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i
ANI CHUKWUNONSO CALEB
PG/M.ENG/13/66409
AN INSULATION CO-ORDINATION
PROCEDURE FOR POWER SYSTEM
EQUIPMENT
FACULTY OF ENGINEERING
DEPARTMENT OF ELECTRICAL ENGINEERING
Azuka Ijomah
Digitally Signed by: Content manager’s Name
DN : CN = Webmaster’s name
O= University of Nigeria, Nsukka
OU = Innovation Centre
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DEPARTMENT OF ELECTRICAL ENGINEERING
UNIVERSITY OF NIGERIA NSUKKA
A THESIS SUBMITTED IN PARTIAL FULFILMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
Master of Engineering
TOPIC
AN INSULATION CO-ORDINATION PROCEDURE FOR POWER
SYSTEM EQUIPMENT
BY
ANI CHUKWUNONSO CALEB
PG/M.ENG/13/66409
iii
SUPERVISOR: PROF. T.C. MADUEME
OCTOBER, 2015
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CERTIFICATION
This is to certify that this project work titled “AN INSULATION COORDINATION
PROCEDURE FOR POWER SYSTEM EQUIPMENT” was carried out by ANI
CHUKWUNONSO CALEB, with Reg. No.: PG/M.ENG/13/66409 in the department of
Electrical Engineering, University of Nigeria Nsukka and meets the regulations governing the
Award of Degree of Master of Engineering(M.ENG) of the University of Nigeria Nsukka
………………………………… ……………..
Engr. Prof. T.C. Madueme Date
(Project Supervisor)
……………………………….. …………….
Engr. Prof E.C Ejiogu Date
(Head of Department)
……………………………… …………….
Prof. A. O. Ibe Date
v
External Examiner
………………………………… ……………..
Engr. Prof. E. S. Obe Date
Faculty PG Rep.
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APPROVAL
The contentS of this report are true reflection of the project undertaken by Ani Chukwunonso
Caleb (PG/M.ENG/13/66409). It is hereby accepted by the Department of Electrical
Engineering, Faculty of Engineering, University of Nigeria, Nsukka in partial fulfillment of
the requirement of for the award of master of engineering in Electrical Engineering
(M.ENG.) of University of Nigeria, Nsukka.
………………………………… ……………..
Ani Chukwunonso Caleb Date
Student
………………………………… ……………..
Engr. Prof. T.C. Madueme Date
Project Supervisor
……………………………….. …………….
Engr. Prof E.C Ejiogu Date
Head of Department
vii
……………………………… …………….
Prof. A. O. Ibe Date
External Examiner
………………………………… ……………..
Engr. Prof. E. S. Obe Date
P.G. Faculty Rep.
viii
DEDICATION
This work is dedicated to the Almighty God and to my Parents; Mr and Mrs Chibuzo Ani.
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ACKNOWLEDGEMENTS
I would like to use this opportunity to express my profound gratitude to my supervisor Prof
T.C. Madueme, for his guidance, encouragement, and total support throughout the course of
this thesis work. It was an extremely useful learning experience for me to be one of his
students. From him I have gained not only extensive knowledge, but also a careful research
attitude.
To Prof E.C. Ejiogu; who taught me that hard work and persistence is an important
research instrument. I also admire the motivation you gave me during my research period.
I also want to appreciate Prof S. E. Obe who has been my guidance and a counselor
during this research period. Moreover, I thank Dr. C.U. Ogbuka, Dr. B.N Nnadi and Engr.
Dr. C.M. Nwosu for your persistent advice as regards my research work. I appreciate all staff
of electrical engineering department and my colleagues in the division of power electronics
group and all the post graduate students in general for their support.
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ABSTRACT
Generally, for existing Insulation co-ordination studies the power system has been modeled
either by deterministic mathematical techniques or by statistical methods. The shortcoming of
the existing conventional mathematical technique of Insulation co-ordination analysis is that
it assumes that the power system dynamics is linear. This makes analysis of over voltage
response of the system under transients less optimal for determining over voltage withstand
of system elements. Thus, this work seeks to model a lightning induced over voltage transient
in a High voltage power system substation(132/33KV) used as a case study) using Hidden
Markov Model, to determine the maximum likelihood lightning surge signal. The station
data and configuration was modeled/simulated (in a MATLAB environment), which
implements the algorithms used in the work. The Hidden Markov algorithm(which makes use
of observable parameters to study what is happening at the hidden states), was used to
formulate the problem, while the Baum-welch and Viterbi algorithm were used to
find/identify the maximum likelihood lightning overvoltage waveform. These hidden states
are represented with different scenarios introduced in the work and the waveform identified,
is used to determine the Basic Insulation level(BIL), which is used to determine other
parameters accurately, which in turn helps to ensure an optimal/novel Insulation coordination
procedure for power system equipment in the station.
The results showed that the minimum required margin(15%) exceeded by a little value(i.e.
about 1.08) and the evaluation carried out to raise the protection margin to 18% meant the
relocation of the arrester to within 5.56m of the transformer.
xi
TABLE OF CONTENTS
Pages
Title Page i
Certification ii
Approval iii
Dedication iv
Acknowledgements vi
Abstract vii
Table Of Contents viii
List Of Figures xi
List Of Tables xii
List Of Symbols And Abbreviation xiii
Chapter One: Introduction
1.1 Background of the Study 1
1.2 Statement of the Problem
2
1.3 Objectives of the Study 3
1.4 Significance of the Study 4
xii
1.5 Scope of the Study 5
Chapter Two: Literature Review
2.1 Historical Trends 6
2.2 Definition of Terminology 8
2.3 Over Voltages 11
2.3.1 Power Frequency Overvoltages 13
2.3.2 Overvoltage Caused by an Insulation Fault 13
2.3.3 Overvoltage by Ferromagnetic Resonance 13
2.3.4 Switching Overvoltages 14
2.3.5 Normal Load Switching Overvoltage 14
2.4 Insulation Coordination Principle 14
2.4.1 Highest Power Frequency System Voltage(Continuous) 15
2.4.2 Temporary Power-Frequency Overvoltages 15
2.4.3 Transient Overvoltage Surges 15
2.4.4 Withstand Levels of the Equipment 16
2.5 Line Insulation Coordination 18
2.6 Station Insulation Coordination 20
2.7 Strategy of Insulation Co-Ordination 23
2.7.1 Conventional Method of Insulation Co-Ordination 24
xiii
2.7.2 Statistical Approach to Insulation Coordination 26
2.8 Hidden Markov Model 30
2.8.1 Brief History of Markov Process and Markov Chain 31
2.8.2 Brief History of Algorithms Need to Develop Hidden Markov Models 32
2.8.3 The Expectation-Maximization (E-m) Algorithm 33
2.8.4 The Baum-Welch Algorithm 34
2.8.5 The Viterbi Algorithm 34
2.9 Mathematical Basics of Hidden Markov Models 35
2.9.1 Definition of Hidden Markov Models 35
2.10 Summary of Related Literatures 36
Chapter Three: Research Methodology
3.0 Model Design 37
3.1 The Model Design Strategy 37
3.2 Scenario Description 39
3.2.1 Surge Event Scenario A 39
3.2.2 Surge Event Scenario B 39
3.2.3 Surge Event Scenario C 39
3.3 The Overvoltage Transient Assessment Based on the Hmm 39
3.4 The Overvoltage Training Disturbance Classification 40
3.4.1 The Processing Block 43
xiv
3.5 Computing for the Insulation Coordination 50
3.6 Modeling the Power System 53
3.6.1 Transmission Line Conductors Model 53
3.6.2 Transmission Line Towers Model 54
3.6.3 Surge Arresters Model 54
3.6.4 Transformer Model 54
3.6.5 Lightning Surge Model 54
3.7 Assumption for Lightning Surge 55
Chapter Four: Simulation and Result Evaluation
4.0 Simulation and Result Evaluation 56
4.1 Simulation of the Three Lightning Overvoltage Transient Scenarios 56
4.1.1 Surge Event Scenario A 60
4.1.2 Surge Event Scenario B 61
4.1.3 Surge Event Scenario C 61
4.2 Waveform at the Strike Point 63
Chapter Five: Recommendation and Conclusion
5.1 Summary 70
xv
5.2 Conclusion 71
5.3 Recommendation 71
5.4 Suggestion for Further Studies 72
References 73
Appendix 76
LIST OF FIGURES
Figure
Pages
2.1 Statistical Impulse Withstand Voltage 10
2.2 Stastical Impulse Voltage 11
2.3 Allegheny Power System's 500-kV Tower. 19
2.4: 330kv Nigeria Power Transmission Tower 20
xvi
2.5 The Strike Distances and Insulation Lengths in a Substation. 21
2.6 Margin of Protection and Insulation Withstand Level 24
2.7 Coordination Using Gaps 25
2.8 Coordination of Bils and Protection Levels Classical Approach) 26
2.9 Method of Describing the Risk of Failure. 28
2.10 Reference Probabilities for Overvoltage and for Insulation Withstand Strength 29
2.11 The Statistical Safety Factor and its Relation to the Risk of Failure 30
3.1: Flow Chart of Proposed Logarithm for Insulation Coordination 42
3.2: Steps for the Signal Processing and Observation Evaluation Problem 43
3.3: Flow Chart of the Hmm Training Process for the Observation Evaluation Problem 46
4.1 Model of the 330kV/132kV Power Station
At New Haven Enugu Nigeria 57
4.2 The illustration of incoming transmission surge wave of scenario A 60
4.3. Resultant Waveform for Surge Event Scenario A 61
4.4. The illustration of incoming transmission surge wave of scenario B1 60
4.5. Resultant Waveform for Surge Event Scenario B 62
4.6 The illustration of incoming transmission surge wave of scenario C 63
4.7. Resultant Waveform for Surge Event Scenario C 64
4.8 Resultant Waveform Of Three Surge Event Scenarios (The Combined Plot) 65
4.9 Resultant Waveform At The Strike Point 66
4.10 Location Of Arrester 4 (On Phase A) To The 132/33kv Transformer Supplying The
Kingsway Line I 68
xvii
LIST OF TABLES
2.1: Characteristics of the various Overvoltages types 12
2.2: Basic Impulse Insulation Levels 16
3.1: Observed electrical feature for HMM classification of the lighting overvoltage transients
of the power system. 44
4.1: Station Parameters/Data supplied by PHCN 58
4.2: Transmission Line data 59
4.3: Corona damping constant 𝐾𝑐𝑜 65
xviii
LIST OF SYMBOLS AND ABBREVIATIONS
HMM: Hidden Markov Model
BIL: Basic Insulation Level
BSL: Basic Switching Level
MV: Mega Volts
PF: Power Frequency
LOV: Lightning Over Voltage:
SOV: Switching Over Voltages
E.H.V: Extra High Voltages
U.H.V: Ultra High Voltages
𝑉𝑆: Statistical Overvoltage
BW: Baum Welch
xix
P(𝑂|λ): Maximum Likelihood Probability
F(𝐼𝑚): Lightning Current Probability
𝐾𝑐𝑜: Corona damping Constant. µs/(KV.m)
IEC: International Electro-technical Commission
IG: Impulse Generator
𝑋𝑝: Limit Overhead line distance within which lightning event occurs, m
T: Longest Travel time of Surge Current, (µs)
𝑈𝑝𝑙 is the lightning impulse protective level of the arrester, KV
U: Overvoltage Amplitude, KV.
𝛽: Reflection Coefficient
𝑆: Steepness of Surge Voltage, Kv/µs.
𝐸𝑡: Surge Voltage at the Transformer Terminal.
𝑙𝑡: Separation between Transformer and the Arrester.
𝐸𝑎: Arrester BIL.
MOP: Margin of Protection.
CFOV: Critical Flashover Voltage.
xx
CIGRE: Conseil International Des Grands Reseaux Electriques(International Council on
Large Electric Systems).
NEMA: National Electrical Manufacturers Association
NELA: Nigeria Electric Light Association
AIEE: Advanced International Electronic Equipment.
EEI: Edison Electric Institute
CDMA: Code Division Multiple Access
GSM: Global System for Mobile Communication
LAN: Local Area Network
CVT: Capacitor Voltage Transformer.
PHCN: Power Holding Company of Nigeria.
CFO: Critical Flash Over
1
CHAPTER ONE
INTRODUCTION
1.0 Background of the Study
The demand for the generation and transmission of large amounts of electric power today,
necessitates its transmission at extra-high voltages. In modern times, high voltages are used
for a wide variety of applications covering the power systems, Industry and research
Laboratories. Such applications have become essential to sustain modern civilization[1].
The diverse conditions under which a high voltage apparatus is used necessitate careful
design of its insulation and the electrostatic field profiles[2]. This entails the analysis of the
electrical power system to determine the probability of post insulation flashovers. For
instance, analysis must be carried out to determine that the insulation contained within power
system components like transformers has the acceptable margin of protection. Since the
internal insulation is not self-restoring, a failure is completely unacceptable. An insulation co-
ordination study of a substation will present all the probabilities and margins for all transients
entering the station.
Over voltages are phenomena which occur in power system networks either externally or
internally. The selection of certain level of over voltages which are based on equipment
strength for operation is known as Insulation co-ordination[3]. It is essential for electrical
power engineers to reduce the number of outages and preserve the continuity of service and
electric supply. In another perspective, Insulation co-ordination is a discipline aiming at
achieving the best possible techno-economic compromise for protection of persons and
equipment against over voltages, whether caused by the network or lightning, occurring on
2
electrical installations. The purpose of Insulation co-ordination is to determine the necessary
and sufficient insulation characteristics of the various network components in order to obtain
uniform withstand to normal voltages and to over voltages of various origins.
However over voltages are extremely hard to calculate. They cannot generally be
predetermined, since they involve incalculable elements which vary from site to site. Hence
effective Insulation co-ordination requires accurate modeling of the power system. Modeling
transmission lines and substations help engineers understand how protection systems behave
during disturbances and faults.
Though a number of techniques have been developed for modeling transient disturbances in
power systems, the problem of doing optimal Insulation co-ordination is still limited by
accurate model of the power system. Generally, for existing Insulation co-ordination studies
the power system has been modeled either by deterministic mathematical techniques or by
statistical methods. The shortcoming of the existing conventional mathematical technique of
Insulation co-ordination analysis is that it assumes that the power system dynamics is linear.
This makes analysis of over voltage response of the system under transients less optimal for
determining over voltage withstand of system elements. While the statistical technique,
though more accurate[4][5][6], is known that the statistical evaluation of the risk cannot be
assessed if the breakdown behavior of the insulation is unknown or if it is referred only to the
basic Impulse level(BIL) of the power system component.
Hence a novel Insulation Co-ordination procedure for power system equipment is proposed in
this work.
1.1 Statement of Problem
3
With reference to the limitation of the deterministic mathematical and statistical approach of
power system insulation co-ordination, as highlighted in the background of this study. Thus
given a high voltage(HV) power station and its associated transmission line, the problem to
be tackled by this work is to model overvoltage transient disturbance from lightning using
Hidden Markov Model(HMM), to determine the maximum likelihood lightning surge
waveform. This is to enable the determination of voltage stresses within the station during
surge event and to determine voltage withstand of systems insulation elements; i.e. the Basic
Impulse Insulation(BII) in order to determine protection margin based on equipment data and
to make optimal placements of protection devices within the system.
1.2 Objectives of the Study
The major objective of this work is to develop a model that enables the investigation of over
voltages due to lightning voltages in order to effectively carry out insulation Co-ordination of
a high voltage substation power system. Hence, this work realizes the following specific
objectives:
1. To model a lightning induced over voltage transient in a High voltage power system
substation using Hidden Markov Model, to determine the maximum likelihood
lightning surge signal.
2. To carry out simulation of the response of the power system to lightning over voltages
and determining over voltages induced at specific junctions of the substation.
3. To carry out evaluation of the results of the simulation to determine voltage withstand
capabilities(Basic Impulse insulation; BIL), evaluating protection margin based on the
systems equipment data and optimal placement of protection devices throughout the
substation.
4
4. To carryout validation of the findings and make recommendation for both actual
implementation of the proposed insulation co-ordination technique and
recommendations for further improvement of the technique.
1.3 Significance of the Study
The power system constitutes a huge factor in the national and global economy. When
power system equipment is not properly protected during over voltage, this equipment
gets damaged necessitating repairs. Hence improper equipment protection against
over voltages increases causes of repairs and cost of power system maintenance. This
means substantial impact on the economy. Hence the realization of the objectives of
this study to develop a novel model to enhance the reliability of insulation co-
ordination of power systems is significant to the reduction of system downtime,
reduction of power system repair and maintenance cost. This means the success of
this work helps to enhance the economy, since all modern services (including
banking, telecommunication, agriculture, manufacturing, health care etc.) that depend
on reliable electric energy benefits from interruptible supply of power.
High voltage insulation failure poses danger to persons and equipment. Hence the
significance of a research that seeks to enhance protection technique for persons and
equipment is in no doubt. Therefore, the proposed study presents much promise for
the enhancement of human and equipment safety from over voltages within electric
power systems.
One of the things that hamper effective administration of electric power generation,
transmission and distribution is planning and control. These activities are in turn
5
hampered by inaccurate evaluation and prediction of equipment and systems failure
rates and lack of reliable probability estimate of post insulation flashovers. This
problem is substantially caused by lack of accurate model of power systems. With
accurate modeling of power system for insulation co-ordination activities, it would be
possible to estimate proper withstand capabilities of power system limits, estimate of
probabilities of failures and proper equipment protection margin. Thus, proper
planning and control of power systems can be done, ensuring effective administration
of electric power systems.
Also, with reference to the modeling of the power system proposed in this study, this
would help increase the understanding of power system engineers about the behavior
of power system components under lightning induced disturbances.
This work makes a contribution regarding the use of Hidden markov model
(HMM), in determining the probabilistic maximum likelihood of surge wave signal,
based on the digital model of a power system. Therefore, this contribution would
benefit further research on both power systems modeling and insulation co-ordination
studies of high voltage power systems.
1.4 Scope of the Study
This work covers modeling of lightning induced overvoltage transients in HV power
substation and its associated transmission lines. It covers insulation coordination, involving
lightning arresters, their placement relative to substation transformers and the evaluation of
protection margin. However, insulation coordination for switching overvoltage and substation
shielding are not considered. PHCN 330/132/33KV Transmission station switch yard New
Haven Enugu, was used as a case study.
6
7
CHAPTER TWO
LITERATURE REVIEW
2.1 Historical Trends
Coordination of insulation was not given serious consideration until after the First World
War, mainly because of lack of information on the nature of lightning surges and the surge
strength of apparatus insulation. Since concrete data were lacking on the actual surge strength
of insulation or the discharge characteristics of protective equipment, early attempts at
coordination were rule-of-thumb methods based on experience and individual ideas. The
result was that some parts of the station were over-insulated while others were under-
insulated. Also, the gradual increasing of line insulation in an attempt to prevent line
flashovers were eliminated at the expense of apparatus failures. Growth of power systems
demands for improved power service, and more economical system operation focused more
and more attention on the problems of surge voltages, adequate insulation, and its protection.
Thus, during the period from about 1918 to 1930 considerable work was done by individual
investigators and laboratories in collecting data on natural lightning and in developing
insulation testing methods and technique. Although progress was seemingly slow, it resulted
in a fair knowledge of the nature of lightning surges and the establishment of universal surge
producing and measuring devices. Very little correlation between laboratories was attempted
during that period[7].
In 1930, the NEMA-NELA Joint Committee on Insulation Coordination was formed to
consider laboratory testing technique and data, to determine the insulation levels in common
use, to establish the insulation strength of all classes of equipment, and to establish insulation
levels for various voltage classifications. After ten years of study and collection of data this
8
schedule was fairly well completed. Numerous articles in trade magazines show the results.
In a report dated January 1941, the committee, now known as the joint AIEE-EEI-NEMA
Committee on Insulation Coordination, rounded out the program by specifying basic impulse
insulation levels for the different voltage classifications.
Test specifications for apparatus are prepared on the basis of demonstrating that the
insulation strength of the equipment will be equal to or greater than the selected basic
insulation level and the protective equipment for the station should be chosen to give the
insulation meeting these levels as good protection as economically justified[7].
The following are the basic definition of insulation coordination in its most fundamental and
simple form:
(a). Insulation coordination is the selection of the insulation strength.
If desired, a reliability criterion and something about the stress placed on the insulation could
be added to the definition. In this case the definition would become
(b). Insulation coordination is the "selection of the insulation strength consistent with the
expected overvoltages to obtain an acceptable risk of failure"[6].
In some cases, engineers prefer to add something concerning surge arresters, thus, the
definition is expanded to
(c). Insulation coordination is the "process of bringing the insulation strengths of electrical
equipment into the proper relationship with expected overvoltages and with the
characteristics of surge protective devices"[8].
The definition could be expanded further to
9
(d). Insulation coordination is the "selection of the dielectric strength of equipment in relation
to the voltages which can appear on the system for which equipment is intended and taking
into account the service environment and the characteristics of the available protective
devices" [9].
(e). "Insulation coordination comprises the selection of the electric strength of equipment and
its application, in relation to the voltages which can appear on the system for which the
equipment is intended and taking into account the characteristics of available protective
devices, so as to reduce to an economically and operationally acceptable level the probability
that the resulting voltage stresses imposed on the equipment will cause damage to equipment
insulation or affect continuity of service" [10].
2.2 Definition of Terminology used in Insulation Coordination
(i). Nominal System Voltage: It is the r.m.s. phase-to-phase voltage by which a system is
designated. Also it is the phase to phase voltage of the system for which the system is
normally designed. S as 11KV,. S as 11KV,33KV, 132KV, 220KV, 400KV systems[11].
(ii). Maximum System Voltage: It is the maximum rise of the r.m.s. phase-to-phase system
voltage.
(iii). Factor of Earthing: This is the ratio of the highest r.m.s. phase-to-earth power
frequency voltage on a sound phase during an earth fault to the r.m.s. phase-to-phase power
frequency voltage which would be obtained at the selected location without the fault. This
ratio characterizes, in general terms, the earthing conditions of a system as viewed from the
selected fault location.
(iv). Effectively Earthed System
10
A system is said to be effectively earthed if the factor of earthing does not exceed 80%.
Factor of earthing is 100% for an isolated neutral system, while it is 57.7% (1/√3 = 0.577) for
solidly earthed system.
(v). Insulation Level: Every electrical equipment has to undergo different abnormal transient
over voltage situation in different times during its total service life period. The equipment
may have to withstand lightning impulses, switching impulses and/or short duration power
frequency over voltages. Depending upon the maximum level of impulse voltages and short
duration power frequency over voltages that one power system component can withstand, the
insulation level of high voltage power system is determined.
(vi). Lightning Impulse Voltage: The system disturbances occur due to natural lightning can
be represented by three different basic wave shapes. If a lightning impulse voltage travels
some distance along the transmission line before it reaches to an insulator, its wave shaped
approaches to full wave, and this wave is referred as 1.2/50 wave. If during travelling, the
lightning disturbance wave causes flash over across an insulator the shape of the wave
becomes chopped wave. If a lightning stroke hits directly on the insulator then the lightning
impulse voltage may rise steep until it is relieved by flash over, causing sudden, very steep
collapse in voltage. These three waves are quite different in duration and in shapes[11].
(vii). Switching Impulse: During switching operation a uni-polar voltage appears in the
system. The waveform of which may be periodically damped or oscillating. Switching
impulse wave form has steep front and long damped oscillating tail.
(viii). Short duration power frequency withstand voltage: This is the prescribed rms value
of sinusoidal power frequency voltage that the electrical equipment shall withstand for a
specific period of time normally 60 seconds.
11
(ix). Protective Level of Protective Device: These are the highest peak voltage value which
should not be exceeded at the terminals of a protective device when switching impulses and
lightning impulses of standard shape and rate values are applied under specific conditions.
(x). Conventional Impulse Withstand Voltages: This is the peak value of the switching or
lightning impulse test voltage at which an insulation shall not show any disruptive discharge
when subjected to a specified number of applications of this impulse under specified
conditions.
(xi). Conventional Maximum Impulse Voltage: This is the peak value of the switching or
lightning overvoltage which is adopted as the maximum overvoltage in the conventional
procedure of insulation co-ordination.
(xii). Statistical Impulse Withstand Voltage: This is the peak value of a switching or
lightning impulse test voltage at which insulation exhibits, under the specified conditions, a
90% probability of withstand. In practice, there is no 100% probability of withstand voltage.
Thus the value chosen is that which has a 10% probability of breakdown[12].
12
Figure 2.1: Statistical impulse withstand voltage
(xiii). Statistical Impulse Voltage: This is the switching or lightning overvoltage applied to
equipment as a result of an event of one specific type on the system (line energizing,
reclosing, fault occurrence, lightning discharge, etc.), the peak value of which has a 2%
probability of being exceeded[12].
Figure 2.2: Statistical Impulse voltage
Insulation coordination is a discipline aiming at achieving the best possible technico-
economic compromise for protection of persons and equipment against over voltages,
whether caused by the network or lightning, occurring on electrical installations. It helps
ensure a high degree of availability of electrical power. Its value is doubled by the fact that it
concerns high voltage networks. To control insulation coordination:
the level of the possible over voltages occurring on the network must be known;
the right protective devices must be used when necessary;
the correct overvoltage withstand level must be chosen for the various network
components from among the insulating voltages satisfying the particular
constraints[13].
13
2.3 OVER VOLTAGES
An overvoltage is an abnormal voltage between two points of a system that is greater than the
highest value appearing between the same two points under normal service conditions.
• Overvoltages are the primary “metric” for “measuring” and “quantifying” power system
transients and thus insulation stress.
Also, these are disturbances superimposed on circuit rated voltage. They may occur:
• between different phases or circuits and are said to be differential mode;
• between live conductors and the frame or earth and are said to be common mode.
Their varied and random nature makes them hard to characterize, allowing only a statistical
approach to their duration, amplitudes and effects. Table 2.1 presents the main characteristics
of these disturbances.
In point of fact, the main risks are malfunctions, destruction of the equipment and,
consequently, lack of continuity of service. These effects may occur on the installations of
both energy distributors and users.
Table 2.1: Characteristics of the various Overvoltages types
Overvoltage Type (Cause) MV-HV
overvoltage
coefficient
Time Steepness of
Frequency
front
Damping
At Power frequency (Insulation
Fault
≤ √3
Long > 1s Power
frequency
low
14
Switching (short-circuit
disconnection)
2 to 4 Short 1ms Medium 1 to
200KHZ
medium
Atmospheric (direct lightning
stroke)
> 4 Very short
1 to 10µs
Very high
1,000KV/µs
high
Source:[13]
Disturbances may result in:
- Short disconnections (automatic reclosing on MV public distribution networks by overhead
lines);
- long disconnections (intervention for changing damaged insulators or even replacement of
equipment).
Protective devices limit these risks. Their use calls for careful drawing up of consistent
insulation and protection levels. For this, prior understanding of the various types of over
voltages is vital[13].
2.3.1 Power frequency overvoltages
This term includes all over voltages with frequencies under 500 Hz. The most common
network frequencies are: 50, 60 and 400 Hz. In normal operating conditions, network voltage
may present short duration power frequency overvoltages (a fraction of a second to a few
hours: depending on network protection and operating mode). Voltage withstand checked by
the standard one-minute dielectric tests is normally sufficient. Determination of this category
of characteristics is simple, and the various insulators are easy to compare.
15
2.3.2 Overvoltage caused by an insulation fault
An overvoltage due to an insulation fault occurs on a three-phase network when the neutral is
unearthed or impedance-earthed. In actual fact, when an insulation fault occurs between a
phase and the frame or earth (a damaged underground cable, earthing of an overhead
conductor by branches, equipment fault, ...), the phase in question is placed at earth potential
and the remaining two phases are then subjected, with respect to earth, to the phase-to-phase
voltage
U = V √3. (2.1)
Where U is the Line Voltage and V is the phase voltage.
More precisely, when an insulation fault occurs on phase A, an earth fault factor, 𝑆𝑑, is
defined by the ratio of the voltage of phases B and C with respect to earth, to network phase
to neutral voltage.
The following equation is used to calculate𝑆𝑑:
𝑆𝑑 =√3 (𝐾2 + 𝐾 + 1)
𝐾 + 2 (2.2)
2.3.3 Overvoltage by ferromagnetic resonance
In this case the overvoltage is the result of a special resonance which occurs when a circuit
contains both a capacitor (voluntary or stray) and an inductance with saturable magnetic
circuit (e.g. a transformer). This resonance occurs particularly when an operation (circuit
opening or closing) is performed on the network with a device having poles either separate or
with non-simultaneous operation.
2.3.4 Switching overvoltages
Sudden changes in electrical network structure give rise to transient phenomena frequently
resulting in the creation of an overvoltage or of a high frequency wave train of a periodic or
oscillating type with rapid damping[13].
16
2.3.5 Normal load switching overvoltage
A normal load is mainly resistive, i.e. its power factor is greater than 0.7. In this case,
breaking or making of load currents does not present a major problem. The overvoltage factor
(transient voltage amplitude/operating voltage ratio) varies between 1.2 and 1.5.
2.4 Insulation coordination Principle
Study of insulation coordination of an electrical installation is thus the definition, based on
the possible voltage and overvoltage levels on this installation, of one or more overvoltage
protection levels. Installation equipment and protective devices are thus chosen accordingly.
Protection level is determined by the following conditions:
• Installation
• Environment
• Equipment use.
Study of these conditions determines the overvoltage level to which the equipment could be
subjected during use. Choice of the right insulation level will ensure that, at least as far as
power frequency and switching impulses are concerned, this level will never be overshot.
As regards lightning, a compromise must generally be found between Insulation level,
protection level of arresters, if any, and acceptable failure risk. Proper control of the
protection levels provided by surge limiters requires thorough knowledge of their
characteristics and behavior.
17
The Insulation requirements are determined by considering the following:
2.4.1 Highest Power Frequency System Voltage(Continuous):
AC network has different nominal power-frequency voltage level(e.g. 400V, 3.3kV, 6.6kV,
11kV, 22kV, 33kV, 66kV, 110kV, 132kV, 220kV, 220kV, 400kV r.m.s. continuous, at 50Hz).
During light-load period, the power frequency voltage at the receiving end of the
transmission line rises. In a well regulated system, the permissible maximum system voltage
allowed is called the highest system voltage. Each nominal voltage level has certain
corresponding highest system voltage(400V, 3.6kV, 7.2kV, 12kV, 24kV, 36kV, 72.5kV,
123kV, 145kV, 245kV and 420kV rms continuous). Each equipment is designed and tested
to withstand the corresponding highest power frequency voltage of that voltage level
continuously without internal/external insulation failure[14].
2.4.2 Temporary Power-Frequency overvoltages:
These overvoltages are caused by load throw-off, faults, resonance, etc. However, there is a
difference between the characteristics of power frequency overvoltages and transient voltage
surges and the corresponding stresses on equipment and surge arresters. The temporary
power-frequency (PF) overvoltages are of 50Hz and of lesser peak, lesser rate of rise and of
longer duration(seconds or even minutes). The protection against temporary PF overvolages
is provided by Inverse definite minimum time(IDMT) overvoltage relays connected to
secondary of bus potential transformer and circuit breakers. The relay and breakers action is
within several tens of milliseconds to a few seconds. The circuit breakers open and the
equipment(such as transformer or bus) is protected against the temporary overvoltage[14].
2.4.3 Transient Overvoltage Surges:
18
It is caused by lightning, switching, restrikes, travelling waves, etc. Surges in the power
system are of comparatively high peak, high rate of rise and last for a few tens/hundreds of
milliseconds and are therefore called transients. Surges can cause spark-over and flash over
at sharp corners, flash over between phase and earth at the weakest point, breakdown of
gaseous/liquid/solid insulation, failure of transformers and rotating electrical machines. The
failure rate due to lightning and switching has been minimized by proper insulation co-
ordination and surge arrester protection. Several protective devices are installed in the
network to intercept lightning strokes and minimize the peak/rate of rise of surges reaching
the equipment[14].
2.4.4 Withstand Levels of the Equipment:
The BIL (Basic impulse insulation level) is specified and other withstand levels are then
selected from relevant tables provided in standard specifications .
Basic impulse levels are reference levels expressed in impulse crest voltage with a standard
wave not longer than 1.2/50μs wave. Apparatus/equipment should be capable of
withstanding test waves above BIL.
Table 2.2 gives the BIL for various reference class voltages (kV).
Table 2.2: Basic Impulse Insulation Levels
Reference Class kV Standard Basic Impulse
Level kV
Reduced Insulation Levels kV
23 150
34.5 200
46 250
69 350
92 450
115 550 450
138 650 550
161 750 650
19
196 900
230 1,050 900
287 1,300 1,050
345 1,550 1,300
Source: [14]
The problem of insulation coordination involves not only the protection of equipment but the
protection of the protective devices too. To achieve this, a lightning arrester must be applied
and used on the system in such a way that it will discharge excessive voltage safely to the
ground very quickly and then restore itself as an insulator and protect the equipment
insulation.
For safe operation of the equipment, it should have insulation strength equal to or greater than
the basic standard insulation level and the protective equipment for a station/substation
should be chosen to give the insulation good protection corresponding to the working of these
levels as economically as possible.
To assist in the process of insulation coordination, standard insulation levels have been
recommended.
The problem of insulation co-ordination can be studied under the following three steps:
(i) Selection of a suitable insulation which is a function of reference class voltage (i.e., 1.05 x
working voltage of the system). The table shown above gives the basic impulse insulation
levels (BIL) for various reference class voltages.
(ii) The design of the various equipment must be such that the breakdown or flashover
strength of all insulation in the station equals or exceeds the selected levels as in Table 2.2
above.
20
(iii) Selection of protective devices that will provide the apparatus as good protection as can
be justified economically.
The above procedure requires that the apparatus under protection shall have a withstand test
value not less than the kV magnitude given in the second column of Table 2.2, irrespective of
the polarity of wave (positive or negative) and irrespective of how the system was earthed.
The third column of Table 2.2 gives the reduced insulation levels which are employed for
selecting insulation levels of solidly grounded system and for systems operating above 345kV
where switching surges are of more importance than the lightning surges.
Usually, insulation coordination is separated into two major parts:
(i) Line insulation coordination, which can be further separated into transmission and
distribution lines.
(ii) Station insulation coordination, which includes generation, transmission, and distribution
substations.
To these two major categories must be added a myriad of other areas such as insulation
coordination of rotating machines, and shunt and series capacitor banks. Let us examine the
two major categories.
2.5 LINE INSULATION COORDINATION
For line insulation coordination, the task is to specify all dimensions or characteristics of the
transmission or distribution line towers that affect the reliability of the line:
(i). The tower strike distances or clearances between the phase conductor and the grounded
tower sides and upper truss.
21
(ii). The insulator string length.
(iii). The number and type of insulators.
(iv). The need for and type of supplemental tower grounding.
(v). The location and number of overhead ground or shield wires.
(vi). The phase-to-ground midspan clearance.
(vii). The phase-phase strike distance or clearance.
(viii). The need for, rating, and location of line surge arresters.
To illustrate the various strike distances of a tower, a typical 500-kV tower is shown in
Figure 2.3[15].
Considering the center phase, the sag of the phase conductor from the tower center to the
edge of the tower is appreciable. Also the vibration damper is usually connected to the
conductor at the tower's edge. These two factors result in the minimum strike distance from
the damper to the edge of the tower. The strike distance from the conductor yoke to the upper
truss is usually larger. In this design, the strike distance for the outside phase exceeds that for
the center phase. The insulator string length is about 11.5 feet, about 3% greater than the
minimum center phase strike distance[15].
22
Figure 2.3: Allegheny Power System's 500-kV tower.
23
Also the Nigeria 330kV Transmission tower is shown in fig. 2.4 below
Figure 2.4: 330kV Nigeria Power Transmission Tower
8.55m
12m
9m 9m
12.82m
24
2.6 STATION INSULATION COORDINATION
For station insulation coordination, the task is similar in nature. It is to specify
(i). The equipment insulation strength, that is, the BIL and BSL of all equipment.
(ii). The phase-ground and phase-phase clearances or strike distances. Figure 2.5 illustrates
the various strike distances or clearances that should be considered in a substation.
(iii). The need for, the location, the rating, and the number of surge arresters.
(iv). The need for, the location, the configuration, and the spacing of protective gaps.
(v). The need for, the location, and the type (masts or shield wires) of substation shielding.
(vi). The need for the amount, and the method of achieving an improvement in lightning
performance of the lines immediately adjacent to the station.
In these lists, the method of obtaining the specifications has not been stated. To the person
receiving this information, how the engineer decides on these specifications is not of primary
importance, only that these specifications result in the desired degree of reliability[15]. It is
true that the engineer must consider all sources of stress that may be placed on the equipment
or on the tower. That is, he must consider
(a). Lightning overvoltages (LOV), as produced by lightning flashes
(b). Switching overvoltages (SOV), as produced by switching breakers or disconnecting
switches[15].
25
Figure 2.5: The strike distances and insulation lengths in a substation.
𝑺𝒑𝒑 is phase-phase Clearance/distances, 𝑺𝒑𝒈 is phase-ground clearance/distance.
(c). Temporary overvoltages (TOV) as produced by faults, generator over speed, Ferro-
resonance etc.
(d). Normal power frequency voltage in the presence of contamination
For some of the specifications required, only one of these stresses is of importance.
For example, considering the transmission line, lightning will dictate the location and number
of shield wires and the need for and specification of supplemental tower grounding.
Considering the station, lightning will dictate the location of shield wires or masts. However,
subjective judgment must be used to specify whether shield wires or masts should be used.
The arrester rating is dictated by temporary overvoltages.
26
In addition, the number and location of surge arresters will primarily be dictated by lightning.
Also, for the line and station, the number and type of insulators will be dictated by the
contamination.
However, in many of the specifications, two or more of the overvoltages must be considered.
For transmission lines, for example, switching overvoltages, lightning, or contamination may
dictate the strike distances and insulator string length. In the substation, however, lightning,
switching surges, or contamination may dictate the BIL, BSL, and clearances.
Since the primary objective is to specify the minimum insulation strength, no one of the
overvoltages should dominate the design. That is, if a consideration of switching overvoltages
results in a specification of tower strike distances, methods should be sought to decrease the
switching overvoltages. In this area, the objective is not to permit one source of overvoltage
stress to dictate design. Carrying this philosophy to the ultimate, results in the objective that
the insulation strength will be dictated only by the power frequency voltage. Although this
may seem ridiculous, it has essentially been achieved with regard to transformers, for which
the 1-hour power frequency test is considered by many to be the most severe test on the
insulation.
In addition, in most cases, switching surges are important only for voltages of 345kV and
above. That is, for these lower voltages, lightning dictates larger clearances and insulator
lengths than do switching overvoltages. As a caution, this may be untrue for "compact"
designs[15].
2.7 Strategy of Insulation Co-ordination:
The problem of overvoltages and insulation co-ordination can be solved by the following
steps:
27
(i). Each equipment/apparatus has specified power-frequency withstand level and impulse
Withstand levels.
(ii). The Withstand levels of Equipment/apparatus/machines are co-ordinated with the
protective voltage level of the nearest lightning arrester. Protective levels of lightning
arrester at each voltage level shall be coordinated.
(iii). Every equipment is well protected and overall economy and reliability is achieved.
In the event of occurrence of severe voltage surge the damage is to the least costly
equipment.
(iv). Duplicate surge protection is provided in substations, one lightning arrester per phase
at incoming bus and another lightning arrester at transformer terminals for each phase.
(v). System neutral is grounded at every voltage level to reduce coefficient of grounding
and to discharge the surges.
Insulation coordination covers the following aspects:
a. The causes and effects of transient overvoltages (surges) and the protection of
electrical equipment insulation.
b. Standardization of nominal voltage levels and highest voltage levels in the network.
c. Choices of power frequency withstand values for equipment insulation.
d. Choice of BIL and switching impulse withstand levels for equipment insulation.
2.7.1 Conventional method of insulation co-ordination
28
In order to avoid insulation failure, the insulation level of different types of equipment
connected to the system has to be higher than the magnitude of transient overvoltages that
appear on the system. The magnitude of transient over-voltages are usually limited to a
protective level by protective devices. Thus the insulation level has to be above the protective
level by a safe margin. Normally the impulse insulation level is established at a value 15-
25% above the protective level. Figure 2.5 below illustrates the margin of protection and
insulation level[15]:
Figure 2.6: Margin of Protection and Insulation Withstand level
Consider the typical co-ordination of a 132 kV transmission line between the transformer
insulation, a line gap (across an insulator string) and a co-coordinating gap (across the
transformer bushing) as shown in Fig. 2.7.
29
Figure 2.7: Coordination using gaps
[Note: In a rural distribution transformer, a lightning arrester may not be used on account of
the high cost and a coordinating gap mounted on the transformer bushing may be the main
surge limiting device]
In coordinating the system under consideration, we have to ensure that the equipment used is
protected, and that inadvertent interruptions are kept to a minimum. The coordinating gap
must be chosen so as to provide protection of the transformer under all conditions. However,
the line gaps protecting the line insulation can be set to a higher characteristic to reduce
unnecessary interruptions.
A typical set of characteristics for insulation co-ordination by conventional methods, in
which lightning impulse voltages are the main source of insulation failure.
30
For the higher system voltages, the simple approach used above is inadequate. Also,
economic considerations dictate that insulation co-ordination be placed on a more scientific
basis.
2.7.2 Statistical approach to insulation coordination
In the early days insulation levels for lightning surges were determined by evaluating the 50
per cent flashover values (BIL) for all insulations and providing a sufficiently high withstand
level that all insulations would withstand.
For those values a volt–time characteristic was constructed. Similarly the protection levels
provided by protective devices were determined. The two volt–time characteristics are shown
in Figure 2.8. The upper curve represents the common BIL for all insulations present, while
the lower represents the protective voltage level provided by the protective devices. The
difference between the two curves provides the safety margin for the insulation system[16].
Thus the
Protection ratio = Max.voltage it permits
Max.surge voltage equipment withstands (2.3)
A: Protecting device
B: device to be protected
Safety margin
Time (µs)
Voltage (KV)
B
A
31
Figure 2.8: Coordination of BILs and protection levels (classical approach)
This approach is difficult to apply at e.h.v. and u.h.v. levels, particularly for external
insulations.
Present-day practices of insulation coordination rely on a statistical approach which relates
directly the electrical stress and the electrical strength. This approach requires a knowledge of
the distribution of both the anticipated stresses and the electrical strengths.
The statistical nature of overvoltages, in particular switching overvoltages, makes it
necessary to compute a large number of overvoltages in order to determine with some degree
of confidence the statistical overvoltages on a system. The e.h.v. and u.h.v. systems employ a
number of non-linear elements, but with today’s availability of digital computers the
distribution of overvoltages can be calculated. A more practical approach to determine the
32
required probability distributions of a system’s overvoltages employs a comprehensive
systems simulator, the older types using analogue units, while the newer employ real time
digital simulators (RTDS).
For the purpose of coordinating the electrical stresses with electrical strengths it is convenient
to represent the overvoltage distribution in the form of probability density function (Gaussian
distribution curve) and the insulation breakdown probability by the cumulative distribution
function. The knowledge of these distributions enables us to determine the ‘risk of failure’. As
an example, let us consider a case of a spark gap for which the two characteristics apply and
plot these as shown in Fig. 2.9[16]
Figure 2.9: Method of describing the risk of failure. 1. Overvoltage distribution–Gaussian
function. 2. Insulation breakdown probability–cumulative distribution)
If 𝑉𝑎 is the average value of overvoltage, 𝑉𝑘 is the kth value of overvoltage, the probability of
occurrence of overvoltage is 𝑃𝑜(𝑉𝑘) du, whereas the probability of breakdown is 𝑃𝑏(𝑉𝑘) or the
33
probability that the gap will break down at an overvoltage 𝑉𝑘 is 𝑃𝑏(𝑉𝑘)𝑃𝑜(𝑉𝑘)du. For the total
voltage range we obtain for the total probability of failure or ‘risk of failure’[16].
R = ∫ 𝑃𝑏(𝑉𝑘)𝑃𝑜(𝑉𝑘) du.∞
0 (2.4)
The risk of failure will thus be given by the shaded area under the curve R.
In engineering practice it would become uneconomical to use the complete distribution
functions for the occurrence of overvoltage and for the withstand of insulation and a
compromise solution is accepted as shown in Figs 2.10(a) and (b) for guidance. Curve (a)
represents probability of occurrence of overvoltages of such amplitude (𝑉𝑠) that only 2 per
cent (shaded area) has a chance to cause breakdown. 𝑉𝑠 is known as the ‘statistical
overvoltage’. In Fig. 2.10(b) the voltage 𝑉𝑤 is so low that in 90 per cent of applied impulses,
breakdown does not occur and such voltage is known as the ‘statistical withstand voltage’ 𝑉𝑤.
Figure 2.10: Reference probabilities for overvoltage and for insulation withstand strength
In addition to the parameters statistical overvoltage ‘𝑉𝑆’ and the statistical withstand voltage
‘VW’ we may introduce the concept of statistical safety factor 𝛾. This parameter becomes
readily understood by inspecting Figs. 2.11(a) to (c) in which the functions 𝑃𝑏 (V) and 𝑃𝑜 (𝑉𝑘)
34
are plotted for three different cases of insulation strength but keeping the distribution of
overvoltage occurrence the same. The density function 𝑃𝑜 (𝑉𝑘) is the same in (a) to (c) and the
cumulative function giving the yet undetermined withstand voltage is gradually shifted along
the V-axis towards high values of V. This corresponds to increasing the insulation strength by
either using thicker insulation or material of higher insulation strength. As a result of the
relative shift of the two curves [𝑃𝑏 (V) and 𝑃𝑂(𝑉𝑘)] the ratio of the values 𝑉𝑊/𝑉𝑠 will vary.
This ratio is known as the statistical safety factor or
𝛾 = 𝑉𝑤
𝑉𝑠 (2.5)
Figure 2.11: The statistical safety factor and its relation to the risk of failure (R)
In the same figure (d) is plotted the relation of this parameter to the ‘risk of failure’. It is clear
that increasing the statistical safety factor will reduce the risk of failure (R), but at the same
35
time will cause an increase in insulation costs. The above treatment applies to self-restoring
insulations. In the case of non-self-restoring insulations, the electrical withstand is expressed
in terms of actual breakdown values. The statistical approach to insulation, presented here,
leads to withstand voltages (i.e. probability of breakdown is very small), thus giving us a
method for establishing the ‘insulation level’[16].
2.8 HIDDEN MARKOV MODEL
Hidden Markov Models (HMMs) are learnable finite stochastic automates. Nowadays, they
are considered as a specific form of dynamic Bayesian networks. Dynamic Bayesian
networks are based on the theory of Bayes[17].
A Hidden Markov Model consists of two stochastic processes. The first stochastic process is
a Markov chain that is characterized by states and transition probabilities. The states of the
chain are externally not visible, therefore “hidden”. The second stochastic process produces
emissions observable at each moment, depending on a state-dependent probability
distribution. It is important to notice that the denomination “hidden” while defining a Hidden
Markov Model is referred to the states of the Markov chain, not to the parameters of the
model.
The history of the HMMs consists of two parts. On the one hand there is the history of
Markov process and Markov chains, and on the other hand there is the history of algorithms
needed to develop Hidden Markov Models in order to solve problems in the modern applied
sciences by using for example a computer or similar electronic devices[17].
2.8.1 Brief history of Markov process and Markov chains
Andrey Andreyevich Markov (June 14, 1856 – July 20, 1922) was a Russian mathematician.
36
He is best known for his work on the theory of stochastic Markov processes. His research
area later became known as Markov process and Markov chains.
Andrey Andreyevich Markov introduced the Markov chains in 1906 when he produced the
first theoretical results for stochastic processes by using the term “chain” for the first time. In
1913 he calculated letter sequences of the Russian language[17].
A generalization to countable infinite state spaces was given by Kolmogorov (1931). Markov
chains are related to Brownian motion and the ergodic hypothesis, two topics in physics
which were important in the early years of the twentieth century. But Markov appears to have
pursued this out of a mathematical motivation, namely the extension of the law of large
numbers to dependent events.
Out of this approach grew a general statistical instrument, the so-called stochastic Markov
process. In mathematics generally, probability theory and statistics particularly, a Markov
process can be considered as a time-varying random phenomenon for which Markov
properties are achieved. In a common description, a stochastic process with the Markov
property, or memorylessness, is one for which conditions on the present state of the system,
its future and past are independent[17].
Markov processes arise in probability and statistics in one of two ways. A stochastic process,
defined via a separate argument, may be shown (mathematically) to have the Markov
property and as a consequence to have the properties that can be deduced from this for all
Markov processes. Of more practical importance is the use of the assumption that the Markov
property holds for a certain random process in order to construct a stochastic model for that
process. In modeling terms, assuming that the Markov property holds is one of a limited
number of simple ways of introducing statistical dependence into a model for a stochastic
37
process in such a way that allows the strength of dependence at different lags to decline as the
lag increases.
Often, the term Markov chain is used to mean a Markov process which has a discrete (finite
or countable) state-space. Usually a Markov chain would be defined for a discrete set of times
(i.e. a discrete-time Markov Chain) although some authors use the same terminology where
"time" can take continuous values.
2.8.2 Brief history of algorithms needed to develop Hidden Markov Models
With the strong development of computer sciences in the 1940's, after research results of
scientist like John von Neuman, Turing, Conrad Zuse, the scientists all over the world tried to
find algorithms solutions in order to solve many problems in real live by using deterministic
automate as well as stochastic automate. Near the classical filter theory dominated by the
linear filter theory, the non-linear and stochastic filter theory became more and more
important. At the end of the 1950's and the 1960's we can notice in this category the
domination of the "Luenberger-Observer", the "Wiener-Filter", the „Kalman-Filter" or the
"Extended Kalman-Filter" as well as its derivatives[17].
At the same period in the middle of the 20th century, Claude Shannon (1916 – 2001), an
American mathematician and electronic engineer, introduced in his paper "A mathematical
theory of communication'', first published in two parts in the July and October 1948 editions
of the Bell System Technical Journal, a very important historical step, that boosted the need
of implementation and integration of the deterministic as well as stochastic automate in
computer and electrical devices.
38
Further important elements in the History of Algorithm Development are also needed in order
to create, apply or understand Hidden Markov Models:
2.8.3 The expectation-maximization (EM) algorithm:
The recent history of the expectation maximization algorithm is related with history of the
Maximum-likelihood at the beginning of the 20th century[17]. R. A. Fisher strongly used to
recommend, analyze and make the Maximum-likelihood popular between 1912 and 1922,
although it had been used earlier by Gauss, Laplace, Thiele, and F. Y. Edgeworth. Several
years later the EM algorithm was explained and given its name in a paper in 1977 by Arthur
Dempster, Nan Laird, and Donald Rubin in the Journal of the Royal Statistical Society. They
pointed out that the method had been "proposed many times in special circumstances" by
other authors, but the 1977 paper generalized the method and developed the theory behind it.
An expectation-maximization (EM) algorithm is used in statistics for finding maximum
likelihood estimates of parameters in probabilistic models, where the model depends on
unobserved latent variables. EM alternates between performing an expectation (E) step,
which computes an expectation of the likelihood by including the latent variables as if they
were observed, and maximization (M) step, which computes the maximum likelihood
estimates of the parameters by maximizing the expected likelihood found on the E step. The
parameters found on the M step are then used to begin another E step, and the process is
repeated. EM is frequently used for data clustering in machine learning and computer vision.
In natural language processing, two prominent instances of the algorithm are the Baum-
Welch algorithm (also known as "forward-backward") and the inside-outside algorithm for
unsupervised induction of probabilistic context-free grammars. Mathematical and algorithmic
basics of Expectation Maximization algorithm, specifically for HMM Applications, will be
introduced in the following parts of this chapter.
39
2.8.4 The Baum-Welch algorithm:
The Baum–Welch algorithm is a particular case of a generalized expectation-
maximization[17]. The Baum–Welch algorithm is used to find the unknown parameters of a
hidden Markov model (HMM). It makes use of the forward-backward algorithm and is
named by Leonard E. Baum and Lloyd R. Welch. One of the introducing papers for the
Baum-Welch algorithm was presented 1970 "A maximization technique occurring in the
statistical analysis of probabilistic functions of Markov chains",[17]. Mathematical and
algorithmic basics of the Baum-Welch algorithm specifically for HMM-Applications will be
introduced in the following parts of this chapter.
2.8.5 The Viterbi Algorithm:
The Viterbi algorithm was conceived by Andrew Viterbi in 1967 as a decoding algorithm for
convolution codes over noisy digital communication links. It is a dynamic programming
algorithm[17]. For finding the most likely sequence of hidden states, called the Viterbi path
that results in a sequence of observed events. During the last years, this algorithm has found
universal application in decoding the convolution codes, used for example in CDMA and
GSM digital cellular, dial-up modems, satellite, deep-space communications, and 802.11
wireless LANs. It is now also commonly used in speech recognition applications, keyword
spotting, computational linguistics, and bioinformatics. For example, in certain speech-to-text
recognition devices, the acoustic signal is treated as the observed sequence of events, and a
string of text is considered to be the "hidden cause" of the acoustic signal. The Viterbi
algorithm finds the most likely string of text given the acoustic signal[17]. Mathematical and
algorithmic basics of the Viterbi-Algorithm for HMM-Applications.
2.9 Mathematical basics of Hidden Markov Models
40
2.9.1 Definition of Hidden Markov Models
A Hidden Markov Model is a finite learnable stochastic automate.
It can be summarized as a kind of double stochastic process with the two following aspects:
• The first stochastic process is a finite set of states, where each of them is generally
associated with a multidimensional probability distribution. The transitions between the
different states are statistically organized by a set of probabilities called transition
probabilities[17].
• In the second stochastic process, in any state an event can be observed. Since we will just
analyze what we observe without seeing at which states it occurred, the states are "hidden" to
the observer, therefore the name "Hidden Markov Model".
Each Hidden Markov Model is defined by states, state probabilities, transition probabilities,
emission probabilities and initial probabilities.
In order to define an HMM completely, the following five Elements have to be defined:
(i). The N states of the Model, defined by equation 2.6
S = {S1,…,SN} (2.6)
(ii). The M observation symbols per state V = {𝑉1,…,𝑉𝑚}. If the observations are continuous
then M is infinite.
(iii). The state transition probability distribution A = {𝑎𝑖𝑗}, where 𝑎𝑖𝑗 is the probability that
the state at time t + 1 is 𝑆𝑗, is given when the state at time t is Si. The structure of this
41
stochastic matrix defines the connection structure of the model. If a coefficient aij is zero, it
will remain zero even through the training process, so there will never be a transition from
state Si to
𝑆𝑗 . 𝑎𝑖𝑗 = P{𝑞𝑡+1 = j ǀ 𝑞𝑡 = i}, 1≤ i, j ≤N (2.7)
Where 𝑞𝑡 denotes the current state. The transition probabilities should satisfy the normal
stochastic constraints, 𝑎𝑖𝑗 ≥ 0, 1≤ i, j ≤N and ∑ 𝑎𝑖𝑗 = 1,𝑁𝑗=1 1≤ i ≤N. (2.8)
(iv). The Observation symbol probability distribution in each state, B = {𝑏𝑗 (k)} where 𝑏𝑗 (k)
is the probability that symbol vk is emitted in state 𝑆𝑗 [17].
𝑏𝑗 (k) = P{𝑂𝑡 = 𝑣𝑘|𝑞𝑡 = 𝑗}, 1≤ j ≤N, 1≤ k ≤M (2.9)
Where 𝑣𝑘 denotes the 𝐾𝑡ℎ observation symbol in the alphabet, and Ot the current parameter
vector. The following stochastic constraints must be satisfied:
𝑏𝑗(k)≥0, 1≤ j ≤N, 1≤ k ≤M and ∑ 𝑏𝑗(𝑘) = 1,𝑀𝐾=1 1≤ j ≤N (2.10)
If the observations are continuous, then we will have to use a continuous probability density
function, instead of a set of discrete probabilities. In this case we specify the parameters of
the probability density function. Usually the probability density is approximated by a
weighted sum of M Gaussian distributions N.
2.10 SUMMARY OF RELATED LITERATURES
From the literatures reviewed, it is was observed that Insulation Coordination is squarely
based on Probability, due to the complex/random events that take place in the power system,
especially in the event of surge. This Probabilistic theory is used to determine the various
42
withstand voltage levels, BIL and other Insulation levels of power equipment. However,
despite the great contributions made by researchers over the years, it is obvious that these
earlier works make use of worst case scenarios, which is based on deterministic approach.
This deterministic approach is not comprehensive and flexible, to take into consideration
several factors that will ensure a balance between economic and technical/safety
factors(which Insulation Coordination intends to achieve). Thus, this work seeks to solve this
problem by introducing Stochastic processes with the instrumentality of Hidden Markov
model, which is very robust in handling, computing, analyzing and observing
complex/randomness experienced in power systems, especially at the event of surge.
CHAPTER THREE
RESEARCH METHODOLOGY
3.0 MODEL DESIGN
The summary of the highlights of the model design strategy of this work, for the insulation
coordination of a power station is given with the classification ability of Hidden Markov
Model(HMM), which is used to identify the travelling wave structure that exhibits the highest
likelihood probability on the power system under investigation. This identified transient wave
model is used to compute for the insulation coordination of the power system based on the
IS/IEC 60071-2 guidelines and standard.
3.1 THE MODEL DESIGN STRATEGY
For effective insulation coordination, a model of the dynamics of power system is required. A
model that includes the most likely combination of transient behavior that the power system
43
would be subjected to[18]. This gives the ideal basis for the conduct of insulation. The power
system is a complex, dynamic and nonlinear system, which is in disturbance all the time.
The probability distribution of the representative lightning overvoltage amplitude at the
power station can be determined by transient overvoltage calculations, taking into account the
lightning performance of the transmission lines. The travelling wave behavior of overhead
lines and substation and the performance of the equipment insulation and the surge arresters
are dependent on the overvoltage amplitude and shape.
The shape of the travelling wave resulting from a lightning strike on the transmission line
within a particular distance of a substation would be different from the one that occurred with
a different distance of the station. Furthermore, the wave structure of a lightning stroke on the
particular line within a distance of the station, or protection arrester coupled with a protective
circuit breaker open, would have different measure of impact on the system insulation
protection. The insulation coordination of the power system then has to be carried out using
transient model(s) that reflects the most probable situation the system would be exposed to.
Hence, the modeling of a number of likely event scenarios (different transient disturbance
dynamics for the power system) and then using the training and classification power of
Hidden Markov Model (HMM) to identify the highest likelihood probabilities is the strategy
adopted by this work. This technique would provide the optimal transient disturbance model
within the limit of available data for the insulation coordination of a given power system.
The proposed HMM strategy involves training a set of three system transient model that
represents the dynamics of the network during a lightning strike and observing certain
electrical parameters. Based on the evaluation of the maximum likelihood probabilities, the
surge wave structure which has more representation of the highest impact of lightning surge
44
on the system can be determined, from which the required parameters are obtained for the
insulation coordination of the system.
The likely power system event scenarios will provide different travelling wave signals for the
training and classification using HMM. This provides the different HMM model of the
system’s travelling wave shape, from which the optimum is selected based on the evaluation
of the maximum likelihood probabilities.
Therefore, simulating different impact on the power system by using station data, different
configuration of station components and lightning initiations, about three different
disturbance event scenarios are produced. An online model of these scenarios is obtained,
from which the one having the maximum likelihood probability is identified by HMM. The
identified scenario represents the travelling wave having the highest probable impact on the
power system. Thus, insulation coordination of the power station is then carried out using the
identified wave shape.
3.2 SCENARIO DESCRIPTION
3.2.1 Surge Event Scenario A:
The structure of the surge transient wave with lightning strike at location x on phase
conductor, with circuit breaker open; with station transformer protection arrester installed at
both sides of the transformer.
3.2.2 Surge Event Scenario B:
45
The structure of the surge transient wave with lightning strike at location x on phase
conductor, with circuit breaker closed; station transformer protection arrester installed and
followed by a secondary strike (i.e. another strike).
3.2.3 Surge Event Scenario C:
The structure of the surge transient wave with lightning strike at location y on the phase
conductor, arrester at the transformer and also at the line entrance.
3.3 THE OVERVOLTAGE TRANSIENT ASSESSMENT BASED ON THE HMM
The power system transient assessment of the lightning induced overvoltage (for which
insulation coordination is required) is a complicated process. According to the perspective of
time sequence, the process of lightning induced overvoltage disturbance in the system is
identified as 5 states: Normal operation, disturbance occurrence (overvoltage transient
occurrence), disturbance development, system swing and system resuming. It is quite difficult
to identify every beginning time and ending time of the 5 states, which could be considered
“hidden”.
However, the 5 states could be described by some electrical parameters, which mean that the
states could be observed, and such electrical parameters are the feature sets of the
observations. In HMM, observation is probabilistic function of the related state and its
probability distribution function[19]. The hidden markov model is used to describe such state
transitions and the observations are encoded into digital signals.
3.4 The Overvoltage Training Disturbance Classification
46
The proposed hidden markov model, classifies the destructive impact of the lightning
induced overvoltage transient on the power system, by comparing the maximum likelihood
probability of the overvoltage signal for trained models. A HMM model is trained for each of
the three overvoltage transient disturbance scenarios identified earlier on.
A HMM is defined as λ = (N, M, π, A, B), where N is the number of states, M is the number
of distinct observation symbols per state, π and B is the initial state distribution probability
and observation probability matrices respectively. The elements of matrix A, 𝑎𝑖𝑗, is the
transition probability from state i to state j, which are defined in equations (3.1) and (3.3) [19]
in these equations, 𝑞𝑡 is the actual state S at time t.
𝑎𝑖𝑗 = 𝑃[𝑞𝑡+1 = 𝑆𝑗|𝑞𝑡 = 𝑆𝑖], 1≤ 𝑖, 𝑗 ≤ 𝑁 …………………………….(3.1)
𝑎𝑖𝑗 ≥ 0, ∑𝑎𝑖𝑗
𝑁
𝑗=1
= 1………………… .. ………………(3.2)
The elements of matrix B, 𝑏𝑗(k), are defined by equation (3.3) where 𝑉𝑘 is the 𝐾𝑡ℎobservation
in the state [19] matrix B and vector π elements follow the rules presented in equation (3.4)
[19]
𝑏𝑗(𝑘) = 𝑃[(𝑂𝑡 = 𝑉𝑘|𝑞𝑡 = 𝑆𝑗)], 1≤ j ≤ N, 1≤ k ≤ M…………………… (3.3)
𝑏𝑗(𝑘) ≥ 0, ∑ 𝑏𝑗(𝑘)
𝑀
𝑘=1
= 1,∑𝜋1 = 1)
𝑁
𝑖=1
…………………… . (3.4)
Where 𝑂𝑡 indicates observation at time t. Equation (3.3) calculates the probability of
observation 𝑉𝑘 at time t, where 𝑞𝑡 = 𝑆𝑗.
47
The HMM training process is identical to finding the appropriate parameters of A, B and π.
For convenience the HMM is denoted as a triplet:
λ = (A, B, π).
Thus, the flow chart of the proposed algorithm for the novel Insulation Coordination
procedure is shown in Figure 3.1 below.
No
O
Yes
Fundamental harmonic of the lighting
stroke phase (V)
C
Start
These-phase of the power system
Over
voltage?
Select window
Processing
Scenario A
HMM model
Scenario B
HMM model
Scenario C
HMM model
48
A
Yes Yes Yes Yes Yes Scenario
A?
Comparator(Maximum likelihood)
Effective Power
system insulation
coordinating using
Scenario A
Transient response
49
C
Figure 3.1: Flow chart of proposed Algorithm for Insulation Coordination
No
Yes
Yes
C
No
No
50
When a lightning induced overvoltage incidence occurs, a windowed fundamental harmonic
of the overvoltage transient waveform of about a quarter of a cycle is sampled. Each window
consists of about ‘400’ samples of which 50% of them are taken as the HMM training data
while the other half are going to be classified by the HMM.
3.4.1 The Processing Block
The steps that make up the processing block is depicted in Figure 3.2
Start
Original feature set
Output signal waveform for
insulation coordination
Obtain HMM parameters
Comparator(maximum
likelihood)
Quantization (coding)
Classification (identification)
mode
Training mode
Feature subset Based on
Relative sensitivity method.
51
Figure 3.2: Steps for the Signal Processing and Observation Evaluation Problem P(𝑂|λ)
From Figure 3.2, the electrical parameters that represent the feature set of the observation are
selected. The selections of the observation are selected. The selection is programmed in the
modeling program. This work uses the MATLAB software environment. The modeling of the
case study power system in MATLAB enables the extraction of electrical features of the
disturbance wave system. The features in Table 3.1 are selected from candidate feature set
from the overvoltage transient features.
3.1: Observed electrical feature for HMM classification of the lightning overvoltage
transients of the power system.
ITEM FEATURE NAME
1. Surge Impedance of phase conductors
2. Surge impedance of bus system
3. Surge impedance of transformer
4. Steepness of lightning current impinging on substation components.
5. Surge current
6. Travel time of lightning surge
7. Lightning crest current
8. Representative steepness of lightning impinging surge
9. Surge impedance of arresters
10. Surge impedance of circuit breakers
11. Phase conductor steady state voltage
12 Bus system steady state voltage
13 Capacitance of station transformer
52
14 Station component overvoltage
15 Positive segment resistance of station components
16 Negative segment resistance of station components
17 Steady state frequently of power system
From Table 3.1 above, the feature observed a feature subset based on Relative sensitivity
method is obtained. The feature subset is selected to decrease the dimension of the candidate
feature set.
Equation (3.5) [20] shown below is utilized by the MATLAB to implement this.
Program/formula used to calculate the dynamic volume under different disturbances is.
𝑊𝑥 = ∆𝑊
𝑊0× 100% =
𝑊1 − 𝑊0
𝑊0 × 100%………………………… . (3.5)
𝑊0 is the basic value before the disturbances,
𝑊1 is the value under disturbances, and 𝑊𝑥 describes the relative sensitivity.
If the |𝑊𝑥| ≥ 100%, this feature would be selected.
The selected feature subset data is divided into two parts: one is the training data, including
stable (normal) and unstable ones (surge), the other is the data to be classified.
53
The identification (classification) pre-process starts through the quantization (coding) of the
inputs observation signal (the surge signal). The reason for the quantization (coding) is that
the selected) features are a set of continuous vectors according to the time domain. These
vectors need to be transferred into a set of scalars using a coding technique so as to meet the
HMM training requirements. For this the appropriate MATLAB binary is used. The
MATLAB modeling environment has the signal discretization box to discretize (i.e. quantize.
Or encode continuous signal into digital signals).
The HMM training is executed to obtain the HMM parameter. The steps in the HMM
processing are depicted in the flowchart shown in Figure 3.3.
P(0׀𝜆𝑗) calculation
Viterbi Algorithm
Compute 𝑎𝑖𝑗 and 𝑏𝑗𝑘 based on
the Baum-Welch (BW)
Algorithm
Initialization
Training Data
Start
54
Figure 3.3: Flow Chart of the HMM Training Process for the observation Evaluation Problem
Initialization
Initialize the π, A parameters of the HMM.
The initial state distribution vector π and the state transition on probability distribution A,
could be set as shown in equation (3.6) and (3.8) [20]
π = [1 0 0 0 0] ………………………………………..(3.6)
Noting π = {𝜋𝑖} where 𝜋𝑖 = 𝑃(𝑞1 = 𝜃𝑖), 1 ≤ 𝑖 ≤ 𝑁 ………… . (3.7)
Where 𝜃1, 𝜃2, 𝜃3, … , 𝜃𝑁 are marked as the markov chain at time instant t, and 𝑞𝑡 ∈
(𝜃1, 𝜃2, 𝜃3, …… , 𝜃𝑁) being the actual state S at time t.
Yes
No
55
𝐴 =
[
0.50000
0.50.5000
00.50.500
00
0.50.50
000
0.51 ]
……….……………...(3.8)
After the initialization step, the new parameters of the HMM are calculated using the Baum-
Welch (BW) algorithm.
The HMM training blocks (fig. 3.3) inputs are observation vectors
O = 𝑂1, 𝑂2, …… , 𝑂𝑇, which as pointed out are feature (electrical parameters) signal samples
(of overvoltage transient waveform). In the training process, the maximum likelihood
probability denoted by equation (3.9a) should be maximized indirectly using the logarithm of
the above probability (Log lik), which is presented in equation (3.9b)[19].
𝑃(𝑂|λ) = ∑ 𝑃(𝑂|𝑄, λ)𝑃(𝑄, λ)………………… (3.9a)
𝐴𝑙𝑙 𝑄
Log lik = Log P(𝑂|λ) ……………………………………………….(3.9b)]
Where Ө = 𝑞1, 𝑞2, 𝑞3, …… . . , 𝑞𝑇 is a fixed state sequence (i.e. sequence of actual state for the
sampling duration) and T is the number of observations.
56
The Baum-Welch algorithm first defines 𝑦𝑡(𝑖, 𝑗)(the posteriori probability of transitions being
in state i at time t and making a transition to state j at time t + 1, given the observation
sequence). It can be computed as equation (3.10), and the variable 𝛾𝑡 (the posteriori
probability of being in state i at time t, given the observation sequence and model λ) is
defined by equation (3.11)[19].
𝛾𝑡(𝑖, 𝑗) = 𝑃(𝑆𝑡 = 𝑖, 𝑆𝑡+1 = (𝑗|𝑂), λ) = 𝛼𝑡(𝑖)𝑎𝑖𝑗𝑏𝑗(𝑂𝑡+1)𝛽𝑡+1(𝑗)
𝑃(𝑂|λ)=
𝛼𝑡(𝑖)𝑎𝑖𝑗𝑏𝑗(𝑂𝑡+1)𝛽𝑡+1(𝑗)
∑ 𝛼𝑇(𝑘)𝑘𝜖𝑄𝑓
…….……. (3.10)
𝛾𝑡(𝑖) = 𝑃(𝑆𝑡 = (𝑖|𝑂), 𝛾 = 𝛼𝑡(𝑖)𝛽𝑡(𝑖)
𝑃(𝑂|λ)
= 𝛼𝑡(𝑖)𝛽𝑡(𝑖)
∑ 𝛼𝑇(𝑘)𝑘𝜖𝑄𝑓
…………………………………… . . … (3.11)
Where 𝛼𝑡(𝑖) is the forward variable for mode λ (one of the scenario overvoltage wave
model). This is the probability of the partial observation sequence O (until time t) and state 𝑆𝑖
at time t. another parameter is 𝛽𝑡(𝑖), which is a backward variable that refers to the
probability of the partial observation sequence from t +1 to the end, given 𝑆𝑖 at time t and the
model λ. 𝑄𝐹 is a set of final states.
𝛼𝑡 = 𝑃(𝑂1, 𝑂2, … . 𝑂𝑡, 𝑞𝑡 = (𝑆𝑖|λ))………………………………… . (3.12)
This means the probability of the partial observation sequence
𝑂1, 𝑂2, …… . . 𝑂𝑡 with state 𝑞𝑡 = 𝑆𝑖, given mode λ.
57
.𝛽𝑡(𝑖) = 𝑃(𝑂𝑡+1, 𝑂𝑡+ 2, … . , (𝑂𝑇|𝑞𝑡) = (𝑆𝑖|λ))…… .………………(3.13)
If 𝛼1(𝑖) = 𝜋𝑖𝑏𝑖(𝑂1), then α can be calculated as follows:
𝛼𝑡+1(𝑗) = |∑𝛼𝑡(𝑖)𝑎𝑖𝑗
𝑁
𝑖=1
| 𝑏𝑗(𝑂𝑡+1)…… . . ……… (3.14)
If 𝛽𝑇(𝑖) = 1 (initialization), then the following holds true[21]:
𝛽𝑡(𝑖) = ∑𝑎𝑖𝑗𝑏𝑗(𝑂𝑡+1)𝛽𝑡+1(𝑗)……………………… . (3.15)
𝑁
𝑗=1
Parameters 𝑎𝑖𝑗 , 𝑏𝑗 , 𝜋𝑖 of the re-estimated new mode ǀ λ can be computed as follows:
𝑎𝑖𝑗 = ∑ 𝛾𝑡(𝑖, 𝑗)
𝑇−1𝑡=1
∑ 𝛾𝑡(𝑖)𝑇−1𝑡=1
……………(3.16)
𝑏𝑗(𝑘) = ∑ 𝛾𝑡(𝑗)
𝑇𝑡=1
∑ 𝛾𝑡(𝑗)𝑇𝑡=1
………………………(3.17)
𝜋𝑖 = 𝛾1(𝑖)…………………… . . (3.18)
The logarithm of the model’s output probabilities are then computed in the recognition stage.
Recognition or classification(identification) means finding the best path in each trained
model and selecting the one that maximizes the path probability for a given input observation
O and the model λ𝑖 = (𝐴𝑖, 𝐵𝑖, 𝜋𝑖), 𝑖 = 1,2, … . . , 𝐷, where D represents the number of voltage
58
transient waveform shapes. This means computing the optimal conditional probability
P((𝑂|λ𝑗). Therefore, overvoltage transient model λ∗ should satisfy the following equation:
λ∗ = 𝑚𝑎𝑥𝑖[𝑚𝑎𝑥𝑄P(Q, (𝑂|λ𝑖))]…………… . . (3.19)
At this stage, the Viterbi algorithm[22] is used to find the best path probability (i.e. the
maximum likelihood).
Initialization for all state i:
δ1(𝑖) = 𝜋𝑖𝑏𝑖(𝑂1), 𝛹1(𝑖) = 0. . . … (3.20)
Recursion from time t = 2 to T and all states j:
δ𝑡(𝑗) = 𝑚𝑎𝑥𝑖[δ𝑡−1(𝑖)𝑎𝑖𝑗]𝑏𝑗(𝑂𝑡)…… . (3.21)
𝛹𝑡(𝑗) = 𝑎𝑟𝑔𝑖𝑚𝑎𝑥 [δ𝑡−1(𝑖)𝑎𝑖𝑗]……………… .…… . . (3.22)
Termination;
𝑃∗ = max[δ𝑇(𝑖)] , 𝑞𝑇∗ = 𝑎𝑟𝑔𝑚𝑎𝑥[δ𝑇(𝑖)]…………(3.23)
State sequence backtracking from T-1 to 1:
𝑞𝑡∗ = 𝛹𝑡+1(𝑞𝑡+1
∗ )…………………………………… . . (3.24)
The maximum likelihood probability P(𝑂|λ) could be achieved, given the best path O and
observation O (observation vector of the lightning induced overvoltage transient signal). The
required optimal disturbance transient required for optimal insulation coordination can then
59
be identified by comparing the logarithm of the likelihood probabilities (log lik) of the
transient models. The model with highest probability likelihood gives the optimal (within the
limit of available data) disturbance waveform for the insulation coordination of the power
system.
The lightning overvoltage transient scenario that gives this optimal probability is used as
input for the computation of the insulation coordination for the power station. That is, the
selected scenario would be used to determine voltage stresses and on this basis insulation
strength is selected to achieve the desired voltage withstand.
3.5 Computing for the Insulation Coordination
The overvoltage transient model identified by the HMM as presented above, is the input for
the computation of the insulation coordination. Since the overvoltages in the power system
(in the case of this work the transmission station) depend on the amplitude and shape of the
overvoltage impinging on the station from the overhead line conductor, as well as on the
travelling wave behavior of the station.
The MATLAB program developed for the purpose of this computation in this work
adheres to the IS/IEC 60071-2 guide for the determination of withstand voltages for
insulation coordination. Based on this the program algorithm follows the following main four
steps:
STEP 1: Determination of the Representative Overvoltage
60
The representative over voltages are not the over voltages that occur in the system but are
overvoltages that represent the electric stress on the equipment as the actual overvoltages.
Hence the need for the representative model to be optimal. This explains the use of the HMM
identified optimal likelihood model of the disturbance. The HMM identified model is used at
this step of the evaluation. This implies that the representative voltages are determined from
the HMM classified transient model.
The procedure adopted in the evaluation software consists in calculating a lightning current
with the desired return rate, and calculating the overvoltage by travelling wave calculations in
the substation.
The lightning current determining surge is determined from the shielding penetration rate
within the limit distance and its probability to be exceeded[23]:
F(I) = F(𝐼𝑚) + (𝑅𝑡
𝑅𝑝⁄ )……………………………..…(3.26)
Where
F(𝐼𝑚) is the lightning current probability corresponding to the maximum shielding current;
𝑅𝑡 is the considered return rate;
𝑅𝑝 is the shielding penetration rate within the limit distance.
NOTE: The shielding penetration rate can be obtained from the shielding failure flashover
rate by:
𝑅𝑝 = 𝑅𝑠𝑓
𝐹(𝐼𝑐𝑟) − 𝐹(𝐼𝑚)………………… . (3.27)
61
Where
𝑅𝑠𝑓 is the shielding failure flashover rate;
𝐹(𝐼𝑐𝑟) is the probability corresponding to the current causing line insulation flashover at
negative polarity.
MATLAB program determines the amplitude of the impinging overvoltage surge using
equation (3.28) and determine its Steepness to correspond to equation (3.29) [23]:
𝑈𝐼 = 𝑍𝐿𝐼
2………………………………………(3.28)
𝑈𝐼: Amplitude of the impinging lightning overvoltage surge.
𝑍𝐿: Surge impedance of the overhead line
I: Lightning current amplitude
S = 1
𝐾𝑐𝑜𝑋𝑇 …………………………………….(3.29)
Where 𝐾𝑐𝑜 is the corona damping constant;
𝑋𝑇 = 𝑋𝑝
4
62
𝑋𝑝: limit overhead line distance within which lightning events have to be considered.
The MATLAB program uses the impinging voltage surge to perform a travelling wave
calculation with the model of the power station and the representative overvoltages are
obtained for this return rate for the various locations in the system.
STEP 2: Determination of the Co-ordination Withstand Voltages
According to the Funde (IS/IEC 60071-1) different factors have to be applied to the
determined values of the representative overvoltages. Those factors, which may vary with the
shape of the overvoltage, take into account the adopted performance criteria and the in
accuracies in the input data (e.g. arrester data).
The co-ordination withstand voltages: 𝐾𝑐𝑑 × 𝑈𝑟𝑝 = 𝑈𝑐𝑤
𝑈𝑟𝑝: Amplitude of the representative overvoltage [3.19 of IEC 71-1]
𝐾𝑐𝑑: Determination co-ordinating factor
STEP 3: Determination of the Required Withstand Voltages
Based on the referenced guideline, the required withstand voltages are obtained by applying
to the co-ordination withstand voltages two correction factors: factor 𝐾𝑎 which take into
account the altitude of the installation, and a safety factor 𝐾𝑠.
𝐾𝑠: Safety factor [3.29 of IEC 71-1]
𝐾𝑎: Atmospheric correction factor [3.25 of IEC 71-1)
The factor is applicable to any type of overvoltage.
63
𝑈𝑟𝑤 = 𝑈𝑐𝑤𝐾𝑠𝐾𝑎 …………………………………… . (3.30)
𝑈𝑐𝑤: Co-ordination withstand voltage of equipment
𝑈𝑟𝑤: required withstand voltage [3.17 of IEC 71-1]
STEP 4: Determination of the Standard Withstand Voltages.
The standard withstand voltages are obtained from the required withstand voltage by
choosing the next highest value from the standard values listed in IEC 71-1.
3.6 Modeling the Power System
For effecting the insulation coordination, the simulation program requires the digital model of
the power station. This is needed to carry out the travelling wave calculation required for the
HMM optimum likelihood classification and to estimate the overvoltage at different locations
in the power system.
Insulation co-ordination models differ greatly from conventional power frequency power
system models used for load flow and fault analysis. Hence the components of the power
station are modeled in MATLAB as follows:
3.6.1 Transmission Line Conductors Model
The transmission line conductors are modeled with surge impedance and a travel time, not
conventional impedance. This is because the stroke currents and associated surge voltages or
actually travelling waves that move along the conductors and split and reflect from points of
different surge impedance. This creates numerous travelling waves back and forth, which are
64
summed or are subtracted as they meet when such travelling waves are summed up at a
junction or line end, this can cause significant overvoltages.
In MATLAB the transmission line is modeled using a frequency dependent travelling wave
model with the frequency fitting curve within a range, with the steady state frequency set to a
value.
In the MATLAB simulation, the transmission line models are constructed using conductor
data and line geometry information.
3.6.2 Transmission Line Towers Model
The transmission line model needs to include back flashover models of the transmission
towers and insulators. It also needs the tower structure and earthing of the overhead earth
wire included. The simulation of the tower models are added to the transmission line
conductor models.
3.6.3 Surge Arresters Model
Surge arresters are modeled as non-linear elements using the MATLAB plug in for metal
oxide surge arresters component along with R, L and C components in line with the IEEE fast
front arrester model described in [24].
The surge arresters are modeled with downleads to the earth grid. The downleads are
modeled as travelling wave models with a surge impedance and a propagation velocity.
3.6.4 Transformer Model
65
Under Lightning conditions, the transformers act as surge capacitance[25]. Hence for the
MATLAB modeling purposes, transformers are presented by winding surge capacitance
between each phase and earth.
Under lightning conditions the other equipment in the power station such as disconnector
insulators, CVT’s station post insulators etc., as surge capacitances. Hence for the modeling
purpose they are represented by surge capacitance between each phase and earth.
3.6.5 Lightning Surge Model
Lightning strokes are most basically described in terms of two values, crest current and front
steepness. The crest current is the maximum current value that the stroke achieves (measured
in KA/µs). Strictly speaking front steepness is the time taken for the stroke current to rise
from 10% to 90% of the crest current. For modeling and evaluating lightning stroke,
according to[25] the CIGRE probability data is considered to be superior to other data. Hence
in the simulation of the lightning stroke, the stroke current and steepness value is varied in
the software following the probability function of the form:
P(x) = 𝐼
2πBI 𝑒−0.5𝑧2
- - - - - - - - - - - - - - - - - - - - - - - - - - -(3.31)
Z = 𝑙𝑛 𝐼
𝑀
𝐵 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - (3.32)
I is the stroke current in kA or front steepness in kA/µs, M is the median value of stroke
current or front steepness and B is the log standard deviation of the stroke current or front
steepness.
66
The CIGRE data suggest that the median value of stroke current crest is 34kA and the log
standard deviation is 0.74. The median front steepness value is considered to be 24.3kA/µs
with log standard deviation of 0.6[25].
3.7 Assumptions for lightning surge
For computer modeling purpose, the following assumptions are held:
1. The station is shielded and no lightning enters the station directly, only via the lines
when a back flashover occurs within a few spans of the station.
2. Transformer margin of protection of 20% is a minimum for lightning surges(IS/IEC
6007-1 recommendation).
67
CHAPTER FOUR
4.0 SIMULATION AND RESULT EVALUATION
The 330/132kv substation at New Haven Enugu Nigeria was used to evaluate the proposed
novel insulation coordination technique. The time domain simulation carried out with
MATLAB, is used to assess(based on the HMM identified maximum likelihood) whether the
combination of surge arrester and their location with respect to the transformer provides
adequate margin of protection. The substation is modeled in MATLAB/Simulink, using
drawings supplied by Power Holding Company of Nigeria(PHCN)Transmission station. The
voltage values at a chosen arrester protection zone in the station, is determined with a
simulated lightning surge entering the station from the incoming line. Three (3) lightning
surge disturbance scenarios are observed by the HMM algorithm. From the training of these
three transient disturbance model (using about n iterations), HMM identifies from among the
surge signals, a waveform structure having the maximum likelihood at location of the
substation being investigated. The identified maximum likelihood wave is used to calculate
the protection margin based on equipment data supplied by PHCN.
The MATLAB/Simulink model of the power system is given in Figure 4.1. The MATLAB
m-file source code that implements the HMM algorithm is given in appendix A. The Name
plates of arresters and transformers at the power substation is given on appendix B and C.
Also the single line diagram of the station is in appendix D.
4.1 Simulation of the three lightning overvoltage transient scenarios
The simulation of the three scenarios provides the parameters associated with the HMM
algorithm. The HMM uses the observation electrical parameters, associated with the dynamic
of the network, during the lightning disturbance to access the probability densities of the
68
associated waves and to determine the maximum likelihood wave. Lightning strokes
occurring at the overhead transmission lines are simulated as impulse current waveform. This
can be simulated by means of CIGRE wave shape [27].
69
70
In simulation studies, the lightning flash is substituted with impulse current generator.
Impulse generator(IG) generates very steep-front wave shapes , known as impulse waves, that
are similar to lightning waves[28].
For the simulation carried out in this chapter, impulse current waveforms have been
generated in the MATLAB. This is provided by the lightning impulse current source in the
model of figure 4.1. A lightning current wave of 30KA is injected into the phase conductors
and propagated into the system during operation. The 132/33KV New Haven Power
Transmission Station Parameters/data used in this work are shown in Table 4.1 below.
Table 4.1: Station Parameters/Data supplied by PHCN
S/N PARAMETERS VALUES
1 Transformer BIL 850V
2 Arrester BIL, 𝐸𝑎 or 𝑈𝑝𝑙 650V
3 Surge Impedance of Line 400 Ω
4 Arrester-Transformer Separation distance 6.5m
5 Ground Clearance 6.10m
6 Vertical distance between conductors 3.96m
7 Horizontal Space between conductors 7.0m
8 Mid-Span clearance 6.1m
9 Vertical distance from overhead conductor to Arrester, 𝑎1 2m
10 Active length of Arrester, 𝑎4 3.6m
11 Vertical distance of Arrester conductor to earth, 𝑎2 15m
12 Length of Phase conductor between Arrester and Protected equipment, 𝑎3 6.5m
13 No. of lines per circuit 2
14 Travelling wave velocity 300m/µs
15 Rated Frequency 50Hz
71
16 Steady state voltage 132KV
72
Table 4.2 shows lines data of a transmission line from new haven 330/132KV to other stations like Aliade, Apir, Nkalagu, Abakaliki, Oji River,
Otukpo and Yandev.
Table 4.2: TRANSMISSION LINE DATA
S/
N
From
Station
To
Station
Voltage
(KV)
Circuit
NO
Conductor
Configuration
Length
(Km)
Positive
Imped.
Negative
Sequenc
e Imped
CCC Conductor
Positive
Susceptanc
e
Negative
Susceptanc
e
Zero Seq.
Imped
1. Onitsh
a
New
Haven
330 113N 2x350mm2(Biso
n)
106.2 0.003773 0.026377 0.14203782
7
0.04074220 0.0296198
2. Apir Aliade 330 1.ID 2x350mm2(Biso
n)
49.32 0.0428 0.349 0.065963 0.0189209 0.336
3. Oji
River,
New
Haven
132 40N 150mm2(Wolf) 43.75 0.051476
5
0.102944 400A 0.0585137 0.0167847 0.1155082
4. New
Haven
Nkalagu 132 H44L,
H45L
150mm2(Wolf) 38.5 0.045299
3
0.090591 0.5149205 0.0147700 0.1016472
73
5. Nkalag
u
Abakaliki 132 H43L 150mm2(Wolf) 53.9 0.006341
9
0.124709 0.07208887 0.0206780 0.1423061
6. New
Haven
Otukpo 132 N64F 150mm2(Wolf) 160 0.188198 0.276362 0.21399296 0.06138185
1
0.4222981
7. Otukpo Yandev 132 F65G 150mm2(Wolf) 114.8 0.135074
3
0.270124 0.1583994 0.0440414 0.3030936
74
4.1.1 Surge Event Scenario A:
In relation to the corresponding location of station electrical components as contained in the
MATLAB model of figure 4.1., this scenario can be visualized by figure 4.2.
The lightning strike occurs at 45m to the A-phase entrance to the 132/33kV segment of the
system. This is on the line of protection of arrester 4. The distances are electrically modeled
by the Simulink 𝜋-sections (i.e.feeders). In this lightning strike scenario, the downstream
circuit breakers are open. On the model of Figure 4.1, the breakers are situated as follows: the
three-phase circuit breaker 5 is close to Kingsway 33kV line I, the breaker 6 is close to the
Kingsway 33kV line II, Breaker 8 is close to the lines: Government house, Independence
layout, NNPC 33kV line and Emene 33kV line. Finally Breaker 7 is close to Thinker’s
A
B
C
a
b
c
com
45m
Lightning
source
132kV/33kV Transformer
132kV/33kV Transformer
Lightning arrester 4
Figure 4. 2. The illustration of incoming transmission surge wave of scenario A
75
corner, Ituku/Ozalla, Amechi lines. For scenario A, the lightning overvoltage waveform at the
arrester 4(i.e. phase A arrester) is as depicted in figure 4.3.
4.1.2 Surge Event Scenario B
In relation to the corresponding location of station electrical components as contained in the
MATLAB model of figure 4.1., this scenario can be visualized by figure 4.4.
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018-400
-200
0
200
400
600
800
Time(µs)
VO
LT
AG
E(K
V)
0
0.5
1
Fig. 4.3: RESULTANT WAVEFORM FOR SURGE EVENT SCENARIO A
A
B
C
a
b
c
com
45m
Lightning source
132kV/33kV Transformer
132kV/33kV Transformer
Lightning arrester 4
A secondary strike after 0.05𝜇s
(the programmed delay of the impulse generator)
Figure 4. 4. The illustration of incoming transmission surge wave of scenario B
76
The lightning strike occurs at 45m to the entrance arresters(i.e. arrester 4 on phase A, arrester
5 on phase B and arrester 6 on phase C). This is followed by a secondary strike. For this
scenario, the lightning overvoltage waveform at arrester 4(i.e. phase A arrester) is given on
Figure 4.5.
77
4.1.3 Surge Event Scenario C
In relation to the corresponding location of station electrical components as contained in the
MATLAB model of figure 4.1., this scenario can be visualized by figure 4.4.
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018-800
-600
-400
-200
0
200
400
600
800
TIME (µS)
VO
LT
AG
E(K
V)
Fig. 4.5: RESULTANT WAVEFORM FOR SURGE EVENT SCENARIO B
78
The lightning strike occurs at 90m to the entrance arresters, linking to the Kingsway 33kV
line(i.e. arresters 4, arrester 5, arrester 6). The lightning overvoltage waveform at arrester
4(i.e. phase A arrester) is given in figure 4.7. The time domain values of the signals resulting
from the simulated scenarios are extracted into vectors and matrix structures buffered in the
MATLAB workspace in memory. This data structures are accessed by the HMM algorithm.
From the values, HMM computation runs iteratively and identifies the waveform with the
maximum likelihood. The identified signal is used to obtain the surge steepness(kV/µs). This
value is used to compute the insulation coordination withstand voltage.
The computed value is compared analytically with the residual or discharge of the arrester
and the Basic Insulation Level(BIL) of the transformer to access the margin of protection
based on the maximum likelihood surge wave.
A
B
C
a
b
c
com
90m
Lightning source
132kV/33kV Transformer
132kV/33kV Transformer
Lightning arrester 4
Figure 4. 6. The illustration of incoming transmission surge wave of scenario C
79
From the simulation studies, the waveform identifies as having maximum likelihood is that of
figure 4.5. But it should be noticed by comparing the maximum amplitude of Figure 4.3 and
4.5 that the surge wave of Figure 4.3 is of a higher amplitude. This amplitude comparison
becomes clearer in the combined plot given in Figure 4.8. Though the amplitude of the surge
signal of Figure 4.3 of highest magnitude of the three, the HMM algorithm still identified that
of figure 4.5 as having the highest maximum likelihood.
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018-400
-200
0
200
400
600
800
TIME(µS)
VO
LT
AG
E (K
V)
Fig. 4.7: RESULTANT WAVEFORM OF SURGE EVENT SCENARIO C
80
This can be understood from the fact that HMM is based on probability distribution, rather on
deterministic measurement. This means from the iterations, the signal waveform of Figure
4.3 has the highest probability strength than the other signals, based on the complex structure
of the power system dynamics as seen by the algorithm.
4.2 Waveform at the Strike point
The waveform at the lightning strike point is given by Figure 4.9. At the strike point is
given(of 45m to the entrance arresters), the wave shape is that of impulse wave with an
exponential curve that rises quickly to the peak and falls comparatively slowly towards zero
with respect to time.
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018-800
-600
-400
-200
0
200
400
600
800
TIME(µS)
VO
LT
AG
E(K
V)
HMM identified maximum likelihood surge signal
Fig 4.8: RESULTANT WAVEFORM OF THE THREE SURGE EVENT SECNARIOS(THE COMBINED PLOT)
81
Comparing the wave at the strike point with those given on Figure 4.8 (i.e. those at the 132kV
entrance arresters). It can be seen that the amplitude(referring to the crest of the wave at the
strike point) is greater than those at the station entrance(132kV side) arresters. In other words,
the rate of rise of the surge wave at the strike point was very high, but by the time it reached
the station entrance(to the 132kV side), it was reduced by corona and the capacitance of the
line[23]. It is important to note that the steepness of the incoming surge into a station is a
crucial factor on how well the arresters are able to protect the equipment at the station.
The steepness S of the surge is given by[23];
0 0.005 0.01 0.015 0.02 0.025 0.030
200
400
600
800
1000
1200
1400
1600
1800
2000
TIME(µS)
VO
LT
AG
E(K
V)
Fig. 4.9: RESULTANT WAVEFORM AT THE STRIKE POINT
82
S = 1
𝐾𝑐𝑜 𝑋𝑇…………………………………………………(4.1)
Where 𝑋𝑇 = 𝑋𝑝
4………………………………………..(4.2)
𝑋𝑝 = 2𝑇
[𝑛𝐾𝑐𝑜(𝑈 − 𝑈𝑝𝑙)]……………………… .………… . (4.3)
Where 𝐾𝑐𝑜 is the corona damping constant according to table to table 4.1(µs/(kV.m)):
𝑋𝑝 is the limit overhead line distance within which lightning events have to be
considered(m).
n is the number of overhead lines connected to the substation.
T is the longest travel time between the point to be protected and the closest arrester(µs).
𝑈𝑝𝑙 is the lightning impulse protective level of the arrester.
U is the considered overvoltage amplitude.
Table 4.3: Corona damping constant 𝐾𝑐𝑜
Conductor Configuration 𝑲𝒄𝒐(µs/(KV.m))
Single conductor 1.5 × 10−6
Double Conductor bundle 1.0 × 10−6
Three or four conductor bundle 0.6 × 10−6
Six or eight conductor bundle 0.4 × 10−6
Source: [27]
83
From the HMM identified maximum likelihood surge wave (Figure 4.5), the highest
amplitude of the signal is 721.42kV. Also from the station’s supplied data, the arrester spark
over level(i.e. discharge voltage level) or BIL is 650kV. This is the equipment name plate
supplied by PHCN on appendix B. Moreover, the make or model of the arrester is “Siemens
3AP1FG”. The transformer surge impedance is 1600Ω, surge impedance of line is 400Ω.
Arrester- transformer separation distance is 6.5m. The reference is to arrester 4 in Figure 4.1.
To understand the insulation coordination distance relationship between lightning arrester 4
and the protected 132/33kV transformer on Figure 4.1, the following illustration in Figure
4.10 depicts the arrester – transformer relationship.
The 132/33kV
protected transformer
𝑍𝑂 = 1600 Ω
•
•
Zo = 400Ω
β a4
a1 a3 α
ARRESTER 4
U
Surge wave front
84
T is determined as follows:
T = 𝐿
𝐶 ………………………………………………………………………… (4.4)
a2
Earth mat
𝑍𝑔 = earthing impedance
Figure 4.10 location of arrester 4 (on phase A) to the 132/33kV transformer
supplying the Kingsway line I
85
Where:
C is the velocity of light (300m/µs);
L = 𝑎1 + 𝑎2 + 𝑎3 + 𝑎4: distance as indicated in Figure 4.7
𝑎1: length of the lead connecting the surge arrester to the line.
𝑎2: length of the lead connecting the surge arrester to earth.
𝑎14: length of the active part of the surge.
𝑎3: length of the phase conductor between the surge arrester and the protected equipment.
From the data obtained from PHCN:
𝑎1 = 2m, 𝑎2 = 15m, 𝑎3 6.5m, 𝑎4 = 3.6m
Thus, T = 27.1
300 = 0.0903µs……………………………………………………… (4.5)
Transmission coefficient 𝛼 = 2 ×1600
1600 +400= 1.6………………………………… (4.6)
Reflection coefficient 𝛽 = 1.6 − 1 = 0.6……………………………………… (4.7)
Data supplied indicate the use of double line at the switch yard, hence n = 2. Then from the
table 4.1, 𝐾𝑐𝑜 = 1.0 × 10−6µs/(ku.m)
Referring to Figure 4.5(i.e. the HMM identified maximum likelihood surge wave),
U = 721.42kV, the arrester discharge voltage(i.e. arrester BIL) = 650kV, hence 𝑈𝑝𝑙 = 650kV.
Substituting using equation (4.3)
86
𝑋𝑝 = 2 ×0.0903
(2×1.0×10−6×(721.42 −650)= 1264.351………………………………… (4.8)
𝑋𝑇 = 1264.351
4 = 316.09 ………………………………………………………. (4.9)
𝑆 = 1
(1.0×10−6×316.09 ………………………………….………………………..... (4.10)
S = 3163.68kV/µs
This is the steepness of the surge voltage 𝐸𝑡 at the terminal of the transformer can e
determined from [ 30 ]:
𝐸𝑡 = 𝐸𝑎 + 𝛽𝑑𝑒
𝑑𝑡 ×
2𝐿𝑡
300……………………………(4.11)
Equation (4.11) gives the maximum voltage at the terminal of a line as a result of the first
reflection of a travelling wave. This gives the maximum voltage up to 2𝛽𝐸𝑎. The factor 2
arises from the return length from arrester to transformer, and the factor 300 is based on a
travelling wave velocity of 300m/µs in the overhead line. 𝑙𝑡 is the separation between the
arrester and the transformer location (for figure 4.10 𝑙𝑡 = 𝑎3, 𝛽 is the reflection coefficient at
the transformer location, 𝐸𝑎(i.e. arrester BIL), and 𝑑𝑒
𝑑𝑡 is the steepness(i.e. the rate of rise) of
the wave front. When the value of 𝛽 is not known, it may be assumed to be 1 without much
loss of accuracy [30 ]
From the data supplied, 𝐸𝑎 = 650𝑘𝑉, 𝑎3(separation of arrester 4 from transformer) = 6.5m.
𝑑𝑒
𝑑𝑡= 𝑆 =
3163.68𝑘𝑉
𝜇𝑠………………………………(4.12)
𝐸𝑡 = 650 + 0.6 × 3163.68 × 26.5
300……………… . . (4.13)
87
𝐸𝑡 = 732.26𝑘𝑉
The BIL of the transformer, as per supplied data is 850kV. The transformer insulation
withstand voltage is greater than the maximum surge voltage appearing at its terminals. The
residual voltage of the arrester should be below the BIL of the protected equipment by a
suitable margin. The IEEE13131.2[28] and the IS/IEC 60071-2[6] recommended margin is
between 15% and 25%. However, emphasis is placed on achieving a good margin above the
15% minimum[29].
Thus, using the obtained maximum value of surge voltage at the protected equipment, and the
BIL of the protected equipment, the margin of protection can be evaluated:
The margin of protection = 850 −732.26
732.26 × 100% = 16.08%………………(4.14)
Moreover from the simulation, the BIL(Basic Insulation Level) to the withstand of the
transformer is higher than the maximum overvoltage(as per HMM identification), appearing
at its terminals during the lighting strike. The 16.08% margin of protection (i.e. by how much
the transformer withstand is greater than the maximum likelihood surge) is just a little above
the minimum recommended margin (i.e. 15%).
However, adjusting the separation of the arrester from the transformer might improve the
margin of protection. For instance, to achieve a protection margin of 18% at the switch yard,
the maximum permissible surge at the transformer
= 850
1.18 = 720.34KV. ……………………………………………………… (4.15)
Substituting in equation (4.11)
88
720.34 = 650 + 0.6 × 3163.68 ×2𝑙𝑡300
∴ 𝑙𝑡 = 5.56𝑚
The lightning surge arrester 4 has to be placed 5.56m to the transformer in order to achieve a
protection margin of 18%.
89
CHAPTER FIVE
5.0 CONCLUSION AND RECOMMENDATION
5.1 SUMMARY
The proposed HMM based insulation coordination technique is applied to a 132/33kV Power
transmission switchyard in New Haven Enugu Nigeria. Insulation coordination is carried out
to evaluate the arrester rating/arrester placement, that will adequately protect the substation’s
transformer from flashover during a lightning strike. The focus is on determining the margin
of protection, with reference to the recommended margin as per IEEE 1313.2/IS/IEC 60021.
The station was modeled in MATLAB/Simulink using single line drawings, supplied by
PHCN. Lightning surge simulated was based on the CIGRE wave shape using impulse
current generator. This was used to inject a lightning surge of 30KA, propagated into the
switchyard. The maximum surge voltage at a specific arrester – transformer location was
determined.
The work assumed that the substation was properly shielded. Otherwise, insulation
coordination involving substation overhead shield wire, should have been considered in the
evaluation carried out in Chapter four. Hence, the work considered, focused on Insulation
coordination of the arrester – transformer pair.
Moreover, Insulation coordination often entails evaluating a trade off between economy and
safety(i.e. technical aspect) margins. Often, for mainly economic reasons, arresters are
located at a distance from transformer, in order to include other station equipment within its
protection zone. Hence the more the margin of protection is increased by shortening the
separation between lightning arrester and protected equipment, the increase in the likelihood
90
of more arresters being required. This is because the more the closer an arrester is moved
towards a protected equipment, gaps are created that affects the protection of other substation
equipment within the protection zone.
However, the location adjustment might push the arrester, to a location in which its protection
for other equipment falls below the recommended protection margin, hence more arresters
would then be required.
5.2 CONCLUSION
Based on the HMM identified maximum likelihood lightning surge waves, resulting from the
three lightning disturbance scenarios at the power station investigated, the arrester –
transformer placement meets the minimum margin of placement. The minimum required
margin(of 15%) exceeded by a little value(about 1.08%). Also, evaluation carried out to raise
the protection margin to 18% meant the relocation of the arrester to within 5.56m of the
transformer. Without the HMM, the work would have to coordinate for each of the lightning
disturbance scenario with different results. This would mean different configuration of
location of arresters, discharge voltage of arresters, different determination of BIL for
protected equipment. Insulation having been established as an engineering practice has
matured to the point of knowing that it is a combination of economic and technical safety
consideration. Sequel to this, the computation, configuration, selection of values as regards
insulation coordination, has its foundation in probability and statistical sciences. Thus, basing
the selection of coordination, lightning surge wave signal on probabilistic maximum
likelihood is an optimal approach in providing the economic – technical safety trade off.
5.3. RECOMMENDATION
91
The technical information provided in this thesis forms a veritable database for future work
towards improved Nigeria power system operation.
The following are recommended to ensure efficient operation of the Nigeria grid system:
a) Insulation Coordination should be conducted in the station on routine basis(for
instance once in 5 years). This is crucial due to equipment ageing.
b) The station must be properly shielded.
c) A High voltage meter that retains Over Voltage readings should be installed in the
station.
d) However, it is also recommended that the strength, occurrence and distribution of
lightning strikes within the geographical area should be collated for insulation
coordination of power system in the country.
5.4 SUGGESTION FOR FURTHER STUDIES
a) The insulation coordination technique proposed in this work should be applied to
substation insulation coordination for switching overvoltages in subsequent studies.
b) The training process in the HMM algorithm should factor in environmental effects.
Since for instance flashover voltages for air gaps depend on moisture content and
density of air. Therefore, in the determination of withstand voltages, correction factors
for humidity and ambient temperature variation should be considered if subsequent
work delves into substation shielding, since critical flashover voltage(CFO) of line
insulators can be reduced by as much as 20% at higher elevations. Such collated data
on environmental effects can be encoded and used in the HMM algorithm for the
identification of more realistic maximum likelihood surge wave for the optimal
insulation coordination of power systems in the country.
92
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93
[8] ANSI C92.1-1982, American national standard for power systems-insulation
coordination.
[9] IEC 71-1-19-12, Insulation coordination Part 1 : Definitions, principles and rules, 1993.
[10] IEC Publication 71-1-1976, Insulation coordination, Part 1: Terms, definitions and rules.
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www.electrical4u.com edition, 2014.
[12] J. Rohan Lucas. “High Voltage Engineering”. Department of Electrical Engineering,
University of Moratuwa, Sri Lanka Third edition, pp 174, 2001.
[13] D. Fulchiron. “ Overvoltages and Insulation Coordination in MV and HV”, Cahier
Technique Merlin GerinE/CT. pp 3,4,5, 1995.
[14] J.B. Gupta. “A course in Electrical Power”, S.K. Kataria Part III pp 457 – 463, 2007-08.
[15] A. R. Hileman. “ Insulation Coordination for Power Systems”. CRC Press, Taylor and
Francis group pp 11 – 13, 1999.
[16] E. Kuffel, W.S. Zaengl, J. Kuffel. “High Voltage Engineering Fundamentals”.
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9, 51000 Rijeka, Croatia. ISBN 978-953-307-208-1, 2011.
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on Dielectric and Electrical,6(2): pp 259 – 266, 1999.
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[19] L. Xiaolin , M. Parizean, R. Plamordon “Training Hidden Markov models with multiple
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4, pp 371–377, April 2000.
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[22] Lawrence and A. Rabiner “A Tutorial on hidden markov models and selected
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[23] IS/IEC 60071 – 2: Insulation Coordination, part 2: Application Guide [ETD 19: High
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96
APPENDIX A
MATLAB M-FILE SOURCE CODE THAT IMPLEMENT HMM ALGORITHM
%the default false value
FALSEVALUE = -1.0 ;
%in baum-welch algorithm, the stop-condition is set using ratio( that is (probFinal-
probInit)/probInit )
RATIOLIMIT = 0.001 ;
%in baum-welch algorithm, when the circle of do...while exceed certain number, break it and
return the
%result
ROUNDLIMIT = 5 ;
%in baum-welch algorithm, in case the denominator is zero, so set it to a very very small
double number
DENOMINATORLIMIT = 10e-70 ;
%******** these are variables in Hmm itself **********************%
%the number of states : Q={1,2,...,N}
int N ;
//the number of observation symbols : V={1,2,...,M}
int M ;
%the probability transition matrix : A[1..N][1..N]
%A[i][j] is the probability from state i to j
double A ;
%the probablity emition matrix : B[1..N][1..M]
%B[j][k] is the probabiltiy of the observation symbol k in the state j
double U = [OUT_PUT_IMPEDANCE SURGE_IMPEDANCE EARTH_IMPEDANCE ] ;
%the initial state distribution
%pi[i] is the initial state probability
vector<double> pi ;
%********** these are variables used(created) in Hmm ****************%
%the T value of the last time
int iPreT ;
%the alpha variable used in forward procedure and Baum-Welch procedure
%alpha[t][i] is the probability of the observation sequence O1,O2....Ot and reach state i given
%modul u
alpha
= [] ;
%the beta variable used in forward procedure and Baum-Welch procedure
%beta[t][i] is the probability of the observation sequence Ot,...OT given modul u and state i
double beta =[];
%the delta variable used in viterbi algorithm
%delat[t][j] = max P(X1...Xt,O1...Ot,Xt=j | u )
double delta =[];
%the gamma variable used in baum-welch algorithm
97
%gamma[t][i] = P( Xt=i | O,u )
double gamma = [];
%some allocating memory function to 2-dimonsion array
nrerror( string errStr ) ;
iMatrix( int irLow, int irHigh, int icLow, int icHigh ) ;
float** fMatrix( int irLow, int irHigh, int icLow, int icHigh ) ;
double** dMatrix( int irLow, int irHigh, int icLow, int icHigh ) ;
%the functions to free memory
iFreeMatrix( int** iMatrix, int irLow, int irHigh, int icLow, int icHigh ) ;
fFreeMatrix( float** fMatrix, int irLow, int irHigh, int icLow, int icHigh ) ;
dFreeMatrix( double** dMatrix, int irLow, int irHigh, int icLow, int icHigh ) ;
%the initialize function
%random set the matrixes to the value between 0 and 1
InitHmm( int iSeed ) ;
%output Hmm to the file,espcially for SIMULINK
WriteHmm( string strFileName ) ;
% output Hmm to the file,espcially for SIMULINK
WriteHmm( char* sFileName ) ;
%read a Hmm from the file named "strFileName", for SIMULINK
void ReadHmm( string strFileName ) ;
%read a Hmm from the file named "strFileName",
void ReadHmm( char* sFileName ) ;
%read the observation sequence to the vector sequence, espcially for SIMULINK
ReadSequence( ifstream& in, vector<int>& sequence ) ;
%read the observation sequence to the array sequence, espcially for c
ReadSequence( FILE* pFile, int*& sequence, int& iNum ) ;
%generate sequence function, it's not much use in fact, but funny
%generate the sequence according Hmm for SIMULINK
%parameters : iSeed : the seed to generate random number
% O : the returned observation sequence
% S : the returned state sequence
GenerateSequence( int iSeed, int T, vector<int>& O, vector<int>& S ) ;
%generate the sequence according Hmm for c
%parameters : iSeed : the seed to generate random number
% O : the returned observation sequence
% S : the returned state sequence
GenerateSequence( int iSeed, int T, int* O, int* S ) ;
%the functions serve GenerateSequence( int iSeed, vector<int>& O, vector<int>& S )
%get the initial state using iSeed
% GetInitialState( int iSeed ) ;
%generate an output symbol according to the given state
int GetSymbol( int iState ) ;
%get the next state according to the transittion probability and given state
int GetNextState( int iState ) ;
%the core functions of Hmm
%such as Forward and Backward functions and viterbi function and Baum-Welch function
%public:
%the forward function for SIMULINK interface
98
double Forward( int T, vector<int>& O ) ;
%the forward function for c interface
double Forward( int T, int* O ) ;
%the forward function with scale ( been normalized ) and return the log value of the
probability
%the reason using a log value, i think, is to smooth the original value which is much small
%this function is designed especially for SIMULINK interface
ForwardNormalized( int T, vector<int>& O) ;
%the forward function with scale ( been normalized ) and return the log value of the
probability
%the reason using a log value, i think, is to smooth the original value which is much small
%this function is designed especially for c interface
ForwardNormalized( int T, int* O) ;
%the backward function for SIMULINK interface
Backward( int T, vector<int>& O ) ;
%the backward function for c interface
Backward( int T, int* O ) ;
%the backward function with scale to normalize and return the log value of the probability
%the
reason using a log value, is the same with forwardnormalized procedure
%it's very similar to the forwardnormalized procedure
%this function is designed especially for SIMULINK interface
BackwardNormalized( int T, vector<int>& O ) ;
%the backward function with scale to normalize and return the log value of the probability
%the reason using a log value, is the same with forwardnormalized procedure
%it's very similar to the forwardnormalized procedure
%this function is designed especially for c interface
BackwardNormalized( int T, int* O ) ;
%the viterbi algorithm for SIMULINK interface
%parameter: T : the number of the observation sequence % O :
the observation sequence % S :
the most likely state sequence as return value
%return value : the probability of the state sequence
Viterbi( int T, vector<int>& O, vector<int>& S ) ;
%the viterbi algorithm for c interface
%parameter: T : the number of the observation sequence % O :
the observation sequence % S :
the most likely state sequence as return value
%return value : the probability of the state sequence
Viterbi( int T, int* O, int*& S ) ;
%the baum-welch algorithm, for SIMULINK interface
%parameter: T: the number of the observation sequence
% O: the observation sequence
% probInit : the probability of the observation sequence calculated by the origin model
% probFinal : the probability of the observation sequence calculated by the adjusted
%model
% note: this algorithm is often not used and it' also the most complex one in hmm
BaumWelch( int T, vector<int>& O, double& probInit, double& probFinal ) ;
%the baum-welch algorithm, for c interface
%parameter: T: the number of the observation sequence
99
% O: the observation sequence
% probInit : the probability of the observation sequence calculated by the origin model
% probFinal : the probability of the observation sequence calculated by the
adjusted
%model
%note
: this algorithm is often not used and it' also the most complex one in hmm
void BaumWelch( int T, int* O, double& probInit, double& probFinal ) ;
%the function called by baum-welch algorithm
%allocate gamma memory and calculate it
ComputeGamma( int T, int N, double probTemp ) ;
%allocate p memory and calculate it, for c++ interface
%p[t][i][j] = p( Xt=i,Xt+1=j | O,u ), is the probability of transitting from state i to state j
double*** ComputeP( double*** p,int T, int N, vector<int>& O, double prob ) ;
%allocate p memory and calculate it, for c interface
%p[t][i][j] = p( Xt=i,Xt+1=j | O,u ), is the probability of transitting from state i to state j
double*** ComputeP( double*** p,int T, int N, int* O, double prob ) ;
%recalculate the probability of hmm parameters( pi, A and B ), for transient vectors
RecomputeParameter( double***& p, int T, vector<int>& O, double probInit, double&
probFinal ) ;
%recalculate the probability of hmm parameters( pi, A and B ), for c++ interface
RecomputeParameter( double***& p, int T, int* O, double probInit, double& probFinal ) ;
%free the memory of 3-diminson matrix
PFreeMatrix( double*** p, int T ) ;
Hmm(scenario_A);
Hmm(scenario_B);
Hmm(scenario_C);
%There are two methods to initialize a Hmm:
%One way is to read a Hmm from a file which store it
% ( of course, you can state a Hmm object and explicitly call the function of
Hmm::ReadHmm(char* sFileName) )
%The other is to set the size of state set and output alphabet set and initialize it with random
value
Hmm( WORKSPACE[] strFileName ) ; % for SIMULINK interface
Hmm( [surge_impedance ] sFileName ) ; % for interface
Hmm( int NHmm, int MHmm, int iSeed ) ;
//and there is the third one : to initialize Hmm with every variable in it
Hmm( int NHmm, int MHmm, double** AHmm, double** BHmm, vector<double>&
piHmm ) ; };
%some allocating memory function to 2-dimonsion array
nrerror( string errStr ) ;
int** iMatrix( int irLow, int irHigh, int icLow, int icHigh ) ;
float** fMatrix( int irLow, int irHigh, int icLow, int icHigh ) ;
double** dMatrix( int irLow, int irHigh, int icLow, int icHigh ) ;
% the functions to free memory
% iFreeMatrix( int** iMatrix, int irLow, int irHigh, int icLow, int icHigh ) ;
% fFreeMatrix( float** fMatrix, int irLow, int irHigh, int icLow, int icHigh ) ;
% dFreeMatrix( double** dMatrix, int irLow, int irHigh, int icLow, int icHigh ) ;
BlockType Reference
Name "Three-Phase\nSeries RLC Load2"
100
Ports [0, 0, 0, 0, 0, 3]
Position [240, 747, 305, 803]
Orientation "left"
NamePlacement "alternate"
AttributesFormatString "\\n"
DialogController "POWERSYS.PowerSysDialog"
FontName "Verdana"
FontSize 11
SourceBlock "powerlib/Elements/Three-Phase\nSeries RLC Load"
SourceType "Three-Phase Series RLC Load"
PhysicalDomain "powersysdomain"
SubClassName "unknown"
LeftPortType "p1"
RightPortType "p1"
LConnTagsString "A|B|C"
Configuration "Y (grounded)"
NominalVoltage "33e3"
NominalFrequency "60"
ActivePower "250e6"
InductivePower "200e6"
CapacitivePower "0"
Measurements "None"
Block {}
BlockType Reference
Name "Three-Phase\nSeries RLC Load3"
Ports [0, 0, 0, 0, 0, 3]
Position [1372, 1135, 1428, 1200]
Orientation "down"
AttributesFormatString "\\n"
DialogController "POWERSYS.PowerSysDialog"
FontName "Verdana"
FontSize 11
SourceBlock "powerlib/Elements/Three-Phase\nSeries RLC Load"
SourceType "Three-Phase Series RLC Load"
PhysicalDomain "powersysdomain"
SubClassName "unknown"
LeftPortType "p1"
RightPortType "p1"
LConnTagsString "A|B|C"
Configuration "Y (grounded)"
NominalVoltage "33e3"
NominalFrequency "60"
ActivePower "250e6"
InductivePower "200e6"
CapacitivePower "0"
Measurements "None"
Branch {}
ConnectType "SRC_DEST"
SrcBlock "Three-Phase Breaker"
SrcPort RConn1
101
Points [90, 0; 0, 80; 60, 0]
}
Branch {
ConnectType "SRC_DEST"
SrcBlock "Surge Arrester4"
SrcPort RConn1
Points [45, 0; 0, 5]
Line {}
LineType "Connection"
SrcBlock "Surge Arrester8"
SrcPort RConn1
Points [60, 0]
Branch {
ConnectType "DEST_SRC"
DstBlock "Ground5"
DstPort LConn1
}
Branch {
ConnectType "DEST_DEST"
Points [1700, 470; 25, 0]
Branch {
ConnectType "SRC_DEST"
SrcBlock "Surge Arrester9"
SrcPort RConn1
Points [50, 0; 0, -35]
}
Branch {
ConnectType "SRC_DEST"
SrcBlock "Surge Arrester7"
SrcPort RConn1
Points [50, 0; 0, 55]
}
}
Line {
LineType "Connection"
SrcBlock "Surge Arrester11"
SrcPort RConn1
Points [60, 0]
Branch {
ConnectType "DEST_SRC"
DstBlock "Ground6"
Line {
LineType "Connection"
SrcBlock "132KV/33KV_4"
SrcPort RConn1
Points [-10, 0]
Branch {
ConnectType "DEST_SRC"
DstBlock " 22"
DstPort RConn1
102
Line {
LineType "Connection"
SrcBlock "Lightning Impulse Current \nSource"
SrcPort LConn1
Points [-25, 0]
DstBlock "Ground11"
DstPort LConn1
}
Line {
SrcBlock " 25"
SrcPort 1
Points [-25, 0; 0, -65]
DstBlock "Scope1"
DstPort 1
}
Line {
LineType "Connection"
SrcBlock "Ground12"
SrcPort LConn1
DstBlock " 25"
DstPort LConn2
}
Line {
LineType "Connection"
SrcBlock "Lightning Impulse Current \nSource"
SrcPort RConn1
Points [10, 0; 0, 55]
DstBlock "Current Measurement"
DstPort LConn1
103
APPENDIX B: ARRESTER NAME PLATE
104
APPENDIX C: TRANSFORMER NAME PLATE
105
106
V
107
APPENDIX C