Development of on-line diagnostic methods for medium voltage XLPE power cables

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VALENTINAS DUBICKAS

Doctoral Thesis in Electrical Systems Stockholm, Sweden 2009

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TRITA-EE 2009:002 ISBN 978-91-7415-220-3

Electromagnetic engineering KTH School of Electrical Engineering 100 44 Stockholm SWEDEN Akademisk avhandling som med tillst˚and av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen den 13 februari 2009 klockan 10.15 i sal F3, Lindstedtsvägen 26, Kungl Tekniska högskolan Stockholm.

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Abstract

On-line diagnostics of power system components is an important area since it allows the diagnostics to be performed at regular intervals during the normal operation of the components. This combined with reliability centered maintenance could lead to reduced customer outages. In this thesis the on-line diagnostic methods for medium voltage cross-linked polyethylene (XLPE) cables are investigated based on Time Domain Reflectometry (TDR).

Degradation of XLPE insulated power cables by water-trees (WT) is a primary cause of failure of these cables. The detection of WT and information about the severity of the degradation can be obtained with off-line measurements using dielectric spectroscopy. In many situations only a limited part of the cable may be degraded by the WT. In such a situation a method for localization of this WT section would be desirable.

The developed high frequency measurements superimposed on HV system is presented. It was used to measure the propagation constant of the WT aged cables as a function of the applied HV. This was done in order to study the diagnostic criteria, which could be used for on-line TDR diagnostics of WT aged cables.

A physically based dielectric model of WT was developed in order to explain qualitatively and quantitatively the permittivity and loss of WT at different frequencies and voltages.

The sensors applicable for the on-line TDR were investigated in terms of sensi- tivity and bandwidth. High frequency models were built and the simulation results in frequency and time domains were verified by measurements.

The developed on-line TDR systems are presented. Their applicability to detect water penetration under the cable sheath and localize the broken screen wires was investigated during the measurements in laboratory environment.

The results of field measurements with on-line TDR are presented. Variations due to load cycling of the cable were observed, where an increase in the cable temperature cause an increase of the pulse propagation velocity in the cable. The temperature dependent wave propagation in the cable is investigated and explained by modeling.

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Acknowledgments

This thesis is part of a Ph.D. project carried out at KTH, School of Electrical Engineering, division of Electromagnetic Engineering. The project was financially supported by national research programme Elektra.

I would like to thank the following people for their help during the work:

My supervisors Dr. Hans Edin and Prof. Roland Eriksson for guidance, nu- merous valuable advises, interesting and productive discussions, enjoyable early morning measurements in-field and also for giving the freedom to experiment with my own ideas.

Former members of the diagnostic group Dr. Ruslan Papazyan, Dr. Gavita Mugala, Dr. Peter Werelius, Dr. Per Pettersson and also Kenneth Johansson at ABB Corporate Research for detailed and rewarding discussions on power cable diagnostics area.

Dr. Johan ˚Ahman and Henric Magnusson at Ericsson Network Technologies AB are greatly acknowledged for providing the cable for the experiment.

Kjell Oberger, Olle Hansson at Fortum Distribution AB, Henrik Flodqvist, Lennart Andersson, Hans L¨owegren, at Vattenfall Eldistribution AB and Henrik Svensson at Eker¨o Energi AB for productive cooperation during in-field and on-line measurements.

I would like to thank my roommates Nathaniel Taylor, Kristian Winter and late-lunch-team David Ribbenfjärd, Héctor Latorre and Nadja Jäverberg for enjoyable discussions on a very wide range of subjects. Also I would like to thank all present and former colleagues Dmitry Svechkarenko, Dr. Valerij Knazkin, Dr.

Cecilia Forsén, Dr. Patrik Hilber, Dr. Tommie Lindquist, Johan Setréus, Julia Nils- son, Carl Johan Wallnerström, Fran¸cois Besnard, Mohsen Torabzadeh-tari, Hanif Tavakoli and other colleagues and personnel at Teknikringen 33 for friendly and enjoyable atmosphere during these years.

Many thanks to friends Jurga, Evaldas, Narine, Aliaksandr, Vilija, Mantas, Pernilla, David, Agn˙e and Tomas for friendship and good company during the trips and skiing, performances and other events.

Last, but not least, I would like to thank my wife Aurelija for support, encour- agement and understanding during these years.

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List of papers

1. V. Dubickas and H. Edin, ”Couplers for on-line time domain reflectometry di- agnostics of power cables”, Proceedings of Conference on Electrical Insulation and Dielectric Phenomena, pp. 210 - 214, Boulder, Colorado, USA, October 2004.

2. V. Dubickas and H. Edin, ”Technique employing inductive coupler for prop- agation constant extraction on power cables with twisted screen wires”, Pro- ceedings of the Nordic Insulation Symposium (Nord-Is), pp. 242 - 245, Trond- heim, Norway, July 2005.

3. V. Dubickas and H. Edin, ”On-line time domain reflectometry measurements of temperature variations of an XLPE power cable”, Proceedings of Conference on Electrical Insulation and Dielectric Phenomena, pp. 47 - 50, Kansas City, Missouri, USA, October 2006.

4. V. Dubickas and H. Edin, ”High frequency model of Rogowski coil with small number of turns”, IEEE Transactions on Instrumentation and Measurements, vol. 56, no. 6, pp. 2284 - 2288, December 2007.

5. V. Dubickas and H. Edin, ”Dielectric model of water trees in an XLPE cable”, International Symposium on Electrical Insulating Materials (ISEIM), pp. 448 - 451, Yokkaichi, Japan, September 2008.

6. V. Dubickas and H. Edin, ”Temperature influence on wave propagation in XLPE power cables: on-line and laboratory measurements”, submitted to IET Science, Measurement & Technology, 2008.

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Contents

Introduction

1.1 Background

Power cables are an elegant solution for the electric power transmission and distribution. They have advantages in esthetic, environmental and safety aspects compared with the overhead transmission lines. Therefore most of distribution networks of medium and low voltages are constructed with power cables. However, a majority of the distribution grid failures are also attributed to the power cables [1, 2].

Power cable technology beginnings are traced to 1880 [3]. Early insulating materials used in power cables were natural rubber, gutta-percha, oil and wax.

Appearance of oil-impregnated-paper cables in 1890 was a significant improvement to the cable design. The oil-impregnated Paper Insulated Lead Covered (PILC) cables have been characterized by their long in-service lifetimes that often exceed 65 years [3]. The development of polyethylene (PE) insulated power cables in early 1950s had the following advantages: high dielectric strength, low insulation permittivity and losses, good mechanical properties and thermal conductivity. The thermoplastic Low Density PE (LDPE) cables have a maximum work temperature of 70^◦C, which was increased to 90^◦C by introduction of thermosetting cross-linked PE (XLPE) in mid 1960s. The quality of XLPE cables was further increased by ensuring cleanliness of the interface between insulation and shields, substituting wet curing by dry curing and introduction of triple extrusion.

The primary cause of insulation degradation in both PILC and XLPE cables is due to moisture. In PILC cables moisture causes premature insulation ageing.

Moisture diffusion into the XLPE cable in combination with an alternating electric field initiates a water-tree (WT) growth in the insulation, which during the years reduces the strength of the insulation and consequently leads to cable failure. At the time of introduction of XLPE cables the WT phenomenon was still unknown, thus older generation cables, especially those with graphite tape insulation shields, are prone to this degradation. Mechanical damage of the cables by digging is also considerable [1]. In order to detect the degradation cable diagnostics could be used.

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1. Introduction

The cable insulation diagnostics are performed in frequency and time domains.

Frequency domain diagnostics include measurements of capacitance and loss tangent at fixed frequency using for example Schering bridge or at several frequencies using Dielectric Spectroscopy (DS)[4]. Time domain measurements include polarization/depolarization current measurements and recovery voltage measurements.

Time Domain Reflectometry proved to be a useful technique to localize the joints along the cables and even to localize water penetration into PILC cable [5]. Some attempts have also been done to localize WT along the XLPE cable using TDR [5, 6]. Another common degradation mechanism is Partial Discharges (PD). PD measurements is a common diagnostic tool for PILC cables. PD measurements are performed both off-line using the external High Voltage (HV) supply and on-line on the cables in service using high frequency sensors [7]. A more comprehensive description of cable diagnostics can be found in section 2.4.

1.2 Research on power cable diagnostics at KTH

The division of Electromagnetic Engineering at Royal Institute of Technology (Kung- liga Tekniska H¨ogskolan)(KTH) has over a number of years built up high compe- tence in the power cable diagnostics. In this department the DS diagnostic system was developed for condition estimation of WT degraded XLPE cables. This re- sulted in the publication of the following thesis [8, 9, 10]. The high frequency characteristics of medium voltage XLPE cables were investigated in terms of high frequency measurements of cable materials and cable modeling [11]. High frequency diagnostic techniques based on TDR were investigated for localization of insulation degradation along medium voltage power cables [5]. The development of on-line TDR systems is presented in the licentiate thesis [12].

1.3 Aim

The main aim of this thesis was to develop on-line diagnostic methods for power cables based on TDR, which would allow to detect or even locate the defects along the cable, that can not be detected as PDs.

In order to reach the main aim, a number of prerequisites had to be accom- plished, which can be summarized as:

Investigation of diagnostic criteria for localization of WT degraded insulation and defects caused by mechanical cable damage.

Investigation of sensors applicable for on-line diagnostics.

Development of on-line cable characterization methods.

Development of on-line diagnostic systems based on TDR.

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1.4. Main contributions

1.4 Main contributions

Low voltage high frequency measurement techniques for power cables are well es- tablished [13, 14]. A novel high frequency measurements superimposed on high voltage system was developed. The developed system was used to measure the propagation constant of the WT aged cables as a function of the applied HV. This was done in order to investigate the diagnostic criterium which could be used to localize WT with on-line TDR.

Models of WT are usually developed to simulate the low voltage dielectric measurements at a constant voltage [15, 16, 17]. A qualitative model explaining voltage dependent dielectric properties of WT was developed by [18]. In this thesis a physically based dielectric model of WT was developed. The model agrees with the DS measurements and can explain the increase in the permittivity and loss at low frequencies with the increase of applied HV. The model also stands in line with the high frequency measurements superimposed on HV of WT aged XLPE insulation.

The sensors used for on-line PD diagnostics of power cables are rather well investigated and their descriptions can be found in the literature [19, 20, 21, 22, 23]. However a direct comparison of the sensor models and the measurements is seldom presented. In this thesis four types of the on-line sensors were modeled and simulation results were compared with the measurements in both frequency and time domains. A physically based high frequency model of Rogowski coil sensor with a small number of turns was developed, there the input parameters are the coil dimensions and material properties. The model could be used as a tool for the Rogowski coil design. Both simulations in frequency and time domains showed good agreement with the measurements.

Two modifications of the on-line TDR system, presented in [11], were developed and used for the measurements in-field. On-line PD measurements on cables are common [24, 2, 7, 25], however on-line TDR is a new technique. The changes in the cable temperature were observed with the developed systems on-line as the variation in the pulse velocity caused by the load cycling.

The developed on-line TDR systems proved to be capable to detect water penetration under the cable sheath and localize broken screen wires along the cable.

1.5 Thesis outline

Chapter 2 gives an overview to cable design, water treeing phenomenon and diagnostic techniques.

Chapter 3 presents a brief review of dielectric polarization, transmission line theory and high frequency measurement techniques.

In Chapter 4 the properties of sample cables with water trees are presented in terms of optical water tree analysis, low frequency dielectric spectroscopy measurements and high frequency measurements superimposed on high voltage.

A dielectric model of water trees is presented in Chapter 5. The model is based

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1. Introduction

on the physical structure of water trees where voltage dependent permittivity and loss of degraded insulation is modeled by changes in the water tree microstructure.

The chapter presents the model reported in Paper 5.

Chapter 6 investigates phenomena affecting wave propagation in the power cable, namely influence of cable’s temperature and water presence between the insulation shield and screen wires. The chapter contains the results presented in Papers 3 and 6.

In Chapter 7 the sensors relevant for on-line power cable diagnostics are investigated and modeled both in frequency and time domains. The chapter summarizes the results of Papers 1 and 4.

A method for a propagation constant extraction of a selected part of a cable with the twisted screen wires is presented in Chapter 8. This chapter is a review of Paper 2.

The developed on-line TDR systems are presented in Chapter 9. This chapter reviews the systems presented in Papers 3 and 6.

In Chapter 10 the application of on-line TDR is investigated to detect broken screen wires along the cable and water penetration under the cable sheath.

The results of on-line TDR measurements are presented in Chapter 11, where the developed systems were used to detect the temperature changes of the cable caused by the load cycling. The chapter summarizes the results of Papers 3 and 6.

Chapter 12 contains summary and general conclusions, while Chapter 13 pro- poses some topics of interest for future work.

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Chapter 2

Power cables and diagnostics

2.1 Power cables

Power cable history begins at the end of the 19th century [3]. Different materials were used as an insulation: natural rubber, vulcanized rubber, oil and wax, cotton and other.

PILC cables

One of the most successful designs were paper insulated lead covered (PILC) cables.

Use of paper insulated power cables can be traced back to 1891 in London. During the years the paper impregnation was improved by changing vegetable substances by mineral oil, later by wax-filled compounds. The sheath protecting the cable from moisture ingress progressed from lead to aluminium [3].

XLPE cables

Development of synthetic polymer materials boosted the birth of extruded power cables. The growth of solid dielectric insulated medium voltage cables began in the early 1950s, with the introduction of butyl rubber and thermoplastic high molec- ular weight polyethylene. Introduction of crosslinked polyethylene (XLPE) as an insulation material in the mid-1960s seemed to be very promising due to good electrical, thermal and mechanical properties. XLPE has low permittivity, high dielectric strength and low dielectric loss. Maximal continuous operating temperature of XLPE is 90^◦C, while during emergency overload and short-circuit the temperature of 130^◦C and 250^◦C respectively can be permitted. Good mechanical properties eliminated the tendency to stress-cracking. Therefore, introduction of XLPE increased the capability of polymeric insulated cables because of their higher temperature ratings, resulting replacement of PILC cables by XLPE.

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2. Power cables and diagnostics

Oversheath Metallic screen Screen bed Insulation shield XLPE insulation Conductor shield Conductor

Figure 2.1: Common design of second generation XLPE cable.

First generation XLPE cables

XLPE cables in Sweden were introduced in late 1960s [26, 27]. The first type of the introduced cables had an extruded conductor shield providing a smooth boundary between the conductor and the XLPE insulation. An insulation shield was made of conducting tape, or graphite paint on the XLPE with conducting textile tape wound on it. The oversheath usually was made of PVC. This type of cables are referred to as the first generation XLPE cables.

Second generation XLPE cables

Due to developments in extrusion techniques, tandem and later triple extrusion in the middle 1970s, conductor shield, XLPE insulation and also insulation shield could be extruded at the same time. This caused an improved boundary between XLPE and metallic screen and reduced the number of polluting particles at the boundary. A dry curing of XLPE as well as cleaner insulation materials started to be used. PE replaced PVC for cable’s sheath in this way reducing water diffusion into the cable.

Third generation XLPE cables

Further improvements to stop water diffusion into the cable were introduced in 1990s. An aluminium foil with a water absorbing powder or tape was placed under the cable sheath. The stranded conductors were filled with the water absorbing powder in order to stop moisture movement along them.

2.2 Water trees

When XLPE power cables were introduced the phenomenon of water treeing was still unknown. XLPE is an hydrophobic material and therefore the first generation 6

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2.2. Water trees

cables could allow water diffusive sheath to be used, usually PVC. However water diffusion into the XLPE cable in combination with an alternating electric field initiates a water tree growth [28, 29]. The water trees are tree or bush shape diffuse structures in the insulation. Two types of water trees are distinguished: vented, see Figure 2.2, and bow-tie. Vented water trees are initiated at the insulation surfaces, while bow-tie are initiated inside the insulation. However vented water trees are considered far more dangerous than bow-tie, as vented trees grow through the insulation. The growth of the bow-tie trees is strongly reduced after some time.

Water tree growth mechanisms

Bow-tie trees are initiated at impurities in the insulation. Vented water tree initiation could begin from one of the following factors:

Mechanical damage of the cable insulation, for example scratching the insulation may initiate treeing.

Irregularity in semiconducting shield where it contacts with the insulation.

Water treeing phenomenon was discovered in 1969 [30] and their growth mechanisms are still under investigation. A water tree growth mechanism can not be distinguished as a single process, it is most probably an effect of several processes taking place simultaneously [28]:

Osmosis. Water-soluble substances in micro-voids attract water from environment.

Capillary action. Water will not enter a narrow channel of pure PE. However if walls of these channels become polar, their surface tension will change. Thus a certain amount of polar material on the walls is required to get an intrusion of water.

Coulomb forces. These are forces on electric charges that are caused by an electric stress.

Dielectophoresis. Water droplets tend to move to higher electric field point.

Electrochemical degradation. Oxidation of amorphous phase of polymer by free radicals or oxidizing agents produced by electrolysis.

Osmosis and capillary action are not related to electric stress, thus they can not be considered as the cause of water tree growth. However both processes may play a secondary role by pushing water into a polarized channel.

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Figure 2.2: Vented water trees in power cable insulation.

Properties of water trees

Water trees are considered as an insulating material [28]. Nevertheless they are called water trees, water content is only ∼1% of water trees in field aged cables [31]. Dielectric properties of water trees are similar to insulating material with a permittivity ε⁰_r= 2.3−3.6 and loss-factor around tanδ = 0.002−0.02 [29, 31]. How- ever the electric breakdown strength of the insulation is reduced by the water trees.

The breakdown stress of the water treed insulation can be restored up to 50% of the initial value by drying the insulation [28, 32], but as soon water is present it will be re-absorbed consequently reducing the breakdown strength. Water tree initiated failures are not clearly understood. Water trees cause local stress enhancements that could be initiation sites for electrical trees, either at power frequency or from transient overvoltages. XLPE is also susceptible to localized degradation caused by Partial Discharges (PD). The degradation of the XLPE appears as an erosion of the surface within the cavities and a breakdown appears after a period of time when a certain degree of surface roughness is attained manifesting the initiation of electrical trees.

2.3 Countermeasures to water treeing in power cables

Water is one of the necessary agents for water treeing. Therefore different cable designs were introduced to protect against water ingress and propagation in the cable [33]. Three water blocking constructions can be distinguished:

Longitudinal water-blocked conductors. Moisture propagation inside of the stranded conductor is blocked by filling the space between the strands with 8

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2.4. Power cable diagnostics

semiconducting or insulating materials, placing water absorbing powder between the strands or using solid conductors.

Longitudinal water-blocking at the insulation shield is achieved using water absorbing tapes.

Radial water blocking. Usually radial water-blocking is implemented by using metallic laminated tapes. Aluminium or lead tapes are laminated between insulating or semiconducting material depending where they are placed on the shield wires or the insulation shield.

The introduction of water Tree Retardant XLPE (TR-XLPE) reduced the size and amount of the water trees in the cables. TR-XLPE consists of XLPE insulation with tree retardant additive [34].

2.4 Power cable diagnostics

The third generation cables are well protected from the water ingress and therefore water treeing is seldom the cause of faults in these cables. However the second generation and especially the first generation power cables are susceptible to water treeing [27]. In Sweden ∼50% of the totally installed 2500 km XLPE cables during the 1965-75 are still in service. The replacement of these cables alone would cost 500 million SEK [10]. This motivates the need for the cable diagnostics, which would allow to estimate condition of old and aged cables. The aim of using the diagnostics is to achieve a strategy for condition based maintenance where good enough cables are kept but bad cables are replaced. Overview of the available power cable diagnostic methods and testing can be found in [35], while non-destructive diagnostics are summarized in the following section.

2.4.1 Off-line diagnostics

Off-line diagnostics are performed on the cables disconnected form the power grid.

Loss tangent

The measurements can be performed using classical Schering bridge measurements of loss tangent. These measurements are usually performed at power frequency [3, 36].

Dielectric spectroscopy

In Dielectric Spectroscopy (DS) measurements of complex permittivity are performed at several frequencies enabling a frequency spectrum of permittivity to be analyzed. The spectrum reflects the properties of the dielectric material in the measured frequency range. Water trees increase the loss and the capacitance of

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the dielectric material sample. These two parameters are also voltage dependent.

The voltage dependence of the loss and the capacitance of the water treed cable are used as a differentiating factor in the dielectric spectroscopy diagnostics. The dielectric spectroscopy system for medium voltage XLPE power cables was developed in Electromagnetic Engineering department at Royal Institute of Technology [10, 8, 9, 4].

Polarisation/depolarisation current

The measurements are performed by charging the sample by DC voltage and measuring the polarization current. After applying DC voltage for a long period of time the sample is short-circuited and depolarization current is measured [36, 37].

Return voltage

measurements are similar to depolarization current measurements. The DC voltage charges the sample; after a relatively short period of time during which the sample is short-circuited, the test object is left in open-circuit condition and the recovery voltage is measured [36, 37].

Partial discharge diagnostics

Partial Discharge (PD) diagnostics is a widely used technique to detect discharges appearing in cavities or on surfaces of the insulation [38, 39, 3, 36]. Off-line PD diagnostics on the power cables are usually performed by energizing the cable with a High Voltage (HV) supply. The measuring equipment is coupled to the cable using a coupling capacitor [38, 24]. The method enables the PD to be detected and localized.

Time Domain Reflectometry

Time Domain Reflectometry (TDR) is pulse-radar similar technique. It is implemented by injecting the pulse into the cable and measuring the reflections along the cable. The reflections arise due to joints along the cable but also due to small irregularities in the cable itself. TDR for medium voltage XLPE power cable diagnostics was also developed in Electromagnetic Engineering department at Royal Institute of Technology [5, 13]. More detailed description of TDR can be found in section 3.8.

2.4.2 On-line diagnostics

On-line diagnostics are performed on the cables in operation.

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2.5. Transient protection devices

DC current measurement

The method was possible to implement in Japan where the distribution power cables operate mostly at relatively low voltages 6.6 kV and are non-grounded. DC voltage is applied to the cable conductor through an inductance and is superimposed on the grid voltage. The AC component of the current which passes thought the insulation of the cable is eliminated by a filter and only the DC component is measured. The reduction of the insulation resistance indicates the presence of water trees [40, 41].

Partial discharge diagnostics

On-line partial discharges on the cables are detected using high frequency sensors [24, 2, 7, 25]. The sensors are of capacitive or inductive type. The capacitive sensors are usually made of conductive tape placed on the insulation shield between the HV termination and the screen wires. Another option is to place the capacitive sensor on the insulation shield in the cable joint, under the metallic screen. The inductive sensors usually used for on-line PD diagnostics are Rogowski coils. They can be placed on the power cable after the earth connection, before the high voltage termination, or on the power cable’s earth connection conductor.

2.5 Transient protection devices

On-line diagnostic systems are usually connected to the power cable through high frequency sensors. Therefore the diagnostic systems are decoupled from the power frequency HV, however they are still susceptible to HV transients in the power cable. The HV transients appear during the cable switching to grid and also during cable failure. These transients usually are not dangerous for the sensors however the output voltage from the sensors could damage the sensitive measurement equipment. To protect the measurement equipment the transient protection devices can be connected on the sensor’s output. The following are properties of common transient protection devices for electronic circuits [42]:

Spark gaps

Can safely conduct large currents (20 kA for 8/20 µs impulse) Very small parasitic capacitance (< 2 pF)

Low voltage in arc mode

Requires large voltage to conduct (> 75 V) Relatively slow to conduct

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Metal oxide varistors Fast response (< 0.5 ns) Large energy absorbtion

Can safely conduct large currents (1 kA for 20 µs) Large parasitic capacitance (1−10 nF)

Avalanche diodes Fast response (< 0.1 ns)

Selection of precisely determined clamping voltages (6.8−200 V) Small max allowable current (6 100 A for 100 µs)

Large parasitic capacitance (1−3 nF)

Zener diodes

Similar characteristics to avalanche diodes however clamping voltage is less than about 5 V.

Quarter-wave stub

High frequency systems operating in narrow frequency band or at fixed frequency f can be protected from transient overvoltages using a quarter-wave stub, which is generally a transmission line with short-circuited and grounded end. A short- circuited quarter-wave line at frequency f appears as an open circuit at at the input terminals, thus another end can be connected for example through T-connection to the cable connecting the sensor and the measurement equipment. The length of the quarter-wave stub l_λ/4 is selected according to f and wave velocity v in the stub: l_λ/4= _4f^v.

High frequency relays

The high frequency relays connected between the sensor and the measurement equipment can provide partial protection from transient overvoltages. Such design allows the measurement equipment to be connected to the sensor only when the actual measurements are performed and disconnected during the remaining time including the cable switching to the grid.

In summary, it could be said that there are no optimal broadband, high frequency transient protection devices and thus the design of the high frequency protection circuit is usually the process involving tradeoff between the max transient current, response speed and the size of the parasitic capacitance.

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Chapter 3

Theory review

In this chapter the theory is reviewed which is later used and referred to in the thesis. The chapter consists of overview of polarization processes, transmission line theory and high frequency measurement techniques.

3.1 Dielectric polarization

Dielectric polarization is a result of a relative displacement of the positive and negative charges. It is produced by the electric field through orientation of permanent dipoles and induced polarization of individual atoms and ions. The macroscopic polarization P and the electric field E in linear and isotropic medium are related by [43]:

P = ε0χE (3.1)

where, χ is susceptibility of material and ε0= 8.854·10⁻¹²(F/m) is permittivity of free space.

The main mechanisms that produce macroscopic polarization are:

Electronic polarization is effective in every atom or molecule as the center of gravity of the electrons surrounding the positive nucleus will be displaced by the electric field E. The effect is effective up to optical frequencies.

Ionic polarization occurs in materials containing molecules forming ions e.g.

NaCl, KCl. Apart from electronic polarization induced in such molecules, relative displacements between positive and negative ions appear giving rise to polarization up to infra-red frequencies.

Dipolar polarization appears in materials possessing molecules with permanent dipole moments even in the absence of the external polarizing field. Such molecules

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3. Theory review

usually consist of two or more dissimilar atoms. An example is the water molecule where hydrogen atoms do not lie exactly on diametrically opposite sides of the oxygen atom. In absence of E the orientations of these molecules are random due to the action of thermal energy. When E field is applied, the distance between charges of the dipole remains constant, however, the dipole itself rotates. The velocity of rotation depends on the torque and the surrounding local viscosity of the molecules. The delay of the response to the change of E causes friction and heat. Dipolar polarization is active up to MHz or GHz frequencies.

Interfacial polarization is effective in non-homogeneous insulating materials.

The mismatch of permittivities and conductivities of the dielectrics give rise to charge accumulation on the interfaces under the influence of E, by this forming the dipoles. The phenomenon is in general slow and active in the power frequency range and below.

Trapping and hopping of charge carriers between localized charge sites also can create polarization. The process is slow and strongly temperature dependent, found mostly in solids.

3.2 Dielectric response in time domain

The dielectric materials exhibit delayed responses due to inertia of all physical pro- cesses. Therefore as the time dependent polarization P(t) is not the same function as the time dependent driving field E(t). The dielectric displacement representing the total surface charge density induced on the electrodes is a sum of the instanta- neous free space ε0E and delayed material polarization P(t):

D(t) = ε0E(t) + P(t) (3.2)

The material polarization P(t) is dependent on the applied E(t) and its history.

In order to relate P(t) and E(t) the additional dielectric response function f (t) is defined, which characterizes the response of the dielectric to specified electric excitation. The requirements on f (t) are:

causality f (t) ≡ 0 for t < 0 (no reaction before action), no permanent polarization when E is removed lim

t→∞f (t) = 0 (every polarization relaxes in the end),

and ^∞R

0

f (t)dt < ∞ (finite polarization in the material).

The time dependent polarization of linear dielectric can be described by f (t) and related to E(t) by the following expression:

P(t) = ε0

Z∞

0

f (τ )E(t − τ )dτ (3.3)

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3.3. Dielectric response in frequency domain

It is common to measure the dielectric response in time domain by applying the step electric field. The polarization P(t) defined by the convolution integral in equation 3.3 induced by the step electric field E0 at t = 0 becomes:

P(t) = ε0E0

Zt

0

f (τ )dτ (3.4)

Combining equations 3.2 and 3.4 dielectric displacement is obtained:

D(t) = ε0E0



1(t) + Zt

0

f (τ )dτ



 (3.5)

And the current density in the dielectric is:

J(t) =∂D(t)

∂t + σ0E0= ε0E0(δ(t) + f (t)) + σ0E0 (3.6) The delta function δ(t) represents the instantaneous response of the free space while σ0E0 term represents direct current. The dielectric response in time domain is normally dominated by the function f (t) which is observed as the time dependence of the polarizing current. This provides an important means of determining the function f (t) experimentally as the response of the dielectric to the step function of E.

3.3 Dielectric response in frequency domain

The dielectric response measurements in frequency domain can be performed with high accuracy. It is because such measurements can be performed at narrow bandwidth thus minimizing the noise in the system.

The Fourier transform of the convolution integral in equation 3.3 can be written as the product of Fourier transforms of the two functions under the integral:

P(ω) = ε0χ(ω)E(ω) (3.7)

where frequency dependent susceptibility is defined as Fourier transform of f (t):

χ(ω) = χ⁰(ω) − jχ⁰⁰(ω) = F {f (t)} = Z∞

0

f (t)e^−jωtdt (3.8)

at zero frequency real and imaginary parts of susceptibility become:

χ⁰(0) = Z∞

0

f (t)dt χ⁰⁰(0) = 0 (3.9)

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3. Theory review

The current density in the dielectric in frequency domain is:

J(ω) = σ0E(ω) + jωD(ω) (3.10)

while displacement:

D(ω) = ε0E(ω) + P(ω) (3.11)

Combining equations 3.10, 3.11, 3.7 and 3.8 results in:

J(ω) = µ

1 + χ⁰(ω) − j µ

χ⁰⁰(ω) + σ0

ωε0

¶¶

jωε0E(ω) (3.12) where imaginary current density part jωε0(1 + χ⁰(ω))E(ω) is in quadrature with E and does not contribute to the loss, while the real part ωε0(χ⁰⁰(ω) + _ωε^σ⁰

0)E(ω) is in phase with E and thus generates loss. By defining real ε⁰_r(ω) = 1 + χ⁰(ω) and imaginary ε⁰⁰_r(ω) = χ⁰⁰(ω) parts of complex relative permittivity the following equation is obtained:

J(ω) = µ

ε⁰_r(ω) − j µ

ε⁰⁰_r(ω) + σ0

ωε0

¶¶

jωε0E(ω) (3.13) Then current ¯I(ω) in the capacitor with the applied voltage V (ω) on the elec- trodes can be expressed as:

I(ω) =¯ µ

ε⁰_r(ω) − j µ

ε⁰⁰_r(ω) + σ0

ωε0

¶¶

jωC0V (ω) (3.14) For a parallel plate capacitor free space capacitance is: C0= ε0A

d , A electrode surface area,

d dielectric thickness between electrodes.

Equation 3.14 can be rearranged and expressed as the sum of capacitive ¯ICand resistive ¯IR currents, see Figure 3.1:

I(ω) = jωε¯ ⁰_r(ω)C0V (ω) + µ

ε⁰⁰_r(ω) + σ0

ωε0

¶

ωC0V (ω) = ¯IC+ ¯IR (3.15)

3.4 Loss tangent

Loss tangent is a measure of the power loss in the dielectric. It is also called dissipation factor or simply tan δ. It is defined as the ratio of the resistive IR and capacitive IC currents in the dielectric, see equation 3.15 and Figure 3.1:

tan δ = IR

IC =ε⁰⁰_r(ω) + _ε^σ⁰

0ω

ε⁰_r(ω) (3.16)

Sometimes loss tangent is confused with the power factor, which is defined as cos φ = ^I_I^R, see Figure 3.1. Confusion could arise due to the fact that in low loss dielectrics I_R¿ I_C, therefore I → I_C, which results in cos φ ≈ tan δ.

16

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3.5. Kramers-Kronig relations

δ

φ IR

IC I

V

Figure 3.1: Vector diagram of voltage and current components in lossy dielectric.

3.5 Kramers-Kronig relations

The Kramers-Kronig relations are mathematical properties, connecting the real and imaginary parts of any complex function which is analytic in the upper half plane.

Since χ(ω) is the Fourier transform of dielectric function f (t) the following relations between χ⁰(ω) and χ⁰⁰(ω) exist:

χ⁰(ω) = 2 π

Z∞

0

xχ⁰⁰(x)

x²− ω²dx (3.17)

χ⁰⁰(ω) = −2ω π

Z∞

0

χ⁰(x)

x²− ω²dx (3.18)

Kramers-Kronig relations are useful in certain experimental situations where they enable the values of one of the functions to be obtained from those of the other.

Evaluation of Kramers-Kronig relations at zero frequency results in:

χ⁰(0) = 2 π

Z∞

0

χ⁰⁰(x) x dx = 2

π Z∞

−∞

χ⁰⁰(x)d(ln x) (3.19)

This indicates that a mechanism leading to strong polarization must inevitably give rise to correspondingly high losses somewhere in the frequency spectrum.

The same conclusion can be reformulated as, it is impossible to have a loss free dielectric material of finite susceptibility.

It is possible to extend that conclusion even further and state that it is impossible to have a dispersion free dielectric material, i.e. which shows frequency independent real and imaginary parts.

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3. Theory review

3.6 Transmission line theory

Transmission lines differ from ordinary electric networks in one essential feature.

The physical dimensions of electric networks are very much smaller than the operating wavelength, however transmission lines are usually a considerable fraction of a wavelength and may even be many wavelengths long. Therefore the transmission line should be described by circuit parameters that are distributed through its length. The equivalent distributed elements circuit of a two wire transmission line is shown in Figure 3.2.

( , )

i x+ ∆x t

( , ) v x t

( , ) i x t

( , )

v x+ ∆x t

∆x R x∆ L x∆

G x∆ C x∆

Figure 3.2: Equivalent circuit of a two conductor transmission line of length ∆x.

The distributed elements circuit in Figure 3.2 can be described by a pair of first- order partial differential equations 3.20 and 3.21, which are called the transmission line equations [44, 45].

−∂v(x, t)

∂x = Ri(x, t) + L∂i(x, t)

∂t (3.20)

−∂i(x, t)

∂x = Gv(x, t) + C∂v(x, t)

∂t (3.21)

For harmonic time dependence the use of phasors simplifies the transmission line equations to ordinary differential equations.

−dV (x)

dx = (R + jωL)I(x) (3.22)

−dI(x)

dx = (G + jωC)V (x) (3.23)

Solving equations 3.22 and 3.23 for V (x) and I(x) the following equations are obtained.

d²V (x)

dx² = γ²V (x) (3.24)

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3.7. Finite transmission lines

d²I(x)

dx² = γ²I(x) (3.25)

where:

γ(ω) = α + jβ =p

(R + jωL)(G + jωC) (3.26)

is the propagation constant which is composed of real and imaginary parts. α and β, are the attenuation constant (N p/m) and phase constant (rad/m) respec- tively. Solution of equations 3.24 and 3.25 are of the form:

V (x) = V⁺(x) + V⁻(x) = V₀⁺e^−γx+ V₀⁻e^+γx (3.27)

I(x) = I⁺(x) + I⁻(x) = I₀⁺e^−γx+ I₀⁻e^+γx (3.28) where the plus and minus superscripts denote waves traveling in the positive and negative x directions respectively. The ratio of the voltage and the current at any x for an infinitely long line is independent of x and is called the characteristic impedance of the line.

Z0= V₀⁺

I₀⁺ = −V₀⁻ I₀⁻ =

s

R + jωL

G + jωC (3.29)

The phase velocity of the wave at given angular frequency ω in the transmission line can be calculated using the following expression:

v_p(ω) = ω

β(ω) (3.30)

The wavelength of the sinusoidal wave of frequency f in the transmission line is by definition:

λ = vp

f (3.31)

3.7 Finite transmission lines

When the transmission line with the characteristic impedance Z0 and the propa- gation constant γ is terminated at the distance l by the load impedance ZL, the generator looking into the line sees an input impedance Zi.

Zi= Z0ZL+ Z0tanh γl

Z₀+ Z_Ltanh γl (3.32)

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3. Theory review

Pulse/step generator

High speed oscilloscope

Z0

ZL

Vi Vr

l

Figure 3.3: Block diagram of a TDR system.

3.8 Time domain reflectometry

Usually time domain measurements provide intuitively understandable results that are easier to interpret, compared with the frequency domain S-parameter measurements. The basic TDR system consists of a fast rise-time pulse (or step) generator and a high speed oscilloscope, see Figure 3.3.

The incident pulse or step Vi is sent into the transmission line Z0. If Z06= ZL, at the interface between Z0 and ZL the reflection of the voltage wave will appear.

The ratio of the reflected voltage wave and the incident voltage wave is called the voltage reflection coefficient and can be expressed as:

Γ = Vr

Vi

=ZL− Z0

ZL+ Z0

(3.33) and voltage transmission coefficient is defined as:

T = 1 + Γ (3.34)

The reflected voltage wave Vr will propagate back to the measuring system and will be recorded by the high speed oscilloscope after a traveling time tr. Know- ing the pulse propagation velocity v in the transmission line the distance to the discontinuity can be obtained as:

l = vtr

2 (3.35)

3.9 Transmission line bifurcation

Voltage wave reflection from the discontinuity in the transmission line is defined by equation 3.33. One more interesting example is the voltage wave reflection in the bifurcated transmission line, see Figure 3.4. The figure considers what happens when traveling wave on a transmission line reaches a point where the line is joined to a second line. Notation (++) denotes that the transmitted (+) wave is resulting 20

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3.10. S-parameters matrix

Z0

V+

Z1

Z2 ⁰

Z V+

Z1

Z2

V−

+ +

V1 + +

V2

Figure 3.4: Traveling voltage wave encountering a line bifurcation.

from the incident (+) wave. Since the propagating wave at the discontinuity point encounters the input impedance of two parallel connected characteristic impedances of transmission lines 1 and 2 the reflection coefficient becomes:

Γ =

Z1Z2

Z1+Z2 − Z0 Z1Z2

Z1+Z2 + Z₀ (3.36)

and thus the transmitted voltage is obtained according to the following relation, where T is transmission coefficient, equation 3.34:

V₁⁺⁺= V₂⁺⁺= V⁺+ V⁻ = V⁺+ ΓV⁺= V⁺(1 + Γ) = V⁺T (3.37) The refracted currents in the bifurcated lines are:

I₁⁺⁺=V₁⁺⁺

Z1 I₂⁺⁺= V₂⁺⁺

Z2 (3.38)

For continuity of current and voltage the following relations must be satisfied:

I⁺+ I⁻ = I₁⁺⁺+ I₂⁺⁺ (3.39)

V⁺+ V⁻= V₁⁺⁺= V₂⁺⁺ (3.40)

3.10 S-parameters matrix

Usually the currents and the voltages can not be measured in a direct manner at microwave frequencies. The directly measurable quantities are the amplitudes and the phase angles of the waves reflected from and transmitted through the test object, relative to the incident wave amplitudes and phase angles. The matrix describing this linear relationship is called the S-parameters matrix [45, 46]. The S-parameters matrix of the twoport, presented in Figure 3.10, is:

· b1

b₂

¸

=

· S11 S12

S₂₁ S₂₂

¸ · a1

a₂

¸

(3.41)

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3. Theory review

11 12

21 22

S S S S

 

 

 

Z1

Z2

V1⁺

V1⁻

V2⁺

V2⁻

Port 1 Port 2

Figure 3.5: Incident and reflected waves in a twoport.

where

b1= ^√^V¹_Z⁻

1 a1=^√^V¹_Z⁺

1

b2= ^√^V²_Z⁻

2 a2=^√^V²_Z⁺

2

(3.42)

Usually impedances Z1and Z2 of the connecting cables of the Vector Network Analyzer (VNA) are matched to VNA’s input impedance Z1= Z2= ZV N A, which is usually ZV N A= 50 Ω. Therefore the S-parameter matrix becomes.

· V₁⁻ V₂⁻

¸

=

· S11 S12

S21 S22

¸ · V₁⁺ V₂⁺

¸

(3.43) The voltages on Port 1 and Port 2 are the sum of the incident and the reflected waves.

V1= V₁⁺+ V₁⁻

V2= V₂⁺+ V₂⁻ (3.44)

3.11 Propagation constant extraction from S-parameters

The propagation constant and the characteristic impedance of the transmission line can be extracted from the measured S-parameters with VNA [14]:

γ(ω) =1 l cosh⁻¹

µ1 − S₁₁² + S₂₁² 2S21

¶

(3.45)

Z0(ω) = ZV N A

s

(1 + S₁₁)²− S₂₁²

(1 − S11)²− S₂₁² (3.46) Usually the Device Under Test (DUT) is connected to the ports or cables of VNA through some type of coaxial connectors. Therefore these connectors introduce a phase shift between the calibration plane at the end of the VNA’s ports or cables and the DUT. The coaxial connectors are used even during the Short-Open-Load- Through (SOLT) calibration of the VNA as adaptors between the VNA and the calibration kit. The phase shift between the calibration plane and DUT can be compensated with the following relation [14]:

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3.12. Z- and ABCD-matrixes

[Scompensated] =

· e^−jθ¹^(ω) 0 0 e^−jθ²^(ω)

¸₋₁·

S11 S12

S21 S22

¸ · e^−jθ¹^(ω) 0 0 e^−jθ²^(ω)

¸₋₁

(3.47) where θ1,2 are the phase shifts at the calibration plane of Port 1 and Port 2. They can be expressed in terms of the phase velocity v1,2 in the connectors and the connectors’ length l1,2:

θ1,2(ω) = β1,2(ω)l1,2 = ω

v_1,2l1,2 (3.48)

In the frequency range under consideration the dielectric properties of the insulation in the connectors is considered to be non-dispersive, and thus v1,2 =const.

The extracted γ(ω) can be represented by the attenuation constant, see equation 3.26, expressed in (dB/m):

α(dB/m) = 20 log₁₀e · α(Np/m) = 8.686α(Np/m) (3.49) and phase velocity, refer to equation 3.30.

Even in the phase compensated propagation constant the residual standing wave pattern is usually present and can be seen as an oscillating shape of the attenuation constant and phase velocity. The presence of the residual standing wave pattern is caused by the systematic measurement error, which is influenced by the parameters of the high frequency connector between the measurement system and the cable [14].

The presence of the residual standing wave pattern in the measurements can be verified as the frequency difference ∆f between the successive minima and maxima and the length of the cable l are related according to:

∆f = vp

2l (3.50)

Equation 3.50 can be derived considering the fact that successive minima and maxima of the standing wave in the transmission line are spaced by λ/2 and equa- tion 3.31.

In order to correct this residual standing wave pattern the technique described in [14] could be used.

3.12 Z- and ABCD-matrixes

The disadvantages of using S-parameters are complicated calculations for some circuits, e.g. cascades. Another possible parameters description of the twoport is the impedance matrix or Z-matrix [46],

· V1

V₂

¸

=

· z11 z12

z₂₁ z₂₂

¸ · I1

I₂

¸

(3.51)

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3. Theory review

Particulary useful representation for cascaded twoports is the ABCD-matrix [46]. The model using ABCD-matrixes can be expanded by multiplying the matrixes in corresponding order.

· V1

I1

¸

=

· A B

C D

¸ · V2

I2

¸

(3.52) ABCD to Z-matrix conversion:

Z = _C¹

· A T

1 −D

¸

T = BC − AD

(3.53)

The Z-matrix can be converted to the transfer function of the twoport, where Rmis the measuring resistor at the end of the twoport.

G(ω) = V2

V1 = Rmz21

z11Rm+ z12z21− z11z22 (3.54)

3.13 Fourier transforms

Fourier transforms are very useful tools for signal modeling, enabling transformation of signal from time domain to frequency domain and vice versa.

F (ω) = Z∞

−∞

f (t) · e^−jωtdt (3.55)

f (t) = 1 2π

Z∞

−∞

F (ω) · e^jωtdω (3.56)

Discrete Fourier transformation is performed on a sampled signal. Integration is replaced by summation of narrow rectangles under the signal function,

X(k) = 1 N

N −1X

n=0

x(n) · e^−j^2πnk^N (3.57)

x(n) =

N −1X

n=0

X(k) · e^j^2πnk^N (3.58)

the frequencies are obtained by

ωk= k · ^2π_T fk =_T^k (3.59)

where:

N number of samples, 24

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3.13. Fourier transforms

n sample index in time domain, k sample index in frequency domain, T signal length in time domain.

The maximal frequency bandwidth using the discrete Fourier transforms is defined by the sampling theorem - sampling frequency must be at least twice the highest frequency component of the signal.

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Chapter 4

Dielectric properties of water trees

In this chapter the dielectric properties of the cables are presented. The measurement objects consist of field aged cables and new cables aged under accelerated conditions. Two types of measurement systems were used: the Dielectric Spec- troscopy (DS) and the developed High Frequency measurements superimposed on High Voltage (HF-o-HV). Water Trees (WT) were also analyzed optically.

4.1 Field aged cables

The measurement objects were made from the field aged cables kept in a dry environment for several years. Thus WT in them were considered to be dried out.

The measurement objects were prepared by separating one of the phases from the 3-phase cables. The general properties of the measurement objects are presented in Table 4.1, while detailed properties can be found in Appendix A.

The cable lengths were rather short, thus in order to obtain accurate results of dielectric spectroscopy measurements high voltage terminations on the cables were guarded and shielded [10, 4]. A tinned copper tubular braid consisting of 396 wires each of 0.2 mm in diameter was used to create a well defined coaxial structure which is needed for high frequency measurements. By the same time it allows water penetration that is important for WT refilling.

The cables were placed in the reservoirs filled with tap water. The temperature of water could be increased from ambient to 45^◦C. In order to accelerate the refilling of WT the temperature of water in reservoirs was increased to 45^◦C and the cables were energized with 50 Hz, nominal phase voltage Uph for 160 days.

4.2 Accelerated aged cables

Measurement objects were prepared form a new one-phase cable consisting of inner conductor, conductor shield, insulation and insulation shield. The screen wires and oversheath were absent. This cable was supplied by Ericsson Network Technologies.