University of Wollongong Thesis Collections

University of Wollongong Thesis Collection

University of Wollongong Year

Transient behaviour modelling of

underground high voltage cable systems

Muhamad Zalani DaudUniversity of Wollongong

Daud, Muhamad Zalani, Transient behaviour modelling of underground high volt-age cable systems, Masters by Research thesis, School of Electrical, Computer andTelecommunications Engineering - Faculty of Informatics, University of Wollongong, 2009.http://ro.uow.edu.au/theses/2032

This paper is posted at Research Online.

Transient Behaviour Modelling of Underground

High Voltage Cable Systems

A thesis submitted in partial fulfilment of the

requirements for the award of the degree

Master of Engineering - Research

from

University of Wollongong

by

Muhamad Zalani Daud, BEng

School of Electrical, Computer and Telecommunications Engineering

July 2009

To my wife, my son and my late mum

Abstract

The behaviour of voltage and current transients when a high voltage (HV) cable is first

energised is a problem of practical significance to utilities. Modelling of this behaviour

on a suitable simulation platform is an attractive approach, in many cases, provided that

the results closely match real-world behaviour. This thesis presents modelling and analysis

of transients resulting from energisation of an unloaded cable using PSCADr/EMTDCTM

simulation software. An assessment of the applicability of existing frequency-dependent

(FD) cable models is given. The impact of transients on a simulated cable system is also

presented and discussed.

In cable system modelling, system components must be accurately modelled, primarily

the underground cable. Two common frequency-dependent cable models are based on the

travelling wave method, namely the FD-Mode and FD-Phase models. These models are

investigated by comparing their ability to predict energisation current transients resulting

from the switching of an unloaded 132 kV underground cable. The simulated results are

validated by comparison with the measurement data. It was found that, the FD-Phase

model provides more accurate results compared to the FD-Mode model. This model is

widely applicable and suitable for use in modelling a wide range of frequencies.

The FD-Phase model was used in this study to analyse the distribution of overvoltages

at sending and receiving ends of the cable system. Specifically, statistical analysis has been

carried out correlating the overvoltage magnitudes induced and the closing behaviour of the

circuit breaker (CB). Two statistical switching techniques have been applied, namely the

deterministic and probabilistic approaches. Based on the approaches studied, results from

probabilistic techniques are recommended owing to the fact that it is closer to reality.

iii

Certification

I, Muhamad Zalani Daud, declare that this thesis, submitted in partial fulfilment of the

requirements for the award of Master of Engineering - Research, in the School of Electrical,

Computer and Telecommunications Engineering at the University of Wollongong, is wholly

my own work unless otherwise referenced or acknowledged. The document has not been

submitted for qualification at any other academic institution.

......................................

Muhamad Zalani Daud

July 7, 2009

iv

Acknowledgements

I would like to express sincere appreciation for the intelligent advise, encouragement and

guidance of my supervisors, Dr Philip Ciufo and Associate Prof. Sarath Perera.

Thanks to Integral Energy (IE) and University of Wollongong Power Quality and Reliability

Centre (IEPQRC) for providing the power system network data and the cable energisation

test results used in this research.

Thanks to Mr Sean Elphick and Mr Neil Browne for their valuable advice and help on

the experimental energisation test data.

My gratitude also should go to all my friends in IEPQRC for their support and friend-

ship.

Thanks also to the Ministry of Higher Education (MoHE) and University Malaysia Tereng-

ganu (UMT), Malaysia for the financial support.

My special thank to my family in Malaysia who has been my inspiration since the pri-

mary school until this stage of my education.

Finally, my deepest feelings and thankfulness I would like to dedicate to my wife for her

love, friendship and endless support and patience during my postgraduate studies.

v

Publications arising from this Thesis

1. M. Z. Daud, P. Ciufo, S. Perera, Investigation on the suitability of PSCADr/EMTDCTM

models to study energisation transients of 132 kV underground cable, Proc. Aus-

tralasian Universities Power Engineering Conference (AUPEC 2008), Paper ID: 037,

December 2008, Sydney, Australia.

2. M. Z. Daud, P. Ciufo, S. Perera, Statistical analysis of overvoltages due to the ener-

gisation of a 132 kV underground cable, Proc. Electrical Engineering/Electronics,

Computer, Telecommunications and Information Technology Conference (ECTI-CON

2009), Paper ID: 1325, May 2009, Bangkok, Thailand.

vi

Table of Contents

Abstract iii

Certification iv

Acknowledgements v

List of Publications vi

List of Abbreviations x

List of Figures xi

List of Tables xiii

1 Introduction 11.1 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Literature Review 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Transients and Travelling Waves . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Cable Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 The Wave Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 Coaxial Cable Electrical Parameters . . . . . . . . . . . . . . . . . . 112.3.3 Impedance and Admittance Matrices . . . . . . . . . . . . . . . . . . 12

2.4 An Overview of Approaches and Existing Models . . . . . . . . . . . . . . . 132.4.1 Electromagnetic Transients Simulation . . . . . . . . . . . . . . . . . 132.4.2 Lumped Pi Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.3 Distributed Parameter Travelling Wave Models . . . . . . . . . . . . 15

2.5 PSCADr/EMTDCTM Cable Models . . . . . . . . . . . . . . . . . . . . . . 172.5.1 The FD-Mode Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5.2 The FD-Phase Model . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.6 Analysis of Switching Transient Overvoltages . . . . . . . . . . . . . . . . . 212.6.1 An Overview of Statistical Switching Studies . . . . . . . . . . . . . 212.6.2 Switching Phenomena and Statistical Methods . . . . . . . . . . . . 22

2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 PSCADr/EMTDCTM Power System Model Development 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Power System Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3 Power System Component Modelling . . . . . . . . . . . . . . . . . . . . . . 27

3.3.1 132 kV Upstream Power Source . . . . . . . . . . . . . . . . . . . . . 273.3.2 Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

vii

viii

3.3.3 Transformer and Capacitor Bank . . . . . . . . . . . . . . . . . . . . 303.4 Underground cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4.1 Physical Construction and Material Properties . . . . . . . . . . . . 313.4.2 Cable Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.5 Inclusion of FD-Mode and FD-Phase Models in the Simulation . . . . . . . 353.5.1 Frequency-dependent Parameter Settings . . . . . . . . . . . . . . . 353.5.2 Simulation Step Size and Simulation Time . . . . . . . . . . . . . . . 37

3.6 Results from Simulation of Preliminary PSCADr/EMTDCTM Model . . . 373.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4 Cable Energisation Transient Behaviour and Assessment of Cable Models 424.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2 Experimental Energisation Tests . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2.1 Measurement Method . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2.2 Measured Current Transient Waveforms . . . . . . . . . . . . . . . . 444.2.3 Data for Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2.4 Analysis of the CB Pole Closing Times . . . . . . . . . . . . . . . . . 48

4.3 Model Refinement and Simulation . . . . . . . . . . . . . . . . . . . . . . . 494.3.1 Implementation of CB Pole Closing Times to the Circuit Model . . . 494.3.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4 Comparison of Results Predicted by FD-Mode and FD-Phase Models . . . . 504.4.1 Simulation using FD-Mode Model . . . . . . . . . . . . . . . . . . . 504.4.2 Simulation using FD-Phase Model . . . . . . . . . . . . . . . . . . . 534.4.3 Implication from Measured and Simulated Data . . . . . . . . . . . . 55

4.5 Overvoltage Transient Behaviour for the System Under Study . . . . . . . . 574.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5 Analysis of Overvoltage Stress due to Cable Energisation 625.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.2 An Overview of Switching Transient Evaluation Methods . . . . . . . . . . 635.3 Simulation Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.3.1 First Approach (Deterministic) . . . . . . . . . . . . . . . . . . . . . 645.3.2 Second Approach (Probabilistic) . . . . . . . . . . . . . . . . . . . . 65

5.4 Model Refinement and Simulation . . . . . . . . . . . . . . . . . . . . . . . 665.4.1 Implementation of Deterministic Approach in Simulation . . . . . . 665.4.2 Implementation of Probabilistic Approach in Simulation . . . . . . . 67

5.5 Analysis of Overvoltage Data from Simulation . . . . . . . . . . . . . . . . . 685.5.1 Results from Deterministic Approach . . . . . . . . . . . . . . . . . . 695.5.2 Results from Probabilistic Approach . . . . . . . . . . . . . . . . . . 705.5.3 Results for the Pole Span below 1 ms . . . . . . . . . . . . . . . . . 72

5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6 Conclusions and Recommendations 766.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Appendices

ix

A Fundamental Equations in Cable Modelling 79A.1 The General Transmission Lines or Wave Equations . . . . . . . . . . . . . 79A.2 Coaxial Cable Electrical Parameters . . . . . . . . . . . . . . . . . . . . . . 81A.3 Impedance and Admittance Matrices . . . . . . . . . . . . . . . . . . . . . . 83

B Power System Component Data 84B.1 Input Parameter Calculation of Surrounding Components . . . . . . . . . . 84B.2 Underground Cable Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

C Measurement Data 95C.1 Current Transients from Experimental Energisation Tests . . . . . . . . . . 95C.2 CB Pole Closing Times from Experimental Energisation Tests . . . . . . . . 99

References 100

List of Abbreviations

HV high voltage

EHV extra high voltage

UHV ultra high voltage

IEC International Electrotechnical Commission

IEEE Institute of Electrical and Electronics Engineers

EMTP electromagnetic transients program

DC direct current

FD frequency-dependent

CB circuit breaker

ULM universal line model

CC cable constant

CF curve fitting

BHTS Baulkham Hills transmission substation

BVZS Bella Vista zone substation

BTTS Blacktown transmission substation

SWTS Sydney West transmission substation

CFTS Carlingford transmission substation

XLPE cross-linked polyethylene

PVC polyvinyl chloride

HDPE high-density polyethylene

SVL sheath voltage limiter

RMS root mean square

FFT fast Fourier transform

VT voltage transformer

TV tertiary voltage

PDF probability density function

CDF cumulative density function

SE sending end

RE receiving end

x

List of Figures

2.1 Single phase frequency domain equivalent circuit of FD-Mode model . . . . 172.2 Weighting Function from J Marti formulation . . . . . . . . . . . . . . . . . 192.3 Typical 2 % slow-front overvoltage values . . . . . . . . . . . . . . . . . . . 23

3.1 Single line schematic diagram of power system network under study . . . . 273.2 Overhead line representation in PSCADr/EMTDCTM . . . . . . . . . . . . 303.3 Cable cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.4 Cable input data in PSCADr/EMTDCTM . . . . . . . . . . . . . . . . . . 333.5 Cross-bonding and configuration of the cable . . . . . . . . . . . . . . . . . 353.6 Current transients from preliminary FD-Mode model at T = 10 kHz . . . . 383.7 Current transients from preliminary FD-Phase model . . . . . . . . . . . . . 383.8 Current transients from preliminary FD-Mode model at T = 50 Hz . . . . 393.9 Overvoltage transients at the sending end of the cable . . . . . . . . . . . . 40

4.1 Cable energisation test set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2 Current transients from measurement data . . . . . . . . . . . . . . . . . . . 454.3 Blue and white phase current transients from third measurement . . . . . . 464.4 Frequency spectrum of blue and white phase current transients . . . . . . . 484.5 Determination of CB pole closing times from third energisation test . . . . 494.6 Establishment of CB pole closing times in PSCADr/EMTDCTM . . . . . . 494.7 Simulated current transients from FD-Mode model . . . . . . . . . . . . . . 524.8 Frequency spectrum of simulated current transients using FD-Mode model . 524.9 Simulated current transients from FD-Phase model . . . . . . . . . . . . . . 544.10 Frequency spectrum of simulated current transients using FD-Phase model 544.11 Steady-state charging current for cable under test . . . . . . . . . . . . . . . 554.12 An example of high frequency transformer model . . . . . . . . . . . . . . . 574.13 Overvoltage transients at sending and receiving end terminals . . . . . . . . 584.14 Busbar voltages during cable energisation . . . . . . . . . . . . . . . . . . . 594.15 Sheath voltages during switching with and without surge arresters . . . . . 60

5.1 Gaussian distribution curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2 Implementation of deterministic approach . . . . . . . . . . . . . . . . . . . 675.3 Results from deterministic approach . . . . . . . . . . . . . . . . . . . . . . 695.4 Results from probabilistic approach for 1 ms, 2 ms and 3 ms spans . . . . . 715.5 Results from probabilistic approach for below 1 ms pole span . . . . . . . . 73

A.1 A x section of a coaxial cable . . . . . . . . . . . . . . . . . . . . . . . . . 80A.2 A simplified coaxial cable cross-sectional area . . . . . . . . . . . . . . . . . 81

B.1 Current transients simulated using two different source models . . . . . . . 86B.2 Overhead line conductor co-ordinates . . . . . . . . . . . . . . . . . . . . . . 87

C.1 Blue and white phase current transients from first measurement . . . . . . . 95C.2 Blue and white phase current transients from second measurement . . . . . 96C.3 Blue and white phase current transients from fourth measurement . . . . . 96C.4 Frequency spectrum of current transients from first measurement . . . . . . 97

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C.5 Frequency spectrum of current transients from second measurement . . . . 97C.6 Frequency spectrum of current transients from fourth measurement . . . . . 98C.7 CB pole closing times for each test . . . . . . . . . . . . . . . . . . . . . . . 99

List of Tables

3.1 Source model input data of voltage source model-2 . . . . . . . . . . . . . . 283.2 Cable layers radial measurements . . . . . . . . . . . . . . . . . . . . . . . . 313.3 Cable dimensions and material properties input data . . . . . . . . . . . . . 343.4 Cable coordinates input data . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.1 CB pole switching times and maximum span from each test . . . . . . . . . 645.2 Red phase magnitudes for different simulation time step . . . . . . . . . . . 665.3 Sending end voltage magnitudes from simultaneous closure of CB . . . . . . 685.4 Significant overvoltage peaks from deterministic approach . . . . . . . . . . 705.5 Relevant statistical information for different cases of pole span . . . . . . . 74

B.1 Calculation of sequence impedances for voltage source model-1 and model-2 85B.2 132 kV overhead line general data . . . . . . . . . . . . . . . . . . . . . . . 86B.3 Conductor and ground wire data . . . . . . . . . . . . . . . . . . . . . . . . 86B.4 Transformer general data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87B.5 Transformer positive sequence leakage reactance data . . . . . . . . . . . . . 87B.6 Cable data from manufacturer . . . . . . . . . . . . . . . . . . . . . . . . . 89

xiii

Chapter 1

Introduction

1.1 Statement of the Problem

In recent times, a steady increase in introduction of underground cables has been seen in new

residential areas across Australia [1]. Their penetration, particularly in urban areas, gives

significant benefits as they can provide additional network capacity without the need for

an expensive overhead transmission easement. They also result in reduced visual impact

as compared to the visual impacts of bulky overhead transmission systems. In certain

situations, the expansion of overhead lines is impossible due to political and environmental

pressures from the public and government. New technology has resulted in underground

cables becoming competitive with overhead lines on technical, environmental and economic

levels.

However, the use of underground cable has a great impact on the quality of power and

has become one of the popular topics of discussion among power engineers and researchers.

Of particular relevance is the high frequency current and voltage transients resulting from

switching operations. The problems depend on several factors, including configuration of the

underground cables, the characteristics of circuit breaker (CB), general network topology,

as well as other external factors. To a certain extent, transients can be worse for the case

of switching at the transition point of overhead to underground transmission. It is crucial

1

2

to address the impact of this switching on the design requirements, not only for extra high

voltage (EHV) systems but also in the case of medium transmission voltages, such as the

132 kV systems [2]. The systems just described are dominant in urban areas in Australia

such as Sydney and Brisbane [3].

Switching operations cause surges to develop and travel within the cable circuit. The

travelling waves result in high frequency damped oscillations in the cable system. Normally,

voltage and current transients are most severe at the receiving end of the cable with unloaded

conditions. This is due to multiple reflections of surges with different magnitudes occurring

at the end terminals of the circuit. The surges continuously travel throughout the circuit

until they are damped out by resistive elements. Generally, these surges are not only

dangerous to the cable being switched, but also to the nearby power system components

and surrounding circuits.

Underground cable energisation may occur anywhere within a transmission and distri-

bution network, with the time and location of occurrences difficult to predict. Normally

the effects of transients are minimised by means of protective and preventive devices and

other switching techniques. The parameters of these devices may be obtained by evaluation

of switching transient voltage and current magnitudes for a particular network. Switch-

ing transients are considered to be one of the more difficult electromagnetic phenomena to

model and predict, and as such has been an ongoing research topic over several decades.

As such, modelling and software simulation of electromagnetic transients to study their

behaviour is one of the key topics of this research.

The Electromagnetic Transients Program (EMTPTM) is one of the most widely used soft-

ware tools for electromagnetic transient analysis. Subsequent and based on the EMTPTM

algorithm, the Electromagnetic Transients including DC (EMTDCTM) program was intro-

duced. To enable easy access and configuration of these programs, they come with computer-

aided design software, such as the Alternative Transients Program (ATPr) and the Power

Systems Computer-Aided Design (PSCADr). Both ATPr/EMTPTM and PSCADr/EMTDCTM

software suites are now major tools in power system studies.

3

There are a number of dedicated models in EMTP-type suites that can be used for cable

and transmission lines. The modelling choices vary from a simple pi model approach to more

complex ones. Some of the models are based on theories developed by early researchers,

which were established over 30 years ago [4–8]. These models are the frequency-dependent

type that take into account the distributed nature and frequency-dependent characteristics

of the cable (or transmission lines) parameters. In other words, they have been formulated

to model transient analysis. However, these models are not general and in some situations

may not be suitable for certain network configurations. For example, it is not always clear

whether the more sophisticated models should always be used in every transient simulation,

as under some circumstances simpler models may provide comparable results.

The literature shows that verification of the suitability of these models has been predomi-

nantly measured for the case of overhead lines, rather than their underground counterparts.

Less rigorous treatment of existing models on cables has raised questions in relation to

their applicability and reliability when applying these models to underground cable ana-

lysis. Such concerns can be addressed by further analysis of existing underground cable

models in terms of accuracy and suitability, specifically when they are intended to be used

under a specific network configuration.

Effort in validating cable models by detailed comparison is found for several cases carried

out in ATPr/EMTPTM [9, 10]. However, the approach used in [9] only gives examples of

single phase energisation of cables. Recently, Nichols et al. [10] carried out a practical com-

parison examining several frequency-dependent models such as KC Lee [11] and Semlyen [4]

approaches for the case of 3-phase energisation. However these models result in inconsisten-

cies in transient magnitudes and introduce numerical instability. Consequently, suggestions

arise from previously studied models which lead to the requirement of studying the more ac-

curate cable model. Such models are currently incorporated in the PSCADr/EMTDCTM,

for instance, one of them is the Universal Line Model (ULM) [8].

The energisation of an underground cable results in high frequency voltage and current

transients. The behaviour of these transients are determined by many factors. For example,

4

the transient peak magnitudes are influenced by the closing span of CB contacts and the

closing angle (point-on-wave) on power frequency voltage [12]. The voltage transients applies

considerable stress on the insulation of cables as well as the insulation systems of nearby

components. These stresses may result from either transients with high magnitudes or cu-

mulative occurrences of low magnitude overvoltages. It is essential to minimise the impact

of these transients. The assessment of peak values is of importance in the evaluation of in-

sulation co-ordination and examination for determination of protection schemes. Due to the

variability of CB contact closure, a statistical method is the most practical means to carry

out such studies. To ensure precise and reliable results from simulation, a carefully crafted

model of the power system network, with inclusion of an accurate frequency-dependent ca-

ble model, is indispensable. The literature shows that these assessments are predominately

carried out for EHV transmission systems using the ATPr/EMTPTM programs [13,14].

In summary, an examination of transient behaviour and switching overvoltages is an

important task in planning and design of a power system. These studies are important as

they have a direct bearing on the insulation requirements, cost and reliability of the designed

network. PSCADr/EMTDCTM is an attractive platform to carry out these studies.

1.2 Objectives of the Thesis

The main aim of this research is to carry out studies on the behaviour of the transients

due to the energisation of a high voltage (HV) underground cable system. The two major

objectives of this research are now presented.

Firstly, in order to facilitate selection of a suitable model of an underground cable, the

goal is to investigate the suitability of the cable models currently incorporated in one of

the EMTP-type simulators - the PSCADr/EMTDCTM software suite. As this work is a

continuation of [15], of particular interest is a study on the applicability and validity of

other models, namely the frequency-dependent mode (FD-Mode) and frequency-dependent

phase (FD-Phase) models [16].

5

Secondly, an extensive study of underground cables is carried out with a view to provide

useful information on switching overvoltage distributions based on the statistical method,

as suggested by the IEC standards [17, 18]. The modelling of a power system network

employing the statistical evaluation of overvoltage data is to be carried out. An accurate

cable model investigated earlier is used to represent the underground systems.

1.3 Contributions

Modelling work presented in this thesis is carried out on PSCADr/EMTDCTM platform.

The network representing the power system connected to the cable under investigation

includes the source, overhead transmission lines, distribution transformers and the capacitor

banks. The two major contributions arising from this work are as follows:

1. Analysis and verification of the suitability of the FD-Mode and FD-phase models

by practical comparison, for the purpose of studying the behaviour of energisation

transients on HV cables.

2. An extensive analysis of overvoltage distributions caused by cable energisation using

statistical analysis for the network under study.

1.4 Outline of the Thesis

The remaining chapters in this thesis are arranged as follows:

Chapter 2 summarises the literature including theoretical aspects of transient pheno-

mena in electrical power systems, electromagnetic transients simulation and cable (trans-

mission line) modelling techniques. The characteristics of existing models, specifically the

FD-Mode and FD-Phase models are further described. At the end of this chapter, analysis

of the switching transient problems is presented.

Chapter 3 explains the modelling process for the power system network under investi-

gation including the underground cable. Treatment of the source model, transformer model

6

and other surrounding components are detailed. Frequency-dependent modelling of trans-

mission lines and underground system are established. Some results from preliminary model

simulations are presented and analysed. Problems arising from the preliminary model are

identified and suggestions for improvement are provided at the end of this chapter.

Chapter 4 focuses on the procedures and methodology undertaken when organising

the experimental tests. Collection of data used in refinement of the preliminary model is

presented. Measurement data of current transients is synthesised to prepare suitable data

for comparison with simulated results. Refinement of the preliminary model and inclusion of

FD-Mode and FD-Phase models for simulation are then presented. Results from simulation

using both models are compared with the measurement data. The analysis of results is

presented in both time and frequency domain. Finally, an overview of overvoltage transients

which stress the underground cable and surrounding network components is presented.

Chapter 5 first provides an overview of switching transient evaluation methods. The

approaches used are also introduced. Then, the refinement of power system model to cater

for two different approaches considered is presented. Particularly, an explanation on the

construction of the multiple run system in PSCADr/EMTDCTM is given. Results from

simulations are presented for the different cases studied.

Chapter 6 provides conclusions based on the work covered in the thesis and provides

recommendations for further work.

Chapter 2

Literature Review

2.1 Introduction

Transient analysis is indispensable in predicting the performance of systems as well as in

designing system insulation. Simulation using electromagnetic transient software suites

is one of the most reliable methods for this purpose. However, it is a difficult task to

model the performance of systems which demonstrate strong frequency dependence. For

example, the parameters of an underground cable are naturally distributed and its non-

linear characteristics change with increase in frequency. Therefore, frequency-dependent

approaches should be catered for in achieving better accuracy. There are a number of

dedicated frequency-dependent cable models currently available, particularly in the EMTP-

type transient simulators. They are formulated based on wave equations derived from the

behaviour of travelling surges in the electrical system.

As the main interest of the work presented in this thesis is to study the transients due

to energisation of a cable system, only switching related issues are considered. This chapter

gives an overview of power system transients, particularly the surges that are caused by

switching operations. Their behaviour is described using mathematical expressions derived

from the wave equations. Coaxial cable modelling, such as the representation of high fre-

quency parameters and impedance matrices, are explained. Several models currently incor-

7

8

porated in EMTP-type platforms are highlighted and compared to emphasise their different

properties and suitability for studying high frequency transients of an underground cable.

Then, modelling approaches of FD-Mode and FD-Phase models are presented. Finally, the

impact of transient overvoltages on the insulation system are reviewed.

2.2 Transients and Travelling Waves

An electrical transient is initiated whenever there is an abrupt change in circuit conditions

due to events such as switching operations. Another definition is the situation of unbalance

that occurs during transition from one steady state to a new steady state condition [19].

It is an electromagnetic phenomena whose behaviour strongly depends on the electrical

parameters of the power system components. The components consist of distributed R, L

and C elements which are in different proportions.

Transients occur in a very short period of time before settling down to a steady state

condition. This short duration cannot be ignored because during such situations, compo-

nents in the system could be subjected to high current and high voltage peaks that place

considerable stress on insulation systems. Extreme cases might damage equipment such

as transformers and circuit breakers. Furthermore, electrical insulation and other sensitive

properties of the components are typically designed to work optimally at rated values and

are therefore susceptible to the deviation from the rated operation.

The classification of transients fall into two major categories - impulsive and oscilla-

tory [20]. Cable energisation belongs to the category of oscillatory transients in which the

instantaneous value of voltage or current changes polarity rapidly. Their occurrence is due

to resonances during switching where parameters are described by magnitude, duration and

spectral content. Evaluation of the peak values and transient frequencies are of primary

importance for assessing the insulation coordination of the system as well as the parameter

of protective schemes intended to be installed in the network.

Cables are designed in such a way to meet their protective and durability requirements

as well as the uniform distribution of currents. Generally, metallic sheaths and screens are

9

used. These layers further worsen the transient due to their coupling effects. Every single

switching operation on a cable may result in the elements of a power system being subjected

to voltages and currents having a wide frequency range which may extend from 50 Hz to

the region of 100 kHz [21]. Over such a frequency range, the parameters of the system and

of the earth path are not constant. Such conditions require the frequency dependent nature

to be accounted for in order to achieve an accurate cable model.

In power system networks, cables are physically long and consist of joints and points of

discontinuity. The complexity of modelling such networks is compounded by the inductive

and capacitive elements that are distributed along its length. As a consequence, the surges

that travel from their origin end up with multiple reflections and refractions at the cable

ends, joints or may be eliminated at surge limiting devices. Furthermore, as the transmission

systems are finite in length, the transmissions and reflections of waves occur iteratively. The

travelling surge is normally referred as an ‘incident wave’ and its reflection and refraction

can be solved using Kirchhoff’s Law [19,22].

Further complications arise when considering the reflection and refraction at various

junctions. These various terminations may consist of many interconnected lines or cable

circuits having different intrinsic impedances. Bewley [23] devised a convenient diagram

(Bewley Lattice Diagram) which shows the position and direction of motion of every inci-

dent, reflected and refracted wave on the system at every instant of time. The multiplicity of

successive reflections at multiple junctions can be monitored. However, it is difficult to ap-

ply the Bewley Lattice Diagram for the case of non linear devices. The graphical method of

Bergeron is suitable instead [24]. This method is valid for both linear and nonlinear models

and helps to calculate the delay of an electromagnetic signal on electrical circuits. Well docu-

mented information on reflected and refracted waves by means of the lattice diagram method

provided valuable contributions toward the development of a digital computer program for

the simulation of electrical transients. The Bergeron method (Method of Characteristics)

of implementing the travelling wave solution technique into the time domain solution has

been applied by Dommel in the development of EMTPTM [25].

10

2.3 Cable Modelling

2.3.1 The Wave Equations

The behaviour of travelling surges can be described mathematically using the wave equa-

tions. These equations govern general two conductor uniform transmission lines including

the coaxial cable. The derivation of these fundamental equations is given in Appendix A

(Section A.1). A set of coupled wave equations to describe the voltage along and the current

through the circuit are [26]

d2V

dx2= γ2V (2.1)

d2I

dx2= γ2I (2.2)

Both voltage, V , and current, I, are characterised by a propagation constant, γ, which is a

complex number defined as

γ = α + jβ =√

(r + jωl)(g + jωc) =√

zy (2.3)

where the real, α, and imaginary, β, parts in (2.3) are known as attenuation and phase

constants respectively. The per unit length parameters of the cable are described as r (re-

sistance), l (inductance), g (conductance) and c (capacitance), whereas ω is the frequency.

Similarly, z and y are the corresponding series impedance and shunt admittance of the cir-

cuit. Another important parameter influencing the wave propagation is the characteristic

impedance, Zc, within the circuit. It is defined as the ratio of circuit’s series parameters to

its corresponding shunt parameters as given by

Zc =

√

r + jωl

g + jωc(2.4)

The general solutions of (2.1) and (2.2) are described using the D’Lambert equations as

V (x) = V +0 e−γx + V −

0 e+γx (2.5)

11

I(x) = I+0 e−γx + I−0 e+γx (2.6)

where the plus and minus signs denote the forward and backward directions of wave prop-

agations respectively.

Depending on the nature of study, modelling of a cable may be described using a constant

or a frequency-dependent parameter approach. Underground cable energisation transient

modelling involves the consideration of frequency variations. Increase in frequency further

increases the non-linear characteristics of cables and the nearby system components which

require frequency-dependency to be accounted for. These greatly increase the burden in

modelling. Marti et al. [27] has postulated several factors that should be treated carefully

in order to achieve better accuracy in modelling such as:

• The distributed nature of transmission system parameters.

• Asymmetrical arrangement of coupled conductors with ground return.

• The strongly frequency-dependent series parameters especially for the ground mode.

2.3.2 Coaxial Cable Electrical Parameters

A copper cross-linked polyethylene (XLPE) cable normally comprises XLPE insulation and

other layers such as semiconducting bedding, copper wire screen (metallic screen) and the

water blocking layers. The metallic screen layers (sheath) of the cable contribute very much

to the high frequency transient currents. In particular cases, the high frequency cable model

requires inner and outer semiconducting screens to be accounted for. Gustavsen [28, 29]

described some procedures for converting geometrical and material data taking into account

other conductive screen layers to be included as an input to electromagnetic transient simu-

lators.

The non-uniformity of ac current distribution is affected greatly by the frequency. At

higher frequencies, skin effects are prevalent where current tends to flow more densely

near the outer surface of the conductor. Similarly, the currents flow primarily along the

inner surface of the outer conductor. The conductor core is stranded in such a way to

12

further minimse the skin effect. In modelling, the resistivity of the stranded core is normally

modified to a new value to account for the air gaps within the core conductors [28].

The proximity effect also greatly affects the non-uniformity of current distribution in

the cable conductor. The conductors in close proximity will produce magnetic flux linkages

which can disturb current distribution amongst each other. Increasing conductor spacing

might reduce such coupled influences. The significance of this effect can be seen particularly

in multi-conductor cable and cables in the same duct. This effect also depends on the size

and length of the conductors. It is another complex and crucial branch in studying electric

cable transient phenomena. Further information on this effect on underground cable can be

found in [30].

In general, the geometrical and material parameters (details of calculation are presented

in Appendix A (Section A.2)) are included as input data in the modelling of a cable system in

PSCADr/EMTDCTM [16,31]. Simplifying assumptions may be considered to overcome the

lengthy and complicated solution of more general ones such as presented in Section 2.3.1. For

instance, in some cases, simple equations which neglect the effect of resistance and conduc-

tance are considered valid since the severity from travelling waves is most pronounced in

the early stages before they become attenuated. Another example is when considering a

lossless transmission cable, such as one with nearly perfect conducting materials [26].

2.3.3 Impedance and Admittance Matrices

The EMTP-type simulators are facilitated with cable constant (CC) routines for the calcu-

lation of the impedance (z) and admittance (y) matrices. The development of this program

was based on the Pollack’s equations [32, 33]. A general solution of parameters for several

cases of underground cables are provided in [34, 35]. The equations form the basis of the

calculation of series and shunt parameters of a cable in EMTP-type simulators. The general

expression of impedance and admittance parameters per unit length for NxN conductors

can be described as matrices as presented in Appendix A (Section A.3). The main dia-

gonal elements of these matrices correspond to the self-impedance (or self-admittance) of

13

each conductor (core and sheath with respect to ground). Similarly, the off-diagonal quan-

tities represent their respective mutual impedance (or admittance). The elements in these

matrices are complex and may be given in Cartesian format such as zij = rij + jxij and

yij = gij + jbij . In some circumstances, a correction algorithm may be applied to these

matrices to account for electrical effects such as long line distances. The type of ideal trans-

position settings may also affect the elements of these matrices [16]. Consequently, the

shunt conductance, g, in some situations can, in general, be ignored as the loss angle of

underground cables is very small. The matrix b is symmetric and has positive values for

main diagonal terms which represent the shunt susceptance while the off-diagonal terms are

zero for underground cables [2].

2.4 An Overview of Approaches and Existing Models

2.4.1 Electromagnetic Transients Simulation

An analogue computer, or transient network analyser (TNA), has been widely used in the

past for the study of transient phenomena in electrical networks. However, since the advent

of digital computers, their application has gradually decreased [21]. Dommel’s work [25] in

programming time domain solution for transmission lines in digital computer has inspired

continuing research in the development of EMTP-type programs. His early attempts in

modelling, based on travelling wave concept, employed the Bergeron’s method [24]. Since

then, a number of models have been developed and are made available particularly in

EMTP-type suites. They are different in ability and applicability due to simplifications and

assumptions used, primarily for achieving computer memory and processing time savings

as well as robustness.

In achieving a high accuracy model, the frequency dependence of power system elements

is indispensable. The approach involves several steps of complex calculation of mathematical

modelling. Time domain model variables are first transferred into the frequency domain so

that their intrinsic response can be derived (allows the rational function fitting of impulse

14

response). A time domain simulation can then be carried out using convolutions that use

the time domain counterpart of their variables, which are obtained from the inverse Fourier

transform [5, 6]. Some of the models prefer the variables to be transformed into z-domain

by means of the z transformation [7]. The computational effort in modelling is greatly

reduced since the introduction of the recursive convolution technique in the solution of the

time domain convolution integrals [4].

The modelling is difficult when multi-phase conductors are considered. Furthermore, the

nature of frequency dependence is strong for the case of underground cables and the asym-

metric structure of transmission lines. In practice, the physical system of conductors (mu-

tually coupled) are firstly decoupled into a mathematically-equivalent decoupled one. The

modal decomposition process [36, 37] increases the burden from the modal transformation

matrices which are also frequency-dependent. Although a constant transformation matrix

can be assumed, it is crucial to consider a frequency-dependent transformation matrix (Tv

or Ti for voltage and current variables respectively) in modelling. L Marti [6] developed a

more accurate model for transmission lines and underground cable which accounted for the

frequency dependence of transformation matrices. However, at the present time and in the

recent past, an increasing effort to overcome difficulties in handling the frequency-dependent

transformation matrix has been evident. Eventually, the direct phase domain models are

much more reliable today [7,8].

In either EMTPTM or EMTDCTM type programs, the models are divided into two broad

categories; the lumped parameter or the distributed parameter travelling wave models. The

suitable approach may be selected depending on the study requirements. A wide range of

models are available including the lumped pi, Bergeron, Noda, KC Lee, Semlyen, L Marti,

J Marti (FD-Mode) and the ULM (FD-Phase) models [11, 31]. The following section pro-

vides an analysis of these models except the FD-Mode and FD-Phase models where detailed

investigations are documented in Section 2.5.

15

2.4.2 Lumped Pi Models

A short transmission line or cable can be described as a lumped pi model with arrangement

of R, L and C parameters of the mutually coupled phases calculated at the steady state

frequency. R and L represent the series impedances where shunt losses are ignored and the

total admittance is divided into two sections lumped at the sending and receiving ends [38].

Such a model can be used to perform accurate steady-state system calculations and is also

suitable for studies which assume constant parameters. Cascading many pi sections can,

in general, represent a long line [31]. However, for predicting a wide range of frequency

variations upon cable energisation, such implementations may not be adequate [10]. Fur-

thermore, cross-bonding of cable sheaths [2] is neglected in this approach.

Another complex model based on the lumped pi approach is applicable, such as the

cross-bonded uniform-pi cable model evaluated by Nagaoka [39]. However it has the same

drawbacks in terms of frequency response. In addition, the sheath voltage is not accessible

at cross-bonding points of a minor section in this model since the cross-bonding is only

considered at the major sections. Another version is the exact-pi model [40], which has the

potential in characterising the frequency dependent effect of transmission lines. However,

for a wider frequency range, this model is not suitable as complications in relation to time

delays result in oscillating functions in frequency domain. Its higher order fitting as the

line length increases results in a considerably longer time taken for the solution in time

domain [41].

2.4.3 Distributed Parameter Travelling Wave Models

The distributed parameter travelling wave models have received much attention over the

pi approach. This is a result of most studies requiring a frequency-dependent approach

to be catered for in calculation. The Bergeron model [21, 31], for instance, represents the

inductance and capacitance of pi sections in a distributed manner. It is a simple constant

frequency method based on travelling wave theory. It incorporates travelling wave delays via

a simple equivalent circuit containing a current source and a constant resistance representing

16

the characteristic impedance. In other words, it is roughly equivalent to using an infinite

number of pi sections with a lumped resistance in the middle and at line ends to represent

losses. An early attempt by Dommel [25] to provide a frequency-dependent transmission

line model was based on this approach. His model forms the basis of the time domain

algorithm used in the development of transmission line models in EMTPTM. However, the

frequency response of Bergeron’s method is only good in the neighborhood of the frequency

at which the parameters are evaluated. It is not recommended for high frequency transient

studies [31].

Noda et al. [7], introduced an Auto-Regressive Moving Average (ARMA) model which

employed the method as a substitute for the existing method in approximating time do-

main convolution. As the modelling is directly performed in the phase domain, it avoided

the use of frequency-dependent transformation matrices. Furthermore, numerical effort is

minimised and stability is greatly increased. However, as the z-transform approach was

used, the resulting model is dependent on the time step settings (t) and is not directly

applicable for an arbitrary time step [42].

KC Lee and Semlyen models are amongst the other dedicated models incorporated in

EMTPTM [4, 11]. The KC Lee approach is suitable for the representation of untransposed

transmission lines. For underground cables, it requires manual calculation of modal trans-

formation matrices [15]. However, as the constant parameter representation is assumed, the

heavily frequency-dependent nature of cable systems means that this method may not be

suitable. The Semlyen model, on the other hand, is theoretically suitable for a wide range

of frequencies. The recursive implementation of convolutions introduced has contributed to

the ongoing research in cable modelling because of the ability in reducing computational

efforts [4]. However, for underground cables, it is very poor in terms of stability of numerical

calculation as proven in recent studies [10].

L Marti [6] has implemented the frequency-dependent calculation of modal transforma-

tion matrices to his model which is suitable for cable systems. The formulation improves the

weakness encountered in the J Marti [5] model, especially for the case of strongly frequency-

17

dependent underground cables and untransposed transmission lines. Unfortunately, this

model is not currently available as a dedicated cable model in PSCADr/EMTDCTM. How-

ever, for certain cases of transient studies, the J Marti or FD-Mode model can be still used,

provided that a suitable frequency is specified for its transformation matrix [5, 31]. This

model will be further explored in Section 2.5 together with the ULM (FD-Phase model).

2.5 PSCADr/EMTDCTM Cable Models

Literature has shown that modelling the distributed nature and frequency-dependent char-

acteristics of underground cables are absolutely necessary in order to achieve better accuracy

of transient modelling. Two distributed parameter travelling wave models in PSCADr will

be treated in this section - the FD-Mode and FD-Phase models. Performance of these

models are to be compared and presented in Chapter 4.

2.5.1 The FD-Mode Model

This model is based on the theory developed by J Marti [5]. To account for the frequency-

dependent characteristics, the frequency-dependent quantities are calculated as discrete

functions in the frequency domain. This yields all variables represented as a function of

frequency. Figure 2.1 illustrates the frequency domain equivalent circuit comprising the

sending (node k) and receiving (node m) end terminals of FD-Mode model. Here, Ekhist

Figure 2.1: Single phase frequency domain equivalent circuit of FD-Mode model [27]

18

and Emhist are the wave transfer sources defined from the change of variables method [43]

used for the simplification of mathematical modelling. For example, they can be represented

as forward travelling wave functions at both sending (Fk) and receiving (Fm) ends by

Ekhist = (Vm + ZCIm)e−γℓ = Fme−γℓ (2.7)

Emhist = (Vk + ZCIk)e−γℓ = Fke

−γℓ (2.8)

where ℓ is the total length of the cable. Whereas, the propagation function, A, as a function

of frequency is described by

A(ω) =1

cosh[γ(ω)ℓ] · sinh[γ(ω)ℓ]= e−γ(ω)ℓ (2.9)

Figure 2.1 depicts a general line model in terms of the characteristic impedance function,

ZC , and the propagation function, A, with the equivalent transfer sources [27,31]. However,

the time domain model is preferred since it is directly compatible with the time domain

solution algorithm in EMTP-type program. Therefore, the time domain form of (2.7) and

(2.8) are evaluated from convolution integrals as

Ekhist(t) =

∫ ∞

τ

fm(t − u)a1(u)du (2.10)

Emhist(t) =

∫ ∞

τ

fk(t − u)a1(u)du (2.11)

The time domain of the propagation constant, a(t) is obtained from inverse Fourier trans-

form and has the form as illustrated in Figure 2.2. The lower limit of the integral, τ ,

is the travel time and is calculated using the phase constant, β (imaginary term), of the

propagation function. Evaluation of the convolution integrals are greatly accelerated using

the recursive convolution [4]. Unlike the constant parameter model, where the constant

parameter lossless line is considered, the characteristic impedance, ZC , in this approach is

synthesised in the frequency domain with an R − C network with constant Rs and Cs.

19

Further details on the evaluation of variables for this model are described in [5], whereas,

detailed explanation on how these variables are implemented in EMTDCTM can be found

in [31].

Figure 2.2: Weighting function from J Marti formulation [5]

So far, the formulation of this model has been discussed for a single line representation.

For the case of polyphase lines (or cables), which are mutually coupled, the variables are

firstly decoupled by means of modal decomposition theory [36] using (2.12), (2.13) and

(2.14).

[Vphase] = [Tv ] · [Vmode] (2.12)

[Iphase] = [Ti] · [Imode] (2.13)

[T ]Tv = [T ]−1i (2.14)

The voltage and current variables can be solved individually in the modal domain which is

identical to the treatment of a single phase line. The modal transformation matrices ([Tv ]

and [Ti]) for matrix diagonalisation used in (2.12) and (2.13) are obtained from eigenvalue

problem and are calculated using cable constant (CC) routines in PSCADr/EMTDCTM.

Consequently, as constant transformation matrices are assumed in this formulation, user

should specify suitable constant frequency for these matrices in PSCADr/EMTDCTM [16].

20

2.5.2 The FD-Phase Model

The FD-Phase approach avoids the matrix diagonalisation and the formulation in modal

domain that occurs in FD-Mode model. Based on the theory by Morched et al. [8], the

formulation of variables is carried out in the phase domain. From the literature, emphasis

has been given to the treatment of the propagation function and characteristic impedance

as they have strong influences on the behaviour of transients in cables. Hence, the critical

part in this formulation is an accurate fitting of the propagation matrix transfer function

(represented as H(ω)) and characteristic admittance (represented as YC(ω)) in the frequency

domain so that the well-known recursive convolution technique [4] can be employed. The

time domain solution of this model is given by (2.15) [8],

YC ∗ V − i = 2

n∑

k=1

H ′k(t − τk) ∗ ifar (2.15)

where V and i are the voltage and current respectively, τk is the travelling time and ifar is

the reflected current wave of the receiving end. H ′k denotes the modal component of H(ω).

Solution for (2.15) requires H(ω) and YC(ω) to be replaced by a low order rational function

approximation to permit a recursive implementation of convolutions [4]. Fitting of YC is

a straightforward task as it has no time delays and it can be fitted directly in the phase

domain using Vector Fitting (VF) [44] as

esτiHmi (s) =

N∑

m=1

cm

s − am(2.16)

However, fitting of H(ω) is quite difficult as its elements contain modal contributions with

widely different time delays. Firstly, a frequency-dependent transformation matrix is used

to calculate its modes. Then, each mode is fitted using (2.16). Finally, with known values

of poles and time delays from modes, each element of H(ω) is fitted of the form [8]

h(s) =

Ng∑

i=1

(N

∑

m=1

cm,i

s − am,i

)e−sτi (2.17)

21

This model is general and theoretically accurate for most overhead lines as well as widely

different modal time delays as found in underground cables. Further detail on the general

aspects of this model are described in [8] and its implementation in PSCADr/EMTDCTM

can be found in [31,41].

2.6 Analysis of Switching Transient Overvoltages

The preceding sections so far described the modelling related problems of an underground

cable. Selection of a proper model is crucial in transient modelling in achieving better accu-

racy, particularly at higher frequencies. In addition to this work in studying the behaviour

of transients in electrical systems, this section will further explore the transient overvoltage

distributions due to cable energisation. The most accurate cable model will be selected

(presented in Chapter 4) for this purpose and detailed analysis is presented in Chapter 5.

The information will be useful for future consideration on design of the protective levels in

relation to this class of cable systems.

2.6.1 An Overview of Statistical Switching Studies

Switching overvoltage studies are of primary importance in electric power insulation co-

ordination. Their role has been widely researched [13, 14, 45, 46]. Studies are normally

performed with particular interest in avoiding breakdown, or minimising transient stress on

the insulation systems as well as the transmission and distribution equipment. In general,

characterisation of overvoltage stress may be performed by the following means [18]:

• the maximum peak values;

• a statistical overvoltage of the peak values;

• a statistical overvoltage value generated by particular events with a peak value that

has a 2 % probability of being exceeded.

Simulation using a reliable cable model is one of the approaches that can be used to obtain

such data. Other than a dedicated simulation approach, the particular general considera-

22

tion which is confirmed by different measurements in field also can be adopted. The latter

method has been used in [46] in studying the influence of the cable length and type of

insulation compound on the risk of insulation failures on MV and HV lines. Some statis-

tical switching studies have also been performed in EMTP-type simulators such as a large

scale statistical switching analysis by Lee and Poon [13] and case studies on the impact

of protective devices carried out in [14]. In the case of a long, cross-bonded cable system,

studies on the overvoltage sensitivity stress on the insulation can be found in [45]. Some

general and specific modelling guidelines in relation to switching overvoltage studies are

also provided [47,48].

2.6.2 Switching Phenomena and Statistical Methods

Switching surges are random in nature as they are affected by many different factors. Two

factors to be further investigated in this work are:

1. The pole span of the circuit breaker (CB) which refers to the time between the first

and the third pole to close.

2. The point-on-wave (POW) of switching angles on the 3-phase closure.

In practice, the breaker poles will not close simultaneously. There will be a small time

gap between poles during the 3-phase closure. The high speed closing of contacts and

their closing times are governed by their mechanical tolerances. Normally, the difference

between the first pole and the third pole to close, especially in extra high voltage (EHV)

and ultra high voltage (UHV) systems, fall in the order of 3 ms to 5 ms [12]. A smaller gap

is expected from medium transmission voltage such as 132 kV system based on the analysis

of measurement data of reference [15].

The second parameter considered is the closing angle, which refers to the point-on-wave

where the CB starts to close. If a contact initiates a close at the peak of the power frequency

(50 Hz) voltage, the corresponding phase will experience higher transient magnitude. Arcing

(pre-strike) might also occur and affect the behaviour of the transient at the circuit breaker

23

terminals. Furthermore, strong coupling effects between phases can cause unexpected high

magnitude and frequency overvoltages. Controlled switching [12], for example, may be used

to make sure closing of contacts at the zero crossings of the power frequency voltage. In

this closing practice, the deviation in pole closing times on 3-phase closing should be small

enough to prevent the pre-strike phenomena. Otherwise, pre-insertion resistors should be

used instead, which cost more [49].

Due to the random behaviour of CB poles during switching, probability analysis is the

most practical way in providing useful data on switching overvoltages. In practice, there

are several analytical methods [50]. However, the statistical study approach is the most

common. Random closing of contacts can be assumed to follow the normal distribution.

Statistics are applied to switching data to derive relevant information suitable for insu-

lation coordination. Cumulative probability distribution of overvoltages is calculated and

compared with the ability of the system to withstand transient overvoltages. An analysis

of several statistical switching evaluation techniques can be found in [51]. Some guidelines

such as the procedures and the reference values are included in the IEC standards [17,18].

For example, the diagram illustrated in Figure 2.3 may be useful.

Figure 2.3: Range of 2 % slow-front overvoltages at the receiving end due to line energisationand re-energisation [18]

Please see print copy for image

24

2.7 Summary

This chapter presented an overview of the behaviour of transients due to switching ope-

ration on transmission systems. The development of EMTP-type simulation programs was

reviewed with focus given primarily on cable modelling issues. In Section 2.6, the importance

of switching studies was addressed. Of particular interest is in providing relevant data for

the evaluation of insulation coordination and protective schemes for the network.

Over the last 30 years, interest has been primarily focused on the accuracy of trans-

mission line modelling. In other words, underground cable models have not been as ex-

haustively examined and validated as their overhead line counterparts. Furthermore, it is

unclear whether more sophisticated models or simpler methods should be used for a ca-

ble, particularly, when considering modelling and simulation of high frequency behaviour

of transients of underground cable system.

There are two common approaches currently in practice to represent a frequency-dependent

cable model. They are either the formulation in modes (FD-Mode model) or the direct for-

mulation in phase domain (FD-Phase model). Theoretical aspects of these models have been

presented. Literature review also highlighted the advantages of phase domain modelling over

the traditional modal domain approach. However, it is crucial to consider assessment of

both approaches particularly when a suitable model is intended to be used in a specific

network, such as the power system network under study.

The issues stated above are to be investigated by careful simulation, employing the FD-

Mode and FD-Phase models to validate their effectiveness against real-world behaviour.

Then, further studies may be performed on the energisation transient behaviour of a cable

using the most accurate model. The modelling work for such purposes is presented in

Chapter 3.

Chapter 3

PSCADr/EMTDC

TM Power System

Model Development

3.1 Introduction

The development of power system network model in PSCADr/EMTDCTM is explained in

this chapter. The majority of data used in this work has been obtained from [15] and [52].

However, conversion of the data from these sources has been made to make the data useable

as input to model described here. The construction of the cable model is the main criteria

in model development where treatment of cable layers is detailed to account for the effect

of semiconducting layers on the system transients.

In this chapter, the power system network located around the underground cable sys-

tem being considered is first introduced. Then, development of models for the power system

components such as a 132 kV source, double-circuit transmission lines and others are es-

tablished. Cable modelling is then presented with detailed dimensions and calculation of

its layered construction, material properties and configuration. Then, description of the

implementation of frequency-dependent models to represent the cable system is presented.

The simulation of preliminary PSCADr/EMTDCTM power system model is carried out

without considering the details of circuit breaker pole closing times as obtained from exper-

25

26

imental measurements. Simulation results obtained from preliminary model for FD-Mode

and FD-Phase approaches are presented and discussed.

3.2 Power System Network

Energising a long cable system is similar to the switching of a capacitive component. This

is due to the complex physical cable construction which has a predominantly capacitive

behaviour. Furthermore, transients developed are influenced by the non-linear characteris-

tics of system components in the vicinity. This means that amplitude, frequency and wave

shape of the current and voltage oscillations are determined by the configuration of the

network as seen from the terminals of switching devices. It is therefore of great importance

to include detailed modelling of these components. For example, as recommended in [53],

specific modelling should be considered on the surrounding network of at least up to one

bus back from the switching location.

The cable to be modelled with a frequency-dependent model is a 132 kV underground

high voltage (HV) cable linking Baulkham Hills transmission substation (BHTS) to Bella

Vista zone substation (BVZS) as illustrated in Figure 3.1 [15]. In this network, power

is supplied by a 132 kV source (upstream) through several kilometres of overhead trans-

mission feeders. Overhead lines are amongst the major components that characterise the

travelling surges from the switching of an underground cable. They are modelled using

the frequency-dependent approach. However, due to lack of detailed modelling data, other

frequency-dependent components such as transformers located near the switching point, are

represented as lumped parameter model. The source and capacitor banks are also developed

based on lumped element models and are included in the circuit. Further details on the

treatment of these components are presented in Section 3.3.

27

Figure 3.1: Single line schematic diagram of power system network under study

3.3 Power System Component Modelling

3.3.1 132 kV Upstream Power Source

From Figure 3.1, beyond the 132 kV source at Sydney West (SWTS) subsystem, there is a

330 kV bus stepped down by two transformers into 132 kV. It is assumed in this practice

that the 132 kV side at Sydney West is a voltage source with some source impedance.

To represent this source, three types of 3-phase voltage source models are available in

PSCADr/EMTDCTM [16]. Voltage source model-3 is not suitable in this exercise as it

permits only external control of voltage.

Based on available source parameter data, either voltage source model-1 or voltage

source model-2 can be used. Model-1 requires its positive and zero sequence impedance

data to be included as series components. While model-2 assumes parallel representation

of its positive and zero sequence impedance values. Care should be taken when selecting

model-1 as the zero sequence parameters need to be included manually using R and L

components attached (at terminal) in series behind the source. Use of the voltage source

model-2 requires conversion of series parameters (valid at 50 Hz) given in the data book [52]

to form the parallel connected R−L circuit. Both parallel and series connected R−L source

28

models have been used in the simulations, where it was noted that the difference between

the results obtained is marginal as will be demonstrated in Section B.1 of Appendix B.

In this work, source model-2 was used to represent the 132 kV upstream voltage source of

the network in Figure 3.1. The values of positive and zero sequence parameters (resistance,

Rp, and inductance, Lp values at 50 Hz) in the parallel circuit can be obtained from series

sequence components (Rs and Ls) using the following expressions

Rp =R2

s + (ωLs)2

Rs(3.1)

Lp =R2

s + (ωLs)2

ω2Ls(3.2)

where ω, is the angular frequency. Table 3.1 provides the input data for the voltage source

model-2, whereas calculation details of sequence impedances are given in Appendix B (Sec-

tion B.1).

Table 3.1: Source model input data of voltage source model-2

Page Input data Values1 Configuration

- Source name Src1- Source impedance type R//L- Source control fixed- Base MVA (3-phase) (MVA) 100- Base voltage (L-L, RMS) (kV) 132- Base frequency (Hz) 50- Voltage input time constant (s) 0.002- Impedance data format RRL values- Specified parameters Behind the source impedance

2 Positive sequence Rrl- Resistance (parallel) (Ω) 0.4513- Inductance (parallel) (H) 0.0000883

3 Zero sequence Rl- Resistance (parallel) (Ω) 0.3048- Inductance (parallel) (H) 0.0001015

4 Source values for fix control- Voltage magnitude (L-L, RMS) (kV) 132- Frequency (Hz) 50- Phase (deg) 0.0

29

3.3.2 Transmission Lines

For the transmission lines, there are four, double-circuit pairs, twin-conductor overhead

feeders included in the circuit model. Two of them connect Sydney West transmission

substation and Blacktown transmission substation (BTTS) busbars and are approximately

10 km in length. Another set is from Blacktown (BTTS) to Baulkham Hills transmission

substation which is about 5 km in length, while approximately 7 km lines also connected

from Baulkham Hills to Carlingford transmission substation (CFTS). They are supported

by double circuit steel towers (DCST) each having a height of approximately 12 to 23 metres

above the ground [52].

Modelling of these lines can be performed in several ways in PSCADr/EMTDCTM. It

depends on the availability of input data as well as the expected study results. A simple

overhead line model can be established employing a double circuit pi section. However,

in taking into account the frequency dependence effect using frequency-dependent models,

more detailed line input data may be required. Either manual entry of sequence impedance

data or details of tower data may be entered to perform a more complex overhead line

model.

In this work, as no suitable pre-defined tower model is available, the universal tower

model was used. The overhead line input data was used by the line constant (LC) calcula-

tion routines for the calculation of line impedance and admittance matrices. Also, in this

work, the FD-phase model has been selected to represent transmission lines because it is

more general and recommended by PSCADr/EMTDCTM [16]. Appendix B (Section B.1)

provides details of the input data for all four sets of transmission lines. Figure 3.2 illustrates

the overhead line geometry data input as used in PSCADr/EMTDCTM.

30

Figure 3.2: Overhead line representation in PSCADr/EMTDCTM

3.3.3 Transformer and Capacitor Bank

In modelling the effect of distribution transformers to switching transients, the high fre-

quency model should be used. However, due to inadequacy of available data, the default

three-phase, three-winding model in PSCADr/EMTDCTM was used to represent the trans-

formers at Baulkham Hills transmission substation.

The effects that the transformer has on the system transient is a significant problem

and has been widely discussed. High frequency transformer model is either modelled using

a detailed internal winding model or terminal model. Further details on the high frequency

modelling of a transformer can be found in [54–56].

There are also shunt capacitor banks installed at the secondary side of each transformer

at Baulkham Hills transmission substation. They are modelled as an equivalent capacitor

to ground. In theory, this lumped model again may not have significant influence on the

behaviour of the transient as the frequency might extend up to the order of tens of kilohertz.

The parameter calculation for including the model of transformers and capacitor banks at

Baulkham Hills busbars (sending end of the cable) is included in Appendix B (Section B.1).

31

3.4 Underground cable

3.4.1 Physical Construction and Material Properties

Modelling of the 132 kV underground cable system has been the main task of this thesis

and it has been carefully treated to account for the frequency-dependent effects and wide

frequency variations of underground cable energisation transients.

The cable is an XLPE type, single core (copper) conductor of 630 mm2 cross-sectional

area. To model the layers and properties that closely resemble a cable in a real system,

the measurement of the radial thickness of the cable has been based on the data stated by

manufacturer (see Appendix B (Section B.2)) and that from the cable sample. Figure 3.3

shows the cross-section of the cable sample, and Table 3.2 gives the radial measurements of

the various layers.

Figure 3.3: Cable cross-section

Table 3.2: Cable layers radial measurements

No. Layer Radius (m)1 Core conductor 0.015252 Inner ins. – semiconducting carbon loaded XLPE 0.016753 Pure XLPE 0.035254 Outer ins. – semiconducting carbon loaded XLPE 0.037255 Copper wire screen (Sheath) 0.039756 Aluminium foil 0.040257 PVC inner serving 0.042758 HDPE outer serving 0.04525

32

The values in Table 3.2 have been used to calculate the capacitance between cylindrical

shells to validate the existing measurements based on example given in [28] (Equation (10)).

It has been found that the new capacitance value was approximately 10 % lower than the

value given by the manufacturer. Apparently in this case, a smaller value of the thickness of

the layer has been provided by the manufacturer. Therefore, from this example, it is impor-

tant to consider measurement of cable layers from both the data stated from manufacturer

and a cable sample.

However, the data given in Table 3.2 are not the final input data required. For the con-

ductor and insulator properties, as well as the sheath radius, it is also necessary to convert

the existing data to a new set of data to account for inner and outer semiconducting layers

and the air gaps that exist within the stranded core. This is a crucial procedure in the tran-

sient simulation of a cable since cable constant (CC) routines in PSCADr/EMTDCTM [31]

only perform calculations based on a simplified configuration of a coaxial cable (detailed

in Appendix A (Section A.2)). It has also been shown that these additional layers have

a significant impact on the wave propagation characteristics in cable system [28]. Figure

3.4 depicts a geometrical representation of a coaxial cable in PSCADr/EMTDCTM. From

Figure 3.4, it is apparent that the cable core is treated as a solid conductor (1st conductor)

rather than stranded wires with air gaps. Similarly, the sheath is represented as a tubu-

lar conductor (2nd conductor). To account for such physical conditions the corrected core

resistivity value, ρ1, can be calculated using (3.3) [28]

ρ1 =ρcπr2

1

A(3.3)

where ρc=1.678E-8 Ωm is the original core resistivity value for copper and A is the cross-

sectional area of the conductor. Similarly for the relative permittivity of XLPE insulator,

ε1, it can be calculated with (3.4)

ε1 =C ln r2

r1

2πε0(3.4)

33

Figure 3.4: Cable input data in PSCADr/EMTDCTM

where C is the cable capacitance as stated by manufacturer and ε0=8.854E-12 F/m. The new

sheath radius, r3, when considering it as a tubular conductor can be obtained from (3.5) [28]

r3 =

√

Ash

π+ r2

2 (3.5)

where Ash is the total cross-sectional area of cable sheath as stated by manufacturer. The

thickness of outer layers (PVC and HDPE) has been measured to be approximately 5 mm.

Therefore, the new value for the 2nd insulator was approximated as 0.043087 m. Values

for the sheath resistivity, ρ2, and the relative electrical permittivity of 2nd insulator, ε2,

remain unchanged as in [15], while the relative magnetic permeability was assumed to be

identical for all layers (µr=1). Table 3.3 depicts the final converted data entered into

PSCADr/EMTDCTM cable model. Impedance (z) and admittance (y) matrices are calcu-

lated by CC routines based on the geometrical and physical properties input data entered

by user. The supporting routines were originally developed based on the simplified coaxial

cable geometry model where details can be found in [34,35].

34

Table 3.3: Cable dimensions and material properties input data

Layer OuterRadius, (m)

Resistivity,(Ωm)

Relative electricalpermittivity

Relative magneticpermeability

Conductor, r1 0.01525 1.946E-8 11st insulator, r2 0.03725 3.052 1Sheath, r3 0.038087 1.678E-8 12nd insulator, r4 0.043087 3.125 1

3.4.2 Cable Configuration

The three, single core cables are buried underground in ducts in a ‘tre-foil’ configuration

as displayed in Figure 3.5 (b). This arrangement is a common practice in HV cables and

is preferred over the flat arrangement, in order to minimise the electromagnetic coupling

effects between conductors. The measurement details of their arrangement are as shown in

Figure 3.5 and Table 3.4 displays the final values of X and Y co-ordinates of all phases.

Table 3.4: Cable coordinates input data

Cable C1 Cable C2 Cable C3

X position (m) 0 0.11 0.22

Y position (m) 1.1985 1.0075 1.1985

The ground resistivity was assumed at 100 Ωm based on default value in PSCADr/EMTDCTM.

It was approximated based on Carson’s homogeneous earth formula [57]. Users can select

either analytical approximation or numerical integration for the solution to the ground

impedance integral. It is recommended to use the analytical approximation due to time

savings and numerical stability. However, if accuracy is concerned, the latter option can be

selected instead [16].

There are more than two joints along the cable route. Therefore, cross-bonding is a

practice for this cable to further minimise transient stress on the joints introduced by cir-

culating current within the sheaths and cable core. Cross-bonding configuration of sheaths

are divided into two major sections as illustrated in Figure 3.5. Each cross-bonded minor

section is terminated by sheath voltage limiters (SVL), which are grounded with the equi-

valent earthing impedances (RSV L). Major sections are directly earthed and represented

35

as resistance to ground (Rmat) for the corresponding substation’s ground mat. The selec-

tion of adequate rating for SVLs and ground resistance values are explained in [2]. The

hypothetical representation of the cross-bonding of the cable and physical configuration of

phases as depicted in Figure 3.5 is adopted from [2,15].

Figure 3.5: Cross-bonding and configuration of the cable

3.5 Inclusion of FD-Mode and FD-Phase Models in the Simulation

3.5.1 Frequency-dependent Parameter Settings

As described in Chapter 2 (Sections 2.5.1 and 2.5.2), accurate modelling of frequency-

dependent systems require evaluation of propagation and surge impedance (or admittance)

transfer functions in the frequency domain. This is achieved through the curve fitting (CF)

algorithm which calculates the poles and zeros of the cable transfer function according to a

known frequency. An explanation on how this program works can be found in [31].

36

In PSCADr/EMTDCTM, the user can freely change some parameters of the curve

fitting algorithm to adapt to the specific requirements. For instance, frequency range can

be defined for the operation of curve fitting. By default, the range is set between 0.5 Hz and

1 MHz. It is important to note that the choice of the lower frequency limit has an influence

on the line or effective conductance of the cable. The number of poles can also be set

based on the simulation requirement. The total number of poles used in the calculation will

depend on the maximum allowed error (in percent) between curves set by the user. Once

the program uses all the poles, a constant approximation will take place for all remaining

higher frequencies.

Another important feature is the least squares weighting factor. It can be set for three

different frequency ranges; 0 to 50 Hz, 50 Hz and 50 Hz to higher. The user can set which

frequency range should be emphasised for more precise calculation. Each factor can be set

as any number (default=1) which implies that the higher the factor, the smaller the error

will be.

The main difference in the implementation of FD-Phase and FD-Mode models is the

specific frequency increment setting required by the FD-Phase model, while for the FD-

Mode model, a constant frequency needs to be specified for the operation of the modal

transformation matrix [16]. This clearly shows the difference between these two models, as

different assumptions are used in the handling of frequency-dependent modal transformation

matrix. In this case, it is possible in the FD-Phase model to set frequency increments of

up to 1000 frequencies (lowest setting is 100 frequencies), which means that cable constants

(CC) will perform the curve fitting for 1000 frequencies equally spaced on a log scale.

For the FD-Mode model, the constant transformation matrix was set to be approximated

in the order of tens of kilohertz. This value was based on previous experience in measurement

that the frequency range extends up to several tens of kilohertz during energisation of cables

in unloaded condition [15]. Care should be taken in setting-up the curve fitting parameters

as instability in the simulation may occur. For example, highly demanding requirements

might slow down the simulation and generate more error warnings. The log file should

37

always be checked as a guide for settings and also to ensure a stable simulation.

3.5.2 Simulation Step Size and Simulation Time

In the determination of adequate solution time step, it is known from Figure 3.5 that the

shortest cable length (referring to shortest cable section defined in model) is approximately

0.855 km. In typical cables, depending on the surge impedance of the cable, the surges will

travel at about half the speed of light which is approximately 1.5×108 m/s. Therefore, the

choice of an appropriate simulation time step should be below 5.7 µs. In this case, 0.1 µs was

used. Accordingly, as the performance of these models will be assessed by comparison with

existing measurement data of the current energisation transient [15], the simulation time

was set to run for 30 ms. This was achieved by simply employing the ‘snapshot’ feature

which allows switching after a stable run (when power frequency voltage peak reached

approximately√

2√3· 132 kV). The output data for the simulation using preliminary power

system model is then processed in MATLABr which is discussed in Section 3.6.

3.6 Results from Simulation of Preliminary PSCADr/EMTDCTM Model

The modelled power system network up to this stage is considered as a preliminary model

since the simulation was performed without the inclusion of details replicating the real

energisation test (as from measurement data). The purpose of simulation is to validate

the stability of the constructed power system model. Observation has been made as to

the behaviour of current and voltage transients during cable energisation. Identification of

potential areas of improvement for the existing model was also sought.

In the simulation, simultaneous closure of the circuit breaker was assumed. Steady

state power was supplied to the downstream with no loads connected at the terminating

connection of the cable as well as at the substation busbars. The cable was then energised by

switching the CB at the sending end at Baulkham Hills transmission substation. Figures 3.6

and 3.7 depict the current transient of each phase predicted by FD-Mode and FD-Phase

models respectively at the instant of switching. From these figures, identical waveforms

38

0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1Simulated current transients of preliminary FD−Mode model ( [ T ] = 10kHz)

0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1

Cur

rent

(kA

)

0 0.005 0.01 0.015 0.02 0.025 0.03−1.5

−1−0.5

00.5

11.5

Time (s)

Figure 3.6: Simulated blue (top), white (middle) and red (bottom) phase current transientsof preliminary model using FD-Mode approach with modal [T ] set at 10 kHz

0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1Simulated current transients of preliminary FD−Phase model

0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1

Cur

rent

(kA

)

0 0.005 0.01 0.015 0.02 0.025 0.03−1.5

−1−0.5

00.5

11.5

Time (s)

Figure 3.7: Simulated blue (top), white (middle) and red (bottom) phase current transientsof preliminary model using FD-Phase approach

39

are observed from both models with only a small deviation (approximately 2 %) of the

transient peak magnitudes for each phase. The transient envelope also decays almost at the

same time in approximately 15 to 20 ms.

Referring to the point-on-wave closing of the CB poles on the respective phases, as in

this case, red phase power frequency voltage was at the highest magnitude compared to

blue and white counterparts. Also, during this instant, blue and white phase instantaneous

magnitudes were negative values. It is evident from these waveforms that the situation is

similar to the behaviour of transients for the case of switching of a capacitor bank [20].

For FD-mode model, it is important to approximate the modal transformation matrix

accurately. For example, as can be seen in Figure 3.8, current transients seem largely dif-

ferent compared to the waveforms in Figures 3.6 and 3.7, where all phases exhibit relatively

higher transient magnitudes. The overvoltage transient at Baulkham Hills transmission

substation is also simulated which is displayed in Figure 3.9. It is clear that the overvoltage

magnitudes, especially of the red phase, rise to nearly 200 kV (1.86 pu).

0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1Simulated current transients of preliminary FD−Mode model ( [ T ] = 50 Hz)

0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1

Cur

rent

(kA

)

0 0.005 0.01 0.015 0.02 0.025 0.03−1.5

−1−0.5

00.5

11.5

Time (s)

Figure 3.8: Simulated blue (top), white (middle) and red (bottom) phase current transientsof preliminary model using FD-Mode approach with modal [T ] set at 50 Hz

40

0 0.005 0.01 0.015 0.02 0.025 0.03−200

−100

0

100

200Simulated BHTS busbar voltage during cable energisation (FD−Phase model)

Time (s)

Vol

tage

(kV

)

Figure 3.9: Overvoltage transients at the sending end of the cable

In the real-world, simultaneous closure of CB contacts rarely occur. There will be small

time gaps between them. The simulation model will be further refined, to include CB pole

closing times that closely match the actual measurement condition. The simulated wave-

forms will be analysed by comparison with measurement data. Furthermore, the frequency

response of each model will be extensively investigated in Chapter 4.

3.7 Summary

In this chapter, the test system for the analysis of FD-Mode and FD-Phase models was

developed. Of primary importance is the frequency-dependent behaviour of system compo-

nents. Accordingly, careful treatment of the underground cable network has been presented.

Particular care was taken in accounting for the effects of semiconducting layers on the sys-

tem transients.

Results from the preliminary simulation indicate the general behaviour of transients

developed which are very similar to the case of switching of a capacitor bank. They also

revealed the general characteristics of FD-Phase approach which is much more consistent

over a wide range of frequencies. FD-Mode model, on the other hand, requires careful

selection of its constant frequency for approximation of the modal transformation matrices.

In Chapter 4, the model is to be further refined to match the real-life behaviour for

the case of switching of an underground cable. The key points include incorporation of

pole switching times of CB and also identification of suitable constant frequency modal

41

transformation of FD-Mode model. For both models, curve fitting (CF) parameters are to

be optimised for better accuracy along with a stable run of simulation program.

Chapter 4

Cable Energisation Transient

Behaviour and Assessment of

Cable Models

4.1 Introduction

The preceding chapter highlighted the treatment of system components in the considered

power system network to develop a sufficiently accurate model in PSCADr/EMTDCTM.

Based on the preliminary model simulation results, some suggestions arise. Particularly,

for the underground cable model, employing the FD-Mode approach would require an ap-

propriate constant frequency to cater for precise operation within the expected frequency

range. On the other hand, FD-Phase model is more general which enables calculation over

a wide range of frequencies. In addition, inclusion of these cable models should be organ-

ised carefully, particularly in the selection of suitable parameters for the curve fitting (CF)

algorithm to avoid unnecessary warning errors and instability in the simulation.

This chapter explains procedures undertaken during cable energisation tests carried out

in August 2007. The measured current transient data are analysed to select one suitable set

of results to be used as a benchmark for the purpose of detailed comparison with simulation

42

43

outcomes from each cable model. Taking into account several issues discussed in Chapter 3,

the power system model is modified accordingly, such as incorporating the pole switching

times of the circuit breaker (CB). For the FD-Mode model, a suitable frequency for constant

modal transformation matrix is also determined. Analysis of results from both cable model

simulations is then presented and compared with measurement data. The main criteria

includes the ability of the models to predict the following:

• Transient amplitudes in time domain.

• Transient envelope times in time domain.

• Frequency domain response.

4.2 Experimental Energisation Tests

4.2.1 Measurement Method

A suitable measuring probe is necessary for the measurement of high frequency current

transients. For the case under study, it should be able to detect the current transients

within the range of up to at least several tens of kilohertz based on the information provided

in [20]. Despite a number of measurement transducers available, the Rogowski coil offers a

range of benefits. It is an ideal apparatus for measuring high frequency current transients,

as it provides an isolated current measurement which does not load the measured circuit.

This high-current transducer has an excellent bandwidth comparable to other measurement

transducers such as the coaxial shunt. For example, the one used in this project has the

capability of measuring current transients of up to 50 kHz, which is considered sufficient for

this test. During the test, two Rogowski coils were attached to the blue and white phases,

close to the CB at Baulkham Hills substation. The overall test set-up is as illustrated in

Figure 4.1.

For the test procedure, the cable was first isolated by opening the sending and remote

end circuit breakers. Then, the loads at sending and remote end busbars were also dis-

connected to reduce their impact on the transient waveforms to be observed. A period of

44

Figure 4.1: Diagram illustrating cable energisation test set-up

time (approximately 10 minutes) was used to allow the capacitive elements to fully dis-

charge. Finally the sending end circuit breaker was closed to energise the cable and the

resulting high frequency current transients data were recorded. An oscilloscope was used

for recording the data. The sampling rate was set at 250 kHz. A total of four energisation

tests were performed. Analyses of these waveforms are presented in Section 4.2.2.

4.2.2 Measured Current Transient Waveforms

The measured blue and white phase current transients from the four energisation tests

undertaken are as displayed in Figure 4.2. As seen from Figure 4.2, all waveforms exhibit

high current magnitudes in the order of 500 A to nearly 1000 A. At the instant of switching,

the phase with higher instantaneous voltage magnitude is likely to force the current to rise

higher than the other phases. The peak values are also dependent on several other factors

such as the degree of electromagnetic coupling among cables, trapped-charge in cables,

pre-strike phenomena as well as mechanical influences inherent in the CB.

Under normal operating conditions, multiple transient stresses may be felt by cables and

nearby system components due to the varying nature of system parameters. The impact of

transients from energisation and re-energisation of cables is introduced by many direct and

indirect factors such as periodical maintenance, system faults, fault clearing, load rejection

45

−0.05 0 0.05 0.1 0.15 0.2−1000

−500

0

500

1000Blue and white phase current transients (test 4)

Cur

rent

(A

)

−0.05 0 0.05 0.1 0.15 0.2−1000

−500

0

500

1000

Time (s)

Cur

rent

(A

)

−0.05 0 0.05 0.1 0.15 0.2−1000

−500

0

500

1000Blue and white phase current transients (test 2)

Cur

rent

(A

)

−0.05 0 0.05 0.1 0.15 0.2−1000

−500

0

500

1000

Time (s)

Cur

rent

(A

)

−0.05 0 0.05 0.1 0.15 0.2−1000

−500

0

500

1000Blue and white phase current transients (test 1)

Cur

rent

(A

)

−0.05 0 0.05 0.1 0.15 0.2−1000

−500

0

500

1000

Time (s)

Cur

rent

(A

)

−0.05 0 0.05 0.1 0.15 0.2−1000

−500

0

500

1000Blue and white phase current transients (test 3)

Cur

rent

(A

)

−0.05 0 0.05 0.1 0.15 0.2−1000

−500

0

500

1000

Time (s)

Cur

rent

(A

)

Figure 4.2: Blue (top) and white (bottom) phase current transients from each measurement

for example. The transient envelope for these tests decays at a repeatable rate. This time

is within approximately 10 ms. The system damping depends on the portion of resistive

elements in the circuit. After approximately 30 ms, the 50 Hz charging current is recorded to

be in the average of 21 A (cable length is approximately 5.6 km long). This data correlates

well with the data quoted by manufacturer which is around 3.7 A/km.

46

4.2.3 Data for Comparison

Based on an analysis of suitability of data in Figure 4.2, the third set of test data was

used as a benchmark for comparison with results simulated from FD-Mode and FD-Phase

models (presented in Section 4.4). It was chosen since the transient peak magnitudes and

the transient envelope times were at the average values. It also has minimal impact in terms

of mechanical influences from the circuit breaker.

The details of the blue and white phase current transient data are depicted in Figure 4.3.

In Figure 4.3, the signals are displayed for 30 ms following the energisation of the cable.

The transient envelope time for the blue phase is approximately 13 ms whereas the white

phase transient envelope is seen to last 10 ms. The blue phase current magnitude peak is

713 A whereas the white phase shows a peak approximately equal to 527 A. Lower peak

magnitude for the white phase current is due to the lower instantaneous voltage magnitude

at switching. The waveforms seem naturally distorted due to strong electromagnetic cou-

pling effects between phases. The mechanical influences from CB contacts are also obvious,

for example, chatter bounce is seen to interfere with the transient waveforms which occur

at time approximately 2 ms. These criteria are to be further discussed in Section 4.4.3.

0 0.005 0.01 0.015 0.02 0.025 0.03−1000

−500

0

500

1000

Time (s)

Cur

rent

(A

)

Measured blue phase current transient (test 3)

0 0.005 0.01 0.015 0.02 0.025 0.03−1000

−500

0

500

1000Measured white phase current transient (test 3)

Time (s)

Cur

rent

(A

)

waveform distorted naturally

impact of CB chatter bounce

Figure 4.3: Blue (top) and white (bottom) phase current transients from third measurement

47

It is also apparent that relatively high frequency transients are confined within the first

millisecond after energisation. At the instant of CB closure initiation, the blue and white

phase current amplitudes varied from zero to -587 A and -247 A respectively. This gives a

clear indication that the power frequency (50 Hz) voltage magnitudes of the blue and white

phases are negative values at the instant of switching. Such information is useful when

incorporating CB switching times in the simulation.

Other than the time domain comparison, the frequency response analysis of cable models

are also to be carried out. The intention is to measure the ability of models in predicting

the dominant peaks in the frequency spectrum. The energy spectral density (ESD) plots

of the current transient signals are provided. In theory, an accurate model should be able

to simulate the component frequency behaviour over the specified calculation range. This

analysis is based on evaluation methodology used in [10,15].

To prepare the frequency domain plots, it is necessary to avoid low frequency signals

from dominating the frequency spectrum. This is achieved by filtering the raw signals using

MATLABr with a third order high pass Butterworth filter with the cut-off frequency set

at 200 Hz. Frequency components below this boundary are then attenuated. It has been

established in [15], that the third order filter is deemed sufficient for this case. The filtered

waveform is then converted into the frequency domain by means of an FFT (Fast Fourier

Transform). The frequency spectrum of the corresponding blue and white phase current

transients are as illustrated in Figure 4.4. From Figure 4.4, it is evident that the frequency

spectrum of blue and white phase signals are dominant in the range of 250 Hz to 10 kHz.

The major peaks of signal energy in this range occur at 1.1 kHz, 1.8 kHz, 2.9 kHz and

5.8 kHz. Measured data (time and frequency domain plots) for the first, second and fourth

tests are included in Appendix C (Section C.1).

The major criteria of measured current transients discussed in this section are to be

compared with results obtained from simulation of both cable models. However, this data

was obtained from measurement in the field where the CB poles no longer behave in an

ideal manner. To include this behaviour in the simulation model, pole closing times were

48

102

103

104

105

0

10

20

30Blue phase frequency spectrum (test 3)

Frequency (Hz)

Mag

nitu

de

102

103

104

105

0

5

10White phase frequency spectrum (test 3)

Frequency (Hz)

Mag

nitu

de

Figure 4.4: Frequency spectrum of blue (top) and white (bottom) phase current transients

measured and analysed. The outcome of this analysis is presented in Section 4.2.4.

4.2.4 Analysis of the CB Pole Closing Times

Identification of the closing time for each pole during the cable energisation test is estab-

lished by measuring the line voltage at the secondary of voltage transformer (VT) located

at the sending end of the cable. The VT has the transformation ratio of 132 kV/110 V.

From analysis of the measured red-to-white and white-to-blue voltage waveforms and based

on [10], it is known that the red phase CB contact is the first to close followed by white

and blue phases. The related waveform with the corresponding pole switching times are as

illustrated in Figure 4.5. The instantaneous peaks are believed to be the times where the

contacts initiate their closure. The closing times are marked for the corresponding phase

poles. From this measurement, the time span between the first and third pole to close

is approximately 0.44 ms. Normally, in HV breakers, the maximum span can be up to 3

ms [12]. Pole closing times for the first, second and fourth measurements are displayed in

Appendix C (Section C.2).

49

−0.5 0 0.5 1 1.5 2 2.5 3

x 10−3

−400

−200

0

200

400

Time (s)V

olta

ge (

V)

Instantaneous line voltage (Vred−white) at secondary of VT (test 3)

4.574E−4 (blue)1.738E−5 (red)

3.894E−4 (white)

Figure 4.5: Determination of CB pole closing times from third energisation test

4.3 Model Refinement and Simulation

4.3.1 Implementation of CB Pole Closing Times to the Circuit Model

The preliminary power system model is modified in such a way that allows the CB pole

switching times to be applied. As explained in Chapter 3 (Section 3.5), snapshot file is

saved (at time t) after the steady state power frequency (50 Hz) voltage peak of each phase

reached the nominal value at√

2√3· 132 kV. Depending on the voltage input time constant

of the source model (set by the user), a stable running simulation may be achieved after

at least one cycle. In this simulation, the snapshot is recorded at the time t=0.0375 s, as

illustrated in Figure 4.6. This value is inferred based on the point-on-wave where the CB

initiates a close as observed in the measurement data. The magnitude and direction of

power frequency voltage of each phase at this instant is similar to the situation as described

in Chapter 3 (Section 3.6), where the blue phase is more negative than the white phase.

In general, it is difficult to anticipate the exact point-on-wave for the closure of the CB.

The technique used in this simulation is based on the available measurement data and

reference [10].

Figure 4.6: Establishment of CB pole closing times in PSCADr/EMTDCTM

50

4.3.2 Simulation

From measurement data, the current transients were recorded for approximately 30 ms after

the energisation. To capture points between zero to 30 ms, the simulation is re-run from

the snapshot file for about 30 ms. Another crucial aspect to be considered is the simulation

time step. Setting up a smaller time step may increase the degree of accuracy as more

points can be calculated. However, it results in a very slow simulation that sometimes

yields numerical instability and produces subsequent error messages. Based on guidelines

described in Chapter 3 (Section 3.5), the simulation time step of 0.1 µs is used and is

considered adequate for this simulation.

4.4 Comparison of Results Predicted by FD-Mode and FD-Phase Models

4.4.1 Simulation using FD-Mode Model

It is obvious from the example discussed in Chapter 3 (Section 3.6) that this model is ca-

pable of simulating high frequency transients provided that a suitable constant frequency is

selected for the model to calculate accurately the cable parameters. Therefore, the impor-

tant task in the inclusion of this model is the selection of suitable frequency for the modal

transformation matrix. Several frequencies ranging from 5 kHz to 30 kHz have been tested.

It was found that the model produces a consistent result for the frequencies ranging between

10 kHz to 20 kHz. Setting up a lower frequency than this range for modal transformation

resulted in excessively high current peaks. In contrast, a lower peak is produced for a con-

stant frequency higher than 20 kHz. This revealed one of the difficulties when incorporating

FD-Mode model. In this simulation, 15 kHz was deemed adequate for its operation.

Consequently, the maximum allowed fitting error for curve fitting (CF) calculation is

set to be as low as 0.1 % for both surge impedance and propagation transfer function.

Employing the model for ac cable generally requires accuracy at fundamental (assumed

50 Hz) and higher frequencies for transient analysis. This range is emphasised for accurate

calculation by setting up a constant value of 1000 for the weighting factor.

51

The time domain current transient results are as shown in Figure 4.7. In Figure 4.7,

the simulated blue, white and red phase current magnitudes are 751 A, 513 A and 1077 A

respectively. Accuracy in applying switching times ensures the blue phase peak is larger

than white phase peak in the simulation. Comparing these values to the experimental

data, especially of the blue and white phases, gives amplitudes of similar order for the

corresponding phases. The difference from measured values are around 5.1 % and 2.7 %

respectively for blue and white phases. Slight differences in the simulated and actual point-

on-wave at which each CB contact closes is one of the major criteria that governed the

behaviour of these transient peaks.

However, the transient envelope times varied significantly. The model approximated

the transient envelope to last 20 ms for blue phase and 15 ms for white and red phases

respectively. This indicates that system damping plays a significant role in dissipating the

energy arising from transients in cable energisation. For the case of measurement data, it

appears that there is still some amount of resistive load near the switching point (sending

end) which help the transients to decay faster. On the other hand, for simulated results,

no resistive components (loads) were added to the simulation model. As a consequence,

the magnitude of oscillation transients was diminishing naturally as a result of system

impedances mostly from the cable, overhead lines and other power system components.

Incorporating system loads is difficult due to their varying characteristics and often detailed

parameters are unavailable.

The consistency of this model is further verified by comparing frequency domain response

as illustrated in Figure 4.8. In this figure, the frequency spectrum seems very poor and

only several dominant peaks can be seen for each phase compared to the measured data

in Figure 4.4. The dominant peaks of blue, white and red phases only occur at 1.5 kHz,

2.2 kHz and 8.7 kHz which is clearly inconsistent with the dominant peaks of the measured

data.

52

0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1Simulated current transients of FD−Mode model ( [T] = 15 kHz )

0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1

Cur

rent

(kA

)

0 0.005 0.01 0.015 0.02 0.025 0.03−1.5

−1−0.5

00.5

11.5

Time (s)

Figure 4.7: Simulated blue (top), white (middle) and red (bottom) phase time domaincurrent transients using FD-Mode model

102

103

104

105

0

0.2

0.4Frequency spectrum of current transients of FD−Mode model

102

103

104

105

0

0.1

0.2

0.3

Mag

nitu

de

102

103

104

105

0

0.1

0.2

0.3

0.4

0.5

Frequency (Hz)

Figure 4.8: Frequency spectrum of simulated blue (top), white (middle) and red (bottom)phase current transients using FD-Mode model

53

4.4.2 Simulation using FD-Phase Model

The FD-Phase model is more general and suitable for a wider range of frequencies. It

may be used for modelling underground dc and ac cables, and is theoretically suitable to

be used for overhead lines of asymmetrical configuration. The advantage of this model

over the FD-Mode model is its flexibility as no constant transformation matrix needs to be

specified. It is directly formulated in the phase domain and assumes frequency dependence

of the internal transformation matrix [16]. Therefore, only the curve fitting (CF) algorithm

parameter needs to be carefully specified for consistent operation of this model.

For the CF controls, this model is set to operate between the range of 0.5 Hz to 1 MHz

(default). Within this range, the cable constant (CC) routines calculate around 500 frequen-

cies spaced evenly on a log scale. A weighting factor is specified to emphasise calculation

around fundamental and higher frequencies which is the same values set for the FD-Mode

model. The maximum fitting error for approximating the surge admittance and propaga-

tion function is set to be as low as 0.8 %. An attempt has been made to set a lower error,

however the model resulted in a significant error in numerical calculations due to unstable

poles [58]. Furthermore, considerably longer run times were required for the solution. The

current transient plots approximated using this model are depicted in Figure 4.9.

The waveforms as seen in Figure 4.9, exhibit identical shape, amplitudes and transient

envelope times compared to the simulated results from FD-Mode model. This implies

good agreement of the modal transformation setting for FD-Mode model at 15 kHz. From

Figure 4.9, the transient envelope times of blue and white phases are around 20 ms and

15 ms respectively. Consequently, the transient peak magnitudes predicted are 736 A,

514 A and 1086 A for blue, white and red phases respectively. This reveals the consistency

of this model, which is only slightly different to amplitudes obtained from measured data,

specifically of the blue and white phases. Only around 3.1 % (blue phase) and 2.5 %

(white phase) deviation to the peaks is observed compared to measurement data. This

discrepancy is explained by the dissimilarity of the point-on-wave closure of CB contacts

between simulated and what actually occurs under experimental test.

54

0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1Simulated current transients of FD−Phase model

0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.5

0

0.5

1

Cur

rent

(kA

)

0 0.005 0.01 0.015 0.02 0.025 0.03−1.5

−1−0.5

00.5

11.5

Time (s)

Figure 4.9: Simulated blue (top), white (middle) and red (bottom) phase time domaincurrent transients using FD-Phase model

102

103

104

105

0

0.2

0.4Frequency spectrum of current transients of FD−Phase model

102

103

104

105

0

0.1

0.2

0.3

Mag

nitu

de

102

103

104

105

0

0.1

0.2

0.3

0.4

0.5

Frequency (Hz)

Figure 4.10: Frequency spectrum of simulated blue (top), white (middle) and red (bottom)phase current transients using FD-Phase model

55

Referring to the frequency response of this model based on the frequency domain plots

displayed in Figure 4.10, it again reveals an inconsistency of this model in predicting domi-

nant peaks for simulated current signals. The resonant peaks are at 1.5 kHz, 2.2 kHz and

8.7 kHz, which are similar to the case approximated by FD-Mode model. Again, there

would appear to be no commonality regarding dominant peaks relative to the measured

data. The discrepancies observed from simulated data of FD-Mode and FD-Phase models

are further discussed in Section 4.4.3.

4.4.3 Implication from Measured and Simulated Data

The simulated data from both models have been practically compared with measured cur-

rent transients resulting from energisation of a 3-phase underground cable. Two major

parameters have been considered for the comparison in the time domain to asses the ability

of models to predict transient amplitudes and the corresponding transient envelope times.

In general, both models give a stable and consistent current transient (especially the peak

magnitudes) with no numerical instabilities for the 30 ms simulation as shown in Figures 4.7

and 4.9. Both models, especially the FD-Phase model, demonstrated a good agreement for

the steady state charging current which is approximately between 19 A and 21 A as illus-

trated in Figure 4.11.

Figure 4.11: Steady-state 50 Hz charging current predicted by FD-Phase model for thecable under test (5651 m long)

However, the wave-shape of simulated data differed considerably from those observed

in the measurement data. The frequency response is also very poor with small number of

dominant frequencies as seen in simulated data. These discrepancies can be explained using

56

several considerations.

Firstly, the strong coupling effects between cables at high frequencies exist, for example,

the impact of cable sheath and conductor on the system transients. At high frequencies,

a cable exhibits strong capacitive behaviour due to the distributed capacitances between

sheath and conductor. Furthermore, when it comes to energising a 3-phase cable, the

conductors and sheaths of all cables are mutually coupled. Increasing the frequency, results

in strong electromagnetic coupling which, as a result, affects the evaluation of the impedance

(z) and admittance (y) matrices of the cable.

The second factor may be due to the existing trapped charges in the cable. As described

in Section 4.2.1, before the cable was energised, it had been isolated for approximately 10

minutes to allow capacitive discharge. In this case, the capacitive energy may not be

completely diminished. This would alter the overall behaviour of transients as seen in

measurement data.

There are also influences from the CB, for example, the arc between the CB contacts.

In this case, there is a tendency for arc to occur at any time between the contact start to

close and its final closure. This phenomena is also known as pre-strike which depends on

the closing speed of CB contacts. Further information regarding this factor can be found

in [49]. Another possibility is the mechanical influences. However, it is beyond the scope of

this study and is not of interest in this work.

Finally, another possible factor is the impact of the frequency-dependent nature of dis-

tribution transformers. It is difficult to model the frequency-dependent transformer be-

haviour. Complexities are pronounced at higher frequencies as the non-linear characteristics

significantly increase due to an increase in frequency. Therefore, transient behaviour affected

by transformers in the vicinity can be modelled provided that both non-linear behaviour

and its frequency-dependent effects are taken into account. These approaches unfortunately

have been neglected due to the unavailability of data such as the nameplate information.

Figure 4.12 shows a useful example of a high frequency transformer model. Using this

model, the winding lumped stray capacitance and the phase to ground capacitance values

57

can be obtained using frequency scan features in PSCADr/EMTDCTM [16].

Figure 4.12: High frequency transformer model suitable for 50 Hz - 20 kHz frequencyintervals [56]

The factors discussed greatly influence the measured current transients in Figure 4.3.

In reality, a large number of frequency components exist, particularly within the first 1 ms

following the energisation. When closely analysed the behaviour of current transients seen

in Figure 4.3, the blue phase current tends to respond and rise quickly at the instant of

white phase contact closure. Such phenomena unfortunately failed to be duplicated by the

simulation model. However, based on the comparison from available data, it is apparent

that the FD-Phase approach is more suitable to simulate energisation transient of the cable.

This is purely because of the ability to predict transient magnitudes more accurately.

4.5 Overvoltage Transient Behaviour for the System Under Study

The short duration current transient produced, as in the case of cable energisation, might

also produce corresponding voltage transients. Considerable transient stress can be felt

across the main insulation of the cable and also the outer casing due to induced voltages.

Transients introduced along cable sheath are also severe which, in many cases, requires

the use of sheath voltage limiters. Suitable surge arresters are normally installed at either

sending or receiving end of cable and sheath or both. Similarly, they are also found in cross-

Please see print copy for image

58

bonded ‘link boxes’ to divert the travelling surges in sheaths of a long cross-bonded cable

systems. The selection of rating of surge arrester and sheath bonding or grounding design

on cables are dictated by parameters set by either manufacturer or the relevant electricity

authority.

To enable analysis of overvoltage behaviour, instantaneous voltages are measured at cer-

tain points within the power system network under study. The simulation was performed

using FD-Phase cable model. Figure 4.13 depicts the voltages across main insulation mea-

sured at sending and receiving ends of the cable near the circuit breakers.

0 0.005 0.01 0.015 0.02 0.025 0.03−200

−100

0

100

200

Time (s)

Vol

tage

(kV

)

Simulated sending end overvoltage transients

0 0.005 0.01 0.015 0.02 0.025 0.03−200

−100

0

100

200Simulated receiving end overvoltage transients

Time (s)

Vol

tage

(kV

)

Figure 4.13: Overvoltage transients at sending and receiving end terminals

From Figure 4.13, once the cable is energised, the surge impedance and the open circuit

end of the cable result in heavily modal reflections causing a large increase in the sheath

voltages. Insulation systems near the switching point (sending end) are subject to a tran-

sient voltage magnitude of the red phase of approximately 181 kV (1.68 pu), whereas at

the receiving end, the voltage rises to a peak of 190 kV (1.76 pu). The travelling surge

continuously propagates within the network up to several kilometres away from switching

point. As can be seen in Figure 4.14, significant amounts of transient also can be measured

at Blacktown and Carlingford transmission substations. However, they are completely at-

tenuated before arriving at Sydney West.

59

0 0.005 0.01 0.015 0.02 0.025 0.03−200

0

200

Time (s)

Vol

tage

(kV

)

SWTS busbar voltage

0 0.005 0.01 0.015 0.02 0.025 0.03−200

0

200

Time (s)

Vol

tage

(kV

)

BTTS busbar voltage

0 0.005 0.01 0.015 0.02 0.025 0.03−200

0

200

Time (s)

Vol

tage

(kV

)

CFTS busbar voltage

0 0.005 0.01 0.015 0.02 0.025 0.03−200

0

200

Time (s)

Vol

tage

(kV

)

BHTS busbar voltage

Figure 4.14: Busbar voltages during cable energisation

Voltages are also induced within the cable sheath. Figure 4.15 shows an example of

instantaneous sheath voltages. In this example, without arresters, the charging current from

main conductor (red phase at approximately 1000 A) causes the induced voltages to rise to

nearly 10 kV. With arresters (rated at 3 kV), some current has been conducted to ground,

thus minimising the voltages to around 6 kV. The magnitude depends on the instant on the

voltage waveform at which the CB contacts close electrically. The higher the instantaneous

voltage, the higher the overvoltage amplitude that will be induced. In practice, evaluation

of insulation co-ordination, and protection schemes is studied by performing a number of

60

energisations over the entire voltage cycle so that the actual peak values can be determined.

Depending on the specific requirement, statistical approaches may be used to evaluate the

required parameters. This method will be further studied in Chapter 5.

0 0.002 0.004 0.006 0.008 0.01−10

−5

0

5

10

Time (s)

Vol

tage

(kV

)

Sheath voltages with SVL turned off

0 0.002 0.004 0.006 0.008 0.01−10

−5

0

5

10

Time (s)

Vol

tage

(kV

)

Sheath voltages with SVL turned on

Figure 4.15: Sheath voltages during switching with and without surge arresters

4.6 Summary

The general behaviour of transient due to energisation of a 132 kV underground cable

considered in this work was studied. A primary issue was to assess the relative merits and

suitability of the frequency-dependent cable models in PSCADr/EMTDCTM. The existing

power system network used for simulation, has been extensively modified to account for the

sensitivity of CB poles during the switching operation. FD-Mode and FD-Phase models

were then included in the replicated network to represent the underground systems.

Inclusion of both cable models has revealed the difficulty in incorporating FD-Mode

model compared to FD-Phase approach. In other words, when incorporating FD-Mode

model to represent the transmission system, the user should know the operating frequency

intervals in order to achieve better accuracy. In this work, it is a straightforward task

since such data are available. However, in the case of limited access to actual measurement

61

data, particularly the expected frequency range, FD-Phase model can be an alternative.

Furthermore, the FD-Phase model was found to give better performance when comparing

the time domain results with measured data. This reveals the suitability of FD-Phase model

especially for studying the high frequency transients on underground cables.

However, inconsistencies have been found in both models in predicting the actual wave

shapes as well as the frequency domain response. Possible discrepancies that contributed

to this situation have been raised and discussed. Apparently in this case, accurate power

system modelling in studying high frequency transients phenomena requires detailed know-

ledge of system parameters. However, often such details are unavailable and in some cases

impractical to obtain such as the system load values during the test. The issues discussed

in Section 4.4.3 are to be further improved in future work.

The impact of energising underground HV cables is of primary interest in electric power

insulation co-ordination and designing protection schemes. Simulation data (based on re-

sults from FD-Phase model) has revealed the direct impact of induced transients on the

insulation systems within the network under study. The behaviour of overvoltages (magni-

tudes) developed are influenced by many factors, but strongly dependent on the point-on-

wave closing of the circuit breaker. The related issues regarding the evaluation of switching

overvoltages are to be presented in Chapter 5.

Chapter 5

Analysis of Overvoltage Stress due

to Cable Energisation

5.1 Introduction

The switching problems associated with cable energisation involve studies that account for

large bandwidth of frequency variations where the cable parameters significantly vary within

that range. Therefore, a detailed model for the cable, such as the distributed parameter

travelling wave model with frequency-dependent approach, should be incorporated in the

simulation. Such models are assessed by practical means as presented in Chapter 4. In gene-

ral, FD-Phase model can be reliably used for instances when the behaviour of overvoltage

magnitudes are intended to be analysed statistically.

It has been established, from the literature, that the behaviour of transients depends

strongly on the network configuration and the characteristics of the switching operation.

The latter is of interest and to be further analysed in this chapter. The study of the sensitiv-

ity of the distribution of transient magnitudes as a function of circuit breaker (CB) charac-

teristics is practically carried out according to a probability approach. Statistical methods

are applied to the switching data following the guidelines such as those given by IEEE

PES Switching Transients Task Force [53]. Useful information is then provided accordingly

62

63

following the recommendations given by the insulation co-ordination standards [17,18].

This chapter first provides an overview of statistical switching studies. The approaches

used in this work are also introduced. Then, network refinement is presented to incorporate

multiple run features to the existing test system. Finally, the results obtained from the

approaches used are analysed, especially the relevant data that may be useful for distribution

system engineers as well as researchers for future planning and design of possible protective

levels related to this class of cable systems.

5.2 An Overview of Switching Transient Evaluation Methods

Switching of a 3-phase CB involve some degree of uncertainty since all poles do not close

simultaneously. In addition, the poles do not always close in the same sequence but are

randomly distributed for every single switching action. The transient voltage magnitudes

generated are also based on the point-on-the-voltage-wave where the contacts initiate a close.

With the help of digital computers and available mathematical tools, several approaches

can be used in the evaluation of switching surges. Common practices found so far can be

categorised as:

• Statistical study approach

• Statistical maximisation approach

• Optimisation approach

The first approach is the most preferred method based on probability concepts and

is adopted in this work. Detailed explanation of the other two approaches can be found

in [50]. In the statistical study approach, statistics are used to evaluate the switching

surges to obtain relevant data such as those suggested by IEC standards for insulation

coordination [18]. The range of values required include the maximum value, 2 % probability

value, mean amplitude as well as the standard deviation. Scattering characteristics of CB

poles, normally assumed as normal distribution (Gaussian), are applied over the full cycle

64

(20 ms) on the voltage wave. The statistical study has proven to be reliable in many

cases including studies on large scale networks [13, 14]. Martinez et al. [51] provide a

comparison of statistical switching results evaluated using several statistical methods such

as the Systematic switching and Gaussian distribution. The latter is an available feature

in PSCADr/EMTDCTM that can be used readily. However, a similar approach to the

systematic switching technique can be applied manually and is detailed in Section 5.3.1.

5.3 Simulation Approaches

5.3.1 First Approach (Deterministic)

In this approach, closing time is varied sequentially from a minimum to a maximum instant

in uniform increments of time. In other words, the pole closing times from each set of

experimental energisation tests are applied uniformly over the duration of one 50 Hz cycle

(full cycle of power frequency voltage). Table 5.1 summarises the four sets of CB pole closure

schemes extracted from measurement data. Total number of overvoltage data generated

will be based on the incremental time step settings. In this case, with incremental time of

0.1 ms, each set of test will generate 200 overvoltage data sequences for a complete cycle of

the power frequency voltage.

Table 5.1: CB pole switching times and maximum span from each test

Tests Phase-A (ms) Phase-B (ms) Phase-C (ms) Max. pole span (ms)

Test 1 0.0095 0.0655 0.1295 0.12Test 2 0.0168 0.5288 0.5968 0.58Test 3 0.0174 0.3894 0.4574 0.44Test 4 0.0173 0.7652 0.8332 0.82

There is also the uncertainty of the pole closing sequence. 3-phase energisation results

in up to six combinations of phase A, B and C poles of each test in Table 5.1. In general,

at least 100 simulations, each using a different set of CB closing times are recommended for

the statistical evaluation of overvoltages [48].

65

5.3.2 Second Approach (Probabilistic)

The randomness of CB poles can be described practically using a probabilistic technique.

This approach is similar to the statistical switches [51], defined as the variation of closing

times applied randomly according to a given probability distribution. In this case, random-

normal distribution (Gaussian) [16] is employed with the curve truncated within the range

of −3σ and 3σ as illustrated in Figure 5.1.

Figure 5.1: Gaussian distribution curve [51]

In this technique, there are two steps involved before the final energisation samples

(data) can be obtained. Firstly, the ‘aiming point’ is established from a random number

(voltage magnitude) generated from simultaneous closure (σ = 0.0) of CB poles over the

full cycle. Assuming closing times are sectionalised by 1 ms, around 20 random number

of peak magnitudes are obtained. Secondly, a new generation is applied in the specified

aiming point to obtain the statistical overvoltage data according to a normal distribution.

The energisation at this aiming point is assumed to generate over 100 samples of peak

magnitudes from random closing times (of each contact). The maximum spans, which is

the time between the first and final contact to close on 3-phase, are varied for the case of

1 ms, 2 ms and 3 ms. These values correspond to nominal span found mostly in high voltage

circuit breakers.

66

5.4 Model Refinement and Simulation

The parameters of the system components and underground systems of the existing power

system network model remain unchanged. However, a larger solution time step is used (1 µs)

to avoid excessive simulation times. This is reasonable since only voltage magnitudes are

of interest. As given in Table 5.2, less than a 1 % deviation (slightly lower) of overvoltage

magnitudes is obtained compared to the 0.1 µs time step setting.

Table 5.2: Red phase magnitudes for different simulation time step

Simulation time step (µs) 0.1 0.5 1

Magnitude (pu) 1.6822 1.6788 1.6700Deviation (%) 0 0.321 0.725

The CB contact timings in Figure 4.6 (Chapter 4) are modified in such a way to make

use of the multiple run component. The multiple run system is programmed to generate

and process the energisation samples. In general, the system allows up to 6 input variables

that can be modified according to a user preference such as the sequential, list, random-flat

or random-normal distribution [16]. It is possible to record up to 6 channels for every run

and a maximum of 10,000 samples can be saved. Auto processing of output data also can

be applied such as the maximum or minimum values.

5.4.1 Implementation of Deterministic Approach in Simulation

Implementing the deterministic approach, requires a sequential run of a fixed time variable

(input V 1 of Figure 5.2) representing pole closing times for each test in Table 5.1. Each

set of pole closing scheme is applied over the full cycle of the power frequency voltage (for

20 ms starting from snapshot time). A total of 6 combinations of pole closing sequence will

generate 1200 energisations for each test. This results in 4800 overvoltage peak magnitudes

(absolute values) recorded for all four set of energisation schemes. Both sending (Vk) and

receiving (Vm) end voltages are measured as illustrated in Figure 5.2.

67

Figure 5.2: An example of implementation of deterministic approach for 3rd energisationscheme

5.4.2 Implementation of Probabilistic Approach in Simulation

In general, it is an unrealistic and time consuming procedure to carry out energisations

anywhere within the full cycle. This is due to peak magnitudes only being produced at

particular point on the voltage wave for each phase [51]. Therefore, the first step in this

technique is to identify the worst switching time (defined as ‘aiming point’) for further

analysis. Sequential run (Figure 5.2) is firstly performed by setting up breaker poles to

close simultaneously (2nd and 3rd pole times equal to zero). The simulation is run from

snapshot file at t = 0.0375 s being set as offset with incremental time of 1 ms. The resulting

overvoltage distribution is presented in Table 5.3. From Table 5.3, it is obvious that the

maximum overvoltage magnitudes are produced when the CB is closed at 1 ms, 8 ms, 11 ms

and 18 ms respectively. Therefore, based on this result, 1 ms is chosen as the aiming point

for further analysis.

Also, in this approach, the input signal is not fixed. Three input variables (V 1, V 2

and V 3) are used to represent phase-A (blue), phase-B (white) and phase-C (red) poles

respectively. The input signals are randomly applied within the specified aiming point

according to random-normal distribution. In the simulation, a total of 125 energisations

are generated from each pole span setting.

68

Table 5.3: Sending end voltage magnitudes from simultaneous closure of CB

Magnitudes (pu)Closing time (ms) Phase-A Phase-B Phase-C Maximum (pu)

1 1.069 1.261 1.719 1.7192 1.120 1.356 1.615 1.6153 1.153 1.570 1.373 1.5704 1.151 1.691 1.088 1.6915 1.263 1.659 1.081 1.6596 1.509 1.472 1.206 1.5097 1.691 1.139 1.308 1.6918 1.708 1.086 1.385 1.7089 1.559 1.044 1.503 1.55910 1.257 1.114 1.680 1.68011 1.069 1.261 1.719 1.71912 1.120 1.356 1.615 1.61513 1.153 1.570 1.373 1.57014 1.151 1.691 1.088 1.69115 1.263 1.659 1.081 1.65916 1.509 1.472 1.206 1.50917 1.691 1.138 1.308 1.69118 1.708 1.086 1.385 1.70819 1.559 1.044 1.503 1.55920 1.257 1.114 1.680 1.680

5.5 Analysis of Overvoltage Data from Simulation

A three phase energisation produces switching overvoltages on all three phases of the cable.

Every single switching operation produces three phase-to-ground with the corresponding

phase-to-phase overvoltages. Based on the guidelines given by IEC 60071-2 [18] standard,

there are two methods currently used in practice:

Phase-peak method: The highest peak value of the overvoltage of each phase-to-ground

or between each combination of phases is taken into account.

Case-peak method: Only the highest peak value of peak magnitudes (either phase-to-

ground or phase-to-phase) generated from all three phases is collected.

In this study, only phase-to-ground overvoltages have been measured at both the sending

and receiving ends of the cable being energised. Both recommended methods are feasible

since the voltage is measured at each individual phase. The data are statistically calculated

by means of multiple run systems and then processed in MATLABr to obtain the statistical

plots. The following section provides results based on the approaches considered.

69

5.5.1 Results from Deterministic Approach

Figure 5.3 compares frequency of occurrence of overvoltage magnitudes obtained from each

energisation scheme. In general, according to [48], the larger the pole span, the more prone

the overvoltage peaks at the CB terminals are to increase up to the high levels. In contrast,

simultaneous close of circuit breaker poles is likely to introduce relatively lower overvoltage

peaks. However, from Figure 5.3, the trend is seen to be distinctly different. Smallest pole

span of Test 1 produces higher overvoltage peaks rather than the larger gap applied in the

case of Test 4. This deficiency is expected due to the inaccuracy of power system model

used to simulate the high frequency phenomena, particularly, the strong coupling effects

between phases, which has been detailed in Chapter 4 (Section 4.4.3). However, only 1.5 %

1 1.2 1.4 1.6 1.8 20

10

20Sending end peaks (Test 1)

1 1.2 1.4 1.6 1.8 20

10

20Receiving end peaks (Test 1)

1 1.2 1.4 1.6 1.8 20

10

20Sending end peaks (Test 2)

1 1.2 1.4 1.6 1.8 20

10

20Receiving end peaks (Test 2)

1 1.2 1.4 1.6 1.8 20

10

20

Fre

quen

cy o

f occ

urre

nce

(%)

Sending end peaks (Test 3)

1 1.2 1.4 1.6 1.8 20

10

20

Fre

quen

cy o

f occ

urre

nce

(%)

Receiving end peaks (Test 3)

1 1.2 1.4 1.6 1.8 20

10

20

Magnitude (pu)

Sending end peaks (Test 4)

1 1.2 1.4 1.6 1.8 20

10

20

Magnitude (pu)

Receiving end peaks (Test 4)

Figure 5.3: Frequency of occurrence of overvoltage peaks from deterministic approach(phase-peak method)

70

difference of sending end overvoltage peaks between the first and the fourth case can still

be considered as a small deficiency.

Based on the overall results of Figure 5.3, the significant overvoltage peaks for each

phase at sending and receiving ends are summarised in Table 5.4. At the sending end,

the highest overvoltage peak is 1.84 pu generated from the third case. Travelling wave

phenomena causes the most severe overvoltage peaks at receiving end when no loads are

connected. This is due to the superposition of voltage waves. For instance, the overvoltage

peak magnitudes, especially in the case of Test 1 and Test 2 energisation schemes, all fall

in the range of 2 pu. Overall, in all of the cases, the sending and receiving ends overvoltage

peak values fall between the range of 1.74 pu to 1.84 pu and 1.84 pu to 2.06 pu respectively.

Table 5.4: Significant overvoltage peaks from deterministic approach

Sending end peaks(pu) Receiving end peaks (pu)Tests Phase-A Phase-B Phase-C Phase-A Phase-B Phase-C

Test 1 1.80 1.76 1.77 2.04 2.06 2.01Test 2 1.79 1.80 1.82 2.01 1.97 2.00Test 3 1.84 1.80 1.78 1.96 1.95 1.88Test 4 1.77 1.75 1.74 1.86 1.84 1.88

5.5.2 Results from Probabilistic Approach

In the probabilistic approach, a more realistic method has been applied. In theory, the

random-normal distribution considered for the scattering effect of CB poles is more suitable

over the uniform or the systematic switching approaches. The frequencies of maximum

value of voltage magnitudes obtained are described using the probability density functions

(PDF) for each case of CB pole span as shown in Figure 5.4. From Figure 5.4, sending

end peak magnitudes fall in the average of 1.85 pu, 1.79 pu and 1.79 pu which occur at

the frequencies of 0.8 %, 1.6 % and 4 % respectively for the corresponding 1 ms, 2 ms

and 3 ms spans. Similarly at the receiving end, 1.6 %, 10 % and 16 % of the time, the

magnitudes tend to vary in the order of 2.05 pu, 1.98 pu and 1.99 pu for 1 ms, 2 ms and

71

1.4 1.5 1.6 1.7 1.8 1.9 20

10

20

30

40

50

Occ

urre

nce

(%)

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.20

10

20

30

40

50

1.4 1.5 1.6 1.7 1.8 1.9 20

10

20

30

40

50O

ccur

renc

e (%

)

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.20

10

20

30

40

50

1.4 1.5 1.6 1.7 1.8 1.9 20

10

20

30

40

50

Magnitude (pu)

Occ

urre

nce

(%)

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.20

10

20

30

40

50

Magnitude (pu)

0

0.2

0.4

0.6

0.8

1Sending end (1 ms span)

0

0.2

0.4

0.6

0.8

1

CD

F

Receiving end (1 ms span)

0

0.2

0.4

0.6

0.8

1Sending end (2 ms span)

0

0.2

0.4

0.6

0.8

1

CD

F

Receiving end (2 ms span)

0

0.2

0.4

0.6

0.8

1Sending end (3 ms span)

0

0.2

0.4

0.6

0.8

1

CD

F

Receiving end (3 ms span)

Figure 5.4: Sending and receiving ends probability density and the corresponding cumula-tive distribution curves for 1 ms, 2 ms and 3 ms pole spans studied based on probabilisticapproach (case-peak method)

3 ms spans respectively. It is obvious that higher magnitudes are obtained from smaller

pole span but the occurrences are very low. Inversely, larger pole spans are more prone to

produce a higher frequency of occurrences of relatively lower voltage magnitudes. Overall,

peak magnitudes are decreasing with increasing pole span settings. However, there is only

a very small percentage difference (overvoltages at sending end) in terms of the 1 ms span

and 3 ms span.

It is apparent that the results observed in Figure 5.4 are more realistic compared to the

deterministic approach as different pole span of CB can be considered. The consistency of

results from simulation can be increased by increasing the number of energisations for each

case. However the variation of pole span studied are based on maximum possible span of

CB in EHV and UHV systems [12]. In this case, the nominal pole span of the CB under

72

study (132 kV CB) is not certain due to unavailability of data from manufacturer. Based

on the data displayed in Table 5.1, the maximum span tends to vary between around 0.1 ms

to around 0.8 ms for each case respectively. Therefore, it is also crucial to consider the pole

span within the range quoted by measurement data since it represents the real situation.

Section 5.5.3 provide the results simulated using smaller pole span.

5.5.3 Results for the Pole Span below 1 ms

In this section, the data provided are based on the simulation of the probabilistic approach

using different breaker pole span ranging among 0.2 ms, 0.4 ms, 0.6 ms and 0.8 ms. It

postulates that the nominal span for the CB under study will vary within this range.

Otherwise, the information from Section 5.5.2 should be considered instead. The results

are as illustrated in Figure 5.5. In Figure 5.5, the sending and receiving end magnitudes are

found to vary between the range of 1.81 pu to 1.88 pu and 2.01 pu to 2.05 pu respectively

with higher frequency of occurrences. These ranges are distinctly higher than the data

quoted in Figure 5.4. Since, the pole span of 0.8 ms is considered close to the Test 4

energisation schemes of the first (deterministic) approach, comparing the related results of

this case gives a very small difference between the two approaches which is around 6 %.

However, the data from second technique (probabilistic) are recommended since they are

based on the approach which is closer to reality.

Based on the statistical information displayed in Figures 5.4 and 5.5, the relevant data

such as mean magnitudes, maximum magnitudes, standard deviation as well as 2 % proba-

bility values are deduced and summarised in Table 5.5.

73

1.4 1.5 1.6 1.7 1.8 1.9 20

10

20

30O

ccur

renc

e (%

)

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.20

10

20

30

1.4 1.5 1.6 1.7 1.8 1.9 20

10

20

30

Occ

urre

nce

(%)

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.20

10

20

30

1.4 1.5 1.6 1.7 1.8 1.9 20

10

20

30

Occ

urre

nce

(%)

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.20

10

20

30

1.4 1.5 1.6 1.7 1.8 1.9 20

10

20

30

Magnitude (pu)

Occ

urre

nce(

%)

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.20

10

20

30

Magnitude (pu)

0

0.2

0.4

0.6

0.8

1Sending end (0.2 ms span)

0

0.2

0.4

0.6

0.8

1

CD

F

Receiving end (0.2 ms span)

0

0.2

0.4

0.6

0.8

1Sending end (0.4 ms span)

0

0.2

0.4

0.6

0.8

1

CD

F

Receiving end (0.4 ms span)

0

0.2

0.4

0.6

0.8

1Sending end (0.6 ms span)

0

0.2

0.4

0.6

0.8

1

CD

F

Receiving end (0.6 ms span)

0

0.2

0.4

0.6

0.8

1Sending end (0.8 ms span)

0

0.2

0.4

0.6

0.8

1

CD

F

Receiving end (0.8 ms span)

Figure 5.5: Sending and receiving ends probability density and the corresponding cumula-tive distribution curves for the pole span below 1 ms (case-peak method)

74

Table 5.5: Relevant statistical information for different cases of pole span

Mean (pu) Max. (pu) Std dev. (pu) 2 % value (pu)CB pole span (ms) SE RE SE RE SE RE SE RE

0.2 1.69 1.90 1.90 2.07 0.09 0.12 1.88 2.150.4 1.65 1.85 1.82 2.06 0.1 0.12 1.85 2.100.6 1.67 1.86 1.85 2.08 0.09 0.10 1.86 2.080.8 1.67 1.85 1.88 2.03 0.08 0.09 1.84 2.051 1.65 1.85 1.87 2.07 0.09 0.10 1.85 2.052 1.64 1.84 1.81 2.00 0.08 0.10 1.81 2.043 1.62 1.82 1.82 2.02 0.11 0.13 1.84 2.09

Of all the results obtained, the 2 % probability values show that the overvoltages due

to cable energisation under current network are at the average level compared to common

cases indicated by IEC standard as displayed in Figure 2.3 (Chapter 2). Therefore, further

studies (to limit the transients) may not be required as the magnitudes, particularly at the

receiving end are not high enough to cause a problem.

5.6 Summary

The energisation of an unloaded cable system causes high overvoltage transients and stresses

the insulation systems. The worst scenario may be experienced for switching of a cable

which is located at the transition point of the overhead to underground system such as the

networks under study. The level of overvoltage experienced is governed by many factors, in

particular, the problems underlying sensitivity of CB contacts as well as the characteristics

of switching operation. In this case, attention has been given to the CB maximum pole

closing span as well as the point-on-wave where the contacts initiate their closure. Due

to statistical characteristics of these variables, it is important to calculate the overvoltage

values by means of statistical methods. Such studies are feasible by manipulating the

multiple run component in PSCADr/EMTDCTM.

Based on two approaches studied, the range of overvoltage magnitudes produced at

sending and receiving ends fall in similar order with slightly higher overvoltage magnitudes

obtained using the probabilistic technique. This revealed the consistency of two methodolo-

75

gies applied. However, probabilistic techniques are more practical as the random nature of

CB contacts can be assumed. It is also flexible because higher number of energisations can

be used to achieve more reliable and optimised overvoltage values. Thus, the data from this

technique are recommended.

According to the data from probabilistic technique, every single energisation at the point

of 1 pu (peak voltage magnitude), will generate approximately 2 pu overvoltage magnitudes

at the receiving end of unloaded cable. Overall, for the cases studied using different pole

spans, all produce transient overvoltage magnitudes at the average level compared to the

values indicated by IEC standard for particular cases of the field results and studies. In

other words, the range of values obtained are within acceptable level and considered to

comply with the standards.

Chapter 6

Conclusions and Recommendations

6.1 Conclusions

Switching problems have been a general concern among utilities in ensuring a consistent

quality of supply, reliability as well as continuous prevention from transients and protection

of system components in the networks. Energising a HV cable system introduces significant

voltage and current transients due to its complex construction, comprising sheath and other

semiconducting layers. Strong electromagnetic coupling among these layers and among the

conductors of 3-phase cable system causes cable parameters to vary significantly as frequency

increases. The impact of transients on insulation systems is vital when considering switching

operation at the transition point of overhead to underground transmission. Therefore,

studies on the switching transient behaviour should be carried out using an accurate model

to represent the cable system. Despite a number of frequency-dependent travelling wave

models provided, all of which can be used for modelling of an underground cable, they are

not always suitable for all cases. Such problems are addressed in two stages of studies of

major interest in analysing the behaviour of transients due to cable energisation.

Firstly, an investigation of the suitability of FD-Mode and FD-Phase models for under-

ground cable under study has been presented by comparing their ability to predict accu-

rately the energisation current transient in terms of magnitude, duration and the spectral

76

77

content. A power system network model that replicates the system under study has been

carefully crafted in PSCADr/EMTDCTM electromagnetic transient simulation platform.

Careful treatment of power system components including the underground cable to cater

for frequency-dependent nature of system transients has been given. In cable modelling,

detailed dimensions and calculation of its layered construction and material properties has

been presented. Cable system was then represented by FD-Mode and FD-Phase models.

The curve fitting (CF) parameters were adjusted for better accuracy for both frequency-

dependent cable models. The simulated results from these models have been compared with

the measurement data. It has been found that there is a very small difference in the perfor-

mance of two models as both are able to predict the current transient magnitude accurately

with fairly good agreement of the transient envelope times. However, no identical dominant

peaks are observed from both models when comparing their performance in the frequency

domain. Overall, of the results studied, the FD-Phase model showed several advantages

over the FD-Mode model. Specifically, the ability to simulate current transient magnitudes

more accurately. Furthermore, the difficulty in incorporating the FD-Mode model becomes

pronounced because a constant frequency for operation of the modal transformation matrix

required to be identified accurately. Conversely, such a problem does not exist for FD-Phase

counterparts as a frequency-dependent internal transformation matrix is assumed.

Secondly, the impact of transients introduced in a HV underground cable has been

further analysed, particularly the statistical distribution of peak magnitude overvoltages at

the sending and receiving ends of the cable respectively. This has been motivated by the

needs for analysis of the impact of circuit breaker (CB) contact closure which are random

in nature. The magnitudes of overvoltages depend strongly on the point-on-wave where the

CB closed and the influence of 3-phase CB pole span which is the time between the first and

the third pole to close. The existing model has been refined according to deterministic and

probabilistic simulation approaches. These approaches are constructed by manipulating the

multiple-run feature in PSCADr/EMTDCTM. The FD-Phase model has been incorporated

to represent the cable system. Results from both approaches revealed that energisation of

78

an unloaded cable at the point of 1 pu of power frequency voltage results in approximately

2 pu of overvoltages at the receiving end of the cable. At the sending end, the magnitudes

may increase to levels as high as approximately 1.8 pu. However, the data particularly of

the receiving end magnitudes obtained from both deterministic and probabilistic techniques

are still at the average level compared to typical values indicated by IEC standard. These

values are not high enough to cause a problem and further studies to limit the transients

may not be required. The data from probabilistic techniques are recommended as their

approach is closer to a realistic scenario.

The accuracy of results obtained depends on the accuracy of the system model as well

as the accuracy of available input data. In some situations, access to specific data of the

system components is limited. Therefore, the assumptions used are critical in gaining higher

accuracy in modelling and simulation.

6.2 Recommendations

Most of the problems arising from the network modelling were addressed in Chapter 4

(Section 4.4.3). It is apparent that one of the problems with the cable modelling is the

significant electromagnetic coupling effects between phases as well as between conductor

and sheath. To get rid of such effects, comparison of results for the case of single phase

energisation may be performed as an alternative. The problem in relation to the existing

trapped charges prior to energisation tests may be avoided by allowing longer time (more

than 10 minutes) when isolating the cable. Finally, a more improved and accurate model

of system components should be developed particularly for the distribution transformers at

the sending end busbars. References [54–56] may be useful as a guideline for such purpose

provided that the required details such as the nameplate data are obtained.

Appendix A

Fundamental Equations in Cable

Modelling

A.1 The General Transmission Lines or Wave Equations

The transmission line equations govern general two conductor uniform transmission lines,

including parallel plates, two-wire lines and coaxial lines. A cable section of x (x −→ 0)

shown in Figure A.1 is described by the parameters representing; r-resistance per unit

length, l-inductance per unit length, g-conductance per unit length and c-capacitance per

unit length. Consequently, rx and lx represent series elements, while gx and cx

represent the corresponding shunt parameters. These parameters are distributed along the

length of the conductor. In general, the line parameters are frequency-dependent where the

series impedance and shunt admittance can be represented as

z = r + jωl (A.1)

y = g + jωc (A.2)

where ω is the angular frequency. The frequency domain equation for voltage and current

drop along x section at any point of x can be written as (applying Kirchhoff’s voltage

79

80

Figure A.1: A x section of a coaxial cable

and current laws)

−dV

dx= zI (A.3)

−dI

dx= yV (A.4)

where V = V (x, ω) and I = I(x, ω). Equations (A.3) and (A.4) are referred to as Telegra-

pher’s equations. Combining these equations yields a set of coupled wave equations

−d2V

dx2= zyV = γ2V (A.5)

−d2I

dx2= yzI = γ2I (A.6)

where γ is the propagation constant which is a complex number defined as

γ = α + jβ =√

(r + jωl)(g + jωc) =√

zy (A.7)

The real part, α, is the attenuation constant in nepers/m and the imaginary part, β, is the

phase constant in radian/m. The wave propagation velocity is the fraction of frequency and

the phase constant given by

u =ω

β(A.8)

81

According to D’lambert’s solution, (A.5) and (A.6) can be given in the form;

V (x) = V +0 e−γx + V −

0 e+γx (A.9)

I(x) = I+0 e−γx + I−0 e+γx (A.10)

where e−γx and e+γx terms represent wave propagation in the positive and negative x direc-

tions respectively. Solving for the unknown voltage (V0) and current (I0) wave amplitudes

in (A.9) and (A.11) results in the definition of characteristic impedance, ZC , which is the

ratio of the voltage to the current amplitude of the travelling waves for each direction as

ZC =V +

0

I+0

= −V −0

I−0=

√

r + jωl

g + jωc(A.11)

A.2 Coaxial Cable Electrical Parameters

The basic geometry, comprising a series of concentric conductor and insulation sections,

are depicted in Figure A.2 where the second conducting element (sheath) is represented as

a third layer of the conductor [26]. For zero frequency, currents are uniformly distributed

Figure A.2: A simplified coaxial cable cross-sectional area

throughout the conductor. Simply, the resistance per unit length can be expressed as

Rdc =ρc

A(A.12)

82

where ρc is the resistivity of conductor and A is the cross-sectional area. However, for

ac, as the frequency increases, the non-uniformity becomes greater where the skin effect

becomes prevalent. With skin effect taken into account, the combined resistance, r (Ω/m)

and inductance, l (H/m) of both conductors per unit length of a coaxial cable in Figure A.2

are described as [26]

r =Rs

2π(1

a+

1

b) (A.13)

l =µ

2πln

b

a(A.14)

where Rs = ρc/δs is the intrinsic resistance (surface resistance) that is varying with fre-

quency and inversely proportional to their skin depth (δs). Consequently, the permeabi-

lity, µ, of the conductor is based on the free space permeability (µ0 = 4π × 10−7 H/m) and

the relative permeability (µr) of the material (i.e. µ = µ0µr).

At higher frequencies, there is a possibility of the current flow from inner conductor

through the insulator to the sheath. In the other words, the shunt conductance (g of the

insulation medium in S/m) may be taken into account because of the existence of shunt

resistance across the insulator. Similarly, there exists shunt capacitance (c of the two

conductors in F/m) as the inner and outer conductor work as two parallel plates along the

coaxial cable. Equations (A.15) and (A.16) describe these shunt quantities per unit length

respectively as [26]

g =2π

ρi lnba

(A.15)

c =2πε

ln ba

(A.16)

where ρi is the resistivity of the insulation material. The electrical permittivity, ε, is

influenced by free space permittivity (ε0 = 8.854×10−12 F/m) and the relative permittivity

(εr) of the material (i.e. ε = ε0εr).

83

A.3 Impedance and Admittance Matrices

The parameters of mutually coupled conductors in general are represented as NxN matrices

as given by (A.17) and (A.18) [16]. The ‘conductors’ refer to both the core and sheath,

which are treated as concentric conductors.

z =

z11 z12 . . z1N

z21 z22 . . z2N

. . . . .

. . . . .

zN1 zN2 . . zNN

(A.17)

y =

y11 y12 . . y1N

y21 y22 . . y2N

. . . . .

. . . . .

yN1 yN2 . . yNN

(A.18)

The diagonal term represent the self impedance per unit length of the loop formed by

conductors and concentric neutrals with ground return. The off-diagonal elements are the

mutual impedances between the respective conductors.

Appendix B

Power System Component Data

B.1 Input Parameter Calculation of Surrounding Components

In this section, calculation of input parameters for 132 kV source, overhead lines, trans-

formers and capacitor banks is given. The original data for these components has been

obtained from the TransGrid Electrical Databook [52] for the corresponding 132 kV systems

commissioned by Integral Energy (IE). Some additional data for cable and transmission lines

are based on the data provided in [15].

To establish the source model, three types of 3-phase voltage source models are available

in PSCADr/EMTDCTM. However, only source model-1 and model-2 are suitable because

source model-3 requires external control of voltage. The main difference between model-1

and model-2 is the connection of sequence impedances (positive and zero sequence) which is

represented in series and parallel form respectively. Table B.1 provides conversion of source

impedance values from the data book [52].

84

85

Table B.1: Calculation of sequence impedances for voltage source model-1 and model-2

Parameter Values Remarks

System base values:-– SLLrmsBase (MVA) 100– VLLrmsBase (kV ) 132

– ZBase (Ω) 174.24V 2

LLrmsBase

SLLrmsBase

– ω (rad/s) 314.16 2πfPositive/Zero sequence impedance:-– Z+% (% on 100 MVA), Angle, θ (deg) 0.0159, 86.4– Z0% (% on 100 MVA), Angle, θ (deg) 0.0183, 84Physical values:-

– Z+ (Ω) 0.0277Z+%

100 ZBase

– Z0 (Ω) 0.0317 Z0%

100 ZBase

Series impedance values (source model-1):-– R+ (Ω) 0.0017 Z+ cos θ

– L+ (mH) 0.0880 Z+sinθω

– R0 (Ω) 0.0033 Z0 cos θ

– L0 (mH) 0.1004 Z0sinθω

Parallel impedance values (source model-2):-– R+ (Ω) 0.4513 refer Eq. (3.1)– L+ (mH) 0.0883 refer Eq. (3.2)– R0 (Ω) 0.3048 refer Eq. (3.1)– L0 (mH) 0.1015 refer Eq. (3.2)

The impact of using either of these two source models on the system transients has been

verified. As can be seen from Figure B.1, only a small difference is noted between the current

transients obtained using the source models. The difference in the peak magnitudes is less

than 1 %. Therefore, either model-1 or model-2 can be used in the simulation. It is also

evident that the source impedance parameters have little impact on the current transients.

This can be attributed to the location of the upstream source which is more than 15 km

away from the origin where the switching takes place.

86

0 0.002 0.004 0.006 0.008 0.01−1

0

1

Time (s)

Cur

rent

(kA

)

Blue phase current transients simulated using source model−1 and model−2

model−1 (series)

model−2 (parallel)

Figure B.1: Energisation current transients of the blue phase of FD-Phase model at sendingend using different source models

Input data for overhead lines are given in Tables B.2 and B.3. Figure B.2 illustrated

the coordinates of all conductors and ground wires.

Table B.2: 132 kV overhead line general data

Feeder name93A/93Z 9J1/9J2 9J3/9J4 930/931

Total length (km) 10.243 10.219 5.470 7.370From SWTS SWTS BTTS BHTSTo BTTS BTTS BHTS CFTS

Owner IE IE IE IEPhase conductor type olive/moose olive/moose moose mooseEarth conductor type opal opal opal opal

Table B.3: Conductor and ground wire data

Specification Input data

Conductor name moose/oliveNumber of conductors 6Conductor radius (m) 0.013

Conductor DC resistance (Ω/km) 0.1Number of sub-conductor in bundle 2

Bundle configuration symmetricalBundle spacing (m) 0.38

SAG for all conductors (m) 5Ground wire name opal

Number of ground wires 2Ground wire radius (m) 0.00653

Ground wire DC resistance (Ω/km) 2.9SAG for all ground wires (m) 5

87

Figure B.2: Overhead line conductor co-ordinates

There are four (132/33/11 kV) 3-phase three winding transformers with star-star-delta

configuration at Baulkham Hills transmission substation which are connected in parallel to

the busbars. Conversion of data is made to represent all parallel connected transformers

into only one transformer with equivalent leakage impedance (positive sequence leakage

reactance). The original reactance data from the data book (in percent on 100 MVA) have

been converted into pu values required by the simulation program. The final data are as

given in Tables B.4 and B.5.

Table B.4: Transformer general data

HV (#1) MV (#3) TV (#2)

Sbase (MVA) 100 100 100Vbase (kV) 132 33 11VLN (kV) 76.21 19.05 11

Zbase 174.24 10.89 1.21Winding star star delta

Table B.5: Transformer positive sequence leakage reactance dataX#1−#3 X#1−#2 X#2−#3

X% 4Tr (%) 31 98.6 67.6Xpu 1Tr (pu) 0.0775 0.2465 0.169

88

Another component included near the Baulkham Hills busbar is the equivalent capacitor

to represent the capacitor banks installed at 33 kV side of the transformers. Rated at

20 MVAr, value of each capacitor is calculated as

C3φ =Q3φ

3ωV 2LN

=20

3(314.16)(19.05)2= 58.47 µF (B.1)

89

B.2 Underground Cable Data

The original data from manufacturer were adopted from [15] and given in Table B.6

Table B.6: Cable data from manufacturer

No. Description Details

1 Manufacturer Iljin Electric Co Cable Divi-

sion

2 Manufacturer address 112-88 Annyoung-Ri, Taean-

Euf, Hwasung-Si Kyunggi-Do,

Korea

3 Cable type Cu/XLPE/CWS/PVC/HDPE

4 Conductor material Copper

5 Conductor stranding 61/3.9

6 Conductor cross-sectional area (mm2) 630

7 Degree of compression or compaction of con-

ductor (%)

92

8 Shape of conductor round

9 Overall conductor diameter (mm) 30.5

10 Details of conductor bedding Semiconducting tape

11 Insulation material details XLPE

12 Radial thickness of insulation (excluding

semiconducting layers) (mm)

Nom. 18.5

continued on next page

90

Table B.6 – continued from previous page

No. Description Details

13 Details of insulation semiconducting layer semiconducting PE and semi-

conducting tape

14 Curing method Dry curing

15 Details of longitudinal water blocking system See attachment 1

16 Details of copper wire screen:-

a) Wire stranding (No./mm) 63/2.0

b) Cross-sectional area (mm2) Approx. 198

17 Details of serving:-

a) Inner serving:

Material PVC

Minimum thickness at any point (mm) 2

Color Orange

b) Outer Serving:

Material HDPE

Minimum thickness at any point (mm) 2

Color Black

18 Cable overall diameter (mm) Approx. 90.3

19 Cable mass (kg/m) Approx. 12.8

20 Method of sealing cable ends Steel cap

21 Impulse withstand voltage 1.2/50 µs full wave

(kV peak)

650

continued on next page

91

Table B.6 – continued from previous page

No. Description Details

22 Power frequency withstand voltage five minu-

tes (kV rms)

190

23 PD routine test. Expected level of discharge

at 2.00 U0(pC)

4

24 Insulation megger readings. 500 metre section

tested with 2.5 kV megger:

a) Expected value (MΩ) 200000

b) Minimum acceptable value (MΩ) 100000

25 Maximum DC resistance of conductor of com-

pleted cable at 20 C (Ω/km)

26 Zero sequence impedance of completed cable

at 20 0C, metallic sheath return only;

resistive and reactive components (R+jX

Ω/km)

0.16+j0.082

27 Positive and negative sequence impedance of

complete cable; resistive and reactive compo-

nents (R+jX Ω/km)

a) at 20 C 0.03+j0.63

b) at normal maximum operating tempera-

ture

0.06+j0.63

28 Core to screen capacitance (µF/km) 0.19

29 Design maximum operating temperature

(R+jX Ω/km)

continued on next page

92

Table B.6 – continued from previous page

No. Description Details

a) Normal (C) 90

b) Emergency (2 hour)(C) 105

c) Short circuit (C) 250

30 Maximum continuous current rating with sin-

gle point earthing or fully cross bonded:

a) Air (40 C ambient)(A) 1047

b) Buried direct (25 C ambient) (A)

– Trefoil, ie touching (A) 798

– Flat, 150 mm spacing (A) 893

c) Ducted (25 C ambient) (A):

– Trefoil, 200 mm spacing (A) 839

– Flat, 200 mm spacing (A) 815

Cable loses at full load (kW/km) 29.1

31 Emergency current rating factor

a) Two hour–cable at 70 % load prior to emer-

gency

2.57

b) Four hour–cable at 75 % load prior to emer-

gency

2.07

32 Maximum short circuit rating for 1 second

a) Core (A) 90.8

continued on next page

93

Table B.6 – continued from previous page

No. Description Details

b) Screen (A) 26.0

c) Maximum temperature at this rating (C) 250

33 Dielectric loss angle of insulation (degrees) max 0.057

34 Maximum dielectric stress at the conductor

(kV/mm)

6.1

35 Sheath voltage (to earth) induced per 100 A

of load current (V/Am) per 100 m of cable

0.5

36 Details of factory serving test According to IEC60840

37 Minimum bending radius adjacent to joints

and termination (m)

1.8

38 Minimum bending radius during installation

(m)

1.8

39 Maximum allowable pulling tension via stock-

inette (Newtons)

43218

40 Maximum allowable pulling tension via stock-

inette (cable under stocking to be disposed of

after installation) (Newtons)

43218

41 Caterpillar hauling machine:

a) Maximum allowable pulling tension (New-

tons)

68600

b) Maximum allowable cable gripping pres-

sure (kPa)

9.8

continued on next page

94

Table B.6 – concluded from previous page

No. Description Details

42 Maximum side wall bearing pressure during

installation (kPa)

2.94

43 Maximum cable drum length that can be sup-

plied (m)

1000

44 Type test copies attached (Yes/No) Yes

Appendix C

Measurement Data

C.1 Current Transients from Experimental Energisation Tests

Figures C.1 to C.6 depict measured current transients and frequency domain plots recorded

for 30 ms following the cable energisation.

0 0.005 0.01 0.015 0.02 0.025 0.03−1000

−500

0

500

1000

Time (s)

Cur

rent

(A

)

Measured blue phase current transient (test 1)

0 0.005 0.01 0.015 0.02 0.025 0.03−1000

−500

0

500

1000Measured white phase current transient (test 1)

Time (s)

Cur

rent

(A

)

Figure C.1: Blue and white phase current transients from first measurement

95

96

0 0.005 0.01 0.015 0.02 0.025 0.03−1000

−500

0

500

1000

Time (s)C

urre

nt (

A)

Measured blue phase current transient (test 2)

0 0.005 0.01 0.015 0.02 0.025 0.03−1000

−500

0

500

1000Measured white phase current transient (test 2)

Time (s)

Cur

rent

(A

)

Figure C.2: Blue and white phase current transients from second measurement

0 0.005 0.01 0.015 0.02 0.025 0.03−1000

−500

0

500

1000

Time (s)

Cur

rent

(A

)

Measured blue phase current transient (test 4)

0 0.005 0.01 0.015 0.02 0.025 0.03−1000

−500

0

500

1000Measured white phase current transient (test 4)

Time (s)

Cur

rent

(A

)

Figure C.3: Blue and white phase current transients from fourth measurement

97

102

103

104

105

0

10

20

30Frequency spectrum of measured blue phase current transient (test 1)

Frequency (Hz)M

agni

tude

102

103

104

105

0

20

40

60Frequency spectrum of measured white phase current transient (test 1)

Frequency (Hz)

Mag

nitu

de

Figure C.4: Frequency spectrum of current transients from first measurement

102

103

104

105

0

20

40

60Frequency spectrum of measured blue phase current transient (test 2)

Frequency (Hz)

Mag

nitu

de

102

103

104

105

0

5

10

15Frequency spectrum of measured white phase current transient (test 2)

Frequency (Hz)

Mag

nitu

de

Figure C.5: Frequency spectrum of current transients from second measurement

98

102

103

104

105

0

10

20

30Frequency spectrum of measured blue phase current transient (test 4)

Frequency (Hz)M

agni

tude

102

103

104

105

0

10

20

30Frequency spectrum of measured white phase current transient (test 4)

Frequency (Hz)

Mag

nitu

de

Figure C.6: Frequency spectrum of current transients from fourth measurement

99

C.2 CB Pole Closing Times from Experimental Energisation Tests

Figure C.7 is the instantaneous line voltage plots measured at secondary of VT during the

energisation test.

−0.5 0 0.5 1 1.5 2 2.5 3

x 10−3

−400−200

0200400

Instantaneous line voltage (Vred−white) at secondary of VT (test 1)

Time (s)

Vol

tage

(V

)

−0.5 0 0.5 1 1.5 2 2.5 3

x 10−3

−400−200

0200400

Instantaneous line voltage (Vred−white) at secondary of VT (test 2)

Time (s)

Vol

tage

(V

)

−0.5 0 0.5 1 1.5 2 2.5 3

x 10−3

−400−200

0200400

Instantaneous line voltage (Vred−white) at secondary of VT (test 4)

Time (s)

Vol

tage

(V

)1.295E−4

6.55E−5

9.502E−6

1.675E−5

1.725E−5

7.652E−4

8.332E−4

5.968E−4

5.288E−4

Figure C.7: CB pole closing times for each test

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