Electrostatic fields and field stress control

SUBJECT:- HIGH VOLTAGE ENGINEERING(2160904)
UNIT: 01
FACULTY:- RAKESH VASANI
1

 Syllabus :- CH-01
 E. Kuffel,W.S. Zaengl,J. Kuffel :- CH-04
 1. Electrical field distribution and breakdown strength
of insulating materials
 2. Fields in homogeneous, isotropic materials
 3. Fields in multi dielectric, isotropic materials
 4. Numerical methods : FEM, FDM, CSM
2

 In response to an increasing demand for electrical
energy, operating transmission level voltages have
increased considerably over the last decades.
 Designers are therefore forced to reduce the size and
weight of electrical equipment in order to remain
competitive.
 This is possible only through a thorough
understanding of the properties of insulating
materials and knowledge of electric fields and
methods of controlling electric stress.
3

 In HV engineering most of the problems concerned
with the electrical insulation of high direct, alternating
and impulse voltages are related to electrostatic and
sometimes electrical conduction fields only.
 The permissible field strengths in the materials are
interlinked with the electrostatic field distributions
and thus the problems may become extremely
difficult to solve.
4

 It is often assumed that a voltage V between two
electrodes may be adequately insulated by placing an
insulating material of breakdown strength Eb
 ; which is considered as a characteristic constant of
the material, between these electrodes.
 The necessary separation d may then simply be
calculated as
d = V/Eb.
5

 Although the electrodes are usually well defined and are
limited in size, the experienced designer will be able to
take care of the entire field distribution between the
electrodes and will realize that
 in many cases only a small portion of the material is
stressed to a particular maximum value Emax.
 One may conclude that the condition Emax = Eb would
provide the optimal solution for the insulation problem.
 This is true only when Eb has a very specific value
directly related to the actual field distribution and can be
calculated for very well-known insulating materials, such
as gases.(Except solid & liquids having approx values) 6

7 Rod-to-plane electrode configuration

8
 Figure represents a rod–plane electrode configuration insulated
by atmospheric air at atmospheric pressure.
 Whereas the gap length and the air density are assumed to
remain constant,
 the diameter D of the hemispherical-shaped rod will change
over a very wide range as indicated by the dashed lines.
 Two field quantities may defined for rods of any diameter D.
 These are the maximum field strength Emax at the rod tip and the
mean value of the field strength
 Emean = V/d.
 ‘field efficiency factor’ is defined as

9
 This factor is clearly a pure quantity related to electrostatic field
analysis only. In a more complex electrode arrangement
 Emax may appear at any point on an electrode,
 not necessarily coinciding with the points providing the shortest
gap distance, d. η equals unity or 100 per cent for a uniform field,
and it approaches zero for an electrode with an edge of zero radius.
 If the breakdown of the gap is caused by Emax only, then the
breakdown voltage Vb is obtained from eqn as
 Vb = Emaxd η = Ebd η (with Emax = Eb)
 This equation illustrates the concept of the field efficiency factor.
As 1 ≥ η 0≥
 for any field distribution, it is obvious that field non-uniformities
reduce the breakdown voltage.

11
 Many electrical insulation systems contain only one type of
dielectric material.
 Most materials may be considered to be isotropic, i.e. the
electric field vector E and the displacement D are parallel.
 At least on the microscopic scale many materials at uniform
temperature may also be assumed to be homogeneous.
 The homogeneity is well confirmed in insulating gases and
purified liquids.
 Solid dielectrics are often composed of large molecular
structures forming crystalline and amorphous regions so that the
homogeneity of the electrical material properties may not be
assured within microscopic structures.
 The permittivity will then simply be a scalar quantityε
correlating D and E, with D = Eε

14
 Electrode configurations providing two-dimensional
cylindrical or three dimensional spherical fields are used in h.v.
equipment as well as in laboratories for fundamental research
or field stress control
 The electrical field distribution is symmetrical with reference to
the centre of the cylinder axis or the centre point of the sphere.
 In both cases the lines of force are radial and the field strength E
is only a function of the distance x from the centres. The
cylinders are then uniformly charged over their surface with a
charge per unit length Q/l, and the spheres with a charge Q, if a
voltage V is applied to the two electrodes.

16
 Using Gauss’s law, the field strength E(x) at x is derived
from the following:
 Coaxial cylinder:
 Coaxial spheres:

17
 For equal geometries (r1 = R1; r2 = R2) Emax will always be
higher in the sphere configuration.:
 Coaxial cylinder:
 Coaxial spheres:

23
 Two spheres of equal diameter 2R separated by distance b
between centres are assumed to have the potential +V and -V
respectively
 Then only the field distribution is completely symmetrical with
reference to an imaginary plane P placed between the two
spheres, if the plane has zero potential
 With a point charge Q0 at the centre of the left sphere (1) the
surface of this sphere would exactly represent an equipotential
surface and could be replaced by a metal conductor, if the right
sphere (2) and the plane were not present.

25
 We choose this electrode configuration for comparison with the
field distribution between two oppositely charged spheres
 If two or more cylindrical conductors would be at the same
potential with reference to predominantly earth potential far
away from the parallel conductors……
 The configuration of so-called ‘bundle conductors’ is formed, a
system extensively applied in h.v. transmission lines.
 Due to the interaction of the single conductors the maximum
field intensity at the conductors is reduced in comparison to a
single cylindrical conductor…..
 so that the corona inception voltage can significantly be
increased

26
Electrostatic field about the spheroidspheroidal coordinates

27
Up to now we have treated ‘microscopic’ fields acting between
conducting electrodes with dimensions suitable to insulate high
voltages by controlling the maximum electrical field strength by
large curvatures of the electrodes.
In actual insulation systems the real surface of any conductor
may not be really plane or shaped as assumed by microscopic
dimensions
or the real homogeneous insulation material may be
contaminated by particles of a more or less conducting nature
Although real shape of particles within the insulating material
may be very complex, the local distortion of the electrical field
which can be assumed to be ‘microscopic’ in dimensions can
easily lead to partial discharges or even to a breakdown of the
whole insulation system.

28
Field distribution produced by a spheroid of high permittivity

29
Many actual h.v. insulation systems, e.g. a transformer
insulation, are composed of various insulation materials, whose
permittivities ε are different from each other
The main reasons for the application of such a multidielectric
system are often mechanical ones, as gaseous or fluid materials are
not able to support or separate the conductors
Layer arrangements may also be applied to control electric
stresses. The aim of this section is, therefore, to treat fundamental
phenomena for such systems.

30
Parallel plate capacitors comprising
two layers of different
materials
Coaxial cable with layers of different
permittivity

31
The law of refraction applied to
field intensities E for ε1 > ε2
Two different
dielectric materials
between plane
electrodes

32
Capacitor bushing. (a) Coaxial capacitor arrangement.

33
•Following methods are used for determination of the potential
distribution
(i) Numerical methods
(ii) Electrolytic tank method.
•Some of the numerical methods used are
(a) Finite difference method (FDM)
(b) Finite element method (FEM)
(c) Charge simulation method (CSM)
(d) Surface charge simulation method (SCSM)

34
(a) Sphere-to-sphere
electrode
arrangement.
(b) Computed
result

35
1. Electrical field distribution and breakdown strength
of insulating materials
2. Fields in homogeneous, isotropic materials
i) Uniform Field Electrode Arrangement
ii) Coaxial Cylindrical and Spherical Fields
iii) Sphere-to-sphere or sphere-to-plane
iv) Two cylindrical conductors in parallel
v) Field distortions by conducting particles
3. Fields in multi dielectric, isotropic materials
i) Simple configurations
ii) Dielectric refraction
iii) Stress control by floating screens
4. Numerical methods:-FEM, FDM, CSM

Electrostatic fields and field stress control

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