0.0086
0.0339
0.1129
0.1276
R1-FO
0.24849
8.5291e-05
3.1035e-04
0.0012
0.0050
0.0223
0.0879
0.1317
R2-FO
ȡavg = 3000 Ÿm
Table 5.3 Risk of single-phase, two-phase and three-phase insulator flashover considering different values of soil resistivity
1.62555
6.8482e-05
2.8269e-04
0.0013
0.0066
0.0389
0.2514
1.3270
R3-FO
70
6. Mitigating the Risk of Medium Voltage
Insulation Flashover
Lightning overvoltages can cause flashovers and failures of insulation along the
overhead lines. Although, the insulation cost is very small compared to the cost of line
and apparatus, the safe operation of the power system is highly dependent on the reliability of line insulation. Since the insulation breakdown can cause permanent damage
to the equipment resulting in interruptions, it is far more important to prevent the conversion of flashovers into such breakdowns of insulation. Thus, the motivation behind
the protection of MV lines is to mitigate the occurrence frequency of momentary interruptions and voltage sags caused by the flashovers of line insulation due to lightninginduced overvoltages. The three protective measures that can be utilized for the mitigation of lightning-initiated flashovers can be identified as [115]-[119]:
1) Upgrading the line insulation level
2) Installation of shield wire
3) Installation of surge arresters
However, it is important to mention that these measures have no appreciable influence in reducing the number of faults due to direct lightning strikes. The reason being
that the direct lightning mostly results in a three-phase flashover or back flashover.
Due to this reason, this study has been conducted in accordance with the induced
overvoltage flashovers.
In Chapter 5, the risk of insulation flashovers for an unprotected insulator subjected
to combined AC and lightning-induced overvoltages is determined. In this Chapter,
the concept of probabilistic risk assessment is extended for the optimum selection of
insulation level against lightning-induced overvoltages. A general cost function is
developed using value-based reliability planning method and the optimum insulation
level is then determined where the cost of excessive insulation level and the cost associated with the risk of insulation flashovers balance each other. Furthermore, the effect
of line transverse discontinuities represented by periodic groundings of shield wire
and surge arresters to mitigate the risk of three-phase flashovers is also evaluated. In
71
this regard, the spacing between the consecutive surge arresters is varied to obtain a
tolerable risk factor. Moreover, it has been also demonstrated that higher spacing between the surge arresters can be allowed if the shield wire is also provided in the distribution system provided the spacing between the consecutive grounding points
should be less than 200 m.
6.1
Risk-based Design Method
Risk-based design is a procedure to integrate risk assessment in the design process
with the mitigation of risk embedded as a design objective. The flowchart presented in
Figure 6.1 depicts the framework of the risk-based design. The procedure is based on
the following steps:
1) Generate the statistical distributions of the stress experienced by the component and its strength, that is, lightning-induced overvoltages and insulator
flashover voltage respectively through experiments and/or literature survey.
2) Determine the risk of insulator flashovers and classify it as low, medium or
high.
3) Generally, the low level of risk is considered to be within the range 10-1-10-4
and satisfies the design requirements.
4) For medium level of risk, a cost-benefit analysis should be performed to justify the cost of modifying the line for the risk reduction against the benefit of
improving the lightning performance of overhead line.
5) In case of high risk, the design should be improved by using suitable mitigation techniques.
Figure 6.1 Flowchart of risk-based design of insulation level.
72
6.2
Upgrading the Line Insulation Level
Increasing the line insulation level has a beneficial effect in reducing the frequency
of faults due to induced overvoltages. For this study, the risk of insulator flashover
computed in Chapter 5 is employed for the selection of optimum insulation level required against lightning-induced overvoltages.
6.2.1
Cost-Benefit Planning Method
In this work, the value-based planning (VBP) method is utilized to maintain a balance between the cost of providing service reliability and the benefits achieved with
the improvements. This balance is achieved by minimizing the total cost that consists
of the investment, losses, maintenance and outage cost. It is obvious that neither high
nor low insulation level is economically desired. Excessive insulation results in higher
capital investment, whereas lower insulation level needs lower capital investment but
larger outage cost due to the insulation flashovers. Thus, the point at which the cost of
excessive insulation level and the cost associated with the risk of insulation flashover
balance each other gives the optimum level of insulation. Thus, the VBP approach
provides a comprehensive view on identifying the cost effective solutions to improve
the reliability of power system.
6.2.2
General Economic Cost Model
Due to the fluctuation in the prices of energy and the equipment of MV line, it is
convenient to develop a general form of the total cost function [120]. The total cost of
an overhead line is formulated by a general function as follows,
CINV CLOSS CMAINT COUT
CTOTAL
(6.1)
where CTOTAL = total annual cost of energy distribution (€), CINV = equivalent annual
line investment cost (€/100 km-year), CLOSS = annual cost of losses (€/100 km-year),
CMAINT = annual maintenance cost of line (€/100 km-year), COUT = annual outage cost
of the line (€/100 km-year).
The annual line investment cost is determined by [121],
CINV
ir ir 1
ir 1
n
n
1
˜ CTI
(6.2)
where ir = interest rate (%), n = economic life of overhead line (years) and CTI = present value of the total investment cost (€/100 km).
The annual cost of losses and maintenance has a minor effect on the total cost and
is negligible [121],
CLOSS
10I m 2 ˜ R
(6.3)
73
C MAINT
(6.4)
0.02.C INV
where Im = peak value of load current in the overhead line (kA) and R = resistance of
the overhead line (Ÿ/km).
The annual outage cost COUT of the line is expressed as [121],
COUT
CU CC
(6.5)
where CU is the annual line outage utility cost and CC is the annual line outage customer cost. The annual line outage utility cost CU and the annual line outage customer
cost CC are calculated using (6.6) and (6.7):
CU
ft
t t
f p t p .CUEU P0 f p CFR
(6.6)
where ft = number of line temporary failures (1/100 km-year), fp = number of line
permanent failures (1/100 km-year), tt = mean duration of line temporary failure (h), tp
= mean duration of line permanent failure (h), CUEU = mean annual cost of undelivered
energy (€/kWh), P0 = power outage caused by line trip-out (kW), CFR = mean cost of
one permanent failure repair (€/fault).
CC
ft qP0 CUPC f p P0 . CUPC CUEC .t p (6.7)
where q = customer participation factor, CUPC = mean annual customer cost of undelivered power (€/kW), CUEC = mean annual customer cost of undelivered energy
(€/kWh).
For a typical 20-kV overhead line in Finland, the values of different parameters in
(6.1)-(6.7) are assumed as follows,
ir = 0.05
n = 20 years
Im = 75 A
R = 0.333 Ÿ/km
ft = 0.9f
tt = 2/60 hrs.
fp = 0.1f
tp = 2 hrs.
CUEU = 0.1142 €/kWh
P0 = 1100 kW
CFR = 1640 €/fault
q = 0.3
CUPC = 0.92 €/kW
CUEC = 9.34 €/kWh
CTI = 2817500 (considering wood poles, insulators and conductors etc.)
Accordingly, the general cost function is expressed in terms of CTI and f can be expressed as,
CTOTAL
0.1CTI 18732 2602f
(6.8)
As the three-phase flashover fault is considered as the worst fault for the power
system, the insulation level is determined by minimizing the total cost associated with
the risk of three-phase flashover. It is worth-mentioning here that the total outage rate
f is calculated by assuming that the lightning contributes to 20% of the total outages
74
and the average annual ground flash density (GFD) in Finland is 0.786 flashes per
km2.
6.2.3
Results and Discussion
Figure 6.2 shows the influence of line CFO voltage on the average risk of threephase flashover over a distance from 50 to 500 m and the cost of line insulation. The
risk of three-phase flashover is acceptable, that is, 10-1 at a line CFO voltage of 190
kV. It can be seen that increasing the insulation level with high CFO voltage leads to
the reduction in the risk of three-phase flashover and hence, the corresponding risk
cost, but at the same time, the cost of line insulation also increases. On the other hand,
low insulation level decreases the cost of insulation but concurrently results in higher
outage cost. Therefore, the optimum point at which the operating cost plus the outages
cost is minimum lies between these two extremes where the annual investment cost
and the risk cost balance each other. Figure 6.3 shows the relation between the cost
associated with the risk of three-phase flashovers as a function of line CFO voltage.
Thus, the minimum point on the curve corresponds to an insulation level of 265 kV
and represents the optimum insulation level.
Sensitivity analysis is also carried out by changing the one input variable while
keeping the other parameters constant to investigate the change in the response of
optimum insulation level. In this regard, the total investment cost CTI and the mean
annual customer cost of undelivered energy CUEC were varied one at a time. Figure 6.4
(a) shows the optimum insulation level as a function of investment cost CTI. It can be
observed that higher insulation level can be provided corresponding to lower investment cost CTI and vice versa. For instance, the change in the total investment cost CTI
to 90% of its original value will result in an optimum insulation level of 285 kV. On
the other hand, the mean annual customer cost of undelivered energy CUEC and the
optimum insulation level is shown in Figure 6.4 (b). In Finland, the mean annual customer cost of undelivered energy CUEC is typically in the range of 2-40 €/kWh from
residential to commercial consumers. Thus, it can be inferred that higher insulation
level should be provided to commercial/industrial consumers due to the high cost of
interruption. In contrast to this, the residential consumers can be provided with lower
insulation level due to the lower interruption cost. In this way, the proposed method
can be utilized for the selection of optimum insulation level considering different
types of electricity consumers.
75
Figure 6.2 (a) Risk of single-phase, two-phase and three-phase flashover (b) Insulation cost as
a function of line CFO voltage.
Figure 6.3 Risk cost of three-phase flashover as a function of line CFO voltage.
Figure 6.4 Sensitivity analysis results based on (a) total investment cost (b) mean annual customer of undelivered energy (€/kWh).
6.3
Installation of Surge Arresters
Next, the mitigation of lightning-induced overvoltages using surge arresters and
shield wire based on risk-based insulation coordination method is analyzed. To accomplish this, surge arresters are installed at different points along the overhead line
76
with variable spacing to achieve tolerable risk of insulation flashover. It is worth mentioning here that the presence of line transverse discontinuities (surge arresters and
shield wire) along the overhead line cannot be treated by analytical models. Thus, the
electromagnetic fields generated by a nearby lightning stroke are computed using the
transmission-line model assuming a perfectly conducting ground and step current
waveform as in [106]. The coupling of electromagnetic fields with the overhead line is
implemented by solving Agarwal’s model in MATLAB as presented in [122], [123]
whereas the line discontinuities were incorporated in accordance with [124].
6.3.1
Configuration of the Overhead Line
The line configuration is shown in Figure 6.5. The length and the height of the
overhead line are assumed to be 2000 m along x-axis and 8 m along z-axis respectively whereas the distance of stroke location from the line is considered along y-axis.
The line was terminated at both ends with matching impedances to prevent reflections.
The simulations have been performed by fixing the location of the lightning stroke at
the mid-point between two consecutive surge arresters considering the worst case scenario. The grounding resistance is considered to be 10 Ÿ. For a typical Finnish MV
line, the V-I curves of 22.5 kV surge arresters were obtained from [67] as shown in
Figure 3.2 (a). The histogram of peak lightning-induced overvoltages was computed
by 5000 Monte Carlo simulations for the following four cases:
x
No surge arresters (SA-0) and lightning stroke is applied at x = 1000 m.
x
Three surge arresters installed, each after 1000 m (SA-1000) and lightning
stroke is applied at x = 500 m.
x
Six surge arresters installed, each after 400 m (SA-400) and lightning
stroke is applied at x = 1000 m.
x
Ten surge arresters installed, each after 200 m (SA-200) and lightning
stroke is applied at x = 1000 m.
6.3.2
Profile of the Peak Lightning-Induced Overvoltages
The peak induced overvoltages reduce not only with increasing distance to the
stroke location but also along the line length. Figure 6.6 shows the reduction in the
median value of the peak lightning-induced overvoltages Um as a function of increasing distance to the stroke location. Although, the curves for SA-0, SA-1000 and SA400 cases appear to lie very close to each other, the curve for SA-200 exhibits slightly
lower values of Um for stroke location up to 150 m.
77
Figure 6.5 Configuration of the overhead line to investigate the mitigation effect of surge arresters on the lightning-induced overvoltages.
Figure 6.6 Median value of the peak lightning-induced overvoltages as a function of stroke
location y.
Figure 6.7 presents the profile of the Um as a function of line length for the case y =
50 m. For the case SA-0, the highest Um observed is 86.94 kV with a standard deviation of 0.4514 at x = 1000 m. This median value Um drops to 78.43 kV at the two line
extremes i.e. at x = 0 and 2000 m. The performance of the line is further deteriorated
when it is equipped with three surge arresters, that is, SA-1000. The highest Um observed is 87.46 kV at x = 500 m and is slightly higher than the unprotected case. The
reason for this increase is that the large separation distance between the surge arresters
results in the summation of the negative surge reflections from the two sides. In this
case, the overvoltage build-up mechanism depends on several factors like surge arrester spacing, line configuration and the stroke location from the line [42], [125]. The
surge arrester limits the overvoltage at its location and the line section beyond the
stroke location from x = 1000 m to 2000 m. But the line section from x = 0 to 1000 m
is highly stressed by the induced overvoltages. Next, protecting the line with six surge
arresters (SA-400) further limits the overvoltage between the line sections x = 0 to 800
78
m and then x = 1200 to 2000 m. However, the line section between x = 800 to 1200
will be under high stress with highest Um of 86.99 kV at x = 1000 m. Finally, lowest
Um of 82.26 kV is observed at x = 1000 m when surge arresters are spaced after every
200 m. Now, high overvoltage stress is limited to only a small section of the line between x = 900 to 1100 m. The remaining line sections are adequately protected by
surge arresters. Therefore, it is concluded that increasing the number of surge arresters
not only reduces the peak induced overvoltages but also the length of the line over
which the induced overvoltage stress is distributed.
6.3.3
Risk Assessment
After evaluating the median value Um and standard deviation of the peak induced
overvoltages, the average risk of insulator flashover over a distance from 50 m to 350
m is computed for the four considered cases. The results are presented in Figure 6.8.
The results indicate that there is no risk of flashover at the surge arrester locations. As
illustrated previously, highest risk is associated with three-phase flashover followed
by single-phase and two-phase flashover. The three-phase flashover has highest risk of
0.1459, 0.1708 and 0.1470 at the points nearest to the stroke location for the cases SA0, SA-1000 and SA-400 respectively. These risk factors are above the tolerable limit
of 10-1 whereas the risk of single-phase flashover is lower than 10-1.
Figure 6.7 Median value of peak lightning-induced overvoltages as a function of distance
along the length of the overhead line for y = 50 m and circles showing the location of surge
arresters.
79
Figure 6.8 Risk of single-phase, two-phase and three-phase insulator flashover as a function of
distance along the length of the overhead line for (a) unprotected line SA-0 (b) three surge
arresters SA-1000 (c) six surge arresters SA-400 (d) eleven surge arresters SA-200.
It can be also observed that increasing the number of surge arresters along the line
reduces the length of the line over which the risk indices are distributed. For instance,
the risk indices are distributed over the whole line length in case of an unprotected line
SA-0. The length of the line sections is reduced to x = 0 to 1000 m and x = 800 m to
1200 m for the cases of SA-1000 and SA-400 respectively. The remaining line sections are adequately protected by surge arresters. In contrast to this, the risk of threephase flashovers is approximately limited to 10-1 when the surge arresters are installed
after every 200 m, that is, SA-200 protection scheme. The risk of single-phase and
two-phase flashover also reduces by 21% and 19% compared to the SA-400 case.
Only small of the line between x = 900 to 1100 m will be subjected to induced overvoltage stress.
Therefore, it can be stated that lightning performance of the overhead line can be
significantly improved by reducing the peak induced overvoltages and confining the
risk indices over a small section of the line. This can be achieved by increasing the
number of surge arresters along the length of line, practically after every 200 m as all
the risk indices are within the threshold limit of 10-1. In this way, the line can be made
more resistant against multi-phase flashover faults. Further reduction in the spacing
between the surge arresters would improve the reliability of overhead line but that
would result in an additional cost.
6.4
Effect of Combined Surge Arresters and Shield Wire
In the previous section, it has been established that the installation of surge arrester
after every 200 m will limit the risk of three-phase flashover to 10-1. It has been de-
80
duced in [126] that the application of combined surge arresters and shield wire protection scheme grounded at the same point has approximately the same mitigation effect
as the surge arresters alone. Hence, the performance of surge arresters in conjunction
with shield wire is now evaluated in this study. The shield wire is generally placed
above the phase conductors and its effectiveness in mitigating the induced overvoltages depends on its distance from the phase conductors. The mitigation effect of shield
wire is considered in the probability distribution of peak induced overvoltage. Using
the modified median value Um and the standard deviation, the PDF of peak induced
overvoltages is combined with the CDF of insulator flashover voltages to obtain new
risk indices.
To analyze the mitigation effect of shield wire, it is assumed that the shield wire is
located at a height of 1 m from the phase conductor. The line configuration is shown in
Figure 6.9 in which the surge arresters are placed after every 400 m whereas the shield
wire is grounded after every 400 m, 200 m, 100 m and 50 m represented by SW-400,
SW-200, SW-100 and SW-50 respectively. The ground resistance is assumed to be 10
Ÿ and the location of the lightning stroke is fixed at x = 1000 m, that is, at the centre
of two adjacent grounding points considering the worst-case scenario.
For the case of SW-400, the highest median value Um at the closest point to the
stroke location is computed to be 77.37 kV with a standard deviation of 0.4519 at x =
1000 for y = 50 m. As the grounding intervals of the shield wire are reduced to 200 m,
100 m and 50 m, the median value Um also decreases to 69.12 kV, 62.17 kV and 54.35
kV for the same x and y. However, the surge arrester limits the overvoltage below the
insulation withstand voltage at its location.
Figure 6.9 Configuration of the overhead line to investigate the performance of surge arresters
in conjunction with shield wire for the cases: (a) SW-400 (b) SW-200 (c) SW-100 (d) SW-50.
The surge arrester location, grounding points of the shield wire and the location of lightning
stroke are represented by green circles, blue squares and red cross respectively.
81
Figure 6.10 presents the average risks of single-phase, two-phase and three-phase
flashover along the line. It can be observed that the risk of single-phase and two-phase
flashover is well below the threshold value of 10-1 for all the cases. When both surge
arresters and shield wire are alternately grounded with a spacing of 400 m, the risk of
three-phase flashover is nearly 10-1. This implies that the lightning protection provided
by combined surge arresters and shield wire protection scheme alternately grounded
after every 400 m is equivalent to case of installing surge arresters after every 200 m.
Thus, lower number of surge arresters is required to protect the overhead line to obtain
tolerable risk index less than 10-1. In addition, a further reduction in the risk of threephase flashover can be achieved by decreasing the grounding intervals of the shield
wire. For instance, the risk of three-phase flashover drops to 0.0736, 0.0410 and
0.0118 when the grounding intervals of the shield wire are reduced to 200, 100 m and
50 m respectively. An important aspect in the design of lightning protection scheme is
the reduction in multi-phase flashover faults especially three-phase flashovers. From
Figure 6.10 (a), it can be observed that risk of three-phase flashover is higher than the
risk of single-phase and two-phase flashover when both surge arresters and shield wire
are alternately grounded with a spacing of 400 m. Decreasing the grounding intervals
of shield wire considerably reduces the risk of three-phase flashover such that it becomes lower than the risk of single-phase flashover as shown in Figure 6.10 (d) where
the shield wire is grounded after every 50 m.
In this manner, the line designer can investigate the performance of various lightning protection schemes by limiting the risk of three-phase flashovers below the
threshold value. The limiting value of the risk of insulation flashover is generally
taken as 10-1 per lightning event [7], [32]. The line designer can further immune the
overhead line against induced overvoltage flashovers by further reducing the threshold
value to 5% but at the same time, the cost of protection will be increased. So, it is desired to achieve a balance between the reliability cost and protection cost.
Figure 6.10 Risk of single-phase, two-phase and three-phase insulator flashover as a function
of distance along the length of the overhead line for the case of surge arresters in conjunction
with shield wire for the cases (a) SW-400 (b) SW-200 (c) SW-100 (d) SW-50.
82
6.5
Application Example
The application of proposed risk-based insulation coordination method is illustrated by estimating the effect of AC voltage on the risk of insulation flashovers in the
presence of surge arresters. The results are shown in Table 6.1. By comparing the risk
of three-phase flashover, it can be noticed that neglecting the effect of AC voltage
results in a higher risk factor of 0.1520. This implies that the distance between the
consecutive surge arresters should be significantly decreased to less than 200 m to
obtain an acceptable risk factor of 10-1. As a result, the overhead line section should be
protected by higher number of surge arresters resulting in a higher investment cost. On
the contrary, the risk of three-phase flashover is calculated to be 0.1067, close to the
acceptable value, when the effect of AC voltage is considered. Thus, the overhead line
section can be adequately protected using surge arresters by reducing the spacing between them to 200 m as proposed in [2]. Thus, the lower number of surge arresters are
required for the protection of line. In this way, the proposed risk-based insulation coordination method can be employed for the design and coordination of various lightning protection schemes.
Table 6.1 Influence of AC voltage on the risk of flashovers at the closest point on the line to
the striking location
Case
SA-0
SA-1000
SA-400
SA-200
With Combined AC and Impulse
Voltage
R1-FO
R2-FO
R3-FO
0.0839
0.0611
0.1459
0.0859
0.0641
0.1708
0.0838
0.0612
0.1470
0.0676
0.0484
0.1067
Without AC Voltage
R1-FO
0.0228
0.0231
0.0227
0.0185
R2-FO
0.0205
0.0211
0.0206
0.0166
R3-FO
0.1976
0.2153
0.1982
0.1520
83
84
7. Conclusions and Future Research
Work
7.1
Conclusions
The response of an unshielded MV overhead line subjected to direct lightning has
been experimentally investigated with different types (metallic and wood) and configurations (grounded and ungrounded) of the cross arm. It has been inferred that the
grounded cross arm configuration of the line may experience a single-phase flashover
fault whereas multi-phase (two-phase or three-phase) flashover faults were observed
for ungrounded cross arm configuration. Accordingly, flashover takes place at higher
voltage level in ungrounded cross arm configuration compared to the grounded cross
arm configuration. The metallic or wood cross arm has no effect on the total CFO
voltage of the line in case of line operated with grounded cross arm configuration as
the dielectric strength to the lightning impulse voltages is provided by only one insulator. On the other hand, the total CFO voltage of the line with ungrounded wood cross
arm configuration is much higher than the corresponding metallic cross arm under dry
conditions. For wet conditions, the CFO voltage of the line with metallic cross arm is
approximately 60-65% of the wood cross arm. Thus, this study has established the
need of cross arm grounding to reduce multi-phase flashover faults due to direct lightning.
The physical mechanisms that govern the flashover phenomena should be dynamically modelled in the evaluation of the lightning performance of overhead distribution
lines. In this regard, the performance of an overhead distribution line subjected to direct lightning have been evaluated by incorporating the dynamic arc model and the
actual volt–time characteristics of the line insulation. An experimental study was carried out to investigate the features of single-phase and two-phase flashover faults using both grounded and ungrounded cross arm configurations respectively. The actual
volt–time characteristics of the line insulators are considered instead of assuming the
simplified 1.5×CFO flashover criterion for the occurrence of flashover. Next, the
flashover arc is modelled by variable resistance controlled by the dynamic arc model
whose parameters were computed using the least square error method. The agreement
85
of experimental and simulated result confirmed the validity of the proposed methodology to accurately predict the lightning overvoltages.
Considering both the first and subsequent direct lightning strokes applied to a typical MV unearthed network, the performance of various lightning protection schemes
of the distribution transformers based on spark gaps (without and with filtering element) and surge arresters (without and with spark gaps) have been studied using ATPEMTP simulations. It has been investigated that the effect of subsequent stroke current
in terms of overvoltage stress on the LV side of the distribution transformer is more
severe compared to the first stroke current. Furthermore, the protection of small distribution transformers (less than 200 kVA) with spark gaps results steep-front overvoltages and the overvoltage transferred to the LV terminals will be increased. The addition of series filtering element can be used to mitigate the steep-front overvoltage as
well as high frequency oscillations appearing on the consumer side. Furthermore, the
simulations also evaluated the performance of surge arresters to limit the transient
overvoltages. Due to the high cost associated with surge arresters, a low rating surge
arrester can be used in series with spark gap of higher energy class.
The evaluation of the dielectric strength of the MV line insulation in terms of
flashover and volt-time characteristics is of significant importance for the risk-based
insulation coordination studies. The flashover characteristics in terms of CFO voltage
and the volt-time curves of the test samples under combined AC and impulse voltages
(both positive and negative SI and STLI voltages) were reported. The results indicate
that the superimposition of the impulse voltage on the AC voltage mainly changes the
shape of probability-voltage curve without significantly affecting the median value of
flashover voltage. The shape of probability-voltage curve has an effect on the risk of
insulation flashover. The designer can underestimate the required insulation level by
neglecting the effect of AC voltage. Therefore, it is recommended to consider the effect of AC voltage for the proper design of insulation level using probabilistic insulation coordination studies.
An investigation based on probabilistic risk assessment was carried out for the occurrence probability of single-phase and multi-phase insulator flashovers due to lightning-induced overvoltages. The study has been made for both perfectly conducting
and lossy ground. In this regard, the modified probabilistic model of insulation flashover is experimentally validated to predict the occurrence probability of single-phase
and multi-phase insulator flashovers for the case of combined AC and impulse voltages. The results of risk assessment indicate that the induced overvoltage due to lightning stroke at a distance of 50 m from the overhead line is sufficiently high to cause a
three-phase flashover. For stroke location greater than 50 m, higher risk is associated
86
with single-phase flashover compared to the two-phase and three-phase flashover. The
situation becomes worse with increasing soil resistivity, that is, in case of lossy ground
with ȡ • 3000 Ÿm where relatively higher induced voltage is observed that is sufficient to cause a three-phase flashover for a stroke location far away from the line. It
can be concluded that the high soil resistivity increases the peak lightning-induced
overvoltages with consequent influence on the risk of insulation flashover. Thus, this
work presents the first attempt to apply risk-based insulation coordination method for
the evaluation of indirect lightning performance of overhead distribution lines. The
proposed methodology presents a comprehensive picture of the flashover phenomenon
in MV lines by taking into consideration the combined effect of AC and lightninginduced voltages with discrimination between single-phase and multi-phase flashover
faults.
The risk-based insulation coordination method has been applied for the selection of
optimum insulation level for MV overhead lines using VBP method. This is achieved
by balancing the cost of insulation with the outages cost. Sensitivity analysis is also
performed to study the dependence of optimum insulation level on the total investment
cost and the mean annual customer cost of undelivered energy. The investigations
proved that the higher insulation level can be provided for the corresponding reduction
in the total investment cost or an increase in the mean annual customer cost of undelivered energy. Finally, the effectiveness of reducing the spacing between the surge
arresters along the length of line to mitigate the risk of insulation flashovers is also
investigated. In this regard, it was observed that reducing the spacing between surge
arresters to less than 200 m will result in highest risk factor less than 10-1. It was also
inferred that higher spacing of 400 m can be permitted between the surge arresters if
they are to be employed in conjunction with shield wire. Accordingly, the lightning
performance of a combined surge arrester and shield wire protection scheme is also
evaluated in this work. It has been demonstrated that a risk factor less than 10-1 can be
obtained by reducing the grounding interval of shield wire to less than 200 m.
7.2
Future Research Work
Finally, the author strongly believes that there are still many research gaps in the
subject of this thesis. The following points suggest some of the research directions that
can be pursued in future:
x
Considering high soil resistivity and high grounding impedance in Finland,
the probabilistic model of insulation flashover should be modified to consider the effect of ground potential rise (GPR) on two-phase and three-
87
phase insulation flashover. This needs more investigation on insulators
testing with combined AC and impulse voltages.
x
Although, 2-D FDTD method has been used for the calculation of lightning-induced overvoltages along the overhead line, additional research efforts are needed to reduce the computational time when dealing with the
realistic line configurations. It would be also advantageous to develop
some simple model that could incorporate the effect of lossy ground along
with the presence of line discontinuities on the induced overvoltages.
x
The effect of seasonal as well as statistical variations in the lightning stroke
parameters like front time, tail time, the polarity of impulse voltage and
stroke multiplicity should be incorporated in the risk assessment of insulation flashovers.
x
In this thesis, the risk-based insulation coordination has been applied for
the overhead lines. The presented methodology could be extended to
evaluate the lightning performance of underground cables as well as aerial
distribution cable lines.
x
The effect of nearby tall grounded objects struck by lightning strokes on
the risk of insulation flashover in overhead lines should be investigated.
88
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