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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.

Certification ii
Approval iii
Dedication iv
Acknowledgements vi
Abstract vii
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
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
viii
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
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
3.5 Computing for the Insulation Coordination 50
ix
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
5.2 Conclusion 71
5.3 Recommendation 71
5.4 Suggestion for Further Studies 72
References 73
Appendix

## 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 coordination
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
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
2
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
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
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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. 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.
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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 coordination
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
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
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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.
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