On-line time domain reflectometry diagnostics of medium voltage XLPE power cables

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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 2006:010 ISSN 1653-5146 ISRN KTH/R-0504-SE ISBN 91-7178-327-X

Elektroteknisk teori och konstruktion KTH SE-100 44 Stockholm SWEDEN Akademisk avhandling som med tillst˚ and av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie licenciatexamen torsdagen den 27 april 2006 klockan 10.00 i sal D2, Kungl Tekniska högskolan, 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 of failure of these cables. The detection of water-trees and information about the severity 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 be degraded by the water-trees. In such a situation a method for localization of this water-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 method opens up as a further step for the development of an on-line TDR method where the diagnostics are performed using pre-mounted sensors on the operating power cable. 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 external high-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 results in frequency and time domains were verified by measurements.

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

The on-line TDR system and the results of a four-days on-line measurement sequence 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 the selected section of the cable to be extracted. The high frequency parameters are extracted from frequency domain measurements of S-parameters as well as from TDR measurements.

iii

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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 experiment with my own ideas.

Prof. Roland Eriksson for giving me the opportunity to perform the work at Royal Institute 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 protection and sensor topics.

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

Mr. Olle Br¨anvall for producing the parts for the sensors.

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

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List of publications

1. V. Dubickas and H. Edin, ”Couplers for on-line time domain reflectometry diagnostics 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”, In Proceedings 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 small number of turns”, Submitted to IEEE Transactions on Instrumentation and Measurements, October, 2005.

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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 compared with the overhead transmission lines. Therefore most of distribution networks of medium and low voltages are constructed with power cables. However, a majority of the distribution grid failures are attributed to the power cables [1, 2].

1.2 Power cables

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

PILC cables

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

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

XLPE cables

Development of synthetic polymer materials boosted the birth of extruded power cables. The growth of solid dielectric insulated medium voltage cables began in the early 1950s, with the introduction of butyl rubber and thermoplastic high molecular weight 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 temperature of XLPE is 90

^◦

C, while during emergency overload and short-circuit voltages the temperature can reach 130

^◦

C and 250

^◦

C respectively. Good mechanical proper- ties eliminated the tendency to stress-cracking. Therefore, introduction of XLPE increased 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 the introduced cables had an extruded conductor screen providing a smooth boundary between a conductor and the XLPE insulation. An insulation screen was made of conducting tape, or graphite paint on XLPE with conducting textile tape wounded on it. The oversheath usually was made of PVC. This type of cables are referred to as the first generation XLPE cables.

Second generation XLPE cables

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

Third generation XLPE cables

Further improvements to stop water diffusion into the cable were introduced in

1990s. An aluminium foil with a water absorbing powder or tape was placed under

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1.3. WATER TREES 3

the cable sheath. The stranded conductors were filled with the water absorbing powder 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 could allow water diffusive sheath to be used, usually PVC. However water diffusion into the XLPE cable in combination with an alternating electric field initiates the water trees 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 Figure 1.2, and bow-tie. Vented water trees are initiated at the insulation surfaces, while bow-tie are initiated inside the insulation. However vented water trees are 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 water tree 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 be distinguished as a single process, it is an effect of several processes taking place simultaneously, 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 are

called 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 a

permittivity ε’=2.3-3.6 and loss-factor around tanδ=0.002-0.02 [7, 9]. However an

electric 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 the initial value by drying the insulation [6, 10]. However as soon water is present it will be re-absorbed consequently reducing the breakdown strength. Water tree initiated failures are not clearly understood. Water trees cause local stress enhancements that could be initiation sites for electrical trees, either at power frequency or from transient overvoltages. XLPE is also susceptible to localized degradation caused by Partial Discharges (PD). The degradation of the XLPE appears as an erosion of the surface within the cavities and a breakdown appears after a period of time when a certain degree of surface roughness is attained manifesting the initiation of electrical trees.

1.4 Countermeasures to water treeing in power cables

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

Longitudinal water-blocked conductors. Moisture propagation inside of the stranded conductor is blocked by filling the strands with semiconducting or insulating materials, placing water absorbing powder between the strands or using solid conductors.

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

Radial water blocking. Usually radial water-blocking is implemented by using

metallic laminated tapes. Aluminium or lead tapes are laminated between

insulating or semiconducting material depending where they are placed on

the shield wires or the insulation shield.

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1.5. POWER CABLE DIAGNOSTICS 5

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

1.5 Power cable diagnostics

The third generation cables are well protected from the water ingress and therefore water treeing is seldom the cause of faults in these cables. However the second generation and especially the first generation power cables are susceptible to water treeing [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 cost 500 million SEK [13]. Overview of the power cable diagnostics and testing can be found 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 bridge measurements of loss factor at a power frequency [3, 15].

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

Polarisation/depolarisation current measurements are performed by charg- ing the sample by DC voltage and measuring polarization current. After applying DC voltage for a long period of time the sample is short-circuited and depolarization current 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 time

during which the sample is short-circuited, the test object is left in open-circuit

condition and the recovery voltage is measured [15].

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6 CHAPTER 1. INTRODUCTION

Partial discharge diagnostics Partial Discharge (PD) diagnostics is a widely used 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 usually performed 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]. The method 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 and measuring the reflections along the cable. The reflections arise due to joints along the cable but also due to small irregularities in the cable itself. TDR for medium voltage XLPE power cable diagnostics was also developed in Electromagnetic En- gineering department at Royal Institute of Technology [22, 23]. More detailed description 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 Japan where the distribution power cables operate mostly at relatively low voltages 6,6kV and are non-grounded. DC voltage is applied to the cable conductor through an inductance and is superimposed on the grid voltage. The AC component of the current which passes thought the insulation of the cable is eliminated by a filter and only the DC component is measured. The reduction of the insulation resistance indicates the presence of water trees [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 or inductive type. The capacitive sensors are usually made of conductive tape placed on 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 cable joint, under the metallic screen. The inductive sensors usually used for on-line PD diagnostics are Rogowski coils. They can be placed on the power cable after the earth connection, before the high voltage termination, or on the power cable’s earth connection conductor. However PD diagnostics do not provide information about the 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 diagnostic methods 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 cable with the twisted screen wires is presented in Chapter 4. Chapter 5 investigates on-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, while

Chapter 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 of a wavelength and may even be many wavelengths long. Therefore the transmission line must be described by circuit parameters that are distributed through its length.

The equivalent distributed elements circuit of a two wire transmission line is shown in Figure 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 transmission line 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

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10 CHAPTER 2. TRANSMISSION LINE THEORY

For harmonic time dependence the use of phasors simplifies the transmission line 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 are obtained.

d

²

V (x)

dx

²

= γ

²

V (x) (2.5)

d

²

I(x)

dx

²

= γ

²

I(x) (2.6)

where:

γ = α + jβ = p

(R + jωL)(G + jωC) (2.7)

is the propagation constant which is composed of real and imaginary parts. α and β, are the attenuation constant (N p/m) and phase constant (rad/m) respec- tively. Solution of equations 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 positive and negative x directions respectively. The ratio of the voltage and the current at any x for and infinitely long line is independent of x and is called the characteristic impedance of the line.

Z

0

= V (x) I(x) =

s

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 = 2π

β (2.12)

When the transmission line with the characteristic impedance Z

0

and the prop- agation constant γ is terminated at the distance l by the load impedance Z

L

, the generator looking into the line sees an input impedance Z

i

.

Z

i

= Z

0

Z

L

+ Z

0

tanh γl

Z

₀

+ Z

_L

tanh γl (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 that are 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) generator and a high speed oscilloscope, see Figure 2.2.

Pulse/step generator

High speed oscilloscope

Z0

ZL

Vi Vr

l

Figure 2.2: Block diagram of a TDR system.

The incident pulse or step V

i

is sent into the transmission line Z

0

. If Z

0

6= Z

L

, at the interface between Z

0

and Z

L

the reflection of the voltage wave will appear.

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

Γ = V

_r

V

i

= Z

_L

− Z

₀

Z

L

+ Z

0

(2.14)

The reflected voltage wave V

r

will propagate back to the measuring system and will be recorded by the high speed oscilloscope after a traveling time t

r

. Knowing the wave propagation velocity v in the transmission line the distance to the discontinuity can be obtained as:

l = v t

r

2 (2.15)

2.3 S-parameters matrix

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

b

1

b

₂

=

S

11

S

12

S

₂₁

S

₂₂

a

1

a

₂

(2.16)

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12 CHAPTER 2. TRANSMISSION LINE THEORY

11 12

21 22

S S S S

 

 

 

Z

1

Z

2

V

1⁺

V

1⁻

V

2⁺

V

2⁻

Port 1 Port 2

Figure 2.3: Incident and reflected waves in a twoport.

where

b

1

=

^√^V¹_Z⁻

1

a

1

=

^√^V¹_Z⁺

1

b

2

=

^√^V²_Z⁻

2

a

2

=

^√^V²_Z⁺

2

(2.17) Usually the impedances Z

1

and Z

2

of the connecting cables of the network analyzers are matched to the input impedance Z

0

of the Network Analyzer (NA) itself i.e. Z

1

= Z

2

= Z

0

. Therefore the S-parameter matrix becomes.

V

₁⁻

V

₂⁻

=

S

11

S

12

S

21

S

22

V

₁⁺

V

₂⁺

(2.18) The voltages on Port1 and Port2 are the sum of the incident and the reflected waves.

V

₁

= V

₁⁺

+ V

₁⁻

V

2

= 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 impedance matrix or Z-matrix [30],

V

1

V

2

=

z

11

z

12

z

21

z

22

I

1

I

2

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

V

1

I

1

=

A B

C D

V

2

I

2

(2.21) ABCD to Z-matrix conversion:

Z =

_C¹

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, where R

m

is the measuring resistor at the end of the twoport.

G(ω) = V

2

V

1

= R

m

z

21

z

11

R

m

+ z

12

z

21

− z

11

z

22

(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) = Z

∞

−∞

f (t) · e

^−jωt

dt (2.24)

f (t) = 1 2π

Z

∞

−∞

F (ω) · e

^jωt

dω (2.25)

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

X(k) = 1 N

N −1

X

n=0

x(n) · e

^−j^2πnk^N

(2.26)

x(n) =

N −1

X

n=0

X(k) · e

^j^2πnk^N

(2.27) the frequencies are obtained by

ω

k

= k ·

^2π_T

f

k

=

_T^k

(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 the

highest 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. The sensors have to be installed without damaging the power cable as it has to operate on-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. The sensors have to be high frequency and broadband as the voltage pulse used for TDR is composed of high frequency components.

The sensors with the higher mentioned characteristics can be found in off-line and on-line PD diagnostics [21, 31, 32, 2, 26]. The sensors can be divided into three groups according to their coupling mechanism to the power cable. Capacitive sen- sors which couple through electric field, inductive sensors couple through magnetic field, and directional couplers couple through both electric and magnetic fields [33].

Usually directional couplers are installed between insulation screen and metallic cable sheath [31]. The technique can be regarded as invasive, and therefore the directional 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.

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16 CHAPTER 3. SENSORS

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.

Rogowski coil couples

U(V)

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 cable are modelled and simulated in frequency and time domains in order to understand their 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, which during the diagnostics is energized by HV. During the TDR diagnostics the pulse is injected and the reflections are measured through the coupling capacitor. The coupling capacitor represents high impedance for low frequency HV, and therefore decouples the measuring equipment from the HV. The high frequency components containing TDR signal meets low impedance and passes through the capacitor. The schematics of the coupling capacitor connected to the cable are presented in Figure 3.2.

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 Z

m

, connected to R, through the coupling capacitor. The

signal is measured at the far end of the power cable on the resistor R

_m

. The cou-

pling capacitor on the cable is described by the ABCD

C

matrix.

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3.2. COUPLING CAPACITOR 17

R C

Z

0

Insulation Screen wires Insulation screen Conductor screen

back Folded

wires screen Coupling

capacitor

L ^D l

wire Ground

Z

m

Figure 3.2: The coupling capacitor connected to the cable.

ABCD

_C

= 1 jωL +

_jωC¹

+ Z

1 1

R

1 +

^jωL+^jωC_R¹ ^+Z¹

!

(3.1) The measurement cable is terminated with the resistor R = Z

m

= 50Ω, therefore in the model they are replaced by equivalent series impedance Z

1

= Z

m

/2 = 25Ω

¹

. At the high frequencies the inductance L between the power cable conductor and the 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 propagation constant γ and the characteristic impedance Z

0

.

ABCD

T

=

cosh(γd) Z

0

sinh(γd)

1

Z0

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 the system 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. The lower frequencies 0-5MHz are cutoff by the coupling capacitor itself. The transfer function 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 is caused by standing waves in the power cable. Using the fact from transmission line theory that the successive maxima and minima in the standing wave pattern are spaced by a half of the wavelength l = λ/2, and equations 2.11 and 2.12 the length of the cable can be expressed. The wave propagation velocity in the investigated cable is approximately v = 150m/µs. The frequency difference between the stand- ing wave maxima is ∆f

λ/2

= 13M Hz. With the later values the calculated length

1Please note that in equation (8) in Paper 1, Z1should be instead of Z0.

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18 CHAPTER 3. SENSORS

0 20 40 60 80 100 120 140 160 180 200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Gain

0 20 40 60 80 100 120 140 160 180 200

−3000

−2500

−2000

−1500

−1000

−500 0 500

Frequency (MHz)

Phase (deg)

Measured Model

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

of the cable is:

l = v

2∆f

_λ/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 ABCD

T

matrix of the 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 it can be concluded that the high frequencies are damped mostly by the inductance L.

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 results

were obtained by the use of Fourier transforms. Fourier transforms enable exact

representation of the input pulse to be used for an exact frequency domain model

of dispersion in the cable. The measurements are compared with the simulation in

Figure 3.5. The first pulse in the Figure 3.5 is the transmitted pulse through the

cable. The successive pulses are the detected reflections propagating in the power

cable due to impedance mismatches at the cable ends.

(33)

3.2. COUPLING CAPACITOR 19

0 20 40 60 80 100 120 140 160 180 200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Gain

0 20 40 60 80 100 120 140 160 180 200

−100

−50 0 50 100

Frequency (MHz)

Phase (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

Output (V)

Time (ns)

Measured Model

Figure 3.5: Comparison of the time domain measurements and simulation of the

coupling capacitor on the power cable.

(34)

20 CHAPTER 3. SENSORS

R2

Insulation

connectorN −type L2

wires screenFoldedback

Insulation screen

Conductor screen

sensor Capacitive wires

Screen

±1( )

C f

±2( )

C f

Figure 3.6: Capacitive strip sensor on the cable.

Limitations

The bandwidth of the coupling capacitor at the high frequencies is limited by the inductance L between the conductor of the cable and the ground wire, see Figure 3.2. Therefore during the measurements the coupling capacitor should be fitted with the minimal distance D and length l of the ground wire. The distance l is usually defined by the cable’s HV termination length. The distance D is limited by safety issues, as the low voltage potential electrode of the coupling capacitor can 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 can be selected relatively high, providing good sensitivity. The sensor can be applied to 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 on

the power cables [34, 35, 36, 37, 38, 39]. Usually the sensors are placed on the HV

terminations or inside of the cable joints. The sensor is made of a metal strip tightly

wound on the insulation screen of the cable, see Figure 3.6. The semi-conductive

material of the insulation screen at low frequencies act as a screen for the HV

electric field, but at high frequencies as a dielectric. Therefore in this region the

50Hz HV electric field will be enclosed by insulation screen, while the high frequency

propagating pulse electric field will penetrate insulation screen and will be detected

by the capacitive strip sensor.

(35)

3.3. CAPACITIVE STRIP SENSOR 21

V

1 ²

I

Rm

R

2

C

2

C1

V

2

L

2

R

1

Cd 1

Rd

2

R

d 2

Cd

I

1

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 capacitances f C

1

(f ), f C

1

(f ) were mod- eled by lumped elements: dc conductivity was modeled with resistors R

1

, R

2

, pure capacitances were modeled with C

1

and C

2

, dielectric response functions were ap- proximated with exponential decay functions - Debye functions, which were modeled with an equivalent circuit consisting of R

d1

in series with C

d1

and R

d2

in series with C

d2

. The inductance of a wire from the coupler to an N-type connection and the N-type connection is modeled with L

2

. R

m

- measuring equipment impedance. The transfer function of the capacitive strip sensor can be expressed:

G

cap

(ω) = V

2

V

1

= Z

4

R

m

Z

3

(Z

1

+ Z

4

) (3.4)

where:

Z

1

= R

1

||

_jωC¹

1

||

R

d1

+

_jωC¹

d1

Z

3

= R

m

+ jωL

2

Z

2

= R

2

||

_jωC¹

2

||

R

d2

+

_jωC¹

d2

Z

4

= Z

2

||Z

3

(3.5)

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

cap cable

was measured with the NA. The transfer function of the sensor was obtained by dividing G

cap cable

with the known transfer function of the power cable G

cable

. As the transfer function G

cable

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 is depicted 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 capacitive

sensor, placed on the far open end of the cable. The sensor has a differentiating

(36)

22 CHAPTER 3. SENSORS

0 50 100 150 200 250 300 350

0 0.2 0.4 0.6 0.8 1

Gain

0 50 100 150 200 250 300 350

−50 0 50 100 150

Phase (deg)

Frequency (MHz)

Measured Model

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

behavior as the elements C

1

and R

m

form a differentiating circuit. Simulations in PSpice were used to verify model in the time domain, see Figure 3.9.

Limitations

The capacitance C

1

of the capacitive strip sensor is proportional to the sensor’s length. The higher C

1

provides stronger coupling and eventually higher sensitivity.

Therefore the sensitivity of the sensor is limited by the available length of insulation screen at the HV termination, see Figure 3.1. Moreover if the sensor is placed close to the shield wires, the sensitivity is reduced by the stray capacitance C

2

. In some designs HV termination is placed close to screen wires leaving no exposed insulation screen. 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.

(37)

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)

Measured Model

Figure 3.9: Comparison of the time domain measurements and simulation of the capacitive 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 be used only on the cables with the twisted screen wires. Return current I

S

flowing in the twisted screen wires can be decomposed into axial I

Z

and radial I

ϕ

compo- nents. Axial magnetic field H

_Z

resulting from the current I

_ϕ

induces a voltage in the inductive strip sensor, which basically is a one turn induction loop, see Figure 3.10.

Frequency domain

The sensor was modelled by a lumped element model, represented in Figure 3.11.

Where the elements represent: Z

0

-characteristic impedance of the power cable, M - mutual inductance between the twisted power cable screen and the sensor, L-self inductance of the sensor, C-capacitance between the power cable screen and the sensor, R

m

-measuring equipment impedance.

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

G

ind

(ω) = V

₂

V

1

= M R

_m

CZ

0

jωL +

_1+jωCR^R^m

m

R

m

+

_jωC¹

(3.6)

(38)

24 CHAPTER 3. SENSORS

conductor Inner

Insulation

Conductor and insulation screens

wire Screen

Oversheath Inductive Coupler

I

S

I

Z

H

Z

Figure 3.10: Inductive strip sensor on the power cable.

M

C R_m

0 L Z

V1

V2

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 rise time, 30ns wide pulse, into the cable and detecting the propagating pulse by the sensor are compared with the model simulated in PSpice in Figure 3.13. The output voltage of the sensor is the derivative of the pulse as the induced voltage is governed by Faraday’s law.

Some of the cables have shield wires with periodically changing twisting direc-

tion. The magnetic field H

Z

resulting from the current I

ϕ

is dependent on the

shield wires spiralization angle. Therefore the induced voltage in the inductive

strip sensor is the highest where the shield wires are maximally twisted, equal to

zero where shield wires go parallel to the cable conductor, and is negative where

the wires are twisted to opposite direction. The phenomenon is depicted in Figure

(39)

3.4. INDUCTIVE STRIP SENSOR 25

0 100 200 300 400 500 600 700

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Gain

0 100 200 300 400 500 600 700

−20 0 20 40 60 80 100

Phase (deg)

Frequency (MHz) Measured

Model

Figure 3.12: Comparison of the measured and modelled transfer functions of the inductive 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)

Measured Model

Figure 3.13: Comparison of the time domain measurements and simulation of the

inductive strip sensor on the power cable.

(40)

26 CHAPTER 3. SENSORS

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

Magnitude (mV)

Distance (m)

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

3.14, where the magnitude of the sensor’s output is measured at specified intervals along 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 sensor along the cable during the diagnostics can sometimes be useful. The production of the 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 magnetic field created by the current circulates around the conductor and also in the toroid core. The magnetic field in the toroid core induces the voltage in the Rogowski coil windings. To provide the shielding from noise interference and to form the constant capacitance to ground the Rogowski coils are usually shielded by metallic enclosures.

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

(41)

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 r

w

N

Rog1 120 40 15 5 0.3 16

Rog2 120 40 30 5 0.3 16

Rog3 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. The schematics are presented in Figure 3.15. Dimensions of the cores, a distance H from the cores to a shield, a winding wire radius r

w

and the number of turns N are presented 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 Figure 3.16, is modelled as a distributed element transmission line [42, 43, 44, 45]. The model is presented in Figure 3.17, where:

Z

c

- characteristic impedance of the cable Z

load

- impedance of the cable load

M

⁰

- distributed mutual inductance between the cable’s conductor and windings of

the Rogowski coil

(42)

28 CHAPTER 3. SENSORS

lc

wires screen

back Folded

coil Rogowski

Zload

Rm

V1

V2

V3

Figure 3.16: Rogowski coil on the power cable.

L

⁰

- distributed windings’ self inductance

Z

_skin⁰

- distributed windings’ wire internal impedance due to skin effect C

⁰

- distributed windings’ stray capacitance to the shield

C

_str⁰

- distributed stray capacitance between the turns R

m

- resistance of measuring equipment

l

c

- length of the cable

l

w

- length of the windings wire

The theoretical values of the elements M

⁰

, L

⁰

, Z

_skin⁰

, C

⁰

can be calculated us- ing the dimensions of the Rogowski coil and the properties of the materials. The expressions are presented in Paper 4.

Transfer function

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

G

rog

(ω) =

^V_V³

2

=

_Z ^jωM⁰^R^m^Z⁰^sinh(γl^w⁾

loadZS(Z0sinh(γlw)+Rmcosh(γlw))

(3.7) where:

Wave impedance of the Rogowski coil

Z

0

= v u

u t− (Z

_skin⁰

+ jωL

⁰

) ω

²

C

_str⁰

C

⁰

Z

_skin⁰

+ jωL

⁰

+

_jωC¹0 str

(3.8)

Propagation constant of the Rogowski coil

γ =

s (Z

_skin⁰

+ jωL

⁰

) Z

_skin⁰

+ jωL

⁰

+

_jωC¹0

str

· C

⁰

C

_str⁰

(3.9)

and,

Z

S

= (Z

_skin⁰

+ jωL

⁰

)

_jωC¹0 str

Z

_skin⁰

+ jωL

⁰

+

_jωC¹0 str

(3.10)

(43)

3.5. ROGOWSKI COIL 29

M ∆' x

L ∆' x

L ∆' x x C'_str∆

x C'_str∆

x Z'_skin∆

C ∆' x

C ∆' x Zload

Zc

Rm

lw

=0 x

lw

x = lc

V1 V₂

I2

V3

∆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 line with shortened far end, and can be described by equation 2.13. To verify the theoretical element values, the impedances of the Rogowski coils Z

R

were measured, and compared with the theoretical ones.

Z

R theor

= jωL

N

+ Z

0

tanh(l

w

γ)

1 + jωC

N

Z

0

tanh(l

w

γ) (3.11)

where, L

N

and C

N

are series inductance and the shunt capacitance of the N-

type connection. In order to improve the model the values of the elements can be

measured and estimated. The measurement and estimation of the element values

is described in detail in Paper 4. The comparison of the theoretical, measured and

estimated Rogowski coil impedances are presented in Figures 3.18, 3.19 and 3.20.

(44)

30 CHAPTER 3. SENSORS

10⁰ 10¹ 10² 10³

10⁰ 10⁵

Frequency (MHz)

Magnitude (Ω)

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

10⁰ 10⁵

Frequency (MHz)

Magnitude (Ω)

10⁰ 10¹ 10² 10³

−100

−50 0 50 100

Frequency (MHz)

Phase (deg)

ZRmeas ZRestm ZRtheor

On-line time domain reflectometry diagnostics of medium voltage XLPE power cables