Transient behaviour modelling of underground high voltage cable systems

Transcription

1 University of Wollongong Thesis Collections University of Wollongong Thesis Collection University of Wollongong Year 29 Transient behaviour modelling of underground high voltage cable systems Muhamad Zalani Daud University of Wollongong Daud, Muhamad Zalani, Transient behaviour modelling of underground high voltage cable systems, Masters by Research thesis, School of Electrical, Computer and Telecommunications Engineering - Faculty of Informatics, University of Wollongong, This paper is posted at Research Online.

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3 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 29

4 To my wife, my son and my late mum

5 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 PSCAD R /EMTDC TM 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

6 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, 29 iv

7 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 friendship. Thanks also to the Ministry of Higher Education (MoHE) and University Malaysia Terengganu (UMT), Malaysia for the financial support. My special thank to my family in Malaysia who has been my inspiration since the primary 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

8 Publications arising from this Thesis 1. M. Z. Daud, P. Ciufo, S. Perera, Investigation on the suitability of PSCAD R /EMTDC TM models to study energisation transients of 132 kv underground cable, Proc. Australasian Universities Power Engineering Conference (AUPEC 28), Paper ID: 37, December 28, Sydney, Australia. 2. M. Z. Daud, P. Ciufo, S. Perera, Statistical analysis of overvoltages due to the energisation of a 132 kv underground cable, Proc. Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology Conference (ECTI-CON 29), Paper ID: 1325, May 29, Bangkok, Thailand. vi

9 Table of Contents Abstract Certification Acknowledgements List of Publications List of Abbreviations List of Figures List of Tables iii iv v vi x xi xiii 1 Introduction Statement of the Problem Objectives of the Thesis Contributions Outline of the Thesis Literature Review Introduction Transients and Travelling Waves Cable Modelling The Wave Equations Coaxial Cable Electrical Parameters Impedance and Admittance Matrices An Overview of Approaches and Existing Models Electromagnetic Transients Simulation Lumped Pi Models Distributed Parameter Travelling Wave Models PSCAD R /EMTDC TM Cable Models The FD-Mode Model The FD-Phase Model Analysis of Switching Transient Overvoltages An Overview of Statistical Switching Studies Switching Phenomena and Statistical Methods Summary PSCAD R /EMTDC TM Power System Model Development Introduction Power System Network Power System Component Modelling kv Upstream Power Source Transmission Lines vii

10 3.3.3 Transformer and Capacitor Bank Underground cable Physical Construction and Material Properties Cable Configuration Inclusion of FD-Mode and FD-Phase Models in the Simulation Frequency-dependent Parameter Settings Simulation Step Size and Simulation Time Results from Simulation of Preliminary PSCAD R /EMTDC TM Model Summary Cable Energisation Transient Behaviour and Assessment of Cable Models Introduction Experimental Energisation Tests Measurement Method Measured Current Transient Waveforms Data for Comparison Analysis of the CB Pole Closing Times Model Refinement and Simulation Implementation of CB Pole Closing Times to the Circuit Model Simulation Comparison of Results Predicted by FD-Mode and FD-Phase Models Simulation using FD-Mode Model Simulation using FD-Phase Model Implication from Measured and Simulated Data Overvoltage Transient Behaviour for the System Under Study Summary Analysis of Overvoltage Stress due to Cable Energisation Introduction An Overview of Switching Transient Evaluation Methods Simulation Approaches First Approach (Deterministic) Second Approach (Probabilistic) Model Refinement and Simulation Implementation of Deterministic Approach in Simulation Implementation of Probabilistic Approach in Simulation Analysis of Overvoltage Data from Simulation Results from Deterministic Approach Results from Probabilistic Approach Results for the Pole Span below 1 ms Summary Conclusions and Recommendations Conclusions Recommendations Appendices viii

11 A Fundamental Equations in Cable Modelling 79 A.1 The General Transmission Lines or Wave Equations A.2 Coaxial Cable Electrical Parameters A.3 Impedance and Admittance Matrices B Power System Component Data 84 B.1 Input Parameter Calculation of Surrounding Components B.2 Underground Cable Data C Measurement Data 95 C.1 Current Transients from Experimental Energisation Tests C.2 CB Pole Closing Times from Experimental Energisation Tests References 1 ix

12 List of Abbreviations HV EHV UHV IEC IEEE EMTP DC FD CB ULM CC CF BHTS BVZS BTTS SWTS CFTS XLPE PVC HDPE SVL RMS FFT VT TV PDF CDF SE RE high voltage extra high voltage ultra high voltage International Electrotechnical Commission Institute of Electrical and Electronics Engineers electromagnetic transients program direct current frequency-dependent circuit breaker universal line model cable constant curve fitting Baulkham Hills transmission substation Bella Vista zone substation Blacktown transmission substation Sydney West transmission substation Carlingford transmission substation cross-linked polyethylene polyvinyl chloride high-density polyethylene sheath voltage limiter root mean square fast Fourier transform voltage transformer tertiary voltage probability density function cumulative density function sending end receiving end x

13 List of Figures 2.1 Single phase frequency domain equivalent circuit of FD-Mode model Weighting Function from J Marti formulation Typical 2 % slow-front overvoltage values Single line schematic diagram of power system network under study Overhead line representation in PSCAD R /EMTDC TM Cable cross-section Cable input data in PSCAD R /EMTDC TM Cross-bonding and configuration of the cable Current transients from preliminary FD-Mode model at T = 1 khz Current transients from preliminary FD-Phase model Current transients from preliminary FD-Mode model at T = 5 Hz Overvoltage transients at the sending end of the cable Cable energisation test set-up Current transients from measurement data Blue and white phase current transients from third measurement Frequency spectrum of blue and white phase current transients Determination of CB pole closing times from third energisation test Establishment of CB pole closing times in PSCAD R /EMTDC TM Simulated current transients from FD-Mode model Frequency spectrum of simulated current transients using FD-Mode model Simulated current transients from FD-Phase model Frequency spectrum of simulated current transients using FD-Phase model Steady-state charging current for cable under test An example of high frequency transformer model Overvoltage transients at sending and receiving end terminals Busbar voltages during cable energisation Sheath voltages during switching with and without surge arresters Gaussian distribution curve Implementation of deterministic approach Results from deterministic approach Results from probabilistic approach for 1 ms, 2 ms and 3 ms spans Results from probabilistic approach for below 1 ms pole span A.1 A x section of a coaxial cable A.2 A simplified coaxial cable cross-sectional area B.1 Current transients simulated using two different source models B.2 Overhead line conductor co-ordinates C.1 Blue and white phase current transients from first measurement C.2 Blue and white phase current transients from second measurement C.3 Blue and white phase current transients from fourth measurement C.4 Frequency spectrum of current transients from first measurement xi

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

15 List of Tables 3.1 Source model input data of voltage source model Cable layers radial measurements Cable dimensions and material properties input data Cable coordinates input data CB pole switching times and maximum span from each test Red phase magnitudes for different simulation time step Sending end voltage magnitudes from simultaneous closure of CB Significant overvoltage peaks from deterministic approach Relevant statistical information for different cases of pole span B.1 Calculation of sequence impedances for voltage source model-1 and model-2 85 B kv overhead line general data B.3 Conductor and ground wire data B.4 Transformer general data B.5 Transformer positive sequence leakage reactance data B.6 Cable data from manufacturer xiii

16 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

17 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 distribution 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. Switching 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 (EMTP TM ) is one of the most widely used software tools for electromagnetic transient analysis. Subsequent and based on the EMTP TM algorithm, the Electromagnetic Transients including DC (EMTDC TM ) program was introduced. To enable easy access and configuration of these programs, they come with computeraided design software, such as the Alternative Transients Program (ATP R ) and the Power Systems Computer-Aided Design (PSCAD R ). Both ATP R /EMTP TM and PSCAD R /EMTDC TM software suites are now major tools in power system studies.

18 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 3 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 predominantly 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 analysis. 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 ATP R /EMTP TM [9,1]. However, the approach used in [9] only gives examples of single phase energisation of cables. Recently, Nichols et al. [1] carried out a practical comparison 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 inconsistencies in transient magnitudes and introduce numerical instability. Consequently, suggestions arise from previously studied models which lead to the requirement of studying the more accurate cable model. Such models are currently incorporated in the PSCAD R /EMTDC TM, 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,

19 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 cumulative 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 insulation 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 cable model, is indispensable. The literature shows that these assessments are predominately carried out for EHV transmission systems using the ATP R /EMTP TM 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. PSCAD R /EMTDC TM 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 PSCAD R /EMTDC TM 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].

20 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 PSCAD R /EMTDC TM 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 phenomena in electrical power systems, electromagnetic transients simulation and cable (transmission 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 investigation including the underground cable. Treatment of the source model, transformer model

21 6 and other surrounding components are detailed. Frequency-dependent modelling of transmission 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 PSCAD R /EMTDC TM 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.

22 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 nonlinear 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 EMTPtype 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 frequency parameters and impedance matrices, are explained. Several models currently incor- 7

23 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, components 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 oscillatory [2]. 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

24 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 5 Hz to the region of 1 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 incident, 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 apply 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 documented 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 EMTP TM [25].

25 1 2.3 Cable Modelling The Wave Equations The behaviour of travelling surges can be described mathematically using the wave equations. 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] d 2 V dx 2 = γ2 V (2.1) d 2 I dx 2 = γ2 I (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 (resistance), 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 circuit. Another important parameter influencing the wave propagation is the characteristic impedance, Z c, within the circuit. It is defined as the ratio of circuit s series parameters to its corresponding shunt parameters as given by Z c = 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 + e γx + V e+γx (2.5)

26 I(x) = I + e γx + I e+γx (2.6) 11 where the plus and minus signs denote the forward and backward directions of wave propagations 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 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 simulators. 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

27 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 [3]. 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 PSCAD R /EMTDC TM [16,31]. Simplifying assumptions may be considered to overcome the lengthy and complicated solution of more general ones such as presented in Section For instance, in some cases, simple equations which neglect the effect of resistance and conductance 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] Impedance and Admittance Matrices The EMTP-type simulators are facilitated with cable constant (CC) routines for the calculation 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 N xn conductors can be described as matrices as presented in Appendix A (Section A.3). The main diagonal elements of these matrices correspond to the self-impedance (or self-admittance) of

28 13 each conductor (core and sheath with respect to ground). Similarly, the off-diagonal quantities represent their respective mutual impedance (or admittance). The elements in these matrices are complex and may be given in Cartesian format such as z ij = r ij + jx ij and y ij = g ij + jb ij. 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 transposition 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 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

29 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 asymmetric structure of transmission lines. In practice, the physical system of conductors (mutually 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 (T v or T i 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 EMTP TM or EMTDC TM 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 provides an analysis of these models except the FD-Mode and FD-Phase models where detailed investigations are documented in Section 2.5.

30 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 [1]. Furthermore, 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 [4], 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] 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

31 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 EMTP TM. 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 domain 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 EMTP TM [4,11]. The KC Lee approach is suitable for the representation of untransposed transmission lines. For underground cables, it requires manual calculation of modal transformation 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 [1]. L Marti [6] has implemented the frequency-dependent calculation of modal transformation 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-

32 17 dependent underground cables and untransposed transmission lines. Unfortunately, this model is not currently available as a dedicated cable model in PSCAD R /EMTDC TM. However, 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 PSCAD R /EMTDC TM Cable Models Literature has shown that modelling the distributed nature and frequency-dependent characteristics of underground cables are absolutely necessary in order to achieve better accuracy of transient modelling. Two distributed parameter travelling wave models in PSCAD R 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 The FD-Mode Model This model is based on the theory developed by J Marti [5]. To account for the frequencydependent 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, E khist Figure 2.1: Single phase frequency domain equivalent circuit of FD-Mode model [27]

33 18 and E mhist 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 (F k ) and receiving (F m ) ends by E khist = (V m + Z C I m )e γl = F m e γl (2.7) E mhist = (V k + Z C I k )e γl = F k e 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, Z C, 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 E khist (t) = E mhist (t) = τ τ f m (t u)a 1 (u)du (2.1) f k (t u)a 1 (u)du (2.11) The time domain of the propagation constant, a(t) is obtained from inverse Fourier transform 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, Z C, in this approach is synthesised in the frequency domain with an R C network with constant Rs and Cs.

34 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 EMTDC TM 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). [V phase ] = [T v ] [V mode ] (2.12) [I phase ] = [T i ] [I mode ] (2.13) [T] T v = [T] 1 i (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 ([T v ] and [T i ]) for matrix diagonalisation used in (2.12) and (2.13) are obtained from eigenvalue problem and are calculated using cable constant (CC) routines in PSCAD R /EMTDC TM. Consequently, as constant transformation matrices are assumed in this formulation, user should specify suitable constant frequency for these matrices in PSCAD R /EMTDC TM [16].

35 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 Y C (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], n Y C V i = 2 H k (t τ k) i far (2.15) k=1 where V and i are the voltage and current respectively, τ k is the travelling time and i far 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 Y C (ω) to be replaced by a low order rational function approximation to permit a recursive implementation of convolutions [4]. Fitting of Y C 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 e sτ i H m i (s) = N m=1 c m s a m (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] Ng N h(s) = ( i=1 m=1 c m,i s a m,i )e sτ i (2.17)

36 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 PSCAD R /EMTDC TM 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 accuracy, 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 An Overview of Statistical Switching Studies Switching overvoltage studies are of primary importance in electric power insulation coordination. 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-

37 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 statistical 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] 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 (5 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

38 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 [5]. 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 insulation 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. Please see print copy for image Figure 2.3: Range of 2 % slow-front overvoltages at the receiving end due to line energisation and re-energisation [18]

39 Summary This chapter presented an overview of the behaviour of transients due to switching operation 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 3 years, interest has been primarily focused on the accuracy of transmission line modelling. In other words, underground cable models have not been as exhaustively examined and validated as their overhead line counterparts. Furthermore, it is unclear whether more sophisticated models or simpler methods should be used for a cable, 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 formulation 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.

40 Chapter 3 PSCAD R /EMTDC TM Power System Model Development 3.1 Introduction The development of power system network model in PSCAD R /EMTDC TM 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 system 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 established. 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 PSCAD R /EMTDC TM power system model is carried out without considering the details of circuit breaker pole closing times as obtained from exper- 25

41 imental measurements. Simulation results obtained from preliminary model for FD-Mode and FD-Phase approaches are presented and discussed 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 characteristics 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 transmission 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.

42 27 Figure 3.1: Single line schematic diagram of power system network under study 3.3 Power System Component Modelling kv Upstream Power Source From Figure 3.1, beyond the 132 kv source at Sydney West (SWTS) subsystem, there is a 33 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 PSCAD R /EMTDC TM [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 5 Hz) given in the data book [52] to form the parallel connected R L circuit. Both parallel and series connected R L source

43 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, R p, and inductance, L p values at 5 Hz) in the parallel circuit can be obtained from series sequence components (R s and L s ) using the following expressions R p = R2 s + (ωl s) 2 R s (3.1) L p = R2 s + (ωl s) 2 ω 2 L s (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 (Section B.1). Table 3.1: Source model input data of voltage source model-2 Page Input data Values 1 Configuration - Source name Src1 - Source impedance type R//L - Source control fixed - Base MVA (3-phase) (MVA) 1 - Base voltage (L-L, RMS) (kv) Base frequency (Hz) 5 - Voltage input time constant (s).2 - Impedance data format RRL values - Specified parameters Behind the source impedance 2 Positive sequence Rrl - Resistance (parallel) (Ω) Inductance (parallel) (H) Zero sequence Rl - Resistance (parallel) (Ω) Inductance (parallel) (H) Source values for fix control - Voltage magnitude (L-L, RMS) (kv) Frequency (Hz) 5 - Phase (deg).

44 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 1 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 PSCAD R /EMTDC TM. 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) calculation 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 PSCAD R /EMTDC TM [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 PSCAD R /EMTDC TM.

45 3 Figure 3.2: Overhead line representation in PSCAD R /EMTDC TM Transformer and Capacitor Bank In modelling the effect of distribution transformers to switching transients, the high frequency model should be used. However, due to inadequacy of available data, the default three-phase, three-winding model in PSCAD R /EMTDC TM was used to represent the transformers 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).

46 Underground cable 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 63 mm 2 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 Inner ins. semiconducting carbon loaded XLPE Pure XLPE Outer ins. semiconducting carbon loaded XLPE Copper wire screen (Sheath) Aluminium foil PVC inner serving HDPE outer serving.4525

47 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 (1)). It has been found that the new capacitance value was approximately 1 % 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 important 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 conductor 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 transient simulation of a cable since cable constant (CC) routines in PSCAD R /EMTDC TM [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 PSCAD R /EMTDC TM. From Figure 3.4, it is apparent that the cable core is treated as a solid conductor (1 st conductor) rather than stranded wires with air gaps. Similarly, the sheath is represented as a tubular conductor (2 nd conductor). To account for such physical conditions the corrected core resistivity value, ρ 1, can be calculated using (3.3) [28] ρ 1 = ρ cπr 2 1 A (3.3) where ρ c =1.678E-8 Ωm is the original core resistivity value for copper and A is the crosssectional area of the conductor. Similarly for the relative permittivity of XLPE insulator, ε 1, it can be calculated with (3.4) ε 1 = C ln r 2 r 1 2πε (3.4)

48 33 Figure 3.4: Cable input data in PSCAD R /EMTDC TM where C is the cable capacitance as stated by manufacturer and ε =8.854E-12 F/m. The new sheath radius, r 3, when considering it as a tubular conductor can be obtained from (3.5) [28] r 3 = Ash π + r2 2 (3.5) where A sh 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 2 nd insulator was approximated as.4387 m. Values for the sheath resistivity, ρ 2, and the relative electrical permittivity of 2 nd insulator, ε 2, remain unchanged as in [15], while the relative magnetic permeability was assumed to be identical for all layers (µ r =1). Table 3.3 depicts the final converted data entered into PSCAD R /EMTDC TM cable model. Impedance (z) and admittance (y) matrices are calculated 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].

49 34 Table 3.3: Cable dimensions and material properties input data Layer Outer Radius, (m) Resistivity, (Ωm) Relative electrical permittivity Relative magnetic permeability Conductor, r E st insulator, r Sheath, r E nd insulator, r 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) Y position (m) The ground resistivity was assumed at 1 Ωm based on default value in PSCAD R /EMTDC TM. 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 circulating 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 equivalent earthing impedances (R SV L ). Major sections are directly earthed and represented

50 35 as resistance to ground (R mat ) for the corresponding substation s ground mat. The selection 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 Frequency-dependent Parameter Settings As described in Chapter 2 (Sections and 2.5.2), accurate modelling of frequencydependent 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].

51 36 In PSCAD R /EMTDC TM, 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.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; to 5 Hz, 5 Hz and 5 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 1 frequencies (lowest setting is 1 frequencies), which means that cable constants (CC) will perform the curve fitting for 1 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

52 37 always be checked as a guide for settings and also to ensure a stable simulation 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.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 m/s. Therefore, the choice of an appropriate simulation time step should be below 5.7 µs. In this case,.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 3 ms. This was achieved by simply employing the snapshot feature which allows switching after a stable run (when power frequency voltage peak reached approximately kv). The output data for the simulation using preliminary power system model is then processed in MATLAB R which is discussed in Section Results from Simulation of Preliminary PSCAD R /EMTDC TM 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

53 38 Current (ka).5.5 Simulated current transients of preliminary FD Mode model ( [ T ] = 1kHz) Time (s) Figure 3.6: Simulated blue (top), white (middle) and red (bottom) phase current transients of preliminary model using FD-Mode approach with modal [T] set at 1 khz Current (ka) Simulated current transients of preliminary FD Phase model Time (s) Figure 3.7: Simulated blue (top), white (middle) and red (bottom) phase current transients of preliminary model using FD-Phase approach

54 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 2 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 [2]. 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 different 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 2 kv (1.86 pu). Current (ka).5.5 Simulated current transients of preliminary FD Mode model ( [ T ] = 5 Hz) Time (s) Figure 3.8: Simulated blue (top), white (middle) and red (bottom) phase current transients of preliminary model using FD-Mode approach with modal [T] set at 5 Hz

55 4 Simulated BHTS busbar voltage during cable energisation (FD Phase model) 2 Voltage (kv) Time (s) 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 waveforms will be analysed by comparison with measurement data. Furthermore, the frequency response of each model will be extensively investigated in Chapter 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 components. 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 system 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

56 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. 41

57 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 PSCAD R /EMTDC TM. Based on the preliminary model simulation results, some suggestions arise. Particularly, for the underground cable model, employing the FD-Mode approach would require an appropriate 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 organised 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 27. 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

58 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 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 [2]. 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 5 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 disconnected to reduce their impact on the transient waveforms to be observed. A period of

59 44 Figure 4.1: Diagram illustrating cable energisation test set-up time (approximately 1 minutes) was used to allow the capacitive elements to fully discharge. 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 25 khz. A total of four energisation tests were performed. Analyses of these waveforms are presented in Section 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 5 A to nearly 1 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

60 45 Blue and white phase current transients (test 1) 1 Blue and white phase current transients (test 2) 1 Current (A) 5 5 Current (A) Current (A) 5 5 Current (A) Time (s) Time (s) Blue and white phase current transients (test 3) 1 Blue and white phase current transients (test 4) 1 Current (A) 5 5 Current (A) Current (A) 5 5 Current (A) Time (s) Time (s) 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 1 ms. The system damping depends on the portion of resistive elements in the circuit. After approximately 3 ms, the 5 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.

61 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 3 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 1 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 coupling 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 Measured blue phase current transient (test 3) Current (A) 5 5 Current (A) Time (s) Measured white phase current transient (test 3) waveform distorted naturally impact of CB chatter bounce Time (s) Figure 4.3: Blue (top) and white (bottom) phase current transients from third measurement

62 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 (5 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 [1,15]. 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 MATLAB R with a third order high pass Butterworth filter with the cut-off frequency set at 2 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 25 Hz to 1 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

63 48 3 Blue phase frequency spectrum (test 3) Magnitude Frequency (Hz) White phase frequency spectrum (test 3) 1 Magnitude Frequency (Hz) 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 Analysis of the CB Pole Closing Times Identification of the closing time for each pole during the cable energisation test is established 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/11 V. From analysis of the measured red-to-white and white-to-blue voltage waveforms and based on [1], 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.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).

64 49 Voltage (V) Instantaneous line voltage (Vred white) at secondary of VT (test 3) 1.738E 5 (red) 4.574E 4 (blue) 3.894E 4 (white) Time (s) x 1 3 Figure 4.5: Determination of CB pole closing times from third energisation test 4.3 Model Refinement and Simulation 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 (5 Hz) voltage peak of each phase reached the nominal value at 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=.375 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 [1]. Figure 4.6: Establishment of CB pole closing times in PSCAD R /EMTDC TM

65 Simulation From measurement data, the current transients were recorded for approximately 3 ms after the energisation. To capture points between zero to 3 ms, the simulation is re-run from the snapshot file for about 3 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.1 µs is used and is considered adequate for this simulation. 4.4 Comparison of Results Predicted by FD-Mode and FD-Phase Models Simulation using FD-Mode Model It is obvious from the example discussed in Chapter 3 (Section 3.6) that this model is capable of simulating high frequency transients provided that a suitable constant frequency is selected for the model to calculate accurately the cable parameters. Therefore, the important 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 3 khz have been tested. It was found that the model produces a consistent result for the frequencies ranging between 1 khz to 2 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 constant frequency higher than 2 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.1 % for both surge impedance and propagation transfer function. Employing the model for ac cable generally requires accuracy at fundamental (assumed 5 Hz) and higher frequencies for transient analysis. This range is emphasised for accurate calculation by setting up a constant value of 1 for the weighting factor.

66 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 177 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 pointon-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 2 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.

67 52 Current (ka) Simulated current transients of FD Mode model ( [T] = 15 khz ) Time (s) Figure 4.7: Simulated blue (top), white (middle) and red (bottom) phase time domain current transients using FD-Mode model.4 Frequency spectrum of current transients of FD Mode model Magnitude Frequency (Hz) Figure 4.8: Frequency spectrum of simulated blue (top), white (middle) and red (bottom) phase current transients using FD-Mode model

68 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.5 Hz to 1 MHz (default). Within this range, the cable constant (CC) routines calculate around 5 frequencies 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 propagation function is set to be as low as.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 2 ms and 15 ms respectively. Consequently, the transient peak magnitudes predicted are 736 A, 514 A and 186 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.

69 54 Current (ka) Simulated current transients of FD Phase model Time (s) Figure 4.9: Simulated blue (top), white (middle) and red (bottom) phase time domain current transients using FD-Phase model.4 Frequency spectrum of current transients of FD Phase model Magnitude Frequency (Hz) Figure 4.1: Frequency spectrum of simulated blue (top), white (middle) and red (bottom) phase current transients using FD-Phase model

70 55 Referring to the frequency response of this model based on the frequency domain plots displayed in Figure 4.1, it again reveals an inconsistency of this model in predicting dominant 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 Implication from Measured and Simulated Data The simulated data from both models have been practically compared with measured current 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 3 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 illustrated in Figure Figure 4.11: Steady-state 5 Hz charging current predicted by FD-Phase model for the cable 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

71 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 1 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 distribution transformers. It is difficult to model the frequency-dependent transformer behaviour. 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

72 57 can be obtained using frequency scan features in PSCAD R /EMTDC TM [16]. Please see print copy for image Figure 4.12: High frequency transformer model suitable for 5 Hz - 2 khz frequency intervals [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-