Dielectric properties and space charge dynamics of polymeric high voltage DC insulating materials

Dielectric Properties and Space

Charge Dynamics of Polymeric High

Dielectric Properties and Space

Charge Dynamics of Polymeric High

Voltage DC Insulating Materials

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. dr. ir. J. T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen,

op maandag 17 december 2007 om 17:30 uur door

BELMA ALIJAGIĆ - JONUZ

Dit proefschrift is goedgekeurd door de promotor: Prof. dr. J. J. Smit

Samenstelling promotiecommissie:

Rector Magnificus, Voorzitter

Prof. dr. J. J. Smit, Technische Universiteit Delft, promotor Prof. dr. E. Ildstad, Norwegian University of Science

Prof. dr. eng. J. A. Ferreira, Technische Universiteit Delft Prof. dr. ir. E. F. Steennis, Technische Universiteit Eindhoven Prof. dr. ir. J. van Turnhout, Technische Universiteit Delft

Prof. ir. W. L. Kling, Technische Universiteit Delft/Eindhoven Dr. ir. P. H. F. Morshuis, Technische Universiteit Delft

This research was funded by the listed companies: Philips Medical Systems, Hamburg

Philips Medical Systems, Heerlen Philips Analytical, Almelo

Philips FEI, Eindhoven

Philips Components, Eindhoven Thales, Hengelo

Tobias Jensen Capacitors, Lyngby PBF Electronics, Almelo

ISBN 978-90-9022561-6

Copyright _{2007 by Belma Alijagić – Jonuz}

Haastige spoed is zelden goed! More haste, less speed! Ko je žurio vrat je slomio!

vii

TABLE OF CONTENTS

TABLE OF CONTENTS

………. vii

1 INTRODUCTION

1.1 General………. 1

1.2 Space charge measurements: state of the art……… 3

1.3 Aim of the thesis……...………... 4

1.4 Outline of the thesis………..………... 5

2 EXPERIMENTAL

2.1 Introduction ………. 9

2.2 Test specimens………. 10

2.3 Pulsed electro-acoustic method……… 11

2.3.1 Description of the method……….. 11

2.3.2 Description of the equipment and measurement procedure…... 12

2.4 Polarization current measurement……… 15

2.4.1 Description of the method……….. 15

2.4.2 Description of the equipment and measurement procedure…… 15

2.5 Dielectric spectroscopy in the frequency domain………. 16

2.5.1 Description of the method……….. 16

2.5.2 Description of the equipment and measurement procedure…… 17

2.6 Breakdown tests……… 20

2.7 Electrical aging tests………. 20

3 THEORETICAL

BACKGROUND

3.1 Introduction……… 23

3.2 Space charge formation……… 23

3.3 Conduction current……… 28

3.4 Dielectric polarization and relaxation……… 29

viii

4.2 Charge dynamics of virgin and pre-stressed PC:

results of the measurements……… 41

4.2.1 Density, polarity and position of the accumulated space charge. 41 4.2.2 Electrical field strength……… 42

4.2.3 ρ vs. E characteristics and electrical threshold for space charge accumulation……….. 44

4.2.4 Space charge accumulation characteristic time……….. 46

4.3 Charge dynamics of virgin and pre-stressed PC-TiO2: results of the measurements……… 48

4.3.1 Density, polarity and position of the accumulated space charge 48 4.3.2 Electrical field strength……… 49

4.3.3 ρ vs. E characteristics and electrical threshold for space charge accumulation………... 51

4.3.4 Space charge accumulation characteristic time……….. 53

4.4 Influence of TiO2 filler……….. 54

4.5 Summary and conclusions……… 56

5

RESULTS OF THE POLARISATION CURRENT

MEASUREMENTS

5.1 Introduction……… 61

5.2 Polarisation and conduction currents in PC: results of the measurements……… 62

5.3 Polarisation and conduction currents in PC-TiO2: results of the measurements……… 65

5.4 Influence of TiO2 filler……….. 67

5.5 Summary and conclusions……… 67

6 MATERIAL

CHARACTERIZATION

BY

DIELECTRIC SPECTROSCOPY IN THE

FREQUENCY DOMAIN

6.1 Introduction……… 71

6.2 DSF on virgin and pre-stressed PC-TiO2: results of the measurements 75 6.2.1 Results of the tan δ measurements……….. 74

6.2.2 Real part of complex permittivity………... 85

6.3 DSF on virgin and pre-stressed PC: results of the measurements……. 86

6.3.1 Results of the tan δ measurements……….. 86

6.3.2 Real part of complex permittivity………... 93

ix

6.4 Summary and conclusions……… 99

7 BREAKDOWN

TESTS

7.1 Introduction………... 101

7.2 Voltage endurance test and pre-stress determination………. 102

7.3 DC breakdown step-up tests………. 103

7.4 Summary………... 103

8

DISCUSSION OF THE RESULTS

8.1 Introduction………... 107

8.2 Summary and discussion of the measurement results………... 109

8.2.1 Space charge measurements……… 109

8.2.2 Polarization current measurements………. 113

8.2.3 Dielectric spectroscopy in frequency domain………. 114

8.2.4 Breakdown tests……….. 116

8.3 Conclusions of the discussion………...………. 117

8.3.1. Influence of TiO2 filler……… 117

8.3.2. Influence of pre-stressing……… 118

8.3.3. Conclusions………. 119

9

CONCLUSIONS AND RECOMENDATIONS

9.1 Introduction………... 121

9.2 Conclusions……… 122

9.3 Recommendations for the future work……….. 125

APPENDICES

Appendix A Practical case ……… 127

Appendix B Results of thermogravimetry ……….. 133

Appendix C Calculation of space charge ……… 137

Appendix D Charge accumulation ………. 139

Appendix E Determination of the threshold field for space charge accumulation ………..……….. 143

Appendix F Polarization current fit ………..………… 151

I

I

n

n

t

t

r

r

o

o

d

d

u

u

c

c

t

t

i

i

o

o

n

n

1

1

1.1 General

The purpose of solid electrical insulating materials [1] is described as: The purpose of electrical insulating materials is to isolate components of an electrical system from each other and from ground, while at the same time providing mechanical support to the component.

and analysis of the dielectric properties of insulating materials for DC driven applications. As a case study, polycarbonate was used, with and without the addition of TiO2 filler. Polycarbonate is frequently used in HVDC applications,

in particular in X-ray applications (Appendix A). The basic idea behind the TiO2

filler addition was to reduce space charge accumulation, by increasing the materials’ ability of transportation of injected charge carriers.

A test method may consist of one material test technique, or a combination of a number of material test techniques. Several material test techniques are available nowadays - destructive, non-destructive, applicable on-line or off-line - providing information about one or more material properties. Each of them has its advantages and disadvantages. For example, the advantage of some destructive techniques is that they often provide a quick answer about a material property. The great disadvantage is that the tested object cannot be used any more. As another example, the insulation condition of an electrical component that supports vital parts of some production process should be tested on-line; however, it might be easier and more favourable to use an off-line technique and to find a solution for temporary support of the vital parts of production, if possible.

The current method under investigation comprises four test techniques: space charge measurements, conduction current measurements, dielectric spectroscopy in the frequency domain and breakdown testing. In the following, a brief overview is given of material properties, which are observed by the mentioned techniques.

Space charge measurements

The internal electrical field of an insulating material can be considerably modified by the presence of space charge. From the measured space charge profile, the distribution of the electric field is derived and as such, space charge measurements are a valuable tool to evaluate a dielectric which is to be used at DC voltage. The occurrence of space charge is often regarded as being detrimental; therefore, a relationship between space charge accumulation and electrical aging is expected. Space charge measurements provide us with a means to detect magnitude, polarity and location of charge trapped in a dielectric. In addition, different dielectrics can be compared regarding their tendency to accumulate charge. It appears that for many dielectrics a threshold field can be defined below which no or hardly any space charge accumulates.

Conduction current measurements

starts to accumulate in a dielectric when the electric field is raised above a threshold level. Theoretical considerations show that this threshold level is quite close –if not identical– to the threshold for space charge accumulation.

Dielectric spectroscopy in the frequency domain

Dielectric changes in material structure can be detected by using dielectric spectroscopy over a wide frequency and temperature range. This technique completes the evaluation method for the characterisation of insulating materials, in particular with respect to aging.

Breakdown testing

Breakdown testing, usually involving step-up tests, is a frequently used insulation testing technique. However, it is very difficult and not completely correct to give a statement about the life expectancy of a polymeric material based on this test alone. The reason for this is that the classical step-up test does not take into account the time needed for space charge accumulation. On the other hand, if this time was taken into account, the test would become very time-consuming and, therefore, expensive. However, combining a breakdown test with some other less time-consuming characterisation techniques would be an appropriate alternative. Even better would be to find a relationship between the results of another characterisation technique and the voltage endurance of the material, which would then make the breakdown test redundant.

In the next section we focused on the space charge phenomenon and its measurement technique, as being the youngest and least known of the four above mentioned test methods.

1.2 Space charge measurements: state of the art

measurement techniques, which use pulse excitation for interaction with accumulated space charge in order to localise and measure it. In most cases, a material specimen is placed in a plane capacitor configuration and charged with a DC voltage, thereby generating space charge in the material. The TSP (thermal step pulse) method [2] uses a temperature step for the displacement of space charge. LIPP (laser induced pressure pulse), PWP (pressure wave propagation), and PPP (piezoelectrically generated pressure pulse) all use the displacement of the space charge pressure pulse that travels as an acoustic wave through the material [3-6]. As a consequence of space charge displacement, the electrode charges change, resulting in an electrical signal in the external circuit of the measuring systems. The PEA (pulsed electro-acoustical) method [5], [7-12] uses short electrical pulses which interact with space charge, and result in an acoustic wave whose intensity and time delay correspond to space charge density and position. Initially, the most common methods used for space charge observation were destructive methods like the field mill and the capacitive probe [13].

Most of the research on space charge accumulation in electrical power engineering has been performed on polyethylene (PE) based materials, which are used in high voltage AC and DC cables [14-20]. There are fewer examples of research on other insulating materials: the most commonly cited are epoxy with or without filler [21-22], impregnated paper [23], polycarbonate with and without filler [24], and PMMA [25]. It has been experimentally proven for PE-based materials that space charge can be considered as one of the causes of failure [26-27]; as already mentioned, electric field enhancement due to space charge accumulation can have deleterious effects on insulation materials. In this sense, it is suitable as a parameter for material testing and ranking. Space charge can also be considered as a consequence [28-29] of electrical aging: the number and distribution of trapping sites where space charge can be captured changes due to electrical aging.

1.3 Aim of the thesis

The aim of the here described research was twofold:

‰ To establish a method to estimate the (future) performance of polymeric insulating materials for DC driven applications.

‰ To evaluate experimentally the dielectric properties of polymeric insulating materials relevant for normal operating conditions in high voltage DC applications.

The following approach was adopted:

As a case study, polycarbonate was used, with and without the addition of TiO2

filler. The specimens were tested when virgin, and after long-term stress at high DC fields. Four test techniques were combined:

‰ Breakdown tests (voltage endurance tests) ‰ Space charge measurements

‰ Polarization current measurements

‰ Dielectric spectroscopy in the frequency domain

1.4 Outline of the thesis

The structural overview of the thesis is given in Figure 1.1.

Chapter 2 describes the technical basis of the four mentioned characterisation techniques.

Chapter 3 covers the physical background and an analytical description of space charge phenomena, conduction current analysis, and dielectric spectroscopy in the frequency domain. The description of the main processes behind the breakdown of insulating materials is assumed to be well-known, and is therefore not repeated. An excellent description can be found in [40-41].

In Chapters 4-7, the experimental results are presented and discussed. Experimental investigation was carried out on virgin and pre-stressed PC and PC-TiO2 specimens. Chapter 4 presents the results of space charge

measurements performed in order to establish the space charge dynamics of PC and PC-TiO2, and to analyse the effect of long-term exposure to a high electric

DC field on the space charge behaviour of the materials. Based on the space charge measurements, the following space charge related quantities were calculated and derived: space charge density, polarity and position; electrical field strength and field enhancement factor; space charge accumulation characteristic times; and the electrical threshold for space charge accumulation, Eth,sc. Results of the polarisation current measurements are shown in Chapter 5.

whether the examined materials show the presence of an electric threshold at which a transition between different conduction mechanisms takes place. The effects of electrical stress on the materials and the influence of TiO2 filler were

also explored. Measurement results of tan

_δ

and the real part of complex permittivity, performed by means of dielectric spectroscopy in the frequency domain are presented in Chapter 6. The objective of the chapter is to probe the dielectric relaxation processes in the tested materials, to explore the effects of electrical stress, and to establish the influence of TiO2 filler on molecular

dynamics. The voltage endurance of new and pre-stressed materials is determined by means of step-up tests as described in Chapter 7.

In Chapter 8, the results of the measurements are discussed in light of the main objective: to arrive at a classification method that evaluates the DC performance of polymeric insulating materials.

Figure 1.1 Structural overview of the thesis Chapter 1 Introduction Chapter 2 Experimental Chapter 3 Theoretical background Chapter 4

The effect of long-term DC stress on space

charge dynamics

Chapter 5

Results of the polarization current measurements

Chapter 6

Material characterisation by dielectric spectroscopy

in the frequency domain

Chapter 7

Breakdown tests

Chapter 8

Discussion of the results

Chapter 9

Conclusions and Recommendations

E

E

x

x

p

p

e

e

r

r

i

i

m

m

e

e

n

n

t

t

a

a

l

l

m

m

e

e

t

t

h

h

o

o

d

d

s

s

2

2

2.1 Introduction

In this chapter, a description is given of the specimens, material test techniques, and measuring set-ups used in this work.

Section 2.2 contains the specimens’ specifications, and details of the specimen treatment procedures that were employed prior to measurements being taken. Sections 2.3 - 2.5 give a description of the following material test techniques: ‰ Pulsed electro-acoustic measurements, used for space charge measurements. ‰ Dielectric spectroscopy in the frequency domain used for tan

δ

and complex

permittivity measurements.

‰ Polarization current measurements, used for the determination of electric field-conduction current characteristics.

The mentioned test techniques were applied to virgin and pre-stressed PC and PC-TiO2 with the objective of analyzing the following aspects:

- Space charge related quantities

- Dielectric relaxations, complex permittivity

- Conduction current; transition field from linear to non-linear regime - Breakdown strength

‰ Influence of 100 kV/mm DC - 1500 hours pre-stressing on above mentioned material parameters.

‰ Influence of the addition of TiO₂ on polycarbonate dielectric properties.

Section 2.6 describes the breakdown tests used for the determination of the electrical pre-stress field, which should be high enough to trigger material deterioration but at the same time low enough not to cause material breakdown. Section 2.7 gives a description of the electrical aging test.

2.2 Test specimens

Experimental investigations were performed on two types of polycarbonate: pure1 polycarbonate (PC) and with TiO2 filler (PC-TiO2).

Polycarbonate is a polymeric, amorphous material with a repeating structure as shown in Figure 2.1. Considering its mechanical response at elevated temperatures, polycarbonate is classified as a thermoplast: it softens when heated and hardens when cooled. The processes are totally reversible and may be repeated. Glass transition temperature of polycarbonate is at approximately 150°C and melting temperature at approximately 265°C [43].

Figure 2.1 Repeating structure of polycarbonate

Some additional data of the material specimens used in this work are given in Table 2.1. The materials were cut from 0.175 mm thick extruded foils. A conditioning procedure was used that consisted of cleaning the specimens with mild soap and de-ionized water; finally, the specimens were dried in an oven at 80°C for 8 hours.

The (series of) measurements always started one day after the specimens had been cleaned; that is, the specimens were exposed to environmental conditions in the high voltage laboratory (20_{°C, 50 % RH) for at least one day. A climate} chamber was used in extreme cases, for example on a rainy summer day when

the temperature and humidity in the high voltage laboratory were very difficult to control and could reach values of 25°C and 80 % RH.

Table 2.1 Specimens’ specification Material

Filler type and

content Thickness [mm] Relative permittivity _εr Glass transition temperature Tg PC none 0.175 3.1 155°C PC-TiO2 TiO2 16.7% wt 0.175 3.7 155°C Specimens used for space charge measurements and dielectric spectroscopy measurements were always space charge free. Discharging of charged specimens was brought about by short-circuit and, if necessary, by heating the specimens at 80_{°C for a couple of days. In extreme cases the specimens were} heated at 150_{°C for a short period of time.}

Specimens that spent some period in insulating oil (for the purposes of electrical-aging tests) were cleaned in the same way. According to Thermogravimetric Analysis (TGA) and dielectric spectroscopy measurements, no detectable amount of oil had penetrated the specimens; therefore, no special cleaning procedure was applied. The results of TGA and dielectric spectroscopy measurements are shown in Appendix B.

2.3 Pulsed electro-acoustic method

2.3.1 Description of the method

A material specimen is put between two electrodes, El1 and El2, as shown in Figure 2.2

([7]-[12], [15], [23], [24]). Given a charge-free specimen, the application of DC voltage (generated by source UDC) causes surface charge densities σ1 and σ2 on the electrodes and a volume

charge density _ρ in the material specimen. During a measurement, a very short, high voltage pulse is applied, generated by a pulse source. When this electric pulse is present, the resulting electric field acts on the space charge inside the material. Due to this field, the space charge and charge at the electrodes experience an electrostatic force, F. The force is of short

duration and, as a result, two acoustic waves propagate in both directions, to El1

and El2. The wave traveling in the direction of El2 is initially transferred to the

electrode material, which acts as a delay block for the acoustic wave until its arrival at a piezoelectric sensor/transducer. The delay is necessary because of the interference of the electromagnetic noise caused by the ignition of the electrical pulse. The piezoelectric transducer detects the acoustic wave and transforms it into an electric signal. The signal is fed into an oscilloscope, and from there into a computer. The computer stores the signal and performs some signal shaping and calibration. The wave in the direction of El1 is first reflected at El1 and then

Figure 2.2 Principle of PEA measurement

The result of a PEA measurement is an electrical, time-dependent signal, u(t). The signal is made space-dependent using a well known relationship between path s[m], velocity

υ

sound [m/s] and time t [s], s =

υ

sound

⋅

t.

The measured voltage signal, u in mV, is converted to a charge signal

_ρ

in C/m3 according to relation (2.1).

(2.1)

where Kcal is the calibration factor.

The calibration factor can be calculated as (2.2) from a known charge, which is in this case the surface electrode charge. A slab of charge [C/m3] is a product of a surface charge

_σ

[C/m2] and the slab thickness b [m],

_ρ

=

_σ

/b. For a detailed description see Appendix C and [23].

( )

specimen cal specimen cal cal U b d t u K

ε

= (2.2)

where: ucal(t) is signal measured during the calibration measurement, dspecimen is

the thickness of the material specimen,

_ε

specimen is the permittivity of the material

and Ucal is the DC voltage during the calibration.

2.3.2 Description of the equipment and measurement procedure

Equipment

The equipment used for PEA measurements in this thesis consisted of: ‰ Electrodes HV: stainless steel covered with semi-con rubber;

LV: aluminum 18 mm, also used as a delay block. A droplet of oil was interposed between the electrodes and the test specimen, to improve acoustical coupling. ‰ Charging DC supply: Heinzinger 40 kV, 15 mA

‰ Pulse DC supply: Heinzinger 10 kV, 5 mA

‰ Spatial resolution Between 13 μm and 17 μm; calculated as: r =

υ⋅

ΔT Where r is the spatial resolution,

_υ

[m/s] is the sound velocity in the material, ΔT is the pulse width.

‰ Sensor/transducer Bi-oriented PVDF foil, 9 μm

‰ Amplifier Two 23 dB amplifiers, bandwidth 0.1 – 500 MHz ‰ Oscilloscope Digital storage 2 GSa/s, HP 54522 A

The high voltage DC circuit and the signal detection circuit are completely separated in the PEA method. Therefore, the output signal is shielded easily and less electric noise enters the detection circuit. Also, the risk of damaging the detection circuit in the event of specimen breakdown is minimal.

The measuring set-up, was placed in an EMC shielded space. A personal computer with a GPIB interface was used for displaying and storing of measured data.

Measurement procedure

There are two possible ways to perform a space charge measurement: a voltage-on or a voltage-off measurement, Figure 2.3. The time-dependent voltage signal u(t) [mV], recorded by the oscilloscope, is called the space charge profile. Space charge density is calculated from this signal (Appendix C). The average space charge density present in the test specimen is calculated from this signal according to the following relationship:

dx ρ(x) d ρ_avg =

_∫

d 0 1 (2.3) ‰ Voltage-on measurement

During a voltage-on measurement, a poling voltage is applied to the test specimen allowing space charge to accumulate. A difficulty with this way is that due to limited spatial resolution and the non-rectangularity of the high-voltage pulse [23], the signals originating from the electrode charges and the signal originating from the space charge may overlap, Figure 2.4.

‰ Voltage-off measurement

To reduce the effect of the electrode charges, a voltage-off measurement is performed: in this case the poling voltage is switched off, the electrode charges’ signals disappear, and on the screen of the oscilloscope the only visible signals are the signals originating from the accumulated space charge and mirror charges at the electrodes.

Sometimes we are interested in measuring the amount of space charge already present in a material prior to poling, for example, as a consequence of electrical aging. In such a case, only a voltage-off measurement is performed.

The duration of a voltage-off measurement depends on its purpose. For the calculation of accumulated space charge, the measurement takes 10 s. To observe the complete process of the discharging of the test specimen can take days.

Figure 2.3 An example of a voltage-on and voltage-off space charge measurement in epoxy [44]:

a) Voltage-on measurement at time t = 0.

b) Voltage-on measurement at time t = 3 hours. It is not possible to identify a difference between electrode charges and space charge at time t = 3 hours in the voltage-on measurement.

c) Voltage-off measurement immediately after switching off the charging voltage. Space charge is clearly visible in the voltage-off measurements.

Accuracy of the PEA measurements

The accuracy of the PEA measured space charge value in this work is approximated to be 15 %. According to [15, 23], two most relevant factors affecting the accuracy of PEA measurements are: the systematic error of the calibration procedure and the statistical error due to the presence of noise in detected signal. In [23] the error is found to account for 12 %, while the statistical error contributes 1 % to 3 % to the total relative error. As the same measurement procedure and data processing were adopted in this work, as well as quite similar equipment, it is assumed that the total relative error also in this case will not exceed 15 %.

2.4 Polarization current measurement

2.4.1 Description of the method

The polarization current measurement is performed by applying a DC voltage to material placed in a parallel plane electrode configuration, Figure 2.4. The polarization processes are thereby started and a small polarization current can be measured. The polarization current has a decreasing character and when all polarization processes are finished only the small conduction current remains.

Figure 2.4 Measurement principle of the polarization current.

2.4.2 Description of the equipment and measurement procedure

Equipment

The experimental set-up used for measurements of polarization current is shown in Figure 2.5. The used equipment is specified below.

‰ Electrodes High voltage: Rogowski-profiled aluminum electrode

Covered with 1 mm semicon rubber Low voltage: aluminum, guarded

‰ Charging DC Heinzinger, 40 kV, 15 mA

‰ Electrometer Keithley 617, programmable electrometer, bipolar 100 V

source, accuracy 0.05 %, connected to the measuring electrode via 10 MΩ resistor.

electrometer

test specimen DC

=

i(t) polarization current

time conduction current

a.u.

The measuring set-up was placed in an EMC shielded cage. A personal computer with a GPIB interface was used for displaying and storing of measured data.

Figure 2.5 Experimental set-up used for measurements of polarization current

Measurement procedure

For the polarization current measurement, a poling voltage is applied to the test specimen for at least 10000 s to make sure that the polarization processes are finished and that the only current which is measured is the conduction current. The polarization current is automatically recorded by a computer.

All polarization current measurements reported in this thesis were performed at ambient temperature.

Accuracy of the measurements

The accuracy of the polarization current measurements in this work is approximated to be 12 %. The error of the measurements caused by uncertainty in DC voltage and dimensions of the test specimens is calculated to be 10 %. Statistical error of 2 % has its origin in the presence of noise, which is introduced in amplifiers and signal cables.

2.5 Dielectric spectroscopy in the frequency domain

2.5.1 Description of the method

Dielectric spectroscopy in the frequency domain makes use of the fact that each dielectric mechanism has a characteristic relaxation frequency or frequency band.

For the purposes of dielectric spectroscopy, a time dependent electric field is used to probe molecular dynamics and charge transport. Reorientation (or relaxation) of dipolar groups, electronic or ionic conductivity, as well as induced

polarization processes contribute to relative complex permittivity

_{ε ε}

_{= −}′ i

_ε

′′.

The complex permittivity can be calculated from the complex impedance measurement, the principle of which is given in Figure 2.6 [45].

Figure 2.6 Principle of a dielectric measurement using a frequency response analyzer.

The sample material with complex permittivity

ε

(

ω

) is placed in a parallel plate

capacitor configuration. The AC voltage U with the frequency of measurement f is applied to the sample capacitor by the generator. The resistor R converts the sample current I into voltage. The amplitude and the phase of U and I are measured by two phase sensitive voltmeters.

I U

Z ₌ (2.4)

Where Z denotes the impedance of the sample capacitor.

Neglecting edge effects, complex permittivity is obtained from the standard equation of a parallel plate capacitor:

A ε d C i ε ε 0 = ′′ − ′ =

ε

(2.5)

where d is the distance between the plates, A is the area of one of the plates,

_ε

0 is

the vacuum permittivity and C is sample capacitance calculated from measured impedance.

2.5.2 Description of the equipment and measurement procedure

Equipment

For the dielectric spectroscopy measurements in the frequency domain a modular measurement system made by Novocontrol was used. The equipment consisted of:

‰ Impedance analyzer: frequency range 3 μHz to 20 MHz, impedance

10-2 _{Ω to 10}14_{Ω, accuracy tan δ ≈ 1·10}-5

‰ Cryostat: temperature range -160°C to 400°C, sensitivity of temperature

controller ± 0.01 K

‰ Temperature control: liquid nitrogen and 4-channel temperature controller

‰ Specimen holder, see Figure 2.8

For frequencies above 1 MHz [46], the sample impedance may become in the same order as the inductive impedance of the BNC cables connecting the specimen holder with the analyzer. This limits the measurements to frequencies below approximately 3 MHz. For high impedance test specimens, long cables cause additional problems due to the electrical noise created by mechanical vibrations. Therefore, cable length should be kept as short as possible. This is achieved by placing the complete analogue electronics at the top of the specimen holder, but not in the impedance analyzer. The connection to the electrodes of the specimen holder is done with solid air insulated lines that have only a tenth of the inductivity of 1 meter of BNC cable, see Figure 2.8.

Depending on the test specimen temperature set point, a heating element builds up a specified pressure in the liquid nitrogen Dewar vessel in order to create a highly constant nitrogen gas flow, Figure 2.7. The pressure and temperature in the Dewar are measured by two of the temperature controller’s channels.

Figure 2.7 Specimen cell and cryostat temperature control.

After being heated by a gas jet, nitrogen gas flows directly through a sample cell that is mounted in a cryostat. The gas and sample temperature are measured by the two remaining channels of the temperature controller.

The cryostat is vacuum isolated by a 2-stage rotary vane vacuum pump, providing thermal isolation by low vacuum (< 10 µbar). All temperature experiments are supported by the Novocontrol software package, providing both isothermal control and temperature ramping.

Sample cell Cryostat

N2 outlet

Vacuum pump Vacuum gauge Dewar PT 100 temperature sensor Dewar temperature sensor Liquid nitrogen evaporator Gas heating module Pressure sensor Ch. 3 Ch. 2 Ch. 1 Ch. 4 Temperature controller

Dewar Gas heater

Measurement procedure

For dielectric spectroscopy in the frequency domain only metallised specimens were used. The measurements reported in this thesis were recorded across broad temperature and frequency ranges. The duration of most measurements was from 5 to 12 hours. The applied voltage was 3 V.

Prior to each measurement, the test specimen’s temperature was kept at 20_{°C for}

approximately 15 minutes in order to achieve thermal equilibrium between the test specimen and the electrodes of the specimen holder. After the temperature stabilization, the measurements were performed in three temperature runs. In

this way, tension in the material or a preference direction2 of polarizable parts

was removed.

Figure 2.8 Active specimen holder.

2 _{A preference direction can be a consequence of long-term exposure to high DC voltages or a consequence of} the manufacturing process.

GEN V1 V2 PT100 Impedance analyser connector PT 100 connector Sample mounting screw Electrode connectors PT 100 temperature sensor Upper electrode, current sense Lower electrode, AC signal source Upper electrode signal Lower electrode signal

2.6 Breakdown tests

The breakdown tests were done by increasing the poling voltage in steps until breakdown occurred. The same set-up as for the electrical aging test was used, Figure 2.9. At least four specimens of each material used in this thesis were tested.

The mode of increase of the voltage was 2 kV/minute. As the start, the voltage was set at 40 % of the probable short-time breakdown voltage. The probable short-time breakdown voltage was obtained in accordance with the following method:

‰ The voltage was raised from zero at a uniform rate until breakdown occurred.

‰ The rate of rise that most commonly caused breakdown to occur within 60

seconds was selected.

If breakdown occurred in less than six levels from the start of the test, a further four specimens were tested using a lower starting voltage.

The electric strength was based on the highest nominal voltage that was withstood for 60 s without breakdown.

2.7 Electrical aging tests

The electrical aging tests were carried out by submerging the test specimens in a vessel filled with mineral insulating oil, type Shell Diala B. The specimens were placed between two stainless steel electrodes in the specimen holder shown in Figure 2.9. Sixteen specimen holders can be used at the same time in the aging set-up.

Figure 2.9 Specimen holder for aging and breakdown test set-ups. Breakdown

detection

Stainless steel Teflon

The specimen holders were connected to a breakdown detection circuit that provided information about the breakdown time and automatically switched off the voltage supply in the event of breakdown.

T

T

h

h

e

e

o

o

r

r

e

e

t

t

i

i

c

c

a

a

l

l

b

b

a

a

c

c

k

k

g

g

r

r

o

o

u

u

n

n

d

d

3

3

3.1 Introduction

In the following section, an overview is given of the main processes whose parameters are measured by means of: space charge measurements, polarisation current measurements, and dielectric spectroscopy in frequency domain. Thereby a physical background is explained and an analytical description is given. The description of the main processes behind the breakdown of insulating materials is assumed to be well known, and is therefore not covered. An excellent description can be found in [40-41].

3.2 Space charge formation

generation of space charge is expressed by the current continuity law, in (3.1) given in 1-dimensional form:

( )

( )

t x ρ x x J 0 d d = ∂ ∂ + (3.1)

where J represents the current density and

_ρ

the space charge density in point x. In other words, any situation where the current density J differs in space, dJ(x)/dx

≠

0, will lead to the generation of space charge. The divergence of the current density is found at various places: at an electrode-dielectric interface, at a dielectric-dielectric interface, in the presence of a temperature gradient, in material in-homogeneity, and in a diverging field.

Electrode-dielectric interface

Considering the electrode-dielectric interface, the build-up of space charge depends on the difference between the flow of the charge carriers through the interface (injection/extraction), and the flow of the charge carriers through the material (transportation). If the flow through the interface equals the flow through the material, there will be no space charge formation. In cases where the injection/extraction rate of the charge carriers is higher than the transportation rate, space charge will primarily build-up in the vicinity of the electrodes. The charge polarity is, in this case, the same as the electrode polarity and this charge is denoted as a homo-charge. The electrical field due to the homo-charge decreases the electrode field, causing a decrease of injection. At the same time, the bulk field increases and, consequently, the transportation current. A steady-state situation is achieved when the injection and transportation of the charge carriers are in equilibrium. The opposite situation is also possible: injection/extraction rate being lower than transportation. The space charge in this case has the opposite polarity from the adjacent electrode and is denoted as a hetero-charge.

Dielectric-dielectric interface

Space charge build-up at the interface of two dielectrics is described by the Maxwell-Wagner theory [48-49]. A hypothetical configuration is used containing two dielectric slabs of thickness dA and dB placed between plane

parallel electrodes (Maxwell capacitor), Figure 3.1. Combining Gauss’ law (3.2), the continuity equation (3.1), and Ohm’s law (3.3) in a homogeneous electrical field, the charge accumulated at the dielectric-dielectric interface can be calculated according to (3.4), [13], [42], Appendix D:

0 1 exp B A A B A B B A t U d d

σ ε

σ ε

κ

σ

σ

τ

− ⎛ ⎛ ⎞⎞ = _⎜ − _⎜− _⎟⎟ + ⎝ ⎝ ⎠⎠ (3.4)

where dA, dB represents material thickness,

σ

is material conductivity,

ε

is

material permittivity, U0 is the applied DC voltage, and

τ

is time constant.

The growth of the charge described by the time constant

_τ

:

A B B A A B B A d d d d

ε

ε

τ

σ

σ

+ = + (3.5)

Figure 3.1 Dielectric-dielectric interface: Maxwell capacitor.

Temperature gradient

Any temperature gradient in a dielectric material will affect conductivity by creating a conductivity gradient. This will influence the ratio of permittivity

_ε

to conductivity

σ

of the material (3.2) and lead to space charge formation.

Material inhomogeneity

Morphological inhomogeneity is often seen in filled materials. The addition of a filler introduces numerous interfaces between the host material matrix and the filler. Space charge formation, as previously described in a dielectric-dielectric interface, is then inevitable. Morphological inhomogeneity occurs in materials that are partly amorphous and partly crystalline. An example is polyethylene, which is often used for cable insulation, Figure 3.2. Space charge will accumulate at the boundary between the amorphous and crystalline part, which is now seen as a dielectric-dielectric interface.

dA dB

U0+ 0

Figure 3.2 Structure of a polymer with crystalline and amorphous parts.

As already mentioned, several physical mechanisms are involved in space charge formation:

Injection/extraction process

The injection/extraction process of charge carriers at an electrode-dielectric interface is possible across or through the metal-dielectric potential barrier, which charge carriers at the electrode have to overcome to enter the dielectric material. The first type of injection is described by the Schottky process [24]. Application of an electric field leads to a reduction of a potential barrier making charge injection possible across the potential barrier. The second type of injection through the potential barrier is described by the Fowler-Nordheim process [24] in which, at fields above approximately 100 kV/mm, the potential barrier becomes very narrow making charge carrier tunnelling possible. Injected charge carriers may also recombine if the opposite charge is present in their proximity.

Trapping

Trapping sites, or more simply traps, are potential wells where the charge carriers can be captured. Traps are always present in an insulating material due to the fact that insulating materials are never perfectly homogeneous: crystalline and amorphous regions may be found in a piece of material. At the atomic level, there will be significant changes in interatomic spacing due to structural disorders in amorphous regions, and this will cause spatial changes in the band gap [24]. Also, incompletely bound atoms in crystal defects give rise to so-called dangling bonds [41]. The dangling bonds can be satisfied by either the removal or donation of an electron (or both) and thus behave as states within the band gap. These localised energy states in the band gap are called trapping sites: donor trapping sites (hole traps) are located immediately above the top of the valence band, acceptor trapping sites (electron traps) are located immediately below the bottom of the conduction band. Electrons or holes crossing over from the valence to the conduction band may enter the trapping sites and may have to

acquire considerable energy before they can leave. So-called self-traps are also possible: the field from an electron or hole can re-orientate the local structure thereby creating a potential well from which escape may be very difficult.

Traps are usually classified according to their location, in the vicinity of physical or chemical defects. Physical defects are conformational; they can be found close to a material surface and in the amorphous parts of materials at the ends of molecular chains. They are responsible for shallow physical trapping sites. Chemical defects consist of additives (for instance, antioxidants), cross-linking by-products, and other impurities. They are responsible for deeper chemical traps.

Charge carriers will be trapped at a rate dependent upon their initial kinetic energy.

Transportation

There will always be a certain amount of injected charge carriers that will be transported through the dielectric and finally extracted. Some of them move free, others are trapped on their way through the dielectric and then, after some time, released. Therefore, the transportation of charge carriers depends also on the density and depth of the trapping sites. This is often denoted as trap limited conduction [50], Figure 3.3.

Figure 3.3 Charge carrier transport through dielectric material is defined by the density and depth of trapping sites. The time a charge carrier spends in a trap is much greater than the time spent travelling between the traps. For example: an electron travels with a velocity of approximately 105 m/s between the traps and spends more than an hour in traps of depth 1 eV.

The time that a charge carrier spends in a trap is much greater than the time spent travelling between the traps. For example: an electron travels with a velocity of approximately 105 m/s between the traps and spends more than an hour in traps of depth 1 eV.

Charge generation

Charge carriers which form space charge are injected from the electrodes or are generated in the material bulk. The internal charge carriers can be electrons or holes that have gained sufficient energy to escape from the valence band into the conduction band. The corresponding excitation energy can be of thermal, electrical, or of some other radiative nature. The charge carriers are sometimes ions, which can be present in the material for various reasons: they can be formed due to the dissociation [51] of additives and impurities that are often found in insulating materials, or they can be a by-product of aging [52].

3.3 Conduction current

Conduction current is the part of a polarisation current that is measured when a DC voltage is applied across the insulating material. The polarisation current has a decreasing character, and when all polarisation processes are finished, it approaches its steady-state value: conduction current. An example of a plot of polarisation current versus polarisation time is given in Figure 3.4.

Figure 3.4 Polarisation current in pre-stressed PCTiO2. Applied electric field

17.1 kV/mm.

Polarisation current is given by expression (3.6), [51], [53], Appendix E:

( )

0 0

( ) ( )

0 P I t U C

σ δ

t f t

ε

⎡ ⎤ = _⎢ + + _⎥ ⎣ ⎦ (3.6)

where: C0 is geometrical capacity, U0 is applied DC voltage,

δ

(t) is a Dirac pulse, f(t) is the dielectric response function related to polarisation processes,

_ε

0 is the vacuum permittivity, and

σ

is the material conductivity.

When the conduction current is plotted against different applied electric fields, the E vs. I characteristic is obtained, as given in Figure 3.5.

Figure 3.5 E vs. I characteristic: change of degree of inclination from 1:1 (ohmic behaviour) to 2:1, indicating the change of conducting mechanisms in the material.

Taking into consideration a parallel plane electrode configuration (which is used in the research described in this thesis), in the absence of space charge, the electric field in the material is uniform and a linear relationship exists between the conduction current through the material and the applied voltage. This linear relationship is described by Ohm’s law. The linear E vs. I characteristic plotted in a log-log plot is a straight line with a degree of inclination (slope) equal to one. The degree of inclination of the characteristic can also change, indicating a change of conduction mechanisms. For instance, in the presence of space charge, the internal electric field in the material is modified and the linear relationship does not hold anymore. Therefore, the threshold field at which the degree of the inclination of the E vs. I characteristic changes, coincides in many cases with the threshold field for space charge accumulation.

3.4 Dielectric polarisation and relaxation

The majority of dielectric materials used in electrical power engineering can be described as being isotropic and linear [53], [55]. For these materials, polarisation P→ is proportional to the applied electric field E→ through the relationship (3.7):

→

P =

ε

0 (

ε

r –1) →

E (3.7)

where

_ε

0 is the vacuum permittivity and

ε

r is the relative permittivity.

The process opposing polarization is called relaxation and each dielectric structure has a characteristic relaxation frequency or frequency band.

The permittivity,

_ε

=

_ε

0

ε

r, in an alternating electric field is a complex quantity and a function of frequency, (3.8):

ε

(

_ω

) =

_ε

΄(

_ω

)- i

_ε

΄΄(

_ω

) (3.8)

ε

΄(

_ω

) is the real part of complex permittivity and represents a measure for the energy stored per period.

ε

΄΄(

ω

) is the imaginary part of complex permittivity and represents energy dissipated per period or dielectric absorption.

The ratio between the real and the imaginary part of complex permittivity is termed tan

_δ

, (3.9). tan

_δ

is actually the phase lag between the alternating voltage V applied at a capacitor and current I through the capacitor1.

tan

_δ

=

_ε

΄΄/

_ε

΄ (3.9)

tan

δ

is frequently used in practice for the testing of insulation materials and the measurements are usually performed at single frequency, 50 Hz. However, a lot more information about the structure and condition of insulating materials is available when complex permittivity is observed in a broad frequency range. Complex permittivity is not only a function of the frequency of an applied electric field, it is also temperature dependent. An example of 3 - D plots of real and imaginary parts of complex permittivity is given in Figure 3.6 [56].

The relationship between complex permittivity, frequency, and temperature [57] was first found by Debye, (3.10):

( )

,T s_i

_{( )}

_T

ωτ

ε

ε

ε

ω

ε

+ − = − ∞ ∞ ₁ (3.10)

where

_ε

_∞ is the dielectric constant at

_ω

_{→ ∞,}

_ε

s is the dielectric constant at

ω

→ 0, and

τ

(T) is the relaxation time.

The real and the imaginary parts of complex permittivity can be written as (3.11) - (3.12):

( )

,T

_{( )}

_T ' s 2 2 1

ω

τ

ε

ε

ε

ω

ε

+ − = − ∞ ∞ (3.11)

( ) (

,T

)

( )

T

_{( )}

_T '' _{s 2 2} 1

ω

τ

ωτ

ε

ε

ω

ε

+ − = _∞ (3.12)

1 _{When an alternating voltage is applied to a capacitor the current through the capacitor will consist of two parts:}

Real (resistive) part which is in phase with the applied voltage, IR = ωC0ε΄΄V

Imaginary (capacitive) part, out of phase, IC = iωC0ε΄V

10 -2 10 0 10 2 10 4 10 6 10 8 Freq uenc_{y [H} z] 3.5 4.0 4.5 5.0 5.5 6.0 Permittivity' 100 150 200 250 300 350 400 Temperature [K] epoxy new 120C to -160C 10 -2 10 0 10 2 10 4 10 6 10 8 Freq_uen cy [H_z] 0.0 0.1 0.2 0.3 0.4 Permittivity'' 100 150 200 250 300 350 400 Tempera ture [K]

The relationship described by (3.10) assumes one specific relaxation time

_τ

(T). Therefore (3.10) is valid for gasses and liquids with a low molecular content where assumption of one polar group is generally acceptable. For a polymer, some modifications are needed.

A polymer often contains different polar groups, and more than one interaction with its neighbours. As a consequence, there is more than one relaxation time, and a certain fluctuation in relaxation time. In other words, a polar group is characterised by a number of relaxation times that are grouped around a certain mean relaxation time. Cole-Cole introduced a modification of (3.10) as given by (3.13):

(

)

( )

, 1 s T i T β

ε ε

ε ω

ε

ωτ

∞ ∞ − − = + ⎡_⎣ ⎤_⎦ (3.13)

The factor

β

makes possible a symmetrical spread of relaxation times along the frequency axis.

Another modification of the Debye expression, which is more general than (3.13), was made by Havriliak and Negami:

(

)

( )

{

}

, 1 s T i T β α

ε ε

ε ω

ε

ωτ

∞ ∞ − − = + ⎡_⎣ ⎤_⎦ (3.14)

Complex permittivity exhibits several types of relaxation, each of them characterised by their own relaxation parameters.

The most pronounced is _{α-relaxation. α-relaxation has a high and narrow peak} in comparison with other relaxations; at higher temperatures the maximum extent of the relaxation shifts to higher frequencies. In polymers, this relaxation is associated with the glass transition temperature, Tg, and it is caused by the

co-operative motion of a number of (polar) segments of the main molecular chain. So-called _{β-relaxation is characterised by a broad relaxation peak, which can} have a width of several decades. The position of the maximum extent of β-relaxation also shifts to higher frequencies if the temperature is increased. This relaxation arises from localised rotational fluctuations of side groups, or fluctuations of localised parts of the main molecule chain.

α-relaxation shows non-Arrhenius temperature dependence, while β-relaxation does.

making a distinction between them quite difficult. An example is given in Figure 3.7.

Figure 3.7 An example of ε΄΄ and contributions of α- and β-relaxations.

T

T

h

h

e

e

e

e

f

f

f

f

e

e

c

c

t

t

o

o

f

f

l

l

o

o

n

n

g

g

-

-

t

t

e

e

r

r

m

m

D

D

C

C

s

s

t

t

r

r

e

e

s

s

s

s

o

o

n

n

s

s

p

p

a

a

c

c

e

e

c

c

h

h

a

a

r

r

g

g

e

e

d

d

y

y

n

n

a

a

m

m

i

i

c

c

s

s

4

4

4.1 Introduction

Space charge measurements provide us with a means to detect magnitude, polarity and location of charge trapped in a dielectric. From the measured space charge profile, the distribution of the electric field is derived and as such, space charge measurements are a valuable tool for dielectric evaluation. Furthermore, different dielectrics can be compared regarding their tendency to accumulate charge: it appears that for many dielectrics a threshold field can be defined below which no or hardly any space charge accumulates.

This chapter presents results of space charge measurements performed in order to establish the space charge dynamics of PC and PC-TiO2, and to analyse the

effect of long-term exposure to a high electric DC field (100 kV/mm DC for 1500 hours) on the space charge behaviour of materials.

Space charge measurements were performed using the PEA method on flat PC and PC-TiO2 specimens as explained in Chapter 2: Experimental. Generally

As a consequence, an acoustic wave is generated which is detected by a piezoelectric sensor. The voltage signal provided by the piezoelectric sensor contains information about the density and location of space charge.

Based on the space charge measurements, a number of space charge related quantities are calculated and derived, as listed below:

‰ Space charge density and polarity, and the position of accumulated space charge.

‰ Electrical field strength in the material.

‰ Space charge accumulation (and depletion) characteristic times.

‰ Characteristics of space charge density as a function of a polarising electric field (

ρ

vs. E characteristics).

‰ Electrical threshold for space charge accumulation, E_th,sc.

In the following, applications of the mentioned quantities are given and their importance is stressed.

Space charge density

Space charge volume density,

ρ

[C/m3] is a basic quantity used for the calculation of the other listed quantities. It is important to note that a quantitative analysis of space charge density does not provide sufficient information for material ranking or characterisation. In other words, the fact that one material accumulates less space charge than another does not provide adequate information to be able to state that one material’s dielectric performance is better than another’s. Space charge volume density is, as its name indicates, a volume quantity, while space charge itself can be concentrated at some points or equally spread throughout the material. Therefore, at the very least, the location and distribution of space charge should be known before any judgment about material performance can be made. The location at which space charge will accumulate is, in turn, closely related to trapping site distribution, the depth of the trapping sites, and the existence of dielectric interfaces, as already explained in Chapter 3.

Homo-charge Hetero-charge

In a flat homogenous specimen, as used in this work, space charge initially accumulates, for the most part, in the vicinity of the electrodes. After some time – depending on the applied field, trapping site distribution, and the depth of the trapping sites – space charge can migrate to the bulk. An often used notation based on space charge polarity is: homo-charge – having the same polarity as the adjacent electrode, and hetero-charge – having the opposite polarity, as shown in Figure 4.1. The polarity of space charge compared to the polarity of the adjacent electrode is an important parameter for the evaluation of insulating materials. Homo-charge results in an enhanced electrical field in the material bulk, while the field at the interface between the material and the electrode drops. In contrast to this, hetero-charge enhances the electrical field at the electrode-insulator interface, while the field in the material bulk drops. In the majority of practical cases, polarity reversal is applied, which makes hetero-charge more critical. [13], [23]. In HVDC applications, homo-hetero-charge prevails, while according to [58] hetero-charge occurs only at quite low poling fields and/or in the presence of a reasonable concentration of intrinsic charge carriers within the insulating material.

Electrical field

The electrical field of a material can be considerably modified by the presence of space charge, Figure 4.2 [15].

a) b)

Figure 4.2 Illustration of an electric field in a homogeneous dielectric, from [15]: a) without space charge, b) in the presence of space charge.

Space charge distorts any electrical field that is present. This effect is expressed through Poisson’s equation (4.1):

( )

t x E r f

ε

ε

ρ

0 1 d d = (4.1)

where E(x) is the electrical field strength at the point x,

_ρ

f is space charge density

at the point x, and

ε

0 and

ε

r are the vacuum and the material permittivity

respectively.

The presence of space charge in a dielectric implies that the dielectric experiences electrical fields above design values in some regions. This additional electrical stress is very hard to take into consideration in the original insulation design, due to the fact that space charge accumulation is influenced by a variety of factors that change during the lifetime of the insulation. Generally speaking, polymeric insulating materials do not indefinitely retain the nature that they possessed on first being manufactured. Over a period of time, both their chemical composition and physical morphology may change, even when not exposed to electrical stress.

An enhancement factor f can be calculated as (4.2):

max DC _100% DC E E f E − = ⋅ (4.2)

where EDC denotes the applied electric field, and Emax is the maximum of the

actual field strength in the test-specimen.

Space charge accumulation and depletion characteristic times

Both charge accumulation and depletion processes are often described with more than one exponential function and corresponding time constants, as schematically depicted in Figure 4.3. The existence of several time constants is brought about by the processes that take place in the material during the accumulation period [23-24]. These are: injection/extraction, transportation, and recombination of the charge carriers.

Figure 4.3 Illustration of space charge accumulation and depletion processes in time.

In analytical form, the processes are described by a superposition of exponential functions according to the following expression (4.3):

where

_ρ

total(t) is the total amount of accumulated charge,

ρ

i(t) is a part of the

total charge accumulated during the process described by an exponential function with the corresponding time constant

_τ

i, and x is a weight factor.

According to [24], since charging phenomena are frequently affected by polarity, time constants can demonstrate polarity dependence. From a practical point of view, it is also interesting to know when the majority of the charging and discharging processes are completed: a limitation can be set at approximately 90 %, which fits quite well in the regions described as fast growth or rapid decay in Figure 4.4. In this way, the accumulation and depletion processes, or 90 % of the processes, are characterised with one exponential function and thus one time constant.

Weather the 90 % accumulation and depletion time constants will be the same or not depends on space charge distribution within the material specimen. In cases where there is absolute space charge symmetry in a homogeneous material specimen, space charge will be driven out of the specimen at the same rate as it was accumulated. In contrast to this, in the most probable unsymmetrical charge distribution, a part of the accumulated charge will be driven out and a part will be forced into the bulk of the specimen. Consequently, depletion will take more time than accumulation. This is illustrated in Figure 4.4 a)-b) from [24].

Figure 4.4 Direction of charge motion in a short-circuited specimen from [24].

a) Symmetrical charge distribution, a zero field plane in the centre of the specimen.

b) Unsymmetrical charge distribution, zero-field planes outside the centre of the specimen

The practical significance of charge depletion time is that it gives the characteristic discharge time needed to release the internal DC stress of the material. It is also related to processes on a microscopic scale: the depth and distribution of trapping sites can be influenced by long-term exposure to a high

Sample

Hetrocharge Homocharge

Zero field plane Direction of charge motion

Sample

Homocharge Homocharge

DC electric field, resulting in different discharging dynamics. Consequently, the charge depletion characteristic time will change.

ρ

vs. E characteristic and electrical threshold for space charge accumulation

By plotting the logarithm of space charge volume density against the logarithm of the applied field, the

_ρ

vs. E characteristic is obtained. From this characteristic, an electrical threshold for the inception of space charge accumulation, Eth,sc, can be determined. Eth,sc and

ρ

vs. E characteristics are

schematically depicted in Figure 4.5. The space charge accumulation threshold is important for several reasons:

‰ The onset of space charge accumulation is also the onset of field modification in the material, triggering the dielectric to experience electrical fields above design values in some regions.

‰ A statement often found in the literature is that this threshold may be close to the threshold field of electrical aging Eth,ag [24, 26-29, 36, 37-39].

Designing an insulation system for an electric stress below Eth,ag would

assure very long life expectancy and high reliability, provided that there were no other significant stresses affecting the insulation [59].

‰ The threshold for space charge accumulation appears to be aging sensitive: it shifts towards lower fields.

‰ The threshold for space charge accumulation shows good agreement with the threshold field at which the I-V characteristic changes from a linear (ohmic) regime to a non-linear one [59].

Figure 4.5 _ρ vs. E characteristics: characteristic of space charge density as a function of the polarising field. Eth,sc: electrical threshold for space charge accumulation.