On-line time domain reflectometry diagnostics of medium voltage ...

On-line time domain reflectometry diagnostics ofmedium voltage XLPE power cables

VALENTINAS DUBICKAS

Licentiate ThesisStockholm, Sweden 2006

TRITA-EE 2006:010ISSN 1653-5146ISRN KTH/R-0504-SEISBN 91-7178-327-X

Elektroteknisk teori och konstruktionKTH

SE-100 44 StockholmSWEDEN

Akademisk avhandling som med tillstand av Kungl Tekniska hogskolan framlaggestill offentlig granskning for avlaggande av teknologie licenciatexamen torsdagenden 27 april 2006 klockan 10.00 i sal D2, Kungl Tekniska hogskolan, Lindstedtsv 5,Stockholm.

© Valentinas Dubickas, 2006

Tryck: Universitetsservice US AB

Abstract

Degradation of XLPE insulated power cables by water-trees is a primary cause offailure of these cables. The detection of water-trees and information about theseverity of the degradation can be obtained with off-line measurement using di-electric spectroscopy. In many situations only a limited part of the cable may bedegraded by the water-trees. In such a situation a method for localization of thiswater-treed section would be desirable. On-voltage Time Domain Reflectometry(TDR) diagnostics proved to be capable of localizing the water-tree degraded sec-tions of the cable. The possibility of using on-voltage TDR as a diagnostic methodopens up as a further step for the development of an on-line TDR method wherethe diagnostics are performed using pre-mounted sensors on the operating powercable. The benefits with such a method are: ability to perform diagnostics with-out disconnecting the cable from a power grid; the diagnostics performed duringa longer period of time could give an extra information; no need for an externalhigh-voltage supply unit.

In this thesis the sensors for the on-line TDR are investigated in terms of sensi-tivity and bandwidth. High frequency models were built and the simulation resultsin frequency and time domains were verified by measurements.

Results of the on-voltage TDR measurements on the degraded XLPE cables inlaboratory as well as on-site are presented.

The on-line TDR system and the results of a four-days on-line measurementsequence 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 propaga-tion velocity in the cable.

A method has been developed for high frequency characterization of power ca-bles with twisted screen wires, where the measurements are performed using in-ductive strip sensors. This technique allows the high frequency parameters of theselected section of the cable to be extracted. The high frequency parameters areextracted from frequency domain measurements of S-parameters as well as fromTDR measurements.

iii

Acknowledgments

First of all I would like to express my gratitude to the following persons and organ-isations for the help and encouragement during the work:

My supervisor Dr. Hans Edin for guidance, interesting and productive discussions,enjoyable measurements together and also for giving the freedom to experimentwith my own ideas.

Prof. Roland Eriksson for giving me the opportunity to perform the work at RoyalInstitute of Technology.

The financial support from the Elektra program of Elforsk AB, Energimyndigheten,ABB AB and Banverket is gratefully acknowledged.

Dr. Ruslan Papazyan, Mr. Kenneth Johansson and Dr. Per Pettersson for interest-ing and rewarding discussions on time domain reflectometry, transient protectionand sensor topics.

Mr. Kjell Oberger, Fortum Distribution and Mr. Henrik Flodqvist, VattenfallEldistribution AB for productive cooperation.

Mr. Olle Branvall for producing the parts for the sensors.

And finally I would like to thank my family and especially Aurelija for supportand encouragement during the work.

v

List of publications

1. V. Dubickas and H. Edin, ”Couplers for on-line time domain reflectometrydiagnostics of power cables”, In Proceedings of Conference on Electrical Insu-lation and Dielectric Phenomena, 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”, InProceedings of the Nordic Insulation Symposium (Nord-Is), Trondheim, Nor-way, July 2005.

3. V.Dubickas and H. Edin, ”High frequency model of Rogowski coil with smallnumber of turns”, Submitted to IEEE Transactions on Instrumentation andMeasurements, October, 2005.

vii

Contents

Abstract iii

Acknowledgments v

List of publications vii

Contents ix

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Power cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Water trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Countermeasures to water treeing in power cables . . . . . . . . . . . 41.5 Power cable diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . 51.6 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.7 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Transmission line theory 92.1 Transmission line equations . . . . . . . . . . . . . . . . . . . . . . . 92.2 Time domain reflectometry . . . . . . . . . . . . . . . . . . . . . . . 112.3 S-parameters matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Z- and ABCD-matrixes . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 Fourier transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

ix

x CONTENTS

3 Sensors 153.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Coupling capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Capacitive strip sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 203.4 Inductive strip sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 233.5 Rogowski coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.6 Comparison of the investigated sensors . . . . . . . . . . . . . . . . . 35

4 Extraction of the propagation constant for a cable with twistedscreen wires 374.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.3 Reference measurements . . . . . . . . . . . . . . . . . . . . . . . . . 374.4 Propagation constant extraction from frequency domain measurements 384.5 Propagation constant extraction from time domain measurements . . 394.6 On-line setup for propagation constant extraction from time domain

measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5 On-voltage TDR 435.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2 High frequency dielectric properties of water-tree degraded insulation 435.3 Measuring system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.4 Measurement objects . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.5 Water tree detection: Cable 1 . . . . . . . . . . . . . . . . . . . . . . 455.6 Water tree detection: Cable 2 . . . . . . . . . . . . . . . . . . . . . . 465.7 Water tree detection: Cable 3 . . . . . . . . . . . . . . . . . . . . . . 485.8 Water tree detection: Cable 4 . . . . . . . . . . . . . . . . . . . . . . 485.9 Influence of non-linear capacitance of the coupling capacitors to the

measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.10 Influence of the connecting loop inductance . . . . . . . . . . . . . . 515.11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6 On-line TDR 536.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.2 Measuring system No.1 . . . . . . . . . . . . . . . . . . . . . . . . . 536.3 On-line measurement results: water trees . . . . . . . . . . . . . . . 556.4 On-line measurement results: temperature variations . . . . . . . . . 566.5 Verification of the pulse propagation velocity in the cable dependence

on the temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.6 Limitations and advantages . . . . . . . . . . . . . . . . . . . . . . . 586.7 Measuring system No.2 . . . . . . . . . . . . . . . . . . . . . . . . . 596.8 High voltage testing of the coupling capacitors . . . . . . . . . . . . 596.9 Limitations and advantages . . . . . . . . . . . . . . . . . . . . . . . 60

xi

7 Summary and conclusions 61

8 Future work 63

Bibliography 65

To Aurelija

Chapter 1

Introduction

1.1 Background

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

1.2 Power cables

Power cable history begins at the end of the 19th century [3]. Different materialswere used as an insulation: natural rubber, vulcanized rubber, oil and wax, cottonand 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. Duringthe years the paper impregnation was improved by changing vegetable substancesby mineral oil, later by wax-filled compounds. The sheath protecting the cable frommoisture ingress progressed from lead to aluminium [3].

XLPE cables

Development of synthetic polymer materials boosted the birth of extruded powercables. The growth of solid dielectric insulated medium voltage cables began in theearly 1950s, with the introduction of butyl rubber and thermoplastic high molecularweight polyethylene. Introduction of crosslinked polyethylene (XLPE) as an insula-tion material in the mid-1960s seemed to be very promising due to good electrical,thermal and mechanical properties. XLPE has low permittivity, high dielectric

1

2 CHAPTER 1. INTRODUCTION

Oversheath

Metallic screen

Screen bed

Insulation screen

XLPE insulation

Conductor screen

Conductor

Figure 1.1: Common design of second generation XLPE cable.

strength and negligible dielectric loss. Maximal continuous operating temperatureof XLPE is 90C, while during emergency overload and short-circuit voltages thetemperature can reach 130C and 250C respectively. Good mechanical proper-ties eliminated the tendency to stress-cracking. Therefore, introduction of XLPEincreased the capability of polymeric insulated cables because of their higher tem-perature ratings, resulting replacement of PILC cables by XLPE.

First generation XLPE cables

XLPE cables in Sweden were introduced in late 1960s [4, 5]. The first type of theintroduced cables had an extruded conductor screen providing a smooth boundarybetween a conductor and the XLPE insulation. An insulation screen was made ofconducting tape, or graphite paint on XLPE with conducting textile tape woundedon it. The oversheath usually was made of PVC. This type of cables are referredto as the first generation XLPE cables.

Second generation XLPE cables

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

Third generation XLPE cables

Further improvements to stop water diffusion into the cable were introduced in1990s. An aluminium foil with a water absorbing powder or tape was placed under

1.3. WATER TREES 3

the cable sheath. The stranded conductors were filled with the water absorbingpowder in order to stop moisture movement along them.

1.3 Water trees

When XLPE power cables were introduced water treing phenomenon was still un-known. XLPE is an hydrophobic material therefore the first generation cables couldallow water diffusive sheath to be used, usually PVC. However water diffusion intothe XLPE cable in combination with an alternating electric field initiates the watertrees growth [6, 7]. The water trees are tree or bush shape diffuse structures in thedielectric insulation. Two types of water trees are distinguished: vented, see Figure1.2, and bow-tie. Vented water trees are initiated at the insulation surfaces, whilebow-tie are initiated inside the insulation. However vented water trees are consid-ered 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

The bow-tie trees are initiated at impurities in the insulation. The vented watertree initiation could begin from one of the following factors:

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

Irregularity in semiconducting screen where it contacts with the insulation.

Water treeing phenomenon was discovered in 1969 [8] and their growth mecha-nisms are still under investigation. A water tree growth mechanism can not bedistinguished as a single process, it is an effect of several processes taking placesimultaneously, e.g.:

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

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

Electrochemical degradation. Amorphous phase of polymer oxidation by freeradicals or oxidizing agents produced by electrolysis.

Properties of water trees

Water trees are considered as an insulating material [6]. Nevertheless they arecalled water trees, water content is only ∼1% of water trees in field aged cables[9]. Dielectric properties of water trees are similar to insulating material with apermittivity ε’=2.3-3.6 and loss-factor around tanδ=0.002-0.02 [7, 9]. However anelectric breakdown strength of the insulation is reduced by the water trees. The


Figure 1.2: Vented water trees in power cable insulation.

breakdown stress of the water treed insulation can be restored up to 50% of theinitial value by drying the insulation [6, 10]. However as soon water is present it willbe re-absorbed consequently reducing the breakdown strength. Water tree initiatedfailures are not clearly understood. Water trees cause local stress enhancementsthat could be initiation sites for electrical trees, either at power frequency or fromtransient overvoltages. XLPE is also susceptible to localized degradation causedby Partial Discharges (PD). The degradation of the XLPE appears as an erosionof the surface within the cavities and a breakdown appears after a period of timewhen a certain degree of surface roughness is attained manifesting the initiation ofelectrical trees.

1.4 Countermeasures to water treeing in power cables

Water is one of the necessary agents for water treeing. Therefore different cabledesigns were introduced to protect against water ingress and propagation in thecable [11]. Three water blocking constructions can be distinguished:

Longitudinal water-blocked conductors. Moisture propagation inside of thestranded conductor is blocked by filling the strands with semiconducting orinsulating materials, placing water absorbing powder between the strands orusing solid conductors.

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

Radial water blocking. Usually radial water-blocking is implemented by usingmetallic laminated tapes. Aluminium or lead tapes are laminated betweeninsulating or semiconducting material depending where they are placed onthe shield wires or the insulation shield.

1.5. POWER CABLE DIAGNOSTICS 5

The introduction of water Tree Retardant XLPE (TR-XLPE) reduced the size andamount of the water trees in the cables. TR-XLPE consists of XLPE insulationwith tree retardant additive [12].

1.5 Power cable diagnostics

The third generation cables are well protected from the water ingress and thereforewater treeing is seldom the cause of faults in these cables. However the secondgeneration and especially the first generation power cables are susceptible to watertreeing [5]. In Sweden ∼50% of the totaly installed 2500km XLPE cables duringthe 1965-75 are still in service. The replacement of these cables alone would cost500 million SEK [13]. Overview of the power cable diagnostics and testing can befound in [14]. In this thesis only non-destructive diagnostics are discussed.

1.5.1 Off-line diagnostics

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

Loss factor The measurements can be performed using classical Schering bridgemeasurements of loss factor at a power frequency [3, 15].

Dielectric spectroscopy In dielectric spectroscopy measurements of complexpermittivity are performed at several frequencies enabling a frequency spectrumof permittivity to be analyzed. The spectrum reflects the properties of the dielec-tric material in the measured frequency range. Water trees increase the loss andthe capacitance of the dielectric material sample. These two parameters are alsovoltage dependent. The voltage dependence of the loss and the capacitance of thewater treed cable are used as a differentiating factor in the dielectric spectroscopydiagnostics. The dielectric spectroscopy system for medium voltage XLPE powercables was developed in Electromagnetic Engineering department at Royal Instituteof Technology [13, 16, 17, 18].

Polarisation/depolarisation current measurements are performed by charg-ing the sample by DC voltage and measuring polarization current. After applyingDC voltage for a long period of time the sample is short-circuited and depolarizationcurrent is measured [15].

Return voltage measurements are similar to depolarization current measure-ments. The DC voltage charges the sample; after a relatively short period of timeduring which the sample is short-circuited, the test object is left in open-circuitcondition and the recovery voltage is measured [15].


Partial discharge diagnostics Partial Discharge (PD) diagnostics is a widelyused technique to detect discharges appearing in cavities or on surfaces of the in-sulation [19, 20, 3, 15]. Off-line PD diagnostics on the power cables are usuallyperformed by energizing the cable with the High Voltage (HV) supply. The mea-suring equipment is coupled to the cable using a coupling capacitor [19, 21]. Themethod enables the PDs 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 andmeasuring the reflections along the cable. The reflections arise due to joints alongthe cable but also due to small irregularities in the cable itself. TDR for mediumvoltage XLPE power cable diagnostics was also developed in Electromagnetic En-gineering department at Royal Institute of Technology [22, 23]. More detaileddescription of TDR can be found in Chapter 2.

1.5.2 On-line diagnostics

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

DC current measurement The method was possible to implement in Japanwhere the distribution power cables operate mostly at relatively low voltages 6,6kVand are non-grounded. DC voltage is applied to the cable conductor through aninductance and is superimposed on the grid voltage. The AC component of thecurrent which passes thought the insulation of the cable is eliminated by a filterand only the DC component is measured. The reduction of the insulation resistanceindicates the presence of water trees [24, 25].

Partial discharge diagnostics On-line partial discharges on the cables are de-tected using high frequency sensors [21, 2, 26, 27]. The sensors are of capacitive orinductive type. The capacitive sensors are usually made of conductive tape placedon the insulation screen between the HV termination and the screen wires. An-other option is to place the capacitive sensor on the insulation screen in the cablejoint, under the metallic screen. The inductive sensors usually used for on-line PDdiagnostics are Rogowski coils. They can be placed on the power cable after theearth connection, before the high voltage termination, or on the power cable’s earthconnection conductor. However PD diagnostics do not provide information aboutthe water tree content and location in the XLPE power cables.

1.6 Aim

The objective of this project was to investigate and apply the TDR diagnosticmethods on the cables on-line. The objective could be divided into three parts:

Investigation and modeling of the sensors.

1.7. THESIS OUTLINE 7

Development of the on-line TDR methods.

Practical application of the on-line TDR on power cables on-site.

1.7 Thesis outline

Chapter 1 gives a background to cable design, water treeing phenomenon and diag-nostic techniques. Chapter 2 presents basic concepts in the transmission line theory.In Chapter 3 sensors are investigated and modeled both in frequency and time do-mains. A method for a propagation constant extraction of a selected part of a cablewith the twisted screen wires is presented in Chapter 4. Chapter 5 investigateson-voltage TDR diagnostics, laboratory and on-site measurements are presented.In Chapter 6 on-line TDR systems are presented and the on-line measurement re-sults are investigated. Chapter 7 contains summary and general conclusions, whileChapter 8 proposes some topics of interest for future work.

Chapter 2

Transmission line theory

2.1 Transmission line equations

Transmission lines differ from ordinary electric networks in one essential feature.The physical dimensions of electric networks are very much smaller than the oper-ating wavelength, however transmission lines are usually a considerable fraction ofa wavelength and may even be many wavelengths long. Therefore the transmissionline must be described by circuit parameters that are distributed through its length.The equivalent distributed elements circuit of a two wire transmission line is shownin Figure 2.1.

( , )i x x t+ ∆

( , )v x t

( , )i x t

( , )v x x t+ ∆

x∆

R x∆ L x∆

G x∆ C x∆

Figure 2.1: Equivalent circuit of a two conductor transmission line of length ∆x.

The distributed elements circuit in Figure 2.1 can be described by a pair of first-order partial differential equations 2.1 and 2.2, which are called the transmissionline equations [28, 29].

−∂v(x, t)∂x

= Ri(x, t) + L∂i(x, t)∂t

(2.1)

−∂i(x, t)∂x

= Gv(x, t) + C∂v(x, t)∂t

(2.2)

9

10 CHAPTER 2. TRANSMISSION LINE THEORY

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

−dV (x)dx

= (R+ jωL)I(x) (2.3)

−dI(x)dx

= (G+ jωC)V (x) (2.4)

Solving equations 2.3 and 2.4 for V (x) and I(x) the following equations areobtained.

d2V (x)dx2

= γ2V (x) (2.5)

d2I(x)dx2

= γ2I(x) (2.6)

where:γ = α+ jβ =

√(R+ jωL)(G+ jωC) (2.7)

is the propagation constant which is composed of real and imaginary parts. αand β, are the attenuation constant (Np/m) and phase constant (rad/m) respec-tively. Solution of equations 2.5 and 2.6 are

V (x) = V +(x) + V −(x) = V +0 e−γx + V −0 e+γx (2.8)

I(x) = I+(x) + I−(x) = I+0 e−γx + I−0 e

+γx (2.9)

where the plus and minus superscripts denote waves traveling in the positiveand negative x directions respectively. The ratio of the voltage and the current atany x for and infinitely long line is independent of x and is called the characteristicimpedance of the line.

Z0 =V (x)I(x)

=

√R+ jωL

G+ jωC(2.10)

The phase velocity of the wave along the line is

v =ω

β(2.11)

And the wavelenght

λ =2πβ

(2.12)

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

Zi = Z0ZL + Z0 tanh γlZ0 + ZL tanh γl

(2.13)

2.2. TIME DOMAIN REFLECTOMETRY 11

2.2 Time domain reflectometry

Usually time domain measurements provide intuitively understandable results thatare easier to interpret, compared with the frequency domain S-parameter measure-ments. The basic TDR system consists of a fast rise-time pulse (or step) generatorand a high speed oscilloscope, see Figure 2.2.

Pulse/step

generator

High speed

oscilloscope

0Z LZ

iV r

V

l

Figure 2.2: Block diagram of a TDR system.

The incident pulse or step Vi is sent into the transmission line Z0. If Z0 6= 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 thevoltage reflection coefficient and can be expressed as:

Γ =VrVi

=ZL − Z0

ZL + Z0(2.14)

The reflected voltage wave Vr will propagate back to the measuring system and willbe recorded by the high speed oscilloscope after a traveling time tr. Knowing thewave propagation velocity v in the transmission line the distance to the discontinuitycan be obtained as:

l = vtr2

(2.15)

2.3 S-parameters matrix

Usually the currents and the voltages can not be measured in a direct mannerat microwave frequencies. The directly measurable quantities are the amplitudesand the phase angles of the waves reflected from and transmitted through the testobject, relative to the incident wave amplitudes and phase angles. The matrixdescribing this linear relationship is called the S-parameters matrix [29, 30]. TheS-parameters matrix of the twoport is:

[b1b2

]=[S11 S12

S21 S22

] [a1

a2

](2.16)

12 CHAPTER 2. TRANSMISSION LINE THEORY

11 12

21 22

S S

S S

1Z

2Z

1V

+

1V

−

2V

+

2V

−

Port 1 Port 2

Figure 2.3: Incident and reflected waves in a twoport.

whereb1 = V −1√

Z1a1 = V +

1√Z1

b2 = V −2√Z2

a2 = V +2√Z2

(2.17)

Usually the impedances Z1 and Z2 of the connecting cables of the networkanalyzers are matched to the input impedance Z0 of the Network Analyzer (NA)itself i.e. Z1 = Z2 = Z0. Therefore the S-parameter matrix becomes.

[V −1V −2

]=[S11 S12

S21 S22

] [V +

1

V +2

](2.18)

The voltages on Port1 and Port2 are the sum of the incident and the reflectedwaves.

V1 = V +1 + V −1

V2 = V +2 + V −2

(2.19)

2.4 Z- and ABCD-matrixes

The disadvantages of S-parameters are complicated calculations for some circuits,e.g. cascades. Another possible parameters description of the twoport is the impedancematrix or Z-matrix [30],

[V1

V2

]=[z11 z12

z21 z22

] [I1I2

](2.20)

Particulary useful representation for cascaded twoports is the ABCD-matrix[30]. The model using ABCD-matrixes can be expanded by multiplying the matrixesin corresponding order.

[V1

I1

]=[A BC D

] [V2

I2

](2.21)

ABCD to Z-matrix conversion:

Z = 1C

[A T1 −D

]

T = BC −AD(2.22)

2.5. FOURIER TRANSFORMS 13

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

G(ω) =V2

V1=

Rmz21

z11Rm + z12z21 − z11z22(2.23)

2.5 Fourier transforms

Fourier transforms are very useful tools for signal modelling, enabling transforma-tion of aperiodic signal from time domain to frequency domain and vice versa.

F (ω) =

∞∫

−∞f(t) · e−jωtdt (2.24)

f(t) =1

2π

∞∫

−∞F (ω) · ejωtdω (2.25)

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

X(k) =1N

N−1∑n=0

x(n) · e−j 2πnkN (2.26)

x(n) =N−1∑n=0

X(k) · ej 2πnkN (2.27)

the frequencies are obtained by

ωk = k · 2πT fk = k

T(2.28)

where:N - number of samples,n - sample index in time domain,k - sample index in frequency domain,T - aperiodic signal length in time domain.

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

Chapter 3

Sensors

3.1 Introduction

The sensors are needed to perform the TDR power cable diagnostics on-line. Thesensors have to be installed without damaging the power cable as it has to operateon-line. The purpose of the sensors is to couple the low voltage measuring equip-ment using electric or magnetic field to the power cable operating at a HV. Thesensors have to be high frequency and broadband as the voltage pulse used for TDRis composed of high frequency components.

The sensors with the higher mentioned characteristics can be found in off-line andon-line PD diagnostics [21, 31, 32, 2, 26]. The sensors can be divided into threegroups according to their coupling mechanism to the power cable. Capacitive sen-sors which couple through electric field, inductive sensors couple through magneticfield, and directional couplers couple through both electric and magnetic fields [33].Usually directional couplers are installed between insulation screen and metalliccable sheath [31]. The technique can be regarded as invasive, and therefore thedirectional couplers are out of the scope of the thesis.

In the thesis are investigated and modelled two capacitive sensors:

Coupling capacitor

Capacitive strip sensor

and two inductive sensors:

Inductive strip sensor

Rogowski coil

Their possible placement positions on the power cable are shown in Figure 3.1.

15

16 CHAPTER 3. SENSORS

U(V)

U(V)

U(V)

Coupling capacitor couples to

the cable conductor through

the electric field between

capacitor plates.

Capacitive sensor couples to the cable conduc-

tor through the electric field between the

sensor and the cable conductor.

Inductive sensor

couples through the

magnetic field induced

from curents the

twisted screen wires.

U(V)Rogowski coil couples

through the magnetic field

induced from currents in the

ground wires.

Figure 3.1: Sensors on the power cable.

The chapter is a summary of papers 1 and 3. The sensors on the power cableare modelled and simulated in frequency and time domains in order to understandtheir properties and limitations. At the end the comparison of the sensors is pre-sented in terms of the sensitivity and the bandwidth.

3.2 Coupling capacitor

The coupling capacitors are widely used for the off-line PD diagnostics on HV cables[3, 15]. The coupling capacitor C is connected to the power cable conductor, whichduring the diagnostics is energized by HV. During the TDR diagnostics the pulseis injected and the reflections are measured through the coupling capacitor. Thecoupling capacitor represents high impedance for low frequency HV, and thereforedecouples the measuring equipment from the HV. The high frequency componentscontaining TDR signal meets low impedance and passes through the capacitor. Theschematics of the coupling capacitor connected to the cable are presented in Figure3.2.

Frequency domain

The coupling capacitor on the power cable is modelled as a lumped element circuit.The model represents the simulation when the signal is injected from the measure-ment equipment cable Zm, connected to R, through the coupling capacitor. Thesignal is measured at the far end of the power cable on the resistor Rm. The cou-pling capacitor on the cable is described by the ABCDC matrix.

3.2. COUPLING CAPACITOR 17

R

C

0Z

Insulation

Screen wires

Insulation screen

Conductor screen

backFoldedwiresscreenCoupling

capacitor

L D

l

wireGroundm

Z

Figure 3.2: The coupling capacitor connected to the cable.

ABCDC =

(1 jωL+ 1

jωC + Z1

1R 1 +

jωL+ 1jωC+Z1

R

)(3.1)

The measurement cable is terminated with the resistor R = Zm = 50Ω, thereforein the model they are replaced by equivalent series impedance Z1 = Zm/2 = 25Ω 1.At the high frequencies the inductance L between the power cable conductor andthe ground wire becomes considerable, and therefore is included in the model.The power cable is modelled as a lossy transmission line of length d and propagationconstant γ and the characteristic impedance Z0.

ABCDT =(

cosh(γd) Z0 sinh(γd)1Z0

sinh(γd) cosh(γd)

)(3.2)

The model of the coupling capacitor and the power cable is obtained by mul-tiplying the ABCD matrixes in corresponding order. The transfer function of thesystem is obtained using equations 2.22 and 2.23.The transfer function obtained from the measurements with the Network Analyzer(NA) is compared with the frequency domain model in Figure 3.3.

Examining the transfer function the following properties can be noticed. Thelower frequencies 0-5MHz are cutoff by the coupling capacitor itself. The transferfunction at frequency above 20MHz is damped by the inductance L and the semi-conductive layers of the cable. The oscillating pattern of the transfer function iscaused by standing waves in the power cable. Using the fact from transmission linetheory that the successive maxima and minima in the standing wave pattern arespaced by a half of the wavelength l = λ/2, and equations 2.11 and 2.12 the lengthof the cable can be expressed. The wave propagation velocity in the investigatedcable is approximately v = 150m/µs. The frequency difference between the stand-ing wave maxima is ∆fλ/2 = 13MHz. With the later values the calculated length

1Please note that in equation (8) in Paper 1, Z1 should be instead of Z0.


0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Gai

n

0 20 40 60 80 100 120 140 160 180 200−3000

−2500

−2000

−1500

−1000

−500

0

500

Frequency (MHz)

Pha

se (

deg)

MeasuredModel

Figure 3.3: Comparison of the measured and modelled transfer functions of thecoupling capacitor on the power cable.

of the cable is:l =

v

2∆fλ/2= 5.77m (3.3)

which is very similar to the real cable length l = 5.85m.The model of the coupling capacitor is obtained removing the ABCDT matrix ofthe power cable from the previous model. The results are presented in Figure 3.4.The high frequencies are only slightly less damped than in Figure 3.3. Therefore itcan be concluded that the high frequencies are damped mostly by the inductanceL.

Time domain

Time domain measurements were performed by injecting a pulse of 0.5V ampli-tude, 200ps rise time, 13ns wide pulse through the coupling capacitor and detect-ing the propagating pulse at the far cable end. Time domain simulation resultswere obtained by the use of Fourier transforms. Fourier transforms enable exactrepresentation of the input pulse to be used for an exact frequency domain modelof dispersion in the cable. The measurements are compared with the simulation inFigure 3.5. The first pulse in the Figure 3.5 is the transmitted pulse through thecable. The successive pulses are the detected reflections propagating in the powercable due to impedance mismatches at the cable ends.

3.2. COUPLING CAPACITOR 19

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Gai

n

0 20 40 60 80 100 120 140 160 180 200−100

−50

0

50

100

Frequency (MHz)

Pha

se (

deg)

Figure 3.4: Transfer function of the coupling capacitor.

0 50 100 150 200 250 300−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Out

put (

V)

Time (ns)

MeasuredModel

Figure 3.5: Comparison of the time domain measurements and simulation of thecoupling capacitor on the power cable.


2R

Insulation

connectortypeN−

2L

wiresscreenbackFolded

Insulation screen

Conductor screen

sensorCapacitive

wiresScreen

±( )1C f

±( )2C f

Figure 3.6: Capacitive strip sensor on the cable.

Limitations

The bandwidth of the coupling capacitor at the high frequencies is limited by theinductance L between the conductor of the cable and the ground wire, see Figure3.2. Therefore during the measurements the coupling capacitor should be fittedwith the minimal distance D and length l of the ground wire. The distance l isusually defined by the cable’s HV termination length. The distance D is limitedby safety issues, as the low voltage potential electrode of the coupling capacitorcan distort the HV electric field from the termination and cause discharges or abreakdown.

Advantages

The main advantage of using the coupling capacitor is that the capacitance C canbe selected relatively high, providing good sensitivity. The sensor can be appliedto any cable independent of the screen wires or HV termination design.

3.3 Capacitive strip sensor

The capacitive strip sensors are used for PD off-line and on-line diagnostics onthe power cables [34, 35, 36, 37, 38, 39]. Usually the sensors are placed on the HVterminations or inside of the cable joints. The sensor is made of a metal strip tightlywound on the insulation screen of the cable, see Figure 3.6. The semi-conductivematerial of the insulation screen at low frequencies act as a screen for the HVelectric field, but at high frequencies as a dielectric. Therefore in this region the50Hz HV electric field will be enclosed by insulation screen, while the high frequencypropagating pulse electric field will penetrate insulation screen and will be detectedby the capacitive strip sensor.

3.3. CAPACITIVE STRIP SENSOR 21

1V

2I

mR

2R

2C

1C

2V

2L

1R

1dC

1dR

2dR

2dC

1I

Figure 3.7: Lumped element model of the capacitive strip sensor.

Frequency domain

The capacitive strip sensor was modeled with the lumped element model [40], seeFigure 3.7. Complex, frequency dependent capacitances C1 (f), C1 (f) were mod-eled by lumped elements: dc conductivity was modeled with resistors R1, R2, purecapacitances were modeled with C1 and C2, dielectric response functions were ap-proximated with exponential decay functions - Debye functions, which were modeledwith an equivalent circuit consisting of Rd1 in series with Cd1 and Rd2 in series withCd2. The inductance of a wire from the coupler to an N-type connection and theN-type connection is modeled with L2. Rm - measuring equipment impedance. Thetransfer function of the capacitive strip sensor can be expressed:

Gcap(ω) =V2

V1=

Z4RmZ3(Z1 + Z4)

(3.4)

where:Z1 = R1|| 1

jωC1||(Rd1 + 1

jωCd1

)Z3 = Rm + jωL2

Z2 = R2|| 1jωC2||(Rd2 + 1

jωCd2

)Z4 = Z2||Z3

(3.5)

The transfer function of the capacitive strip sensor and the power cableGcap cable

was measured with the NA. The transfer function of the sensor was obtained bydividing Gcap cable with the known transfer function of the power cable Gcable. Asthe transfer function Gcable accounts only for the signal attenuation along the cable,the standing wave pattern is left in the extracted transfer function of the capac-itive sensor. The comparison of the measured and modelled transfer functions isdepicted in Figure 3.8.

Time domain

Time Domain measurements were performed by injecting a 0.25V , 200ps rise time,30ns wide pulse into the cable and detecting the propagating pulse by the capacitivesensor, placed on the far open end of the cable. The sensor has a differentiating


0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1

Gai

n

0 50 100 150 200 250 300 350−50

0

50

100

150

Pha

se (

deg)

Frequency (MHz)

MeasuredModel

Figure 3.8: Comparison of the measured and modelled transfer functions of thecapacitive strip sensor.

behavior as the elements C1 and Rm form a differentiating circuit. Simulations inPSpice were used to verify model in the time domain, see Figure 3.9.

Limitations

The capacitance C1 of the capacitive strip sensor is proportional to the sensor’slength. The higher C1 provides stronger coupling and eventually higher sensitivity.Therefore the sensitivity of the sensor is limited by the available length of insulationscreen at the HV termination, see Figure 3.1. Moreover if the sensor is placed closeto the shield wires, the sensitivity is reduced by the stray capacitance C2. In somedesigns HV termination is placed close to screen wires leaving no exposed insulationscreen. In such designs the sensor can not be used.

Advantages

The capacitive strip sensors are made of a thin copper tape that makes their pro-duction very simple and cheap.

3.4. INDUCTIVE STRIP SENSOR 23

20 30 40 50 60 70 80 90 100

−0.1

−0.05

0

0.05

0.1

Time(ns)

V2(V

)

MeasuredModel

Figure 3.9: Comparison of the time domain measurements and simulation of thecapacitive strip sensor on the power cable.

3.4 Inductive strip sensor

The description of the inductive strip sensor and the application for the measure-ments of PD on the power cable can be found in [41]. The sensor is designed to beused only on the cables with the twisted screen wires. Return current IS flowingin the twisted screen wires can be decomposed into axial IZ and radial Iϕ compo-nents. Axial magnetic field HZ resulting from the current Iϕ induces a voltage inthe inductive strip sensor, which basically is a one turn induction loop, see Figure3.10.

Frequency domain

The sensor was modelled by a lumped element model, represented in Figure 3.11.Where the elements represent: Z0-characteristic impedance of the power cable, M -mutual inductance between the twisted power cable screen and the sensor, L-selfinductance of the sensor, C-capacitance between the power cable screen and thesensor, Rm-measuring equipment impedance.

The transfer function of the inductive strip sensor can be expressed in terms ofthe equivalent circuit elements:

Gind(ω) =V2

V1=

MRm

CZ0

(jωL+ Rm

1+jωCRm

)(Rm + 1

jωC

) (3.6)


conductorInner

Insulation

Conductor and

insulation screens

wireScreen

Oversheath

InductiveCoupler

I

SI

ZI

ZH

Figure 3.10: Inductive strip sensor on the power cable.

M

C mR

L0Z

1V

2V

Figure 3.11: Lumped element model of the inductive strip sensor.

The extracted transfer function of the inductive strip sensor from the measure-ments with the NA is compared with the model in Figure 3.12.

Time domain

Time domain measurements performed by injecting a 0.25V amplitude, 200ps risetime, 30ns wide pulse, into the cable and detecting the propagating pulse by thesensor are compared with the model simulated in PSpice in Figure 3.13. The outputvoltage of the sensor is the derivative of the pulse as the induced voltage is governedby Faraday’s law.

Some of the cables have shield wires with periodically changing twisting direc-tion. The magnetic field HZ resulting from the current Iϕ is dependent on theshield wires spiralization angle. Therefore the induced voltage in the inductivestrip sensor is the highest where the shield wires are maximally twisted, equal tozero where shield wires go parallel to the cable conductor, and is negative wherethe wires are twisted to opposite direction. The phenomenon is depicted in Figure

3.4. INDUCTIVE STRIP SENSOR 25

0 100 200 300 400 500 600 7000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Gai

n

0 100 200 300 400 500 600 700−20

0

20

40

60

80

100

Pha

se (

deg)

Frequency (MHz)

MeasuredModel

Figure 3.12: Comparison of the measured and modelled transfer functions of theinductive strip sensor.

−10 0 10 20 30 40 50 60−0.015

−0.01

−0.005

0

0.005

0.01

0.015

V2 (

V)

Time (ns)

MeasuredModel

Figure 3.13: Comparison of the time domain measurements and simulation of theinductive strip sensor on the power cable.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5−300

−200

−100

0

100

200

300

Mag

nitu

de (

mV

)

Distance (m)

Figure 3.14: Magnitude of the inductive strip sensor output measured along thecable with shield wires with periodically changing twisting direction.

3.14, where the magnitude of the sensor’s output is measured at specified intervalsalong the cable.

Limitations

Low sensitivity of the inductive strip sensor is caused by the small mutual induc-tance M .

Advantages

The main advantage of the sensor is its wide bandwidth. Possibility to move sensoralong the cable during the diagnostics can sometimes be useful. The production ofthe sensor is also relatively cheap.

3.5 Rogowski coil

The Rogowski coil basically consists of a winding wound on a toroid shape core.The current carrying conductor goes though the center of the toroid. The magneticfield created by the current circulates around the conductor and also in the toroidcore. The magnetic field in the toroid core induces the voltage in the Rogowskicoil windings. To provide the shielding from noise interference and to form theconstant capacitance to ground the Rogowski coils are usually shielded by metallicenclosures.

The use of the Rogowski coil for on-line PD diagnostics is described in [2, 26, 32].In Figure 3.1 the Rogowski coil is placed on the grounded cable screen wires. An

3.5. ROGOWSKI COIL 27

D

d

h

H

H

Core

Shield

N-type connector

Figure 3.15: Rogowski coil schematics.

Table 3.1: Dimensions and number of turns of the investigated Rogowski coils.Dimensions in mm.

Coil D d h H rw NRog1 120 40 15 5 0.3 16Rog2 120 40 30 5 0.3 16Rog3 74 32 20 3 0.3 20

alternative position is on the power cable where the screen wires are removed,instead of the capacitive strip sensor, or where the screen wires are folded back.

Objects

Three Rogowski coils Rog1, Rog2 and Rog3 were built and investigated. Theschematics are presented in Figure 3.15. Dimensions of the cores, a distance Hfrom the cores to a shield, a winding wire radius rw and the number of turns N arepresented in Table 3.1.

Frequency domain

At high frequencies wave propagation inside of the Rogowski coil becomes consid-erable. Therefore the Rogowski coil mounted on a power cable depicted in Figure3.16, is modelled as a distributed element transmission line [42, 43, 44, 45]. Themodel is presented in Figure 3.17, where:Zc - characteristic impedance of the cableZload - impedance of the cable loadM ′ - distributed mutual inductance between the cable’s conductor and windings ofthe Rogowski coil


cl

wiresscreenbackFolded

coilRogowski

loadZ

mR

1V

2V

3V

Figure 3.16: Rogowski coil on the power cable.

L′ - distributed windings’ self inductanceZ ′skin - distributed windings’ wire internal impedance due to skin effectC ′ - distributed windings’ stray capacitance to the shieldC ′str - distributed stray capacitance between the turnsRm - resistance of measuring equipmentlc - length of the cablelw - length of the windings wire

The theoretical values of the elements M ′, L′, Z ′skin, C ′ can be calculated us-ing the dimensions of the Rogowski coil and the properties of the materials. Theexpressions are presented in Paper 4.

Transfer function

The transfer function of the distributed element model of the Rogowski coil can bederived:

Grog(ω) = V3V2

= jωM ′RmZ0 sinh(γlw)ZloadZS(Z0 sinh(γlw)+Rm cosh(γlw))

(3.7)

where:Wave impedance of the Rogowski coil

Z0 =

√√√√− (Z ′skin + jωL′)

ω2C ′strC ′(Z ′skin + jωL′ + 1

jωC′str

) (3.8)

Propagation constant of the Rogowski coil

γ =

√(Z ′skin + jωL′)

Z ′skin + jωL′ + 1jωC′str

· C′

C ′str(3.9)

and,

ZS =(Z ′skin + jωL′) 1

jωC′str

Z ′skin + jωL′ + 1jωC′str

(3.10)


xM ∆'

xM ∆'

xM ∆'

xL ∆'

xL ∆'

xCstr∆'

xCstr∆'

xZskin∆'

xZskin∆'

xC ∆'

xC ∆'

loadZ

cZ

mR

wl

0=x

wlx =

cl

1V

2V

2I

3V

x∆

Figure 3.17: Model of the cable and the Rogowski coil system.

Impedance of Rogowski coil

At high frequencies the Rogowski coil itself can be viewed as a transmission linewith shortened far end, and can be described by equation 2.13. To verify thetheoretical element values, the impedances of the Rogowski coils ZR were measured,and compared with the theoretical ones.

ZR theor = jωLN +Z0 tanh(lwγ)

1 + jωCNZ0 tanh(lwγ)(3.11)

where, LN and CN are series inductance and the shunt capacitance of the N-type connection. In order to improve the model the values of the elements can bemeasured and estimated. The measurement and estimation of the element valuesis described in detail in Paper 4. The comparison of the theoretical, measured andestimated Rogowski coil impedances are presented in Figures 3.18, 3.19 and 3.20.


100

101

102

103

100

105

Frequency (MHz)

Mag

nitu

de (

Ω)

100

101

102

103

−100

−50

0

50

100

Frequency (MHz)

Pha

se (

deg)

ZRmeas

ZRestm

ZRtheor

Figure 3.18: Impedance of Rog1.

100

101

102

103

100

105

Frequency (MHz)

Mag

nitu

de (

Ω)

100

101

102

103

−100

−50

0

50

100

Frequency (MHz)

Pha

se (

deg)

ZRmeas

ZRestm

ZRtheor



100

101

102

103

100

105

Frequency (MHz)

Mag

nitu

de (

Ω)

100

101

102

103

−100

−50

0

50

100

Frequency (MHz)

Pha

se (

deg)

ZRmeas

Z

Restm

ZRtheor


Transfer impedance of Rogowski coil

A parameter usually used to describe the qualitative properties of the Rogowskicoil is the transfer impedance Zt = V3/I2.

Zt theor =jωM ′RmZ0 sinh(γlw)

ZS(Z0 sinh(γlw) +Rm cosh(γlw))(3.12)

Comparison of the theoretical transfer impedances Zt theor and the ones extractedfrom the measurements with the NA, Zt meas of the Rog1, Rog2 and Rog3 coilscan be found in Figures 3.21, 3.22 and 3.23 correspondingly.

Analyzing the figures with the Rogowski coil impedances and figures with theRogowski transfer impedances the standing wave pattern can be observed. Forthe Rog2 coil the minimums are spaced by ∆fλ/2 = 55MHz. Using the wavepropagation in free space velocity v = 300m/µs and the equation 3.3 the length ofthe transmission line can be obtained.

lestm =v

2∆fλ/2= 2.72m (3.13)

The estimated length lestm is similar to the actual length of Rog2 windings wirelw = 2.24m. The actual winding wire lengths and the ones estimated from standingwave pattern of all the coils are presented in Table 3.2.

Therefore the natural conclusion follows that the wave in the Rogowski coilpropagates along the windings wire.


100

101

102

103

10−2

10−1

100

101

Mag

nitu

de (

Ω)

Frequency (MHz)

100

101

102

103

−150

−100

−50

0

50

100

Pha

se (

deg)

Frequency (MHz)

Zt meas

Zt theor

Figure 3.21: Transfer impedance of Rog1.

100

101

102

103

10−1

100

101

Mag

nitu

de (

Ω)

Frequency (MHz)

100

101

102

103

−100

−50

0

50

100

Pha

se (

deg)

Frequency (MHz)

Zt meas

Zt theor



100

101

102

103

10−2

10−1

100

101

Mag

nitu

de (

Ω)

Frequency (MHz)

100

101

102

103

−150

−100

−50

0

50

100

Frequency (MHz)

Pha

se (

deg)

Zt meas

Zt theor


Table 3.2: Comparison of the actual windings lengths and the ones calculated fromthe standing wave pattern.

Coil Rog1 Rog2 Rog3lestm 2.14 2.72 1.92lw 1.76 2.24 1.76

Time domain

The time domain measurements were performed with the Rogowski coils mountedon the power cable. Both the injected pulse V1(t) of 0.25V, 13ns length and theoutput signal V3(t) of the Rogowski coil were measured with the oscilloscope. Theoutput signal V3(t) is simulated using transfer functions of the cable Gcbl(ω) andRogowski coil Grog(ω), the measured input V1(t) and Fourier transforms. Thecable was modelled as a lossy transmission line. The detailed description of themeasurement setup and the simulation can be found in Paper 4.

V3(t) = F−1 F V1(t) ·Gcbl(ω) ·Grog(ω) (3.14)

The first pulse in Figures 3.24, 3.25 and 3.26 is the detected pulse propagatingin the cable. The following negative repetitive pulses are caused by the signalpropagating inside of the Rogowski coil along the coil windings.


0 20 40 60 80 100 120 140 160 180 200−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025

V3 (

V)

Time (ns)

V3 meas

V3 estm

V3 theor

Figure 3.24: Time domain measurements and simulations of Rog1.

0 20 40 60 80 100 120 140 160 180 200−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025

V3 (

V)

Time (ns)

V3 meas

V3 estm

V3 theor


3.6. COMPARISON OF THE INVESTIGATED SENSORS 35

0 20 40 60 80 100 120 140 160 180 200−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025

V3 (

V)

Time (ns)

V3 meas

V3 estm

V3 theor


Limitations

As mentioned before the signal to the Rogowski coil is coupled through the magneticfield produced by the current passing through the center of the coil. In the practicalapplication depicted in Figure 3.16 the current contour is composed of the cableconductor, the load impedance Zload and earth path. The contour has high enoughinductance to distort and damp the high frequency signals used for the diagnostics.

Advantages

The Rogowski coil design can be optimized for the required bandwidth. The coilscan be clamped-on the operating cable, however it gives rise to safety issues.

3.6 Comparison of the investigated sensors

The sensors are compared in terms of the bandwidth and the sensitivity in Table 3.3.The sensitivity is defined as the ratio: amplitude of the sensor output/amplitudeof the detected pulse propagating in the cable.

The bandwidth is defined as the frequency range where the magnitude of thetransfer function is ≥ 1√

2of the maximum value.

The capacitive strip sensor during the measurements was placed on the openend of the cable. The detected pulse, due to reflection at the open end, had two


Table 3.3: Properties of the investigated sensors

Sensor Bandwidth Sensitivity ZtCoupling capacitor 3.2nF 0.8-30MHz 0.5Capacitive strip sensor 25mm width 100-350MHz 0.2Rogowski coil Rog2 3-50MHz 0.08 2.1Rogowski coil Rog1 6-65MHz 0.07 1.78Rogowski coil Rog3 4-60MHz 0.06 1.76Inductive strip sensor 25mm width Ultra-wide 0.05

times higher amplitude than the propagating pulse in the cable. To compensatethis effect the sensitivity of the capacitive strip sensor is reduced by a factor 0.5.

The sensitivity of the Rogowski coils is influenced by the load impedance. Duringthe time domain measurements with Rogowski coils Zload = 50Ω. A more objectivecriterion of the Rogowski coil sensitivity is the transfer impedance Zt.

The magnitude of transfer function of the inductive strip sensor does not reachthe maximum, but instead it is increasing in the measurements range. Thereforethe bandwidth of the inductive strip sensor is referred to as an ultra-wide.

It is important to note that the high frequency properties of the sensors are notonly defined by the sensors’ design alone. Instead the properties are defined by thewhole sensor-cable system design. The factors such as:

the inductive contour of the cable connection to the sensor, or to the load -coupling capacitor and Rogowski coil,

spiralization angle of the screen wires - inductive strip sensor,

thickness of the cable insulation - capacitive strip sensor,

can be mentioned as examples.

Chapter 4

Extraction of the propagationconstant for a cable with twistedscreen wires

4.1 Introduction

Knowledge of a cable’s propagation constant is important for PD [46] and TDR[47], [23] diagnostics of power cables. The TDR pulse or PD attenuation duringpropagation along the cable can be estimated if the propagation constant is known.The propagation constant measurement of a power cable on-site is more complicatedas one has access only to one cable end in a substation. Recently available on-site measurement techniques extract the propagation constant from the full-lengthcable measurements in the time domain [47], [23]. Presence of joints or degradedregions along the cable together with the influence of surrounding medium [48]would affect the propagation constant measurements. However the part of the cablein a substation may operate in a dry surrounding, and therefore can be considerednon-degraded and joints-free. Measurements on the cable part in the substationwould provide the non-corrupted propagation constant.

4.2 Object

The power cable used for the experiments was an XLPE insulated, second gen-eration, 1-phase, 5.75m long, 12kV with the twisted screen wires. The twistingdirection is periodically changing every 0.46m.

4.3 Reference measurements

The reference propagation constant was extracted from the measurements with theNA. The technique is implemented by measuring S-parameters of the whole length

37

38CHAPTER 4. EXTRACTION OF THE PROPAGATION CONSTANT FOR A

CABLE WITH TWISTED SCREEN WIRES

a b

Testconnection

Inductivecoupler

Powercable

albl

abl

Terminatingresistance

−

+

1

1

V

V

−

aV2−

− bV2

Figure 4.1: Measurements setup.

power cable [49].

γ(ω) =1l

cosh−1

(1− S2

11 + S221

2S21

)(4.1)

The attenuation constant and the propagation velocity are obtained using equations2.7 and 2.11 respectively.

4.4 Propagation constant extraction from frequencydomain measurements

An HP8712ES (0.3MHz-1.3GHz) NA was used for measuring the S-parameters.Port1 of the NA was connected to the test connection, while Port2 was connectedto inductive strip sensor. The S-parameters are measured when the sensor is placedat location a, refer to Figure 4.1. Afterwards the sensor is moved to the location band the the measurements are repeated.

The inductive strip sensor was placed at the locations where the screen wiresare maximally twisted, every 0.46m, as the coupling at these locations is the high-est. Because of the changing screen wires direction of twisting the induced voltagepolarity is different at a and b locations.

It can be showed that the propagation constant of the cable part lab can be ex-tracted using equation 4.2, where subscripts a and b denote S-parameters measuredat the respective locations.

γ(ω) = − 1lab

ln(k · S21b(ω)

S21a(ω)

)(4.2)

where: k = −1 if the twisting direction at location a is opposite to b, and k = 1if the twisting direction is the same at the both locations.

The extracted and the reference propagation constants are compared in Figure4.2. It was found that reliable results are obtained from the frequency domainmeasurements when the distance lab is approximately 2m or more.

4.5. PROPAGATION CONSTANT EXTRACTION FROM TIME DOMAINMEASUREMENTS 39

0 200 400 600 800 1000 1200 1400−2

0

2

4

6

8

10

Atte

nuat

ion

cons

tant

(dB

/m)

0 200 400 600 800 1000 1200 1400100

120

140

160

180

200

Pro

paga

tion

velo

city

(m

/µs)

Frequency (MHz)

Referencelab=2.76m

Figure 4.2: Comparison of the propagation constants: the reference and extractedfrom measurements with inductive strip sensor in frequency domain. The distancebetween measurements lab = 2.76m (6 periods).

4.5 Propagation constant extraction from time domainmeasurements

A pulse of 2.5V amplitude, 13ns length is injected to the cable through the testconnection. The signals Vo a and Vo b are measured with the inductive strip sensorat the respective locations. It can be shown that the propagation constant can beextracted using Fourier transforms of signals Vo a and Vo b in equation 4.3.

γ(ω) = − 1lab

ln(F Vo b(t)F Vo a(t)

)(4.3)

The results are compared to the reference propagation constant in Figure 4.3.One of the limitations is the bandwidth of the oscilloscope, which is 500MHz, there-fore the extracted propagation constant was found to be valid only up to 800MHz.

40CHAPTER 4. EXTRACTION OF THE PROPAGATION CONSTANT FOR A

CABLE WITH TWISTED SCREEN WIRES

0 100 200 300 400 500 600 700 800 900−5

0

5

10

Atte

nuat

ion

cons

tant

(dB

/m)

0 100 200 300 400 500 600 700 800 900100

120

140

160

180

200

Pro

paga

tion

velo

city

(m

/µs)

Frequency (MHz)

Referencelab=2.76m

Figure 4.3: Comparison of the propagation constants: the reference and extractedfrom measurements with inductive strip sensor in time domain. The distance be-tween measurements lab = 2.76m (6 periods).

4.6 On-line setup for propagation constant extraction fromtime domain measurements

The time domain measurement setup can be adapted for on-line measurements.The pulse to the cable is injected through the coupling capacitor C = 3.2nF , andthe signals are detected by two identical inductive strip sensors placed at a and blocations. The results are presented in Figure 4.4. The on-line setup reduces theaccuracy of the extracted propagation constant as the coupling capacitor reducesthe magnitude of the injected signal. Therefore the signal detected by the inductivestrip sensor has smaller signal to noise ratio.

4.7 Conclusions

Limitations

As the inductive strip sensor is used for measurements the technique can be appliedonly on the cables with the twisted screen wires.

To extract the reliable results the cable length has to be ∼ 2m or longer. Duringthe on-site measurements the available length of the cable could be constrained bythe substation design.

4.7. CONCLUSIONS 41

0 100 200 300 400 500 600 700 800 900−5

0

5

10

Atte

nuat

ion

cons

tant

(dB

/m)

0 100 200 300 400 500 600 700 800 900100

120

140

160

180

200

Pro

paga

tion

velo

city

(m

/µs)

Frequency (MHz)

Referencelab=2.76m

Figure 4.4: Comparison of the propagation constants: the reference and extractedfrom measurements with inductive coupler in on-line setup. The distance betweenmeasurements lab = 2.76m (6 periods).

Advantages

The main strength of the technique is the possibility to select the section of thecable for the propagation constant extraction.

Chapter 5

On-voltage TDR

5.1 Introduction

On-voltage measurements are performed on the cable disconnected from the grid.The name on-voltage emphasizes the fact that the cable during the diagnosticsis energized with a low-frequency HV. The HV applied to the cable is used as adifferentiating parameter to detect and localize the water trees, which have thevoltage dependent ε′(V ) and ε′′(V ) [13], [16], [18].

5.2 High frequency dielectric properties of water-treedegraded insulation

As mentioned before the permittivity of water-treed insulation is voltage dependent.It was observed that the high frequency real part of permittivity of water-treed in-sulation ε′(V ) decreases when the HV is applied [22]. The phenomenon is explainedthat the charges are trapped in the tips of the water trees during the application ofthe HV. This effect would reduce the mobility of charges and their ability to followthe high frequency field of the TDR pulse. Therefore the TDR pulse propagationvelocity, equation 5.1, is higher in the water-treed section of the cable when thecable is energized by HV. It allows to use the non-linearity of ε′(V ) of the watertrees as a differentiating parameter for the diagnostics.

v =1√

µε′(V )(5.1)

5.3 Measuring system

The pulse generator is synchronized with the HVAC supply unit, refer to Figure 5.1.The pulses are sent to the cable through the coupling capacitors at the specifiedpositions of the applied HVAC: 0, 90, 180 and 270. According to equation 5.1

43

44 CHAPTER 5. ON-VOLTAGE TDR

Ch1

HVAC2kV

1HzTrigering

Synchronised

Pulse generator

DC

Filtering

x100 probe

CC

C

L

Figure 5.1: On-voltage TDR system.

the pulses sent at the phases 90 and 270, when the amplitude of the applied HVACis maximal will propagate faster than the pulses sent at 0 and 180, when theHVAC crosses zero potential. Detailed description of the on-voltage TDR systemcan be found in [22].

5.4 Measurement objects

The measurements were performed on the Cable 1 in the laboratory, while measure-ments on the Cable 2, Cable 3 and Cable 4 were performed on-site, in Strangnasand Tumba respectively.

1. Cable 1; three phase, first generation XLPE insulated, 24kV, ∼110m long.

2. Cable 2; three phase, first generation XLPE insulated, 12kV, ∼1280m long.

3. Cable 3; three phase, 24kV, ∼825m long. The cable consists of the secondand the first generation cables connected with a joint. The first part of thecable, the second generation, is new and considered to be non-degraded.

4. Cable 4; three phase, 24kV, ∼350m long.

5.5. WATER TREE DETECTION: CABLE 1 45

−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6−200

−100

0

100

200

300

Time(µs)

Am

plitu

de(m

V)

090180270

Figure 5.2: On-voltage TDR measurements the Cable 1.

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500−20

−15

−10

−5

0

5

10

Time(ns)

Am

plitu

de(m

V)

090180270

Figure 5.3: Magnified section of the signal in Figure 5.2.

5.5 Water tree detection: Cable 1

During the diagnostics the cable was energized with 6kV , 10Hz HVAC. The pulsesof 100V amplitude, 20ns rise time and 100ns pulse length were injected throughthe coupling capacitors at different phase positions of the HVAC.

The measurement results are presented in Figure 5.2. The first and the lastpulses are the injected pulse and the reflection from the open end of the cable. Theoscillations during 0.1 − 0.6µs are generated in the LC circuit composed of thecoupling capacitors and the inductive loop formed by the capacitors connection tothe cable.

Examining the magnified signal in Figure 5.3 it can be noticed that the pulsesent at the phase positions at 90 and 270 propagate faster, and the reflections aredetected 20ns sooner, than the ones at 0 and 180, this indicates the presence ofwater trees in the cable.


−2 0 2 4 6 8 10 12 14 16 18

−0.04

−0.02

0

0.02

0.04

Time(µs)

Am

plitu

de(V

)

0°90°180°270°

1 2 3

Figure 5.4: On-voltage TDR measurements on Cable 2.



The measurement results are presented in Figure 5.4. The oscillations during1−3µs are generated in the earlier mentioned LC circuit. Oscillations last longer asthe inductance is higher in the on-site setup. The locations 1, 2 and 3 are magnifiedin the Figures 5.5, 5.6 and 5.7.

From the measurements at location 1, in Figure 5.5, it can be noticed thatthe pulse sent at the phases 90 and 270 propagate faster, and the reflections aredetected sooner, than the ones at 0 and 180. The time interval between arrival ofthe 0, 180 and 90, 270 reflections is 19ns. Therefore it can be concluded thatthe water trees are present in this section of the cable.

In location 2, refer to Figure 5.6 the time interval between the reflections isincreased to 25ns, indicating water tree presence in this cable section.

The high frequency components of the propagating pulse in the cable are dampedby the the conductor and insulation screens. The pulse at the location 3 is highlydamped, refer to Figure 5.7, and the time difference between the reflections can notbe detected.

5.6. WATER TREE DETECTION: CABLE 2 47

4 4.05 4.1 4.15 4.2 4.25 4.3 4.35 4.4 4.45 4.5−7

−6

−5

−4

−3

Time(µs)

Am

plitu

de(m

V)

090180270

Figure 5.5: Magnified location 1.

7 7.05 7.1 7.15 7.2 7.25 7.3 7.35 7.4 7.45 7.5−4.5

−4

−3.5

−3

−2.5

Time(µs)

Am

plitu

de(m

V)

090180270


10.5 10.55 10.6 10.65 10.7 10.75 10.8 10.85 10.9 10.95 11

−2.5

−2

−1.5

−1

Time(µs)

Am

plitu

de(m

V)

090180270



−2 0 2 4 6 8 10 12−200

−100

0

100

200

300

Time(µs)

Am

plitu

de(m

V)

090180270



During the diagnostics the cable was energized with 6kV and 9kV , 1Hz HVAC.The pulses of 200V amplitude, 20ns rise time and 100ns pulse length were injectedthrough the coupling capacitors at different phase positions of the HVAC.

The on-voltage TDR measurements on Cable 3 are presented in Figure 5.8 wherethe reflection from the joint is at 4.7µs.

Diagnostics performed using the dielectric spectroscopy indicated presence ofthe water trees, however no shift of the reflections were observed the using on-voltage TDR, refer to Figure 5.12. The possible explanation could be that the highfrequency components of the pulse are damped while the pulse propagates in thenew cable section, and also when the pulse passes the cable joint.



The on-voltage TDR measurements are presented in Figure 5.9 and the magni-fied results are presented in Figure 5.10. Shift of the reflections caused by presenceof the water-trees was not observed. It well agrees with the results of dielectric re-sponse measurements performed on the cable. The tanδ ≈ 4 · 10−4 was at differentvoltage levels, what indicates good condition of the cable.

5.9. INFLUENCE OF NON-LINEAR CAPACITANCE OF THE COUPLINGCAPACITORS TO THE MEASUREMENTS 49

−1 0 1 2 3 4 5 6−50

0

50

100

Time(µs)

Am

plitu

de(m

V)

090180270


2.2 2.25 2.3 2.35 2.4 2.45 2.5 2.55 2.6 2.65 2.7−8

−7

−6

−5

−4

−3

Time(µs)

Am

plitu

de(m

V)

090180270

Figure 5.10: Magnified section of the signal in Figure 5.9.

5.9 Influence of non-linear capacitance of the couplingcapacitors to the measurements

The used coupling capacitors have voltage dependent capacitance. The non-linearcapacitance of the coupling capacitor was measured with the dielectric spectroscopysystem at 3kV, 6kV, 9kV and 12kV. The results are presented in Figure 5.11.

The non-linear capacitance affects the on-voltage measurements and the phe-nomenon can be observed in the measurements of the Cable 3, presented in Figure5.12, as an increased undershoot at higher voltage levels: 0kV (0,180 at 6kV),6kV (90,270 at 6kV) and 9kV (90,270 at 9kV).

The increase in the undershoot can be explained in the following way. Themeasurement system can simplified be viewed as an RC differentiator, where R is thecharacteristic impedance of the cable and C is the coupling capacitor’s capacitance.The corner frequency of this RC differentiator is:

fRC c =1

2πRC=

12π25 · 2 · 10−9

= 3.2MHz (5.2)


1 102.3

2.35

2.4

2.45

2.5

Frequency (Hz)C

apac

itanc

e (n

F)

3kV6kV9kV12kV

Figure 5.11: Dielectric spectroscopy measurements of non-linear capacitance of thecoupling capacitor.

5.5 5.55 5.6 5.65 5.7 5.75 5.8 5.85 5.9 5.95 6−30

−25

−20

−15

−10

−5

Time(µs)

Am

plitu

de(m

V)

0kV (0° 6kV)6kV (90° 6kV)0kV (180° 6kV)6kV (270° 6kV)9kV (90° 9kV)9kV (270° 9kV)

Figure 5.12: Magnified on-voltage TDR measurements on Cable 3.

When the pulse of frequency content 0-70MHz [22] from the pulse generator isinjected to the cable through the coupling capacitor, the part of frequency compo-nents below fRC c are differentiated, while frequency components above fRC c arenot. The differentiating effect to the pulse in the time domain can be seen as theundershoot after the pulse, e.g. during 0.1-0.4 µs in Figure 5.2.

The decrease in capacitance will shift fRC c to higher frequencies. As a con-sequence a wider band of the pulse frequency components are differentiated, whatcan be observed as the stronger undershoot in the time domain.

5.10. INFLUENCE OF THE CONNECTING LOOP INDUCTANCE 51

5.10 Influence of the connecting loop inductance

In order to improve the coupling capacitors connection at the high frequencies theinductance of the loop has to be reduced. It was done by placing the groundedmetallic cone [50] on the HV termination of the cable, see Figure 5.13. Using thecone the length of the connection wires is reduced as the coupling capacitors, thepulse generator and the filter/probe are mounted directly on the cone, close toconnection point to the cable conductor. In Figure 5.14 are compared on-voltageTDR measurement results with and without the cone connection.

Figure 5.13: On-voltage TDR measuring system with the cone.

6 6.5 7 7.5 8 8.5 9 9.5 10−5

0

5

10

15

Time(µs)

Am

plitu

de(m

V)

without the conewith the cone

Figure 5.14: Comparison of the on-voltage TDR with and without the cone.


5.11 Conclusions

The high frequency components of the pulse needed for the water tree detection arestrongly damped by semiconductive layers of the insulation and conductor screens,when the pulse propagates in the cable. The longest distance of the cable the watertrees could be detected from on-site measurements of Cable 2 was ∼ 500m.

The inductance of the coupling capacitor connection loop should be as low aspossible in order to increase the high frequency content of the pulse in the cable;what can be done using the setup with the cone.

If the results of different on-voltage TDR measurements are compared, the samevoltage levels of the applied HVAC should be used during diagnostics, as the mea-surements results are affected by non-linear capacitance of the coupling capacitors.

Chapter 6

On-line TDR

6.1 Introduction

On-line TDR measurements are performed on the operating cable. The pulses areinjected to the cable and the reflections are measured using the sensors. Due tosafety issues the cable is disconnected from the grid when the sensors are mounted.Afterwards the diagnostics could be performed during several days or weeks.

6.2 Measuring system No.1

For the first on-line TDR attempt due to safety issues and comparatively highsensitivity the capacitive strip sensors were used, refer to Figure 6.1. The capacitivesensors are selected as they require no galvanic connection to the conductor of thepower cable. Moreover the sensors are placed on the insulation screen, which at lowfrequencies is regarded as a ground potential, and therefore the insulation screenencloses the low frequency HVAC electric field.

However in reality the potential of the insulation screen rises to several hundredsof millivolts due to its resistance RIS , refer to Figure 6.2. The conductive tapeplaced directly on the insulation screen acts as a contact, while the the insulationscreen itself at 50Hz forms the capacitive sensor; where CLF is a low frequencycapacitance between the cable conductor and the insulation screen. The capacitivecurrent of CLF flowing in RIS creates a voltage rise VPS . As CLF is in the rangeof picofarads and RIS is in the range of ohms, the measured voltage VPS leads theHVAC by angle almost equal to 90.

The insulating tape is placed on the insulation screen, and afterwards the ca-pacitive sensors are placed on the insulating tape, refer to Figure 6.2. Such config-uration decouples 50Hz signal from measurement signal. The insulation screen atthe high frequencies can be regarded a dielectric and therefore the high frequencycomponents containing TDR pulses be injected and detected through the capacitive

53

54 CHAPTER 6. ON-LINE TDR

Ch1 Ch2

HVAC

AC

Pulse generator

DC

Synchronised

50Hz

230V

50HzTrigering

TDR measurements Phase estimation

21 3kV

Figure 6.1: On-line TDR system No.1.

strip sensors. In Figure 6.2 CHF are the high frequency capacitances between thesensors and the cable conductor.

The triggering of the pulse generator is synchronized with the frequency of thepower grid. The reference 50Hz frequency is measured at the 230V outlet. Usuallythere is a phase shift between the reference signal at the outlet and the phase-to-ground HVAC at the cable. The phase shift could occur as consequence of a differentphase connected to the outlet than at the power cable; or due to different powertransformer’s primary and secondary winding’s connection, e.g. ∆-Y. Thereforethe phase of the grid HVAC is measured using a capacitive sensor, the phase shiftis estimated and the triggering is adjusted so that the pulses are sent at 90, 180

and 270 of the grid HVAC.

Insulation screen

XLPE insulation

Conductor screen

Conductor

Insulating tape

LFC

LFC

HFC HF

C ISR

ISR

PSV

Figure 6.2: Capacitances between the cable conductor - capacitive sensor and cableconductor - insulation screen.

6.3. ON-LINE MEASUREMENT RESULTS: WATER TREES 55

6.3 On-line measurement results: water trees

The measurements were performed on the ∼ 2km long, 24kV rated voltage, threephase, second generation XLPE insulated power cable. The on-line TDR measure-ments were performed every 2 hours, during a four-days measurement sequence,with the previously described measurement system No.1.

The measurement results are presented in Figure 6.3. The small reflections inthe cable are numbered as 1, 2, 3, 4. The last reflection 5 is the reflection from thefar end of the cable. Location 4 is magnified in Figure 6.4, where velocity shift of

0 5 10 15 20 25 30 35−40

−35

−30

−25

−20

−15

−10

−5

0

5

Time(µs)

Am

plitu

de(m

V)

90°180°270°

1

2

3

4 5

Figure 6.3: On-line TDR measurements.

the reflections due to water trees was investigated. However no reflection velocityshift at 90 and 270 can be observed due to non-linear properties of water trees.

20.4 20.5 20.6 20.7 20.8−1.5

−1

−0.5

0

0.5

Time (µs)

Am

plitu

de(m

V)

90°180°270°

Figure 6.4: Magnified location 4 of the on-line TDR measurements.


6.4 On-line measurement results: temperature variations

Periodical velocity changes of the reflections were observed during the measure-ments sequence. The velocity changes are presented in Figure 6.5. The pulsespropagate slower at 6:00-8:00 o’clock, and faster 20:00-22:00 o’clock. Therefore itwas concluded that the pulse velocity changes due to temperature variations of thecable caused by a load-cycling. The reflections in Figure 6.5 marked as 6:00 and20:00 are compared in Figure 6.6. The time difference between the reflections is10ns.

0

10

20

30

40

50

60

70

80

90

10020.45 20.5 20.55 20.6 20.65 20.7 20.75 20.8 20.85 20.9

Time (µs)

Tim

e (h

)

6:00

20:00

Figure 6.5: Reflections at location 4 during a four-days measurements sequence.

6.5. VERIFICATION OF THE PULSE PROPAGATION VELOCITY IN THECABLE DEPENDENCE ON THE TEMPERATURE 57

20.4 20.5 20.6 20.7 20.8 20.9−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Time (µs)

Am

plitu

de (

mV

)

6:0020:00

Figure 6.6: Comparison of reflections at 6:00 and 20:00 o’clock, at location 4.

6.5 Verification of the pulse propagation velocity in thecable dependence on the temperature

The TDR system was used for the measurements on the cables placed in the tem-perature chamber, refer to Figure 2.2. The pulse of 1.5V amplitude and 13ns lengthwas sent to the cable, and the reflections from the open end were measured whenthe cable was heated to 30C, 60C and 90C.

The measurements were performed on two cables:

First generation XLPE, 24kV, 6.05m long

Second generation XLPE, 24kV, 5.75m long

The TDR measurements results are presented in Figure 6.7 and the pulse ve-locities are presented in Figure 6.8.

The increase in pulse velocity can be explained by the temperature dependentpermittivities ε′(T ) of the semiconductive layers in the cable. The decrease in ε′(T )of the screen bed and the conductor screen with the increase in temperature wasmeasured by [51], [52].


85 90 95 100

0

0.2

0.4

0.6

0.8

1

1.2

1.4A

mpl

itude

(V)

Time (ns)

30°C60°C90°C

First generation cable

95 100 105 110

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Am

plitu

de(V

)

Time (ns)

30°C60°C90°C

Second generation cable

Figure 6.7: Reflection from the open end at different temperatures in the first andthe second generation cables.

20 40 60 80 100182

183

184

185

186

187

188

Temperature (°C)

Gro

up v

eloc

ity (

m/µ

s)

First generation cable

20 40 60 80 100152

153

154

155

156

157

158

Temperature (°C)

Gro

up v

eloc

ity (

m/µ

s)

Second generation cable

Figure 6.8: Group velocity variation at different temperatures in the first and thesecond generation cables.

6.6 Limitations and advantages

Low capacitance of the capacitive strip sensors implies low sensitivity of the on-lineTDR measuring system No.1. Water trees could not be detected using the the on-line TDR No.1, nevertheless the temperature variations of the cable were observedusing the system. The advantage of the system is cheap and simple installation ofthe capacitive strip sensors.

6.7. MEASURING SYSTEM NO.2 59

6.7 Measuring system No.2

The on-line TDR system No.2, presented in Figure 6.9 is generally a modification ofthe on-voltage TDR system. The triggering of the pulses is synchronized with thegrid frequency. The signal measured with the oscilloscope’s Ch2 is used to estimatethe phase difference between the HVAC and the outlet 230V AC.

Trigering

Synchronised

Pulse generator

DC

Ch1

Filtering

x100 probe

CC

C

AC230V50Hz HVAC

50Hz

Ch2

x100 probe

21 3kV

Figure 6.9: On-line TDR system No.2.

6.8 High voltage testing of the coupling capacitors

The coupling capacitors in the on-line TDR No.2 are connected directly to theconductor of the power cable which is in service. Therefore the capacitors shouldhave the same insulation levels as the equipment to which they are connected.As on-line TDR No.2 is designed for 12kV and 24kV power cables the couplingcapacitors were tested for 24kV equipment standard insulation levels, defined inIEC 71-1 and IEC 358.

According to IEC 71-1 non self-restoring insulation should withstand three ratedlightning impulses and rated short-duration power-frequency voltage during 60 sec-

Table 6.1: IEC 71-1 and IEC 358 standard insulation levels

Highest voltage for Rated lightning impulse Rated short-durationequipment (r.m.s.) withstand voltage (peak) power-frequency

withstand voltage (r.m.s.)24kV 95kV 50kV


onds. To meet the criterions the coupling capacitors connected to the conductor ofthe cable were replaced by banks of the capacitors, each consisting of three 20kV,2nF capacitors connected in series. The coupling capacitors were subjected to andpassed previously defined tests.

6.9 Limitations and advantages

The coupling capacitors will be subjected to high voltage fast transients in thecable generated by switching the cable to/from the grid. The coupling capacitorscan sustain significant overvoltages, defined in IEC 71-1 [53] and IEC 358 [54]standards. However the high voltage fast transients will give rise to overvoltages onthe low voltage side of the capacitors, and therefore can damage the pulse generatorand the measuring equipment.

The main advantage of the system is its higher sensitivity compared with theon-line TDR No.1.

The system has not yet been tested during on-line conditions. The furtherdevelopment of the system is proposed in Chapter 8, Future work.

Chapter 7

Summary and conclusions

The investigated types of sensors differ in terms of bandwidth and sensitivity andplacement position on the cable, however the general tendency could be observedthat the sensors with the higher sensitivity have narrower bandwidth. The highfrequency properties of the sensors on the cable are defined not only by the designof the sensor, but by the whole sensor-cable system design.

A technique was developed for the propagation constant extraction of a selectedpart of the cable with twisted screen wires using the inductive strip sensor. Thetechnique includes the measurements with the inductive strip sensor at two locationsof the cable. In order to achieve good accuracy the minimal distance between thelocations was found to be 2m or more.

The on-voltage TDR system was adapted for on-site measurements by intro-ducing the high-frequency-high-voltage connection. The on-voltage TDR measure-ments are affected by non-linear capacitance of the coupling capacitors, thereforethe same voltage levels of the applied HVAC should be used for the results to becompared. The longest distance the water trees could be detected with the on-voltage TDR without the high-frequency-high-voltage connection was circa 500m.

The sensitivity of the on-line TDR No.1 was not sufficient to detect the watertree degraded regions in the cable. However the temperature variations of the cablecaused by load-cycling were observed on the circa 2km long cable during a four-daymeasurement sequence.

To investigate the possibility of water tree detection on-line, the coupling ca-pacitors should be used, as they have the highest sensitivity among the investigatedsensors. The coupling capacitors introduce minor possibility of failure during di-agnostics as they were tested according IEC 71-1 and IEC 358 standard insulationlevels for 24kV equipment. The issue is the measuring equipment subjection toovervoltages rising on the low-voltage side of the coupling capacitors from highvoltage fast transients in the cable.

61

Chapter 8

Future work

The natural continuation of the project would be a development of the on-line TDRNo.2. The transients caused by cable switching to and from the grid should be mea-sured for the different lengths of the cables and different types of circuit breakers.According to transients appearing in the real-life conditions, the overvoltage pro-tection should be designed at the low-voltage side of the coupling capacitors.

More measurements both on-line and on-voltage should be carried out in orderto investigate the systems’ limitations in the on-site conditions, e.g. the longestdistance the water trees can be detected using the high-voltage-high-frequency con-nection. Another interesting topic is to investigate the systems’ limits of detectingdifferent amount of water trees in the cable by correlating the TDR and the dielec-tric response measurements.

The diagnostics system could be made more compact by building a modularinstrument consisting basically of a high-speed digitizer and a signal generator forthe synchronized triggering.

63

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