on-line time domain reflectometry diagnostics of mv xlpe power cables
TRANSCRIPT
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On-line time domain reflectometry diagnostics of
medium voltage XLPE power cables
VALENTINAS DUBICKAS
Licentiate Thesis
Stockholm, Sweden 2006
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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
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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 during
a 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.
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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.
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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.
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Contents
Abstract iii
Acknowledgments v
List of publications vii
Contents ix
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Power cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Water trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Countermeasures to water treeing in power cables . . . . . . . . . . . 4
1.5 Power cable diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.7 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Transmission line theory 9
2.1 Transmission line equations . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Time domain reflectometry . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 S-parameters matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Z- and ABCD-matrixes . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Fourier transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
ix
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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.4 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 C onclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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
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xi
7 Summary and conclusions 61
8 Future work 63
Bibliography 65
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To Aurelija
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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 cablesPower 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
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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 between
XLPE 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 cables 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
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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 the
dielectric 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 free
radicals 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=2.3-3.6 and loss-factor around tan=0.002-0.02 [7, 9]. However anelectric breakdown strength of the insulation is reduced by the water trees. The
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4 CHAPTER 1. INTRODUCTION
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 or
using 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.
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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 during
the 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].
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6 CHAPTER 1. INTRODUCTION
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 along
the 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 the
current 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 cables earth
connection 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.
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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.
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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)
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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+jL)I(x) (2.3)
dI(x)
dx = (G +jC)V(x) (2.4)
Solving equations 2.3 and 2.4 for V(x) and I(x) the following equations areobtained.
d2V(x)
dx2 =2
V(x) (2.5)
d2I(x)
dx2 =2I(x) (2.6)
where:= +j=
(R+jL)(G +jC) (2.7)
is the propagation constant which is composed of real and imaginary parts. and , 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 ex + V0 e
+x (2.8)
I(x) = I+(x) + I(x) = I+0 ex + I0 e+x (2.9)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 atanyx for and infinitely long line is independent ofx and is called the characteristicimpedance of the line.
Z0=V(x)
I(x) =
R+jL
G +jC (2.10)
The phase velocity of the wave along the line is
v=
(2.11)
And the wavelenght=
2
(2.12)
When the transmission line with the characteristic impedance Z0 and the prop-agation constant is terminated at the distance l by the load impedance ZL, thegenerator looking into the line sees an input impedance Zi.
Zi = Z0ZL+ Z0tanh l
Z0+ ZLtanh l (2.13)
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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 rV
l
Figure 2.2: Block diagram of a TDR system.
The incident pulse or step Vi is sent into the transmission line Z0. IfZ0=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:
= VrVi
=ZL Z0ZL+ Z0
(2.14)
The reflected voltage waveVr will propagate back to the measuring system and willbe recorded by the high speed oscilloscope after a traveling time tr. Knowing thewave propagation velocity vin 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 S12S21 S22
a1a2
(2.16)
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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.
where
b1= V
1Z1
a1= V+
1Z1
b2= V
2Z2
a2= V+
2Z2
(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.
V1V2
=
S11 S12S21 S22
V+1V+2
(2.18)
The voltages on Port1 and Port2 are the sum of the incident and the reflectedwaves.
V1= V+
1 + V1V2= 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],
V1V2
=
z11 z12z21 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.
V1I1
=
A BC D
V2
I2
(2.21)
ABCD to Z-matrix conversion:
Z= 1C
A T
1 D
T =BC AD
(2.22)
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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() = V2V1
= 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() =
f(t) ejt dt (2.24)
f(t) = 1
2
F() ejt d (2.25)
Discrete Fourier transformation is performed on a sampled signal. Integrationis replaced by summation of narrow rectangles under the signal function,
X(k) = 1
N
N1
n=0x(n) ej
2nkN (2.26)
x(n) =N1n=0
X(k) ej2nkN (2.27)
the frequencies are obtained by
k = k 2
T fk = kT
(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.
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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
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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 themagnetic field induced
from curents the
twisted screen wires.
U(V)Rogowski coil couplesthrough 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 capacitorCis 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 ABCDCmatrix.
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3.2. COUPLING CAPACITOR 17
R
C
0Z
Insulation
Screenwires
Insulation screen
Conductor screen
backFoldedwiresscreenCoupling
capacitor
L D
l
wireGroundm
Z
Figure 3.2: The coupling capacitor connected to the cable.
ABCDC=
1 jL + 1
jC + Z1
1R 1 +
jL+ 1jC
+Z1R
(3.1)
The measurement cable is terminated with the resistorR= Zm= 50, thereforein the model they are replaced by equivalent series impedance Z1= Zm/2 = 25
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 dand propagationconstant and the characteristic impedance Z0.
ABCDT =
cosh(d) Z0sinh(d)1
Z0sinh(d) cosh(d)
(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 wavelengthl = /2, and equations 2.11 and 2.12 the lengthof the cable can be expressed. The wave propagation velocity in the investigatedcable is approximatelyv = 150m/s. The frequency difference between the stand-ing wave maxima is f/2 = 13MHz. With the later values the calculated length
1Please note that in equation (8) in Paper 1, Z1 should be instead ofZ0.
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18 CHAPTER 3. SENSORS
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
Gain
0 20 40 60 80 100 120 140 160 180 2003000
2500
2000
1500
1000
500
0
500
Frequency (MHz)
Phase(d
eg)
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
2f/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, 13nswide 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.
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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
Gain
0 20 40 60 80 100 120 140 160 180 200100
50
0
50
100
Frequency (MHz)
Phase(deg)
Figure 3.4: Transfer function of the coupling capacitor.
0 50 100 150 200 250 3000.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Output(V)
Time (ns)
MeasuredModel
Figure 3.5: Comparison of the time domain measurements and simulation of thecoupling capacitor on the power cable.
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20 CHAPTER 3. SENSORS
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 theinductanceL 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 cables 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 a
breakdown.
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.
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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], see
Figure 3.7. Complex, frequency dependent capacitancesC1(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 ofRd1in series withCd1and Rd2in series withCd2. The inductance of a wire from the coupler to an N-type connection and theN-type connection is modeled withL2. Rm- measuring equipment impedance. The
transfer function of the capacitive strip sensor can be expressed:
Gcap() = V2V1
= Z4Rm
Z3(Z1+ Z4) (3.4)
where:
Z1= R1|| 1
jC1||
Rd1+ 1
jCd1
Z3= Rm+jL2
Z2= R2|| 1
jC2||
Rd2+ 1
jCd2
Z4= Z2||Z3
(3.5)
The transfer function of the capacitive strip sensor and the power cable Gcap cablewas measured with the NA. The transfer function of the sensor was obtained bydividingGcap cable with the known transfer function of the power cable Gcable. Asthe transfer functionGcableaccounts 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, 200psrise time,30nswide 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
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22 CHAPTER 3. SENSORS
0 50 100 150 200 250 300 3500
0.2
0.4
0.6
0.8
1
Gain
0 50 100 150 200 250 300 35050
0
50
100
150
Phase(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 sensorslength. The higherC1 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 some
designs 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.
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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 currentIS flowingin the twisted screen wires can be decomposed into axial IZ and radial I compo-nents. Axial magnetic fieldHZ resulting from the current I 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() = V2V1
= MRm
CZ0
jL + Rm
1+jCRm
Rm+
1jC
(3.6)
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24 CHAPTER 3. SENSORS
conductorInner
Insulation
Conductor and
insulation screens
wireScreen
Oversheath
Inductive
Coupler
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 Faradays law.
Some of the cables have shield wires with periodically changing twisting direc-tion. The magnetic field HZ resulting from the current I 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
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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
Gain
0 100 200 300 400 500 600 70020
0
20
40
60
80
100
Phase(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 50 600.015
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.
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26 CHAPTER 3. SENSORS
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5300
200
100
0
100
200
300
Magnitude(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 sensors output is measured at specified intervalsalong the cable.
Limitations
Low sensitivity of the inductive strip sensor is caused by the small mutual induc-tanceM.
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
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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 cables conductor and windings ofthe Rogowski coil
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28 CHAPTER 3. SENSORS
cl
wiresscreen
backFolded
coilRogowski
loadZ
mR
1V
2V
3V
Figure 3.16: Rogowski coil on the power cable.
L - distributed windings self inductanceZskin - distributed windings wire internal impedance due to skin effectC - distributed windings stray capacitance to the shieldCstr - 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, Zskin, 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 () = V3V2
= jMRmZ0sinh(lw)
ZloadZS(Z0sinh(lw)+Rmcosh(lw)) (3.7)
where:Wave impedance of the Rogowski coil
Z0=
(Zskin+j L)2CstrC
Zskin+ jL
+ 1jCstr
(3.8)Propagation constant of the Rogowski coil
=
(Zskin+jL
)
Zskin+ jL+ 1jCstr
C
Cstr(3.9)
and,
ZS=(Zskin +jL
) 1jCstrZskin+ jL
+ 1jCstr(3.10)
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3.5. ROGOWSKI COIL 29
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 ZRwere measured,and compared with the theoretical ones.
ZR theor= jLN+ Z0tanh(lw)
1 +jCNZ0tanh(lw) (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.
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30 CHAPTER 3. SENSORS
100
101
102
103
100
105
Frequency (MHz)
Magnitude()
100
101
102
103
100
50
0
50
100
Frequency (MHz)
Phase(deg)
ZRmeas
ZRestm
ZRtheor
Figure 3.18: Impedance of Rog1.
100
101
102
103
100
10
5
Frequency (MHz)
Magnitude()
100
101
102
103
100
50
0
50
100
Frequency (MHz)
Phas
e(deg)
ZRmeas
ZRestm
ZRtheor
Figure 3.19: Impedance of Rog2.
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3.5. ROGOWSKI COIL 31
100
101
102
103
100
105
Frequency (MHz)
Magnitude()
100
101
102
103
100
50
0
50
100
Frequency (MHz)
Phase(deg)
ZRmeas
ZRestm
ZRtheor
Figure 3.20: Impedance of Rog3.
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= jMRmZ0sinh(lw)
ZS(Z0sinh(lw) + Rmcosh(lw)) (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 f/2 = 55MHz. Using the wavepropagation in free space velocity v = 300m/s and the equation 3.3 the length of
the transmission line can be obtained.
lestm= v
2f/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.
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32 CHAPTER 3. SENSORS
100
101
102
103
102
101
100
101
Magnitude()
Frequency (MHz)
100
101
102
103
150
100
50
0
50
100
Phase(deg)
Frequency (MHz)
Zt meas
Zt theor
Figure 3.21: Transfer impedance of Rog1.
100
101
102
103
101
100
10
1
Magnitude()
Frequency (MHz)
100
101
102
103
100
50
0
50
100
Pha
se(deg)
Frequency (MHz)
Zt meas
Zt theor
Figure 3.22: Transfer impedance of Rog2.
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3.5. ROGOWSKI COIL 33
100
101
102
103
102
101
100
101
Magnitude()
Frequency (MHz)
100
101
102
103
150
100
50
0
50
100
Frequency (MHz)
Phase(deg)
Zt
measZ
t
theor
Figure 3.23: Transfer impedance of Rog3.
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() and
Rogowski coil Grog (), 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) = F1 {F{V1(t)} Gcbl() Grog ()} (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.
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34 CHAPTER 3. SENSORS
0 20 40 60 80 100 120 140 160 180 2000.01
0.005
0
0.005
0.01
0.015
0.02
0.025
V3
(V)
Time (ns)
V3meas
V3estm
V3theor
Figure 3.24: Time domain measurements and simulations of Rog1.
0 20 40 60 80 100 120 140 160 180 2000.01
0.005
0
0.005
0.01
0.015
0.02
0.025
V3
(V)
Time (ns)
V3meas
V3estm
V3theor
Figure 3.25: Time domain measurements and simulations of Rog2.
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3.6. COMPARISON OF THE INVESTIGATED SENSORS 35
0 20 40 60 80 100 120 140 160 180 2000.01
0.005
0
0.005
0.01
0.015
0.02
0.025
V3
(V)
Time (ns)
V3meas
V3estm
V3theor
Figure 3.26: Time domain measurements and simulations of Rog3.
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 impedanceZload 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
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36 CHAPTER 3. SENSORS
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= 50. 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.
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Chapter 4
Extraction of the propagation
constant for a cable with twisted
screen wires
4.1 Introduction
Knowledge of a cables 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
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38
CHAPTER 4. EXTRACTION OF THE PROPAGATION CONSTANT FOR A
CABLE WITH TWISTED SCREEN WIRES
a b
Testconnection
Inductivecoupler
Powercable
al
bl
abl
Terminatingresistance
+
1
1
V
V
aV
2
bV2
Figure 4.1: Measurements setup.
power cable [49].
() =1
lcosh1
1 S211+ S
221
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 frequency
domain 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 subscriptsa and b denote S-parameters measuredat the respective locations.
() = 1
labln
k
S21b()
S21a()
(4.2)
where: k= 1 if the twisting direction at location a is opposite to b, andk = 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.
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4.5. PROPAGATION CONSTANT EXTRACTION FROM TIME DOMAIN
MEASUREMENTS 39
0 200 400 600 800 1000 1200 14002
0
2
4
6
8
10
Attenuationconstant(dB/m)
0 200 400 600 800 1000 1200 1400100
120
140
160
180
200
Propagationvelocity(m/s)
Frequency (MHz)
Referencelab=2.76m
Figure 4.2: Comparison of the propagation constants: the reference and extracted
from measurements with inductive strip sensor in frequency domain. The distancebetween measurements lab = 2.76m(6 periods).
4.5 Propagation constant extraction from time domain
measurements
A pulse of 2.5V amplitude, 13ns length is injected to the cable through the testconnection. The signalsVo a andVo 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.
() = 1
labln
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.
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40
CHAPTER 4. EXTRACTION OF THE PROPAGATION CONSTANT FOR A
CABLE WITH TWISTED SCREEN WIRES
0 100 200 300 400 500 600 700 800 9005
0
5
10
Attenuationconstant(dB/m)
0 100 200 300 400 500 600 700 800 900100
120
140
160
180
200
Propagationvelocity
(m/s)
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 measurementslab = 2.76m (6 periods).
4.6 On-line setup for propagation constant extraction from
time 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 2mor longer. Duringthe on-site measurements the available length of the cable could be constrained bythe substation design.
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4.7. CONCLUSIONS 41
0 100 200 300 400 500 600 700 800 9005
0
5
10
Attenuationconstant(dB/m)
0 100 200 300 400 500 600 700 800 900100
120
140
160
180
200
Propagationvelocity(m/s)
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.
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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 (V) and(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(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(V) of the watertrees as a differentiating parameter for the diagnostics.
v= 1(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
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44 CHAPTER 5. ON-VOLTAGE TDR
Ch1
HVAC 2kV
1HzTrigering
Synchronised
Pulse generator
DC
Filtering
x100 probe
CC
C
L
Figure 5.1: On-voltage TDR system.
the pulses sent at the phases 90and 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 the
cable, the second generation, is new and considered to be non-degraded.4. Cable 4; three phase, 24kV,350m long.
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5.5. WATER TREE DETECTION: CABLE 1 45
0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6200
100
0
100
200
300
Time(s)
Amplitude(mV)
090180270
Figure 5.2: On-voltage TDR measurements the Cable 1.
1000 1050 1100 1150 1200 1250 1300 1350 14 00 1450 150020
15
10
5
0
5
10
Time(ns)
Amplitude(mV)
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 last
pulses are the injected pulse and the reflection from the open end of the cable. Theoscillations during 0.1 0.6s 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 20nssooner, than the ones at 0 and 180, this indicates the presence ofwater trees in the cable.
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46 CHAPTER 5. ON-VOLTAGE TDR
2 0 2 4 6 8 10 12 14 16 18
0.04
0.02
0
0.02
0.04
Time(s)
Amplitude(V)
0
90
180
270
1 2 3
Figure 5.4: On-voltage TDR measurements on Cable 2.
5.6 Water tree detection: Cable 2
During the diagnostics the cable was energized with 2kV, 1Hz 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 5.4. The oscillations during13sare generated in the earlier mentionedLCcircuit. Oscillations last longer asthe inductance is higher in the on-site setup. The locations 1, 2 and 3 are magnified
in the Figures 5.5, 5.6 and 5.7.From the measurements at location 1, in Figure 5.5, it can be noticed that
the 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.
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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 4.57
6
5
4
3
Time(s)
Amplitude(mV)
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 7.54.5
4
3.5
3
2.5
Time(s)
Amplitude(mV)
090180270
Figure 5.6: Magnified location 2.
10 .5 10 .55 10. 6 10. 65 10. 7 10. 75 1 0. 8 1 0. 85 10 .9 10 .9 5 11
2.5
2
1.5
1
Time(s)
Amplitude(mV)
090180270
Figure 5.7: Magnified location 3.
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5.9. INFLUENCE OF NON-LINEAR CAPACITANCE OF THE COUPLING
CAPACITORS TO THE MEASUREMENTS 49
1 0 1 2 3 4 5 650
0
50
100
Time(s)
Amplitude(mV)
090180270
Figure 5.9: On-voltage TDR measurements on Cable 4.
2.2 2.25 2.3 2.35 2.4 2.45 2.5 2.55 2.6 2.65 2.78
7
6
5
4
3
Time(s)
Amplitude(mV)
090180270
Figure 5.10: Magnified section of the signal in Figure 5.9.
5.9 Influence of non-linear capacitance of the coupling
capacitors 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 Figure
5.12, 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 capacitors capacitance.The corner frequency of this RC differentiator is:
fRC c= 1
2RC =
1
225 2 109 = 3.2M Hz (5.2)
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50 CHAPTER 5. ON-VOLTAGE TDR
1 102.3
2.35
2.4
2.45
2.5
Frequency (Hz)
Capacitance(nF)
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 5.95 630
25
20
15
10
5
Time(s)
Amplitude(mV)
0kV (0 6kV)
6kV (90 6kV)
0kV (1806kV)
6kV (2706kV)
9kV (90 9kV)
9kV (2709kV)
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 belowfRC 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 s 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.
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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 9.5 105
0
5
10
15
Time(s)
Amplitude(mV)
without the conewith the cone
Figure 5.14: Comparison of the on-voltage TDR with and without the cone.
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52 CHAPTER 5. ON-VOLTAGE TDR
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.
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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 ofCLF flowing in RIScreates a voltage rise VP S. As CLF is in the rangeof picofarads and RISis in the range of ohms, the measured voltage VP S 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
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54 CHAPTER 6. ON-LINE TDR
Ch1 Ch2
HVAC
AC
Pulse generator
DC
Synchronised
50Hz
230V
50Hz
Trigering
TDR measurements Phase estimation
21 3kV
Figure 6.1: On-line TDR system No.1.
strip sensors. In Figure 6.2CHF 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 different
phase connected to the outlet than at the power cable; or due to different powertransformers primary and secondary windings 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 HFC IS
RIS
R
PSV
Figure 6.2: Capacitances between the cable conductor - capacitive sensor and cableconductor - insulation screen.
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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 3540
35
30
25
20
15
10
5
0
5
Time(s)
Amplitude(mV)
90
180
270
1
2
3
45
Figure 6.3: On-line