Materials and Emerging Test Techniques: Field Grading in Electrical Insulation Systems

 

D1

Materials emerging Materials and emerging test techniques

Field grading in electrical insulation systems Re󰁦erence: Re󰁦erenc e: 794 7 94 March 2020

   

Field grading in electrical  

insulation systems WG D1.56

Members V. HINRICHSEN, Convenor   J. DAS M. HADDAD N. HAYAKAWA I. JOVANOVIC M. KOCH J. LAMBRECHT C. STAUBACH N. ZEBOUCHI

DE US UK JP US DE DE DE FR

D. BACHELLERIE L. DONZEL M. HAGEMEISTER S. JOSEFSSON L. KEHL M. KOZAKO F. PERROT J. WEIDNER M. H. ZINK

FR CH CH NO DE JP UK DE DE

Young members R. HUSSAIN

DE

M. SECKLEHNER

AT

Corresponding Me Member mber D. TABAKOVIC

US

Copyright © 2020 “All rights to this Technical Brochure Brochure are retained by CIGRE. It is strictly prohibited to reproduce or provide this publica publication tion in any form or by any means to any third party. Only CIGRE Collective Members companies are allowed to store their copy on their internal intranet or other company network provided access is restricted to their own employees. No part of this publication may be reproduced or utilized without permission permission from CIGRE”.  CIGRE”.  Disclaimer notice “CIGRE gives no warranty or assurance about the contents of this publication, nor does it accept any responsibility, as to the th e accuracy or exhaustiveness exhaustiveness of the information. All implied warranties and conditions are excluded to the maximum extent permitted by law”.  law”. 

ISBN : 978-2-85873-496-2 978-2-85873-496-2

 

TB 794 - Field grading in electrical insulation systems  

Executive summary High-voltage equipment like bushings and cable accessories require field grading strategies to control and redistribute the electric field more uniformly in the material and at the interfaces of the insulation. Different approaches provide geometrical grading (conductive layers in the insulation material), refractive grading (high permittivity layers in the insulation), resistive grading (semiconductive layers on the surface of insulation) or combinations of them. Semiconductive materials with linear or nonlinear conductance, like carbon black or silicon carbide (SiC), are currently used as fillers for the purpose of field grading. Alternating three-phase system voltage levels and design requirements are emerging. Direct voltage applications with mixed capacitive and resistive field stress require special considerations. New materials like microvaristors open new possibilities for the design of bushings, cable accessories etc., but also for electrical insulation systems in other equipment, such as long rod insulators and rotating electrical machines. The design of a field grading system is a rather complex task, requiring knowledge about the fillers, the matrix materials and their interaction, which often cannot be predicted from the properties of the individual components. The purpose of this Technical Brochure is   to inform about the fundamentals of field grading,   to examine today’s different practices in detail and to give an outlook on possible future developments,   to inform about material characteristics (fillers, matrix materials), and   to disseminate a common understanding of how to optimize electric field distribution and grading of insulation systems and characterize the individual components. c omponents. The present Technical brochure summarizes the work carried out by the Working Group D1.56 and is reported in seven chapters. Following an “Introduction” in Chapter 1, Chapter 2 “Basics of electric field grading” gives the fundamentals of electric field distribution in media. In particular, it introduces the concept of refraction at interfaces between materials with different permittivities and/or conductivities. A classification of the different field grading concepts is given and each concept explained. Chapter 3 “Material systems for field grading systems” starts with a description of the physical phenomena “conductivity” and “permittivity”. A majority of o f materials used in field grading are composite materials. In this chapter, first, a description of typical matrix materials is presented, followed by a comprehensive list of fillers known from products and literature. Then, the topic of measurements and characterization methods for field grading materials is addressed. Especially for DC systems, design rules and a design example are finally given. Chapter 4 “Simulation of field grading systems” presents the different methods that can be used to design and optimize field grading systems. Historically, transient network analysis has been used and is still helpful in special cases. However, nowadays numerical field simulations with the finite element method (FEM) or the finite difference method (FDM) are more widely used. Experimental possibilities to validate the simulation results are presented. The intention of Chapter 5 “Applications” is to give a detailed description of the main electrical devices relying on field grading to function. First, First , cable accessories for both medium- and high-voltage systems are addressed. Secondly, possible designs for terminations, joints and separable connectors (plugin systems) are presented. The third section deals with the special requirements of transformers. The different types of bushings are discussed in Section 5.4. Section 5.5 is dedicated to the end corona protection of rotating electrical machines that are either connected directly to the line or converter fed. Finally, the subject of insulators (line insulators, hollow core insulators, insulators for gas insulated systems) is treated.  After Chapter 6 “Summary and Conclusions”, which summarizes the content of the brochure and gives an outlook to future needs and developments, Chapter 7 “Terms and Definitions” lists all all symbols,  symbols, units and abbreviations that are in use or have been used in this Technical Brochure.

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TB 794 - Field grading in electrical insulation systems  

The Technical Brochure ends with Chapter 8 “References”, a list of the literature that was used to prepare this Technical Brochure. It comprises some 200 publications and might be helpful for all who need more comprehensive information on particular field grading issues.

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TB 794 - Field grading in electrical insulation systems  

Contents Execu ti ve su summ mm ary ................ ................................. .................................. .................................. .................................. ................................... ......................... ....... 3  1. 

Int Intro ro du duct ctio io n ................... .................................... .................................. .................................. .................................. ................................... ......................... ....... 7 

2. 

Basics of electric field grading ................................................................................. 9 

2.12.1.1Capacitive resistive electric field distributions ............................................................................... 9 Basicsand .................................................................................................................................................. 9      2.1.2  Fields at interfaces of layered materials ............................................................................................ 10   2.2  Electr ic fiel d grad in g con cepts ....... ............. ............. .............. ............. ............. .............. ............. ............. .............. ............. ............. .............. ............. ............. .............. .......... ... 11   2.2.1  General .............................................................................................................................................. 11  2.2.2  Bulk field grading ............................................................................................................................... 12  2.2.3  Surface field grading ................................................................................................................... .......................................................... ................................................................ ....... 16  2.2.4  Field grading in coaxial cylinder configurations by layered dielectrics ............................................... 21  

3. 

Material sys tems for field gradin g syst ems ....... ........... ......... ......... ......... .......... ......... ......... .......... ......... ......... .......... ....... 27 

3.1  General ..................................................................................................................................................... 27  3.1.1  Conductivity ....................................................................................................................................... 27  3.1.2  Permittivity ......................................................................................................................................... 28  3.2  Matrix materials ....................................................................................................................................... 31  3.2.1  Glass (resistive glazing) ..................................................... .............................................................................................................. ................................................................ ....... 31  3.2.2  Thermoplastic polymers ..................................................... .............................................................................................................. ................................................................ ....... 32  3.2.3  Thermoset polymers .................................................................................................................................. 32  3.2.4  Elastomers................................................................................................................ .................................................... ..................................................................................... ......................... 33  3.3  Fillers ........................................................................................................................................................ 34  3.3.1  Goal ................................................................................................................................................... 34  3.3.2  Carbon black and carbon nanotubes ................................................................................................. 34  3.3.3  Nonlinear materials ..................................................................................................................... ............................................................ ................................................................ ....... 37  3.3.4  Further approaches under development ......................................................... ............................................................................................ ................................... 42  3.4  Measuremen t metr ics of fiel d g radi ng m ateri als and syst ems ............. .................... .............. .............. ............. ............. .............. ............. ...... 47  3.4.1  Introduction ........................................................................................................................................ 47  3.4.2  Characterization of the polymer matrix .............................................................................................. 48   3.4.3  Characterization of the particulate filler .............................................................................................. ........................................................... ................................... 48  3.4.4  Characterization of the composite material..................................................... ........................................................................................ ................................... 51  3.4.5  Electrical characterization of nonlinear field grading composite materials ......................................... 52  3.4.6  Operating stresses at component/equipment levels .......................................................................... 61 

 

  4.1  Purpose and requirements ..................................................................................................................... 63  4.2  Transi ent Networ k Anal ysis appr oach ....... ............. ............. .............. .............. ............. ............. .............. ............. ............. ............. ............. .............. ............. ............ ...... 63  4.3  Numeri cal fiel d si mul atio n appr oach es ....... .............. ............. ............. .............. ............. ............. .............. ............. ............. .............. ............. ............. .............. .......... ... 64  4.4  Verifi cati on of sim ul atio n resul ts ....... .............. ............. ............. .............. ............. ............. .............. ............. ............. .............. ............. ............. .............. .............. ............. ...... 66  4.4.1  Measurement of potential and temperature distributions .................................................... ................................................................... ............... 66  4.4.2  Measurement of partial discharge (PD) inception voltages ......................................................... ................................................................ ....... 69  4.

Simu lati on of f ield g radi ng syst s yst ems ................. .................................. .................................. ................................... .................... .. 63 63

5. 

 Ap  Appl pl ic ati on s .......... ................... .................. .................. ................... ................... .................. .................. .................. ................... ................... ................ ....... 71  

5.1  Cable accessories ................................................................................................................................... 71  5.1.1  General .............................................................................................................................................. 71  5.1.2   Accessories for MVAC and HVAC extruded cables ........................................................................... ............................................................ ............... 75  5.1.3   Accessories for HVDC extruded cables............................................................................................. .......................................................... ................................... 79  5.2 

Plug -in syst ems / separ able con nect ors ...... ............. ............. ............. .............. .............. ............. ............. ............. ............. .............. .............. ............. ............. ......... .. 83 

5.2.1 5.2.2   5.2.3 

General .............................................................................................................................................. 83 Outer and inner cone systems ........................................................................................................... 84   Further examples of application ......................................................................................................... ........................................................... .............................................. 86  

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TB 794 - Field grading in electrical insulation systems  

5.3  Transformers ........................................................................................................................................... 86  5.3.1  General .............................................................................................................................................. 87  5.3.2  Design criteria for AC and impulse voltages ...................................................................................... 89  5.3.3  Design criteria for DC voltages .......................................................................................................... 90   5.3.4  Special field grading applications a pplications in transformers .............................................................................. ..................................................... ......................... 92  5.4  Bushings .................................................................................................................................................. 93  5.4.1  Basics of field grading within bushings .............................................................................................. 94  5.5  Rotati ng electr ical machi nes ...... ............. .............. ............. ............. .............. ............. ............. ............. ............. .............. .............. ............. ............. .............. ............. ............. ......... 97  5.5.1  General .............................................................................................................................................. 97  5.5.2  Direct line connection ........................................................................................................................ 98  5.5.3  Converter fed drives ........................................................................................................................ 100  5.6  Insulators ............................................................................................................................................... 101  5.6.1  Line insulators ................................................................................................................................. 101  5.6.2  Hollow core insulators ........................................................ ................................................................................................................. .............................................................. ..... 104  5.6.3  GIS insulators .................................................................................................................................. 105 

6. 

Summary and conclusions ....................................................................................109 

7. 

Terms and definitions.............................................................................................114 

7.1 

Symbols and units ................................................................................................................................. 114 

7.2 

 Acr on yms .......................................................................................................................................... ............................................................................... ................................................................ ..... 116 

8. 

.................................. .................................. ................................... ................................... .................................. ........................120 .......120  Referenc es .................

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TB 794 - Field grading in electrical insulation systems  

1. Introduction Electric field grading – grading  – sometimes  sometimes also denoted as stress grading  – refers  – refers to the active control of the distribution of the electric field within or around a device. Especially apparatus for the transport and distribution of electrical energy are facing huge potential differences between their terminals. This cannot be avoided, but the electric field strengths must be kept below a level where partial discharges and breakdowns within the insulating space would occur. Without a well-considered well-considere d design, the voltage and the resulting electric field is likely to not be distributed evenly across the insulating space or surface. Since for high voltage applications one single   weak or overstressed spot may decide over the functionality and reliability of the whole given device, this has to be prevented.  Various different methods of electric field control can be implemented in the design process. Some are seen as “good practice” or even basic knowledge for high voltage engineers, while others are subject of ongoing research. They are all bundled together under the term “electric field grading” and will be explained in this technical brochure. Electric field control includes all measures that serve to lower local electric field strengths to such an extent that the dielectric strength of the insulating materials and related interfaces are not exceeded anywhere in the insulation system. In principle, a distinction is made between field control measures in the volume of an insulating material and along interfaces. As the interfaces typically represent the weakest points in an insulation system the latter is more important i mportant in most cases. Basic differences also exist between time-varying field stress at alternating or surge voltages, constant field stress at steadystate DC voltages or at superimposed transient stress in DC systems. Regarding electric field control in insulating volumes, various fundamental measures for reducing electric field stress are known:      

application of large-radii curvatures for electrodes, e.g. by shielding electrodes, large-diameter conductors or chamfered electrode edges; optimization of radii ratios, e.g. in coaxial power cables, gas insulated systems or spherical capacitor configurations; layering of insulating materials of different permittivities (for time-varying stress) or different conductivities (for steady-state DC stress), e.g. by embedding a strongly curved electrode in a high-permittivity material at alternating voltage or by the displacement of a DC field into a barrier of low conductivity and high dielectric strength.

These measures are in most of the cases easy to implement, in contrast to the electric field control along interfaces, which is typically a more challenging task. As long as interfaces are stressed by an electric field in normal direction, i.e. perpendicular to the interface, field control can easily be achieved by just controlling the maximum field strengths within the different layers. This is simply done by appropriate choices of their permittivities and/or conductivities. When interfaces are also stressed by the tangential electric field, i.e. parallel to the interface, the often lower electrical strength along the interface is detrimental. The dielectric strength of an interface is typically lower than it would be expected from the two adjacent media due to microscopic and macroscopic field displacement effects, which can lead to local increases of the electrical stress. The formation of electron avalanches is facilitated by inhomogeneities of the material structure, and the propagation of electrical discharges is supported by the particular configuration of the insulation. Interfaces and surface discharge configurations can occur o ccur between all types of insulating materials. The most important combinations are solid-solid (e.g. a rubber stress cone of the cable termination on an XLPE cable), solid-liquid (e.g. pressboard barriers in transformer oil), and solid-gaseous (e.g. the outer surface of a bushing or a cable termination). Because of the low dielectric strength, the low permittivity and the low conductivity of gases, special problems arise at interfaces between gases and solid or liquid insulating materials, respectively. They are further intensified if pollution and water are present. These interfaces are often referred to as surfaces. It belongs to the most important and frequently most difficult tasks of high-voltage engineering either to avoid surface discharge arrangements (i.e. such with significant tangential electrical stress) at all or at least to relieve them by adequate field control measures. The following methods are available for this purpose:   geometric field control by the geometric design of electrode contours;

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TB 794 - Field grading in electrical insulation systems  

       

capacitive field control by conductive layers with capacitively determined voltage distribution (at alternating or transient voltages); refractive field control by high-permittivity insulating materials (at alternating and surge voltage); resistive field control by semiconductive coatings with resistively determined voltage distribution; nonlinear resistive field control by materials that relieve themselves in areas of high electric field stress by an increasing conductivity.

 A need for electric field control is also given when potential and field distributions along insulator surfaces are affected by stray capacitances to ground or adjacent live structures (at alternating and transient voltage) or resistive surface currents (at direct voltage), e.g. for long insulators, insulator s, surge arresters or HVDC bushings.  Although it would have been most most likely beneficial for some end users of field grading materials to base their requirements on standards, no attempt was undertaken so far to standardize neither field grading materials nor their components. A reason may be that the general requirements are too diversified to establish a single standard being useful to a reasonable number of users. In this Technical Brochure the basics of electric field control, the different materials materi als used, the numerous methods of characterization, simulation and verification approaches and typical applications are presented and explained. It shall thus help improving the understanding of field grading systems and recognizing the relevance of their individual components, and by this, give technical guidance to designers as well as to users of field grading applications as long as standards do not exist. It may also serve as an input to future standardization.

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TB 794 - Field grading in electrical insulation systems    

2. Ba Basics sics of electric field grading 2.1 2. 1 Ca Capacitive pacitive and resisti ve ele electri ctri c field dist ribut ions 2.1.1

Basics

Free charge carriers within a defined space and exposed to an electric field will move along the electric field lines within this space. The direction of the movement depends on the polarity of the charge and the orientation of the electric field lines. The resulting current density  of the moving charge is defined by the electric field  and the electric conductivity  of the material:

⃗ c

⃗ c ⃗

⃗  

 

Equation 2.1

This type of electric current is basically relevant to both, AC and DC, and therefore al also so to mixed electric fields. However, for AC fields another current, the displacement current, is usually dominant. Maxwell introduced the displacement current when he derived the electromagnetic wave equations. The  then is: total current density  then

  ⃗c ⃗d

⃗ c

 

⃗ 

Equation 2.2

where   represents the conduction current by moving charges, and  represents the displacement current caused by the time-dependent electric field. The displacement current density  is defined by the permittivity  of the material and the rate of change of the electric field

⃗: ⃗ 



⃗ d   ⃗  ⃗   

Equation 2.3

provided that the permittivity  is time-invariant. For rather high frequencies permittivity will decrease (see e.g. Figure e.g. Figure 3.1 and and Figure  Figure 3.2) 3.2).. Electric conductivity  and permittivity  both describe material properties related to the response of materials to applied electric fields. On the basis of the formula for conduction current density  the permittivity  is sometimes also called the  “  “dielectric dielectric conductivity”, conductivity”, which underlines the similarity between conduction and displacement current. Traditionally, permittivity  of a material is specified as a multiple of the permittivity of the vacuum . The factor is called the relative permittivity permitt ivity .









⃗ c



    ⃗c⃗d  ⃗  r ⃗ ⃗     ⃗ c ⃗ 

ε

So the total current density  becomes:

 

Equation 2.4

In general the total current field should be considered when AC electric fields are applied to insulating materials. However, the displacement current  usually dominates this case, and therefore the conduction current  is often neglected. For pure DC electric fields only the conduction current  needs to be considered as far as steady state conditions are concerned. However, transitions between different steady state conditions, like polarity reversal etc., may take significant time and should, therefore, be carefully considered. In a homogeneous isotropic material of well defined linear electric conductivity  and permittivity respectively, both current fields,  and  are oriented in the same way. Further, in case of a purely

 

⃗  ⃗ c ⃗





sinusoidal time-depedency the be electric field as with an angular frequency of  and no DC bias the time-dependent electric fieldofmay expressed a complex quantity

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TB 794 - Field grading in electrical insulation systems    

+ ⃗  ⃗ ∙ ej+

 

Equation 2.5

⃗

with  representing the amplitude and direction of o f the sinusoidal field. The rate of o f change

⃗ ⃗ ∙ ej+ + ⃗

⃗  is:

 

Equation 2.6

The total current  can then be expressed in complex quantities, that is:   c d        ⃗ ⃗  ⃗ ⃗ ⃗   Both current amplitudes, c and  , are proportional to the amplitude  of the electric field under these conditions. It has to be kept in mind, however, that the displacement current ⃗   is not in phase with the  of o f . The amplitude   of conduction current⃗ c and the electric field ⃗  but phase-shifted by a time angle of the total currrent density  , therefore, calculates to      c  d  √     The phase angle between the total current   and  and the displacement current ⃗ d  is called loss angle  . It is typically used to characterize the ratio between power losses  and  and reactive power at a specified and Equation 2.7

Equation 2.8

P 

Q

constant frequency.

tan

tan δδ 

 

Equation 2.9

 is also called “dielectric dissipation factor” or “dielectric power factor”.  factor”.  

tanc tantanc tantatannpolpol  ta∗nc′ ′r

 Apart from the losses caused by the conduction current, dielectrics also show frequency dependent polarization losses. The total dielectric dissipation factor  is then represented by the sum of both contributing components,  due to conduction, and  due to polarization:  due  

Equation 2.10

The dissipation factor due to conduction can be expressed as  

Equation 2.11

The polarization losses can be characterized by introducing introd ucing the complex permittivity  

r′ tan pol

r r r

Equation 2.12

where   represents the earlier introduced relative permittivity dissipation factor   of of the polarization becomes:

′  r tanpol  r′

r

r∗

:

. With this definition the dielectric

 

Equation 2.13

2.1.2 2.1 .2

Fields at int erfaces of layered materials

 As long as electric interfaces between layered materials are stressed in normal direction (perpendicular to the interface between them), the electric field can be described by comparatively simple equations.

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TB 794 - Field grading in electrical insulation systems    

 As soon, however, as tangential components of the field exist, the typically lower dielectric strength of the interfaces and the refraction of field lines have to be considered. Electric fields at interfaces of dielectrics of different permittivities  and/or conductivities  will be refracted depending on the ratios of the mentioned parameters. As long as either permittivity or conductivity are the dominating parameters in both dielectrics dielectri cs the refraction can be easily approximated. The refraction index is defined as:



ttaann   ttaann    



 

Equation 2.14

or

 

Equation 2.15

 

depending on the dominating parameter  or  of the applied stress (DC or AC). Note that in these equations  and  are the angles between the electric field vectors and the normal vectors of the boundary surface, see Figure see Figure 2.1. 2.1.   In case of dielectrics with mixed and different dominating properties the refraction becomes more difficult to describe, since accumulating charges trapped at the interface need to be considered as well.

Figure 2.1: between two di electrics [Küch ler 2017] 2017] 2.1: Tangential and normal electric fi eld compo nents at the in terface between

2.2 2. 2 Ele Electri ctri c field grading concepts 2.2.1

General

Electric field grading aims at insulation. reaching aBy more less homogeneous field distribution thepossible bulk or to at the interfaces of an electric the orapplication of field grading measures in it is increase the operating voltage or to reduce the volume of the insulation as the insulating material can be used in a more efficient way. Basically, there are three different field grading concepts, which can be further sub-divided depending on the type of electrical stress (DC, AC, or transient) and the main parameters influencing the field grading properties. Table 2.1 provides an overview of these concepts. It is extended by two more concepts, based on the basic three ones. For the extended concepts material materi al properties are no longer assumed to t o be linear nor isotropic nor homogeneous. It can further be distinguished between two basic modes of operation: Surface field grading concepts aim at defining a smoothly changing potential distribution along a surface, whereas bulk field grading concepts involve the total volume of the relevant insulating materials. Although functionally graded materials and nonlinear materials applied in the bulk volume will affect the electric field at the t he interfaces, this approach is considered as bulk field grading concept in this context.

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TB 794 - Field grading in electrical insulation systems  

Table Ta ble 2.1: Overview Overview of electric fi eld grading c oncepts (red dashed lines = field li nes, blue dashed lines = equipotential lines)

Significant parameter for Concept

DC

AC

shape of electrode and total current density along electrodes

shape of electrode and total current density along electrodes

conductivity of layer between adjacent grading foils

permittivity of layer between adjacent grading foils

conductivity

conductivity & permittivity

conductivity = f(E )

permittivity = f(E ) conductivity = f(E )

conductivity = f(x ,y, z, E, ϑ , …) …)  

permittivity = f(x, y, z, E, ϑ , …) …)   conductivity = f(x, y, z, E, ϑ , …) …)  

Geometry (bulk field grading) 

Potential grading (capacitive/resistive field grading, bulk field grading) 

Potential grading (surface field grading) 

Nonlinear materials with field dependent conductivity/permittivity (in combination with any of the other concepts) 

Continuous or stepwise discrete functionally graded materials (in combination with any of the other concepts) 

2. 2.2. 2.2 2

Bulk field grading

These concepts aim at defining equipotential surfaces in a way that the field stress within the dielectric located between those surfaces remains below critical levels. The simplest kind of this concept consists of two, either metallic or metallized surfaces, where both are usually connected to defined levels, i.e.

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TB 794 - Field grading in electrical insulation systems  

high voltage and ground, respectively. The (linear) electrical properties of the dielectric are not relevant to the field distribution between these equipotential surfaces. In addition to these two equipotential surfaces with fixed potential, further, floating equipotential surfaces can be introduced. Their potential is defined by the capacitance/resistance between the adjacent equipotential surfaces and the total capacitance/resistance between the grounded and energized surfaces (principle of voltage divider). The (linear) electrical properties of the specific dielectric are again not relevant to the field distribution within the region between the adjacent equipotential surfaces. However, the properties influence the level of floating potential of the additional surfaces, and by selecting a dielectric with higher permittivity/conductivity for a highly stressed region, the maximum field stress in that specific specifi c region can be reduced. The principle of layering dielectrics with different properties prope rties can also be applied without the introduction of additional metallic or metallized equipotential surfaces. However, the shape of the individual layers needs to be well defined since the refraction of field lines at the interface int erface between the layers may have an additional impact on the field distribution where two or more interfaces intersect or converge (triple point effect). 2.2.2.1 2.2.2. 1 Geometric field gradi ng

Provided that there is enough space available within an electric apparatus it is possible to influence the electric field by introducing additional conductive surfaces, which are connected to well defined potentials (typically ground or high voltage). These electrodes guide the equipotential surfaces such that the corresponding dielectric stress remains within a tolerable limit. This way of field grading is called geometric, since suitable geometries are used to influence the electric field. An example for geometric field grading is shown in  in   Figure 2.2. In 2.2. In this case of a gas-filled bushing field grading must be achieved not only inside the bushing, where an insulation gas of high electric strength is used, but also at the outer insulator surface. Particularly position and shape of electrode (6) must, therefore, be carefully chosen.

2.2:: Gas-filled bushing as an example example for geometric fi eld grading [HSP] Figure 2.2

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TB 794 - Field grading in electrical insulation systems  

 Another example of geometric field grading is the stress control1 element typically used in terminations for solid dielectric  cables,  cables, provided in Figure in Figure 2.3. 2.3.  

      

2.3: Typical field co ntrol element (“stress cone”) for solid dielectric cables (left) and distribution of Figure 2.3: equipot ential lines in the cable termination (right) [G&W Electric Electric Company]  

The ground ground electrode (“deflector”) provides extension of the power cable insulation screen and is geometrically shaped to distribute the electrical stress as evenly as possible from the edge of cable screen to the point where the deflector ends. The regions of highest electrical stress are embedded in insulating material with high electric strength, such as silicone rubber or EPDM in case of solid dieletric cables, or oil-impregnated paper in case of laminar insulated cables.  An example of geometric field control for laminar dielectric  systems  systems is provided in Figure in  Figure 2.4. Here 2.4. Here the same principle is used as in the case of solid dielectric cables, but the “ideal” geometry of the electrode is determined by calculation of the longitudinal component of the electrical stress that is critical for laminar (layered) dielectric systems such as oil-impregnated paper insulation.

Figure 2. 2.4: 4: Example of geometric field grading in lamin ar dielectric systems, in thi s case oil-impregnated power cable [G&W Electric Company]  Company]  

Geometric field grading is in principle applicable to AC and DC electric fields. However, it needs to be considered that in case of layered dielectrics between the electrodes any refraction of field lines at the interfaces depends on the type of field and may change the relevant electric field significantly. At AC and transient stress the refraction is controlled mainly but not exclusively by the ratios of the permittivities whereas at DC the ratios of the electric conductivities become the only relevant parameter [Hinrichsen 2011]. Hence in the DC case it has to be taken into account that conductivity of a material is strongly dependent on temperature and also field strength, which makes field control rather challenging for high DC voltages, refer e.g. to [Wirth 2015]. 1 As  As

mentioned earlier, the term “stress grading” is often used synonymously for “field grading”. grading”. This is especially the case f or or cable accessories.

14 

 

TB 794 - Field grading in electrical insulation systems  

2.2.2. 2.2 .2.2 2 Ca Capacit pacit ive field grading (Condenser field grading) Capacitive  (condenser)   (condenser)

field grading can be applied if available space is limited or if size and hence weight shall be kept low. This type of field grading is not limited to AC or impulse electric fields, where the permittivity of the material defines the capacitances between the grading elements. It can be applied to DC as well, were the conductivity of the material defines resistive grading elements (see (see Figure  Figure 2.5) 2.5).. Further, the condenser type field grading is usually limited to rotational-symmetric apparatus for manufacturing related reasons.  As in the geometric field grading concept additional equipotential equipot ential surfaces (electrodes) are introduced to the dielectric. In contrast to the geometric field grading, the electric potential of these additional electrodes is not fixed but floating and will take a level, which ensures that the electric field in all layers between adjacent electrodes (and in their proximity) remains below critical limits. The potential difference between adjacent grading electrodes is given give n by the voltage divider ratios of the impedances between the layers (see Figure (see Figure 2.5) 2.5).. E.g., by changing the lengths of the cylindrical electrodes of a condenser type bushing (see Figure (see Figure 2.6) 2.6) the  the individual capacitances can be adjusted as needed, but it has to be kept in mind that the change of a single electrode also impacts imp acts the potential difference of the other layers, which typically requires an iterative approach to find the optimal design. An example for the radial field distribution in an optimized condenser bushing b ushing is shown in in Figure  Figure 2.7. 2.7. Further  Further information is given in 5.4. in 5.4.   In order to achieve identical capacitances between the individual electrodes, the lengths of the electrodes usually change from inside to outside of the cylindrical structure with the longer one being located closer to the center of the cylindrical structure. This means that a portion of the electrode is exposed to the surrounding electric field and can, therefore, also be used as a geometric field grading electrode. This feature is actually used with air-to-oil and air-to-SF6 condenser bushings, where the exposed length is larger at the air side of the bushing to provide a larger flashover distance in air compared to the other, electrically stronger side (Figure 2.6). 2.6). Hence the capacitive field grading does provide both, a radial (Figure 2.7) 2.7) and  and an axial field grading on the surface of the bushing envelopes, which can be seen at the equipotential lines shown on the right side of the bushing in Figure in Figure 2.6. 2.6.  

Figure 2.5: 2.5: Equivalent circuit of a condenser type field grading arrangement 

2.6: Condenser type bushin g with asymmetric arrangement of electrodes for additional bound ary field grading; Figure 2.6: acc. to [Kü chler 2017] 2017]

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TB 794 - Field grading in electrical insulation systems  

Figure 2.7: 2.7: Typical Typical radial field stress within a cylindr ical condenser type bushing wi th homog eneous dielectric properties

Since the permittivity of the material in condenser ACadjacent application is dominating over its resistivity, the voltage drop acrossused an individual layerbushings betweenfor two electrodes is bascially not influenced by the frequency of the applied electric field. Therefore, this t his type of field grading is also suitable for transient electric fields (impulse voltages). Special care should be taken for very fast transients because they can be split according to the different surge impedances inside and outside the dielectric. This is important especially for bushings in gas insulated switchgear (GIS), because the rate of voltage change is exceptionally high in case of switching, and the dielectric can be overstressed. Theoretically, there is another way of changing the capacitance of individual layers between the electrodes (see Figure (see Figure 2.14) 2.14):: Materials of different dielectric properties could be applied, which would represent a stepwise functional field grading. However, for manufacturing-related reasons this may be done only in very special cases. Even nonlinear field grading material could be used as well, but no related product is known so far. 2.2.3 2.2.3

Surface fi eld gradi ng

This concept aims at defining a suitable potential distribution along a surface or interface between different materials to prevent surface discharges. Theoretically, the thickness of the layer controlling the potential distribution could be infinitesimal. In practice layer thickness varies, which may affect the efficiency of the layer at the interface. However, in most cases the field distribution can be approximated with sufficient accuracy by assuming surface properties only. 2.2. 3.1 1 Cre Creeping eping disch arge confi gurations 2.2.3.

Surface discharges develop along the boundary between two insulating materials with different states of matter e.g. along the surface of a solid insulator kept in air. The main conditions responsible for this phenomenon are electric field lines mainly in parallel to the surface and strong capacitive coupling of conductive surface layers with the counter electrode. Typical examples of such configurations are bushings, cable ends, or the winding terminations of electrical machines. A classical model used for the investigation of surface discharges is the Toepler's configuration   [Toepler 1921], which helps understanding the phenomena. As shown in Figure in  Figure 2.8, 2.8, it  it consists of a simple glass plate connected to a rod electrode at HV potential. The ground electrode is formed by a metal surface on the back side of the glass plate.

Figure 2.8: (left) and cross section 2.8: Surface discharge config uration according t o Toepler : experimental setup (left) depicting surface discharges and surface capacitances (right)  (right) 

Characteristical for such a configuration is that no direct puncture (breakdown) between the electrodes will occur due to the high electric strength of the insulator between the electrodes. Nevertheless, such kind of discharges are quite a strong load for insulating materials, as they can erode the material and lead to a breakdown after a certain time. These discharges dischar ges will occur mainly along the insulator sur surface, face,

16 

TB 794 - Field grading in electrical insulation systems    

fed by capacitive displacement currents through the insulator. The development of breakdown decisively depends upon the specific surface capacitance of the dielectric. diel ectric. Surface discharges can form only when this capacitance has a certain minimum value. Another precondition is that pre-discharges develop at one of the electrodes. Prevention of these pre-discharges is the most effective measure to prevent surface discharges. 2.2.3. 2.2.3.2 2 De Develop velop ment of sur face dis charg es

The inception voltage U  i especially of the above stated Toepler's configuration  depends  depends on the thickness s  of  of the electrode as:

   ∙  

 

Equation 2.16

with U   ii in kV and s  in  in cm. The factor K  can   can be calculated theoretically. But many additional factors (such as the shape of the electrode or the surface insulation resistance) have an influence. Thus it is appropriate to use the empirical values determined for K , listed in Table in Table 2.2: 2.2:   Table 2.2: K  values for different configu rations; acc. to [Böning 1953]

Configuration

Metal edge Metal or graphite edge Graphite edge

K

in air

8

6 inin SF oil in air

21 30 12

If the voltage is increased above the inception voltage, streamer discharges occur. In the Toepler's configuration , these streamers spread out radially around the center of the electrode, whereas in a coaxial cable arrangement (e.g. at cable ends) these streamers spread out in axial direction along the dielectric. This is shown in Figure in Figure 2.9. 2.9. In  In principle, this configuration is also found e.g. on the winding rods of rotating electrical machines, where they leave the stator.

2.9: Appearance of surf ace discharges in Toepler’s configuration (left) and at a Figure 2.9: cable end (right; acc. to [Kü chler 2017]) 2017])

The surface discharges on the insulator surface form a capacitance with the counter electrode. The value of the specific surface capacitance c surface surface of the covered surface A surface surface is given by:

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TB 794 - Field grading in electrical insulation systems    

csurface

C surface 



0



  

r  



 Asurface

 

s

2.17   Equation 2.17

where C surface  the thickness of the dielectric. surface represents the surface capacitance and s  the The current in the discharge channel can be expressed as follows: ichannel



dQsurface

d (usurface C surface ) 



dt

 

d t 

2.18  Equation 2.18 

The voltage u surface surface is thus the voltage between the considered location of the insulator's surface and the counter electrode. In a first approximation, it is same as the voltage u  applied  applied across the electrodes, so that finally, using the product rule, for the applied current in the discharge channel the following holds: ich an an ne ne l



Cs ur ur fa ce ce

d u 

dt



u

d C surface

 

d t 

2.19  Equation 2.19 

For alternating voltages , it can be assumed that the voltage in the interesting time intervals (  10 ns) is constant (i.e. d u   /dt  =  = 0). This leads to: ichannel



u

dCsurface dt



u  csurface



d Asurface

 

d t 

2.20   Equation 2.20

Thus, besides voltage, the discharge current is dependent upon the specific surface capacitance and the rate of change of the surface area covered by surface charges. However, for impulse voltages , the term du   /dt   also also contributes significantly and cannot be ignored. Hence the surface discharge is more intense with impulse voltages than with alternating voltages. Similarly, for direct voltages , both the derivative terms result in zero values. Theoretically there should thus not be any problem of surface discharges in case of DC configurations. However, in reality, there exists a problem of discharges (e.g. bushings or terminations of DC cables) because of non-zero d u   /dt   high frequency components superimposed to the DC voltage as soon as pre-discharges develop. Such pre-discharges are formed due to the low electric strength of the ambient media (e.g. air) covering the surface of the solid insulation.  Already streamer lengths of a few centimetres will result in thermal ionization because of the high displacement currents due to the high specific surface capacitance. As a result, the initial streamer discharges slowly transit into leader discharges even at such small distances of around few centimetres. (It has to be noted that, in a conventional rod-plane arrangement in air, at least one to two meters of discharge length is required for leader discharges.) Leader discharges have low voltage demands because of their negative differential resistance characteristics (decreasing voltage with increasing current). As a comparison:   specific flashover voltage of a post insulator in air (peak value):  5 kV/cm   inception voltage of a streamer surface discharge (peak value):  6 kV/cm = a few 100 V/cm   field intensity for surface leader propagation (peak value): Once the streamer surface discharge transforms into a leader discharge, it requires only a slight further increase in voltage to initiate a flashover. Hence, in the very first place, voltages equal to or above the surface discharge inception voltage U i must be avoided in practical configurations. An empirical formula for U i in air is as below:

  13.u.5u∙10−

 

Equation 2.21  2.21 

surface in F/cm². with U  i given as the r.m.s. value of voltage in kV and c surface

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TB 794 - Field grading in electrical insulation systems  

In [Werdelmann 2009] an inception field strength  of  of 0.64 kV/mm is determined for a clean surface in air. This reference also provides measurement values for different kinds of surface pollution. In [Marusic 1994] [Wheeler 2005] an inception field strength of 0.6 kV/mm is stated, and [Baumann 2011] discusses values between 0.4 – 0.4  – 0.5  0.5 kV/mm. In a theoretical approach [Thienpont 1964] derives an equation for inception voltage of glow and brush discharges at the slot exits of generator stator windings and determines a field strength of 0.39 – 0.39  – 0.41  0.41 kV/mm. 2.2.3. .3.3 3 Mea Measur sur es to avoid sur face dis charg es 2.2

To understand, how surface discharges can be avoided, it is necessary to recall that surface discharges are discharges in the gaseous phase. These discharges creep along the surface in the described manner, and just increasing the length of the surface will not be conducive to avoid or stop the discharges. So, as mentioned already, prevention of pre-discharges is most important. This can be achieved using advanced measures of field control (like using embedded electrodes in the insulating material, metallization of the insulator at the interfaces to the flanges of bushings or capacitive grading like in bushings). Another frequently used counter-measure is resistive field control by using a weakly conductive layer on the insulating surface to limit the power available for the development of a leader discharge, which is exemplarily and principally shown in Figure in  Figure 2.10 and is explained in detail in in 2.2.3.5.  2.2.3.5.   In many cases,  cases,  such as at the winding terminations of electrical machines, not many other measures do exist for suppressing surface discharges.

Figure 2.10: 2.10: Example of a counter measure against surface discharges: resist ive field gr ading [Hinrichsen 201 2011] 1] 

2.2.3.4 2.2.3. 4 Re Refr fr activ e fi eld gradi ng

The least space is typically required for refractive  field  field grading. This type of field grading is mainly used to avoid surface discharges along tangentially stressed interfaces (see Figure 2.11), 2.11), like the cable insulation at the end of the semicon shield within cable terminations or the end corona protection of stator windings. The name “refractive” reflects that the field lines at the interface bbetween etween two different materials having different electric properties (permittivity and conductivity) are refracted (see also 2.1.2).. Although the refraction of the electric field is not limited to interfaces between two mainly 2.1.2) capacitive materials, the name refractive field grading is commonly used for this combination of materials only. The grading capacitive-to-resistive resistive-to-resistive called “resistive”, butfield it should befor kept in mind that the basicorconcept is the same. interfaces is usually Due to naming conventions the term “refractive field grading” is used for AC for  AC electric field grading only, though the physical effect is also present in the DC case. Concept of this type of field grading is to provide a spatially distributed voltage divider divi der (lattice network) along the electrically highly stressed interface. A simplified version of the divider is shown in Figure 2.11. This 2.11.  This model can be applied provided the thickness of the field grading layer is small compared to the thickness of the remaining insulation layer. l ayer. For thick field grading layers permittivity and conductivi conductivity ty perpendicular to the interface have to be taken into account additionally. The equivalent lattice lat tice network may be extended in this case by another lattice network, net work, representing the bulk of field grading material. Efficiency of the field grading layer depends on the characteristic admittance (permittivity and conductitivty) per unit length of the field grading layer versus the insulation layer. The higher the difference the lower will be the electric stress along the interface. In order to keep the field grading layer thin, high permittivity materials are preferred.

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TB 794 - Field grading in electrical insulation systems  

Figure 2.11: Thin mixed “refractive” & resistive (semiconducting) field grading and equivalent electric circuit (spatially (spa tially distri buted mixed divi ders); acc. to [Hinrichsen 2011] 2011] and [Küchler 2017] 2017]

The equivalent suggestsand that in case also of a applies mainly to capacitive grading material the grading will not electric depend circuit on frequency therefore transientfield fields. However, typically high permittivity materials are significantly frequency dependent. The effectiveness of a refractive field grading system exposed to transient fields should therefore always be checked carefully against the frequency dependance of the electric properties. For that reason it may be required to use larger thicknesses of lower permittivity materials or to use a combination of geometrical and resistive field grading as implemented in some cable joints, refer re fer to 5.1.3. 2.2. 3.5 5 Linear and and nonlinear resistive field grading grading syst ems 2.2.3.

 As mentioned mentio ned iinn the previous chapter, a resistive  field   field grading is based on the same concept as the refractive field grading. However, the conductivity of the field grading layer becomes the dominant property, and therefore the thermal balance of the field grading systems needs to be considered carefully.  As shown earlier, the electricatfield lines are has refracted also in this case. The difference is that additionally space charge accumulation the interface to be considered. Depending on the subjacent insulation insulatio n material the resistive field grading can be applied to AC or DC electric fields. For DC field grading the subjacent insulation must exhibit a controlled conductivity in order to achieve a well-defined field grading. This may represent a significant technical challenge since the conductivity is typically highly influenced by temperature. For certain service conditions like polarity reversal and transient electric stresses, also for DC applications the permittivities of the involved materials may need to be coordinated. Otherwise, the field grading system may fail under these conditions. In practice resistive field grading is, therefore, often accompanied by refractive/capacitive or geometric field grading. In order to improve the thermal balance or the response to transient electric fields, the refractive field grading can be extended by using nonlinear field grading gradi ng material (see Figure (see Figure 2.12) 2.12),, which changes its properties to become dominantly conductive when e.g. a certain field strength is exceeded. The losses generated at low or continuous stresses can thus be reduced without affecting the field grading performance at higher overall stresses including transients.  An example for such a field grading system are microvaristors, mixed int intoo either elastomers, hot melt compounds or thermosetting resins to allow for easy application. In addition to the nonlinear resistive field grading, microvaristors also provide a suitable refractive field grading due to the high permittivity of the varistor grains.

2.12: Thin Figure 2.12: Thin non linear field grading and equivalent electric circ uit (spatially dist ribut ed nonlinear dividers); acc. to [Hinrichsen 201 2011] 1]  

In principle permittivity nonlinear materials are be not utilized li mited to limited grading. A dielectric field without dependent, increasing could also to resistive improvefield a linear refractive field with grading the negative impact of higher losses, which is typical for nonlinear resistive field grading. However, such

20 

TB 794 - Field grading in electrical insulation systems    

kind of material with sufficiently high nonlinear permittivity is currently not available, but antiferroelectrica are possible candidates and under investigation, e.g. [FLAME 2019]. Current technology is based on materials with electric field-dependent conductivity. Their response to a field stress exceeding a certain threshold is practically instantaneous. However, other indirect dependencies like increased local temperature due to electric stress could theoretically be exploited as well. They may, however, react slower to high stresses than the currently c urrently used materi materials. als. Typically, a high level of nonlinearity is beneficial, since power losses will be low with currently used materials, as long as the threshold is not exceeded. But when exceeded, the impact on field grading performance is strong. However, a high level of nonlinearity also affects adjacent areas in several ways. Firstly, adjacent will experience a higherinhomogeneous stress once thethe threshold is exceeded somewhere.  As longthe as the initial areas field distribution is distinctly stress will be gradually displaced to adjacent areas. In case of a rather homogeneous field, where all regions are likely to simulaneously exeed the threshold, this concept may not provide an improvement. Secondly, the electric field stress in the adjacent areas will become non-sinusoidal, which may have a negative influence on the field grading properties of the material. The higher the nonlinearity, the larger will be the distortion of the electric stress in the adjacent areas. Therefore, the design of a nonlinear field grading is much more difficult than it is for linear systems. Even if the applied voltage is sinusoidal, the overall displacement and conduction currents and as a result also the electric field may deviate significantly from a sinusoidal shape. The harmonic content of the electric field should be taken into account within the field grading material itself but also in the adjacent insulation since it potentially may cause higher power losses. In 3.4.5 In 3.4.5 an example of a design procedure for nonlinear field grading material is given for the case of a DC application.

2.2.4 2.2. 4

Field grading in coaxial cylin der confi gurations by layere layered d dielectrics 2.2.4. 2.2 .4.1 1 Genera Generall pri nci ple

Basically the electric field distribution can be optimized by chosing permittivity and geometry such that maximum field strength values are kept below the specified ones. Especially in coaxial cylinder configurations use can also be made of coaxially layered dielectrics. In each individual layer the electric field decreases inversely proportional to the radius and makes a step upwards at the next layer if the dielectric constant makes a step downwards, and by varying thickness and the dielectric constant of each layer, taylored field control is possible. A basic configuration consiting of two different layers is shown in Figure in Figure 2.13. 2.13.  

Figure 2.13 2.13:: Coaxially Coaxially l ayere ayered d dielectrics; r 0…radius of inner conductor, r 1….outer radius of layer 1, r 2….outer radius of layer 2, ε r1 constants of layers 1 and 2, respectively  r1  and ε r2 r2….dielectric constants

The maximum field strength, E nn ,  max, in each layer n  is   is found at its inner radius and can be expressed as:

   ∙  ∙ 

 

Equation 2.22

   ∙  ∙  21 

 

TB 794 - Field grading in electrical insulation systems    

Equation 2.23  2.23 

where K c is a constant, determined by the radii and dielectric constants of the overall configuration of N layers:

  ∑=  1∙ ln 

 

 

2.24  Equation 2.24 

The maximum field strengths, E nn ,max , max, in each layer (in this case only two) are identical if r 0·ε rr11 = r 1·ε rr22, or in general if r n -1·ε rn  = const. Following this principle, an ideally constant electric field can be achieved if a material is used that has a dielectric “constant”, which continuously decreases proportional proportional to 1/r   (see Figure 2.14). This approach has become known as “func “functionally graded materials” and is explained in detail in in  2.2.4.2 and 5.6.3.2. In 5.6.3.2.  In some practical applications, like bushings, the ratio between the absolute radius of a grading foil and the distance to its neighboured one is so high, that the field in between can be regarded as nearly constant.

Figure 2.1 2.14: 4: Magnitud Magnitud e of electric field strength i n a coaxial cylinder confi guration; black: not l aye ayered, red, only one homog eneous dielectric; red: four layers of dielectrics opt imized such that all are exposed to the same maximum field stress (by decreasing ε r r  in   in four steps from the inner to the outer conductor); blue: functionally graded insulation system with ε r r   1/r, which co rresponds to an infinit e number of grading l aye ayers; rs; not e: areas areas below the three curves are identical  

The same grading principle can also be applied to DC insulators in the emerging DC GIS and GIL (gas insulated switchgear, gas insulated lines). For insulation layers of different electrical conductivities, the same rules apply as for layers of different permittivities in the AC case. In the equations given above  just the dielectric constants have to be replaced by electric conductivities. Well controlled conductivities in DC systems are much more important than well controlled permittivities in the AC case. This is due to the fact hasup a very dependanceofofthe temperature. Closebetomuch the inner which maythat takeconductivity temperatures to 90strong °C, conductivity insulators may moreconductor, than one order of magnitude higher than at the outer conductor, where the temperature can be significantly lower. Consequently, the electric field strength is reduced close to the inner conductor and increased at the outer conductor. In extreme cases the field stress at the outer conductor becomes higher than that at the inner conductor (“field inversion”). This phenomenon is also well known for DC cables and their accessories, or for DC bushings [Wirth 2015]. 2.2. 4.2 2 Applic ation of func tionally graded graded materials 2.2.4.

Functionally graded materials are characterized by the spatial distribution of dielectric permittivity ( r), denoted here as “ε as “ε-field -field grading”, grading”, and/or  and/or electrical conductivity ( ), denoted here as “-field grading”, of solid insulators in order to change these electrical properties properti es e.g. inversely proportional to the distance to the inner conductor [Kurimoto [K urimoto 2002] [Kurimoto 2010] [Ju 2009]. The concept of ε-field grading with a graded permittivity distribution is shown in Figure in  Figure 2.15. Compared 2.15. Compared with the uniform material in in Figure  Figure 2.15 (a), the in Figure in Figure 2.15 (b)insulation has a spatial grading filler content from material-A material-B in εa-field solidgrading insulator. In gas/solid systems, theofelectric field stress under AC to or

22 

 

TB 794 - Field grading in electrical insulation systems  

impulse voltage application is generally intensified in the gas region, because the permittivity of gas is lower than that of solid material. In order to relax the stress intensification, application applicat ion of ε-field grading is expected to be effective by giving a suitable permittivity distribution inside the solid insulator. Thus, the intensified electric field stress in the limited region can be relaxed and homogenized in the wide region, i.e. ε-field grading can drastically raise the electric field utilization factor in the insulating materials. Material-A

Material- B

Electric field stress Low High

HV electrode



Gas

GND electrode

(a) Uniform material Electric field stress Low High

HV electrode



Gas

GND electrode

(b) -FGM Figure 2.15 2.15:: Concept of ε-field grading [Hayakawa 2014]  

Figure 2.16 shows the fabrication concept of ε-field grading with grading to lower permittivity (GLPFGM) by using the centrifugal force. Two kinds of fillers, such as Al 2O3, SiO2, TiO2, are uniformly mixed into the uncured epoxy resin. One filler has a small particle diameter and high permittivity, and the other one has a large diameter and low permittivity. By application of a centrifugal force, the large diameter fillers (with low permittivity) move towards the direction of centrifugal force during the curing process, whereas the small diameter fillers (with high permittivity) do not move under the centrifugal force. But they can be pushed away by the large diameter fillers and, therefore, relatively relat ively move towards the direction opposed to the centrifugal force. Once the epoxy resin is cured this distribution of filler particless is “frozen”. As particle “frozen”.  As the result, a GLP-FGM with grading to lower permittivity along the centrifugal direction can be obtained. Following the same principle, other kinds of ε-field grading with grading to higher permittivity (GHP-FGM) or U-shape permittivity distribution (U-FGM) can be fabricated by centrifugation [Hayakawa 2014].

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Figure 2.16: Fabrication con cept of GLP-FGM GLP-FGM with g rading to low er permittivity along the centrifugal di rection 2.16: Fabrication [Hayakawa 2014]  

[Hayakawa 2014] shows a calculation model to simulate the filler particle movement in viscous fluid (epoxy resin mixed with hardener) under the impact of a centrifugal force.

Figure 2.17: Calculation model of f iller particl e movement under centrifu ging fo rce [Hayakawa [Hayakawa 2014] 2014] 2.17: Calculation

Using a one dimensional model for the post-type ε-functionally graded materials spacer (Figure 2.17), the flow of particle density due to the centrifugal ce ntrifugal force is calculated in each region. The balance of three forces working on the filler particles, i.e. centrifugal force, buoyancy and drag force, is given by the following equation: 

 ddr      D

 

Equation 2.25

where M is the mass of a filler particle, vr   is the relative velocity of a filler particle, r is the radius of rotation,   is   is the angular speed,    f   and    p  are the mass densities of fluid and particle, and FD  is the /dt = 0, the terminal velocity vt of filler particles is expressed as follows: viscous force. Given dvr /d

  p t  (18p  f )  

 

Equation 2.26

where G is the acceleration by the centrifugal force, Dp is the diameter of a filler particle,   is  is the viscosity of the epoxy resin mixed with filler particles.    is estimated a and nd experimentally verified, considering material, temperature, loading with filler, etc. The permittivity distribution of the ε-functionally graded o f the filler particles in the epox epoxy y resin [Hayakawa material can be calculated by the density distribution of 2016].

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Using TiO2  and SiO2  with the specifications shown in  in  Table 2.3,  a sample of a GLP-FGM post-type insulator was fabricated. The permittivity distribution was calculated and verified on the sample, with the results shown in Figure 2.18  [Hayakawa 2016]. Permittivity distributions of GHP-FGM and U-FGM samples were also verified by calculation and measurement. An arbitrary permittivity distribution of an ε-functionally graded material is expected to be obtained by optimizing the specifications of fillers (material, size, specific gravity, relative permittivity, loading, etc.) and the manufacturing conditions (centrifugal acceleration, time, temperature, their combination pattern with time, etc.). Table 2.3: Specifications ε-functionall y graded material material Specificati ons of filler particles for ε-functionall

Figure 2.18 2.18 : Permittivit y distri butio n of post-type GLP-FGM GLP-FGM (Filler (Filler loading: 10 vol% TiO2 and 40 vol% SiO2, centrifugal conditon: 4 000 G and and 60 minu tes) [Hayakawa 2016]

 An alternative approach to achieve “functional grading” especially in DC systems is to make use of the electric field dependance of functional fillers that provide field dependent conductivity and only moderate and field well as controlled temperature dependance. Typically, conductivity increases with not the applied electric well as with temperature, which is exactly the desired behavior (this would work with permittivity as it typically decreases with increasing electric field). The comparatively high conductivity close to the inner conductor is achieved both by the electric field dependance and the temperature dependance. The fillers may be based on ZnO microvaristors or on antimony doped tin oxide (ATO) and possibly other materials in the future. They are filled into the polymer matrix at a densitiy above the percolation threshold. Such systems, s ystems, which are still under development, can be used to optimize DC GIS/GIL insulation systems. One practical approach of ATO fillers are MFF (“MFF” = Minatec® functional fillers; since 2015 named lriotec 7000®) [Rüger 2012] [Greb 2015]. The electric bulk conductivity of an MFF filled epoxy is in the range (10-13… 10-11 S/m) (Figure 2.20) 2.20),, which is an appropriate range for DC compact GIS insulators in order to achieve the desired field distribution distr ibution and low losses at the same time. An example of achievable field distributions in a DC GIS insulator is shown in Figure in Figure 2.19. 2.19.  

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 A further benefit of the controlled conducti conductivity vity is a faster decay of surface and volume charges, which typically develop in DC insulation insul ation systems [Tenzer 2011] [Tenzer 2013c] [Tenzer 2015] [Winter 2011a] [Secklehner 2013] [Winter 2014] [Winter 2015] [Secklehner 2015]. It is still an open question and under investigation if such sophisticated approaches are necessary or if “conventional” insulating materials of comparatively high intrinsic conductivity may be sufficient for HVDC applications.

Figure 2.20: 2.20: Measured Measured bulk conduc tivit y of MFF filled epoxy [ Winter 2014] 2014]  

2.19: Normalized Figure 2.19: Normalized tangential electric fi eld distri bution at a disc-shaped DC GIS GIS insulator surface for the two cases: “hot” with a temperature gradient  gradient   (ϑ conductor  = 80 °C/ ϑ enclosure = 50 °C) and “cold” with constant low temperature  temperature   (ϑ conductor   = ϑ enclosure °C); MFF = “Minatec® “Minatec® functional fillers” fillers ” [Winter 2014]   c onductor  = e nclosure = 30 °C);

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3. Mate aterial rial syst systems ems for fi fie eld gradin grading g syst syste ems 3.1 General Most field grading materials used today as bulk material or coatings consist of a blend of different unitary materials since the properties of single si ngle unitary materials usually do not meet all the requirements set for modern field grading systems. The typical base material – material  – the  the host matrix – matrix – is  is a polymer (resin, elastomer, hot melt compound, etc.) into which particulate fillers like carbon black are homogeneously dispersed. Inorganic, ceramic type fillers may also be used either together with carbon black or independently. The host matrix is typically selected with the focus on the required mechanical mechanic al properties for easy processing and acts as a carrier and fixation for the filler. It usually encloses the particles almost completely. The filler is typically selected to provide or improve the electrical properties of the host matrix. The effectiveness of a field grading material in general depends on its permittivity or conductivity, respectively. Usually one of these properties is dominating with respect to field grading, although sometimes a well balanced combined system has to be chosen or can provide some additional benefits. In the following these two parameters are considered, and unitary materials are addressed first. 3.1.1

Conductivity

Depending on their level of conductivity, materials are typically classified into groups: -  Insulators -  Semiconductors -  Conductors For solid unitary conductors and semiconductors the conduction mechanism is often determined by the electronic band structure. Charge carriers are mainly electrons and electron-holes. The conduction mechanism in polymers, which are commonly used as host matrix for field grading systems, is rather complex and still under investigation. At low electric electri c fields ionic conduction seems to dominate. Only at high fields close to the breakdown strength electronic conduction takes over and becomes dominant [Bärsch 2008]. Polymers are usually good insulators due to the absence of free and mobile electrons. Depending on the purity of the polymer, free ions may, however, be available, increasing the conductivity. Other reported sources of ions are ionic dissociation by thermal t hermal agitation. The number of ions from this source increases exponentially with temperature as shown in the following Arrhenius Arrheniu s equation [Warfield 1961]:

∙ −   C   k  

3.1  Equation 3.1 

C 

where          

is the number of ions formed is a constant is the activation energy for the formation of an ion is the Boltzmann constant is the absolute temperature.

Furthermore, some ions are formed by background radiation. Conduction in polymers depends not only on the number of ions present but also upon the mobility of the ions. This mobility, which is proportional to the reciprocal of the viscosity of the system, increases exponentially with temperature following also an Arrhenius equation [Warfield 1961]:

 −   C ∙  Equation 3.2  3.2 

where

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C     

is the mobility is a constant   is the activation energy for the mobility of an ion   is the Boltzmann constant   is the absolute temperature. Hence electrical conductivity of a polymer is the product of the number and the mobility of the ions present [Warfield 1961]:  

   − ∙      

  C C 

Equation 3.3  3.3 

where   is the conductivity at absolute temperature .



Conductivity is also influenced by the chain-length of the polymer, the degree of cross-linking and its crystallinity. All of them reduce the mobility mobilit y of ions, which leads to lower conductivity. conducti vity. This is the reason why XLPE cable insulation has a rather low conductivity, and hence the problem of volume charges trapped inside the dielectric has to be considered for a proper design. Special polymers with alternating single and double bonds along the molecular chain, so-called conjugated polymers like e.g. polyacetylene, show a small intrinsic intr insic electric conductivity already at room temperature. It is based on the electrons being able to move along the polymer backbone [Dai 2004]. 3.1.2

Permittivity

With respect to permittvity, materials are contributing usually not classified into permittivity specific groups like conductive materials. However, the polarization modes to the overall lead themselves to a classification in cases where a specific mode of polarization is dominant. Polarization describes the ability of a dielectric material to generate and/or modify electric dipoles under the influence of an electric field. It results from the separation and alignment of electric charges brought about by that field. The larger the dipole moment arm (the separation of charges in the direction of the t he field) and the larger the number of these dipoles, the higher is the material’s permittivity [Ulrich 2000]. 2000].   The following modes of polarization can be distinguished [Bärsch 2008] [Ulrich 2000]: polarization – existing  existing polar molecules (dipoles) aligned by the electric field - Orientational polarization – - Displacement or deformation polarization polarization – slight  slight displacement of electrons with respect to the nucleus   Electronic polarization – polarization  – slight  slight displacement or orientation of ions and nuclei in a   Ionic and atomic polarization – molecule or lattice   e.g. ferroelectric materials – materials – with  with spontaneous ionic polarization Interface and space charge polarization o

o

 All of these modes contribute to the material’s permittivity, depending on the mechanisms relevant to the given dielectric. They do not only determine the value of the relative permittivity, ε r, but also how it varies with frequency, temperature, bias, impurity concentration, and crystal structure [Ulrich 2000]. The four general mechanisms important to candidate materials for field grading are electronic , atomic,  ionic  and   and last but not least interface charge  polarization.   polarization. Since the orientational polarization requires mobile polar molecules it is less important to solid dielectrics. Electronic polarization  involves  involves charge symmetry distortion of an atom or molecule. Under the influence influen ce of an applied electric field the nucleus and the negative charge center of the electron cloud shift in opposite directions, creating a small dipole. This induced dipole effect occurs in all materials, but is usually relatively small compared to other polarization mechanisms since the moment arms of these dipoles are very short, usually a fraction of the size of an a n atom [Ulrich 2000]. The described mechanism is very fast, and, therefore, the polarization is almost independent of the frequency of the applied field.  Atomic polarization   occurs substances made the up of more than type of non-ionic why different elements willinnormally not share electron cloudone equally. The negativeatoms, chargewhich centeris

will be shifted towards the more electronegative atoms resulting in a permanent dipole. An externally

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applied electric field generates opposite forces on various parts of the molecules causing electronic polarization but also the nuclei to t o move relative to each other and to align with the field. It iiss this relative movement of the nuclei within the molecule which is attributed with the atomic polarization. The atomic polarization is, with (1… (1…15) % compared to the electronic polarization, usually not very strong, but can reach up to 30 % under special circumstances [Ulrich 2000] [Gor 2003]. Ionic polarization   is is similar to atomic polarization but involves the movement of ionic species under the influence of the electric field. It can result in very high relative permittivity, up to several thousands, but is, compared to electronic and atomic polarization, much slower. Orientational polarization  requires   requires permanent dipoles to be present, which align themselves with the orientation of thelocal applied electric This rotation a timescaleis,that dependsmostly on theeffective torque and surrounding viscosity of field. the molecules. Thisoccurs type ofonpolarization therefore, with liquids and gases. The most prominent example is the water molecule H 2O, which has a high dipole moment. This is used e.g. in microwave ovens for heating due to the dielectric diel ectric losses. Each mode of polarization has got a typical dispersion area limited by the relaxation frequency, up to which it is effective (see Figure (see  Figure 3.1) 3.1).. At frequencies above the dispersion area the corresponding mode of polarization is unable to contribute contribut e any more to the overall permittivity permitt ivity of the material. Reason is that the electric field is not applied for a time duration long enough to t o allow an earlier polarization of opposite  are polarity to relax. As a consequence, relative permittivity  as well as the dissipation factor frequency dependent [Bärsch 2008].



tan

3.1:: A dielectric permittivi ty spectrum for un itary materials over a wide range of frequencies. Real and imaginary Figure 3.1 parts of permittivi ty are shown, and various processes are are depicted; acc. acc. to [HP 199 1992] 2]  

Frequency dependance of permittivity may impact the efficiency of a field grading material in the time domain significantly, depending on the intended application. In case the field grading shall be effective at transient(50/60 stresses lightningofimpulse voltage, commutation impulses, may etc.)beasbetter well assuited at power frequency Hz),(i.e. a material lower but balanced overall permittivity than one of very high permittivity at low frequencies only. The relaxation frequencies for electronic as well as atomic polarization are typically t ypically above the frequency spectrum relevant to HV apparatus. Often they only matter to optical physics applications. For materials materi als with significant ionic and orientational polarization mechanisms, however, relaxation frequencies may have to be considered. Within the group of dielectrics with dominating ionic polarization two different kind of behaviours can be distinguished. So-called ferroelectric materials will not lose their polarization even when the electric field is removed (often described as spontaneous electric polarization), whereas paraelectric materials will. In the lattice of a ferroelectric material ions may take several different states. An electric field can pull some ions into configurations that do not relax back to the previous state once the field is removed.  As a result, ferroelectric, analogous ttoo ferromagnetic materials, can have a residual polarizati polarization on aft after er the field has been removed. These materials usually provide the highest permittivities and are, therefore, in the focus of scientific research in the field of power energy storage devices.

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Barium titanate is the most popular member of ferroelectric ceramics, although there are others available, which exceed barium titanate’s permittivity by a factor of two (e.g. lead magnesium niobiumlead titanate: PMN-PT; however, lead-free materials need to be developed). Ferrorelectric behaviour can also be observed with polymers where atomic polarization is dominating and where the dipoles can be aligned by the applied electric field. Polyvinylidene fluoride and polytrifluoroethylene are two representatives of this subgroup. Since atomic polarization is weaker compared to the stronger ionic one permittivities of these polymers are somewhat lower.  A commonly named representative for orientational polarization is water. Due to the strong permanent dipole of its molecule the relative permittivity can reach values of more than 80. Unitary high permittivity materials and materials with nonlinear electric properties are typically of ceramic type and, therefore, difficult to apply directly in field grading systems with respect to processability, durability, flexibility and stability. Conducting and semiconducting materials are likewise not directly applicable due to either their excessive conductivity or their brittle structure. Only after being dispersed in a suitable host matrix, which is selected mainly based on mechanical requirements, an easy-to-apply composite is formed. Typical host matrices are varnishes (resins), EPDM and VMQ (elastomers) as well as thermoplastics and thermosets. For these composites interface charge polarization   is typically the most dominant polarization mechanism. It is present when charge carriers can migrate an appreciable distance through the composite but then get trapped e.g. at interface boundaries before they can reach an electrode. This is the case when materials with different dissipation factors  are combined or micro- and macroscopic interfaces like cellulose fibres do exist. Therefore, this mode of polarization applies to almost every material mix like suspensions or colloids, biological materials, phase separated polymers, blends and crystalline or liquid crystalline polymers and the commonly used oil-paper insulation system.

tan

The relaxation frequency for interface polarization quite Figure low and is. determined by the conductivity and permittivity of thecharge involved dielectricsis (see Figure (see 3.2) 3.2). In simplifiedbasically terms the relevant process can be compared to a low-pass RC filter where the conductivity of the material with the higher dissipation factor and the permittivity of the other material determine the limiting limit ing frequency.

Figure 3.2 3.2:: A dielectric permit tivity spectru m for c omposi te materials materials over a wide range of frequencies. Relative Relative permittivity ε  r  and   and dissipation factor tan δ are shown. Compared to unit ary materials interface charge polarization contri butes at low f requencies; acc. to [Beyer 1986] 1986]  

The electrical properties of a composite are in general difficult to predict due to interaction effects between the filler particles’  surface  surface and the host matrix. Also statistical effects have a significant impact.  A number of “effective medium approximation” models have been published published,, from which only the Maxwell-Garnett approximation , the Bruggeman’s model  and  and the Maxwell-Wagner-Sillars model  shall  shall be mentioned in this context. Effective medium approximations are based on the assumption that each filler particle is, in average, surrounded by the host matrix that hasfiller the particles assumed has homogeneous property. With increasing filler level, however, percolation of the to be takenmedium into consideration.

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The Maxwell-Garnett  approximation  usually  usually provides valid results at low volume fractions of fillers with dilute conductivity (below the percolation threshold) of up to 10 % or 20 %, respectively [Steeman 1992] [Beek 1967]. It is based on a mean field approximation covering spherical inclusions according to the Maxwell’s relation embedded in a continuous matrix of polymer [Barber 2009]. The formula can be extended to complex permittivities and then also covers dielectric losses of the composite. Bruggeman’s model  assumes  assumes a binary mixture, composed of repeated units, which in turn are composed of the host matrix and a spherical or ellipsiod ell ipsiod inclusion in the center [Barber 2009]. This mixing model yields better results even though the dispersion is not strongly diluted. The Maxwell-Wagner-Sillars model  is  is finally able to also take into account the effects of interface charge polarization, may occur atpermittivities inner dielectric boundary layers filler2011]. particles and the matrix [Zulkifli 2012]which having different and/or conducti conductivites vitesbetween [Romasanta It was found that with a larger surface area at the interface between filler particles particle s and host matrix the interfacial polarization increases [Salaeh 2012]. Investigations of functionalized graphene sheets with high aspect ratios [Romasanta 2011] and high aspect ratio fillers like barium titanate fibres and graphene platelets [Wang 2012] confirm that a large interface surface area is able to provide higher permittivity levels. It is also reported that by chemically modifying the filler’s surface the typical high power loss related with the Maxwell-Wagner-Sillars process can be significantly reduced [Romasanta 2011]. Such an additional process step can, however, significantly raise the production costs, and thermally expanded graphene sheets are presented as an alternative. The thermal reduction of graphite oxide is reported to provide a chemically modified graphene sheet or so-called functionalized graphene sheet without the need for further modification steps [Romasanta 2011]. Carbon black is the most commonly used filler to increase conductivity as well as permittivity of polymers. At low filling levels and well dispersed particles conductivity usually does not change much since the average distance between the conductive particles is too large to form a continuous conductive path. Maxwell-Garnet approximation  may  may be applied to calculate permittivity and conductivity of such a composite. At increasing filling levels, however, conductivity starts to increase rapidly as the distance between the conductive particels becomes less than 10 nm [Bärsch 2010]. Further details about carbon black, its application as filler and percolation theory are given in 3.3.2. in 3.3.2.   The effective medium approximations and the percolation theory can be combined into a “general effective media (GEM) equation” , which covers most aspects of both theories. t heories. Adapated equations have been proven to provide good results with respect to AC and DC conductivity as well as complex permittivity of composites [Wu 2003]. So far it has been assumed that the particulate fillers are homogeneously dispersed in the composite. Recent development investigates possibilities to disperse fillers inhomogeneously but in a controlled way within an insulation or field grading system. s ystem. This is explained in greater detail in in 2.2.4.2.  2.2.4.2.  

3.2 Ma 3.2 Matri tri x materials 3.2.1 3.2 .1

Glass (resist ive glazing)

Theoretically, the overall axial potential distribution of an insulator can be improved by resistive grading in form of a conductive surface layer. Since Sin ce the 1970s ceramic insulators with weakly conductive glazing have been in use. The first patent was granted in 1940 [Forrest 1940] and the application published shortly afterwards [Forrest 1942]. Semi-conducting glaze properties are obtained by a conducting phase in the glass matrix, usually metal oxide crystallites. crystallit es. In the beginning metal oxides, especially iron oxide, were applied. Partially reduced titanium oxide improved thermal properties but turned out to be instable in the long term [Gubanski 2005]. Finally, an insulator manufacturer developed a glazing system that contains antimony-doped antimony-doped tin oxide, resulting in a constant leakage current flow of (0.5…1) mA across the insulator surface [Fukui 1978] [Naito 1997] [Mizuno 1999]. Further information is given in in 5.6.1  5.6.1

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3.2. 3. 2.2 2

Thermopl The rmopl astic polymers

High molecular polymers consist of one or several different monomers bonded together by polymerization, polyaddition or polycondensation. For thermoplastic polymers the resulting long chain molecules mostly have a linear structure (examples in Figure in  Figure 3.3) 3.3),, interconnected by van der Waals bonds. When heating the material the van der Waals bonds split up, and the polymer melts. When cooling the substance sets again. This reversible behavior allows shaping by thermal treatment, e.g. extrusion processes. Among others, polyethylene (PE), polyvinyl chloride (PVC) and polypropylene (PP) are widely used thermoplastics in high voltage engineering, e.g. as insulators or spacers.

3.3: Molecular structur e of polyethylene, polyprop ylene and polyvinyl chl oride; acc. to [Kü chler 2017] Figure 3.3: 2017]

The copolymer of ethylene and vinyl acetate is called ethylene-vinyl acetate (EVA), or more precisely poly(ethylene-vinyl acetate) (PEVA). Figure 3.4 shows the molecule structure. The content of vinyl acetate determines the chemical and physical properties and thus, the application of EVA. The technical properties of the polymer with about 20 wt% 2   vinyl acetate are very similar to low density PE. Increasing the fraction to (40… (40…50) wt% of vinyl acetate leads to rubber-like materials. EVA is used for cable sheathing and for sheds of various types of insulators as well as for heat shrinking cable accessories [Brinkmann 1975].

Figure 3.4 3.4:: Molecule struct ure of EVA consist ing of ethylene (right) and vinyl acetate (left) (left) monomers ; acc. to [Brinkm ann 1975] 1975]

3.2.3  Thermoset polymers

 As for the thermoplastics the thermosets originate from polymerization, polyaddition or polycondensation reactions. But the resulting long chain molecules are chemically cross-linked to each other, forming a network structure. Thus, those materials do not melt with increasing temperature but soften and show an elastomeric behavior when reaching the glass transition temperature. After curing or crosslinking, respectively, thermosets can only be shaped by mechanical processes. Thermosets, typically used as matrix materials, are epoxy resin, alkyd resin and polyurethane. Epoxy resins (EP) are widely used for electrical engineering purposes mostly as cast resins or as adhesives. They can also be used as basis for varnishes, coatings and tapes. The resin contains more than one epoxide group per molecule. The epoxide group consists of an oxygen atom bonded to two carbon atoms, which are further connected, resulting in a reactive ring structure (Figure 3.5 left). For applications the epoxy resin is mixed with a hardener.

2 wt%

= percentage by weight

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Figure 3.5: 3.5: Structure of epoxy gro up and urethane group; acc. to [ Küchler 2017] 2017]

 Alkyd resins form the basis of varnishes, coatings and tapes. The term “alkyd” reflects the combination of “alc “alcohol” ohol” and organic “acid “ac id”, ”, the main components of the material. Mostly, fatty acids are used. The number of double bonds of the unsaturated fatty acids determines if the resin is air drying or needs baking. Polyurethane (PUR) is synthesized by polyaddition from polyisocyanate with polyhydric alcohols. Polyurethanes are characterized by the urethane group (Figure 3.5 right). If the linear molecules of thermoplastic polyurethanes are cross-linked, this results in a thermoset polymer. Polyurethane is used as basis for varnishes and tapes.  As described above, polyethylene (PE) is a thermoplastic polymer, thus showing low long term temperature stability and creeping of the material. Crosslinking the extruded polyethylene in a subsequent process step by e.g. peroxide crosslinking or electron beam forms the thermoset XLPE. XLPE is commonly used for cable insulations and can be used for warm shrink applications. 3.2.4

Elastomers

Elastomers are wide-meshed thermoset polymers, thus being elastic over a large temperature range. The shaping expanded process isor identical to thermosets. their shape be permanently compressed without losingDue theirtoresilience. Thismemory behaviorelastomers is especiallycan useful for cable accessories where a permanent contact pressure between the body of the accessory and the cable insulation is necessary to maintain the dielectric strength. Silicone rubbers (VMQ) are elastomers widely used in high voltage applications. The silicone macromolecules consist of an inorganic backbone of silicon and oxygen atoms surrounded by organic side groups (Figure 3.6) 3.6).. Depending on the vulcanization process the relevant silicone rubbers are divided into three groups: high temperature vulcanizing silicone rubbers (HTV silicone), room temperature vulcanizing silicone rubbers (RTV silicone), and liquid silicone rubbers (LSR). The widemeshed structure of silicone rubbers allows a comparatively high diffusion of gases, water vapor, and oil molecules. This is an advantage for the use of VMQs in cable accessories, as voids in the interface of cable insulation and insulation body disappear rapidly after installation. Suspension insulators, post insulators and hollow core insulators benefit from the tracking resistance and the excellent hydrophobic surface properties of silicone rubbers. Additionally, silicone rubbers can be used for tapes, coatings and varnishes.

3.6: Chemical Figure 3.6: Chemical struct ure of silicone with org anic side groups

Beside XLPE and silicone rubber, ethylene propylene rubber (EPM, often incorrectly denoted as EPR) is a standard elastomer used for extruded cable insulation and cable accessories. Monomers of ethylene and propylene are randomly combined to synthesize EPM, resulting in a rubber resistant to heat, oxidation, ozone, and weather impact. Due to the comparatively high dielectric losses the use of EPM in AC systems is typically limited to the distribution and sub-transmission voltage levels. Closely related to EPM, the ethylene propylene diene rubber (EPDM rubber) takes diene monomer as third partner in the polymerization process. The resulting elastomer has similar properties as EPM. Widely as EPDM sealingismaterial (e.g. O-rings), is alsomaterial. taken as insulating material. Further, beside silicone used rubber, commonly used as cold itshrink

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3.3 Fillers 3.3.1

Goal

Fillers are particles added to a matrix to modify its physical properties (color, strength, permittivity, resistivity, etc.). In the context of field control, fillers are used to tune either the permittivity or the conductivity of a material. Fillers can be added homogeneously throughout the material mat erial or with a spatial gradient of the concentration (Figure 3.7) 3.7).. In some cases multiple fillers are used; either to obtain specific properties, for example gradient materials (see 2.2.4.2) (see 2.2.4.2) or  or to improve the manufacturability, reduce the cost, etc.

3.7:: Schematic representation of different fi ller types: a) single filler homogeneousl y dispersed, b) single filler Figure 3.7 homogeneously dispersed above percolation limit (the arrow illustrates one possible continuous path from one particle to th e next), next), c) single filler with spatial gradient, d) system of two fillers with spatial gradients

To adjust the electrical conductivity , it is necessary that the filler concentration is above the percolation limit. If the filler is conducting (for example carbon black) the level of conductivity is controlled by the concentration (see 3.3.2) (see 3.3.2).. For semiconducting fillers such as SiC, ZnO microvaristors, or antimony-tin oxide (ATO – (ATO – SnO  SnO2 /Sb  /Sb2O3) the conductivity level is determined by the properties of the filler (see ( see 3.3.3)  3.3.3).. With their help it is possible to provide a kind of self-adaptive field grading systems [Brandes 2008] [Donzel 2011] [Seen 2012] [Rüger 2012] [Greb 2015] [Tenzer 2011] [Tenzer 2013c] [Tenzer 2015] [Winter 2011] [Winter 2014] [Winter 2015] [Secklehner 2013] [Secklehner 2015] [Secklehner 2017a] [Secklehner 2017b]. The commonly applied concept is that the filler particles become more conductive after a certain threshold level of the electric field is exceeded. Further new approaches are addressed in in 3.3.4.  3.3.4.   The permittivity  of   of a composite is tuned by modifying the concentration of high permittivity particles (for example SrTiO3,TiO2, etc.). It is not necessary to be above the percolation limit as the effect relies on polarization. 3.3.2 3.3. 2

Carbon Ca rbon black and carbon nanotubes

For many field grading applications materials with a comparatively low specific volume resistivity of less than 100 cm is required. These materials are usually compounds of a matrix polymer and an electrically conductive filler. The most widely used fillers are carbon blacks, which, with a carbon content of more than 96 %, in principle demonstrate a variety of carbon (C). Carbon blacks with standard conductivity are produced in the so-called acetylene-black-process, a controlled incomplete combustion of acetylene in a special reactor. Other gases and specific technologies are used to produce carbon blacks with a very high electrical conductivity. The size of primary particles of conductive carbon blacks is typically in the range of (1…100) (1… 100) nm. Primary particles in the carbon black do not exist in an isolated i solated form, but rather aggregate in a beadslike manner into aggregates of different sizes. Smaller particles have larger contact surfaces, which lead to a self-aggregation behavior. The individual primary particles are coupled by van der Waals forces and can only be separated by applying very strong mechanical forces. Thus, an aggregate can be defined as a separate, solid, colloidal particle, which is the smallest dispersible unit in the carbon black and, therefore, must be considered as the actual primary particle in a carbon black as it is delivered.

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 Aggregates tend to form agglomerates. The agglomerates of conductive carbon blacks typically show a less spherical appearance then blacks used for pigments. They are rather branched agglomerates (Table 3.1) with 3.1)  with a high specific surface of (80 (80…1200) …1200) m2g-1. Carbon blacks consisting of branched aggregates are easier to incorporate into the bulk material and show a better electrical conductivity in comparison to other aggregate types. Ta Table ble 3.1: Types of carbon aggregate aggregates s

Spherical aggregate

Elliptical aggregate

Linear aggregate

Branched aggregate

Conductivity of carbon black filled polymer composites changes rapidly when the concentration of the homogeneously dispersed carbon black reaches the so-called so- called percolation threshold. Well below and well above the percolation threshold, change of conductivity is negligible. The percolation threshold level in turn is depending on the conductivity of the carbon black, the matrix polymer and the mixing process parameters, but morethe importantly on experimentally the carbon black’s structure. Therefore, it istheory typically required to evaluate parameters and micro then adapt a suitable mixing for predicting the electric properties. The objective of percolation theory is to characterize the connectivity properties in complex and randomly mostly disordered structures that are composed of simple components. It provides a natural frame for the theoretical description of random composites. The percolation theory gives a phenomenological power dependance of the effective property of a diphase composite in the volume fraction range, where one phase has just formed or is about to form a continuous percolation network or infinite cluster. However, the main problem with using the percolation theory in practical cases is that it is only strictly valid when the ratio of the properties of the two phases is infinite or zero [Wu 2003]. The resulting typical behavior of the specific resistivity of a carbon black filled compound is shown in Figure 3.8.  3.8.  The figure shows the resistivity of three polypropylene-carbon black-compounds with different specific surfaces in dependance on the percentage of the added carbon black.

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Figure 3.8: 3.8: Influence of the specific sur face of carbon blacks on th e electrical electrical resisti vity of a carbon bl ack-PP ack-PP-compound (sketch after R. Gilg, DEGUSSA)

Taking into consideration that the electrical conductivity of these compounds is provided by small contact areas between the aggregates, it is easy to understand that the ability of carbon-black-filled materials to carry an electrical current is very limited. Even if the earlier mentioned preconditions for the application of the percolation theory are not perfectly met for carbon black and the typical polymers, it still can provide some useful insight into other effects relevant to e.g. heat- and cold-shrink field grading tubes filled with carbon black particles. When these are mechanically expanded the probability to form a continuous conduction path increases, since expansion in one direction is accompanied with reduction of thickness in other directions. Existing but separated small clusters of carbon black may get connected to each other forming larger conductive clusters. Both, the probability to form a continuous conduction con duction path and conductivity conductivity,, will increase. This effect is reversible, which means conductivity decreases again when the material relaxes. The effect may also cause anisotropic changes of the electric parameters. It should also be taken into consideration that the compounding of carbon black and polymers can lead to a strong increase in the viscosity of the mixture, which may limit the usability.  A promising alternative for future developments with good electrical electrical conductivity are carbon nanotubes (CNT). CNT are microscopic tubular structures (molecular nanotubes) consisting of carbon atoms that are commercially available but have not reached a broad range of application yet. Their walls consist of carbon only, where the carbon atoms form a honeycomb-like structure with hexagons and three binding partners each. The diameter of the tubes is usually in the range of (1…. (1 ….50) 50) nm. In comparison, the longitudinal dimension of the tubes is much higher. Thus, they are more a fiber-like material in comparison to carbon black, but in a nano-scale. A distinction is made between single and multi-walled CNT. Because of the limited data available, the following paragraph should be understood as guiding information. The high electrical conductivity of CNT allows to use rather low amounts of less than 5 % of CNT to achieve about the same electrical resistivity as by conventional filling of a compound. As known from carbon blacks, there is a strong dependance of the resistivity on the filling degree (Figure 3.9) 3.9).. Filling a low viscosity bulk material, e.g. silicone polymer, with CNT leads to a very strong increase of the viscosity of the mixture. This may become a limiting factor for the application, so that the very low resistivity values of compounds reported in the literature are not possible to reach with standard mixing technologies, such as stirring or role-milling. Another measurable effect is the increase of resistivity of a compound with increasing number of mixing cycles (Figure 3.10). 3.10). It can be assumed that the mixing process leads to changes of the orientation of the CNT and the number of contact points to each other, so that the resulting specific volume resistivity increases.

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Figure 3.9: 3.9: Specific volume resistiv ity of a VMQ-C VMQ-CNT NT-compound -compound in dependance on the amount of CNT [Wacker [Wacker Chemie  AG, Mun ich ]

Figure 3.10: 3.10: Specific volume resisti vity of a VMQ-C VMQ-CNT NT-compound -compound in dependance of th e number of mi xing c ycles of the compou nd on a tripl e-rolle-roll-mill mill [Wacker Chemie AG, AG, Munich Munich ]

3.3.3 3.3 .3

Nonli near materials

 As fillers for nonlinear field grading materials either silicon carbide particles or zinc oxide microvaristors microvaristors are used in commercially available products. In the following both systems are described. The use of  ATO is still under investigation. 3.3.3. .3.1 1 Silic on carbi de (SiC) 3.3

SiC is a semiconductor that can take many different crystallographic structures. Depending on the doping (on purpose or due to impurities) SiC is either an n- or a p-semiconductor. Green SiC (doped with nitrogen or phosphor) is an n-semiconductor, while black SiC (doped with Al, B, Ga) is a psemiconductor [Senn 2012]. The SiC powder used for field control is of the same quality tthat hat is produced for grinding application. The SiC grains are typically sharp edged bulky particles and are classified according to their particles size, see Figure see Figure 3.11 [Donzel 2011].

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Figure 3.11: 3.11: Scanning electron m icroscop y pictur e of SiC particles [ Donze Donzell 2011] 2011]  

The macroscopic electrical properties of the SiC Si C based compound depend on the microscopic properties propert ies of the contact zones between SiC grains, see  see  Figure 3.12 [Donzel 2011]. It was shown that these contacts can be modeled by Schottky-like barriers. Tunneling by field emission is the dominant conduction mechanism [Mårtensson 2003]. The size of the SiC particles has direct influence on the electrical properties through the number of contacts of the current path [Onneby 2001], see Figure 3.13. Usually 3.13.  Usually SiC powder with a mean particle size of a few micrometers to few tens of micrometers are used. The percolation limit for SiC based composite lies at about 32 vol% 3 [Seen 2012].

Figure 3. 3.12: 12: Schematic Schematic illust ration of an SiC based composite; interpartic le contacts (responsible for the macroscopic electrical properties of th e composite) highlig hted in red [Donzel 2011] 2011]  

Figure 3.13: Dependance of the electrical prop erties (here: (here: resistivi ty) of SiC based composit es on the particl e size 3.13: Dependance [Seen 2012]  2012]  

The doping of the SiC particles changes their intrinsic conductivity and, therefore, also influences the electrical properties of powder bed4 or composites [Seen 2012] [Mårtensson 2003]. The large range of U-I- characteristics characteristics measured on SiC of different doping and grain size is illustrated in [Brandes 2008],

3 vol% = 4 powder

percent by volume bed: a layer that embeds any solid substance reduced to a state s tate of fine, loose particles by crushing, grinding, disintegration, etc.

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see Figure 3.14. see Figure 3.14. The  The U-I- characteristic characteristic of SiC powder is slightly nonlinear with exponents of nonlinearity, nonl inearity, α , between 2 and 4 (I  =  = k U α ).

3.14: 4: Current vs. voltage characteristics of six diff erent grades of SiC particles, illustrating the large spread of Figure 3.1 electrical properties; m easure easurements ments made on po wder beds [Brandes 2008]  2008] 

The strong effect of impurities on the electrical properties properti es of SiC is an issue for engineering application: applicati on:  “nominally identical” SiC can have very different properties, see Figure see Figure 3.15 (acc. to [Seen 2012]). This is one reason for the large tolerance in the specification of field control elements based on SiC, for example end corona protection tapes, see Figure see  Figure 3.16 [Brandes 2008].

Figure 3.1 3.15: 5: Resistivi Resistivi ty vs. electric fi eld measured on two bl ack-S ack-SiC iC powders of id entical grain size but delivered by two di fferent suppli ers; acc. to [Seen 2012] 2012]

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Figure 3.16: 3.16: Boundaries fo r the current-volt age characteristics of two commercial SiC tapes, tapes, named Type “A” and Type “B” here [Brandes here [Brandes 2008]

SiC is a hard material (9 on the Mohs scale; diamond hardness is 10). This has a practical impact on the production of field control compounds and tapes based on SiC: the equipment is subject to severe abrasion. 3.3.3.2 .2 Metal ox oxid ides es (MO) 3.3.3

Diverse nonlinear ceramics such as for example ZnO, SnO2, or SrTiO3 are known, however doped ZnO is the material of choice for MO surge arresters and state-of-the-art field control industrial applications due to its unmatched properties. The nonlinearity of ZnO originates in the microstructure of the ceramic [Greuter 1995] [Donzel 2011], see Figure see  Figure 3.17: 3.17: conductive  conductive grains (