MODELLING AND ANALYSIS OF FUNCTIONALLY GRADED MATERIAL...
Transcript of MODELLING AND ANALYSIS OF FUNCTIONALLY GRADED MATERIAL...
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MODELLING AND ANALYSIS OF FUNCTIONALLY
GRADED MATERIAL USED IN GAS INSULATED
SUB-STATION FOR THREE PHASE BUS DUCT
CHAPTER-III
The reliability of power transmission and the introduction of
higher voltages to the center of big cities have been the two key
features in the history of GIS. Coping with the requirement in the
power systems, three-phase enclosure type GIS has been developed as
a practical means to realize a GIS with higher reliability in more
compact size. A Three- phase enclosure-type Gas Insulated Bus (GIB)
has widely been applied to minimize the installation space of a sub-
station. Three phase enclosure type GIS is about 65% in area, about
70% in volume, and about 90% in weight in comparison with single
phase type GIS below 145kV[116]. The number of enclosures,
component devices and sealed sections are about one-third of single-
phase type. The compactness makes it possible to transport a unit or
a bay or GIS in full assembly to minimize on-site works. This feature
makes a three-phase enclosure type GIS to be highly reliable.
Compactness, reduction of the number of parts and simple
construction on-site promotes the economy of the GIS.
These days, electric power equipment tends to be compact and be
operated under high voltage. In the equipment, the solid insulators
3.1 INTRODUCTION
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play the most critical role for electrical insulation. To improve the
insulation performance of the solid insulators, there is a need to
control electric field distribution around the solid insulators. However,
conventional techniques for the control of electric field lead to the
complicated structure of insulators and increase the manufacturing
cost. Then, it is necessary to propose a new concept on insulators
while keeping their simple structure and configurations. In the
optimization process, permittivity distribution of the FGM insulator is
sequentially modified for minimizing the electric field stress in and
around FGM insulators.
In the present work Electric Field is obtained by applying FEM
on FGM type spacer for GIS under 650kV switching over voltages
(standard maximum voltage that may occur for a 145kV class of GIS).
A three phase bus duct with aluminum enclosure, aluminum
conductor and different insulator shapes are modeled as shown in
Figs(3.2-3.7) in a two dimensional axis. The dimensional details for
three phase GIB are Thickness of the enclosure is 6.4mm, outer
diameter of enclosure is 508mm, outer diameter of conductor is
89mm, conductor thickness is 12.7mm and filled with SF6 gas. The
analysis is done with various types of spacers as shown in Fig. (3.1).
In type A spacer, the value of the relative permittivity εr = 6 is
constant, where as for type B spacer, the corresponding value of the
permittivity εr = 3 right from high voltage electrode to enclosure. In
3.2 DIFFERENT GEOMETRY’S USED IN THREE PHASE ANALYSIS
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type C spacer, the value of relative permittivity varies linearly from 9
to 3. In type D spacer, the value of relative permittivity varies linearly
from 9 to 3 in a 50 percent radial distance and then it becomes
constant thereafter. The concept of Finite Element Method (FEM) &
Functionally Graded Material (FGM) has been discussed in previous
chapter. Below, six different modeling have been discussed, they are
[81].
1. Bulb-shape insulator
2. Post type insulator
3. Rib-shape insulator
4. V-shape insulator
5. Delta- shape insulator
6. Post inside insulator
For all the above mentioned models fig(3.2 to 3.7), four types of
materials are applied fig(3.1) and the electrical potential and electric
field stresses are plotted along the surface of insulator enscapulating
the conductor along X and Y-axis fig(3.8 to 3.73)
0
3
6
9
A
D
B
C
Radial Co-ordinate (mm) varies from High Voltage to
Enclosure
Rel
ativ
e P
erm
itti
vit
y (ε
r)
Fig-3.1 Distribution of relative
permittivity in spacer
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3.2.1 THE GEOMETRY DETAILS FOR DIFFERENT MODELS
Conductor-3
Conductor-2
Conductor-1
Fig-3.3 Geometry for post shape insulator
SF6 Gas
Insulator
Enclosure
SF6 Gas Conductor-1
Conductor-2
Conductor-3
Fig-3.2 Geometry for Bulb shape Insulator
Enclosure
Insulator
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Conductor-3
Conductor-2 Conductor-1
Fig-3.4 Geometry for Rib shape insulator
SF6 Gas
Insulator
Enclosure
Conductor-1 Conductor-3
Conductor-2
Fig-3.5 Geometry for V-shape insulator
Insulator-2
Insulator-1
Enclosure SF6 Gas
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Conductor-1
Conductor-2
Conductor-3
Fig-3.7 Geometry for Bulb-inside shape insulator
Insulator
Enclosure
SF6 Gas
Conductor-1
Conductor-2
Conductor-3
Fig-3.6 Geometry for Delta shape insulator
Enclosure
Insulator
SF6 Gas
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In type A spacer, the value of the relative permittivity, εr = 3 is
constant right from high voltage electrode to enclosure and the
corresponding electric field plots fig(3.8) and graphs are given in figs
(3.8(a) to 3.8(f))
3.3 MODEL 1: DETAILED ANALYSIS OF BULB SHAPE INSULATOR
3.3.1 TYPE-A SPACER FOR BULB SHAPE INSULATOR
Surface: Electrical Potential (V)
Fig-3.8 Electric field plot with εr=3(constant) for Type-A Bulb
Shape spacer
3.8.1(a) ELECTRIC FIELD GRAPHS FOR TYPE-A SPACER
Fig-3.8(a) Electric Field Distribution of type-A Spacer for conductor-1 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
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Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.8(b) Electric Field Distribution of type-A Spacer for
conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.8(c) Electric Field Distribution of type-A Spacer for
conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.8(d) Electric Field Distribution of type-A Spacer for conductor-2 along Y-axis
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Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.8(e) Electric Field Distribution of type-A Spacer for
conductor-3 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.8(f) Electric Field Distribution of type-A Spacer for
conductor-3 along Y-axis
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In type B spacer, the corresponding value of the relative permittivity,
εr = 6 right from high voltage electrode to enclosure, the corresponding
electric field plots figs(3.9) and graphs are given in figs (3.9(a) to 3.9(f))
3.3.2(a) ELECTRIC FIELD GRAPHS FOR TYPE-B SPACER
3.3.2 TYPE-B SPACER FOR BULB SHAPE INSULATOR
Surface: Electrical Potential (V)
Fig-3.9 Electric field plot with εr=6(constant) for Type-B Bulb
Shape spacer
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.9(a) Electric Field Distribution of type-B Spacer for
conductor-1 along X-axis
Radial Co-ordinate in mm
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Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.9(b) Electric Field Distribution of type-B Spacer for
conductor-1 along Y-axis
Radial Co-ordinate in mm
Fig-3.9(c) Electric Field Distribution of type-B Spacer for
conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.9(d) Electric Field Distribution of type-B Spacer for
conductor-2 along Y-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
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Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.9(e) Electric Field Distribution of type-B Spacer for
conductor-3 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.9(f) Electric Field Distribution of type-B Spacer for
conductor-3 along Y-axis
Radial Co-ordinate in mm
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In type C spacer, the value of relative permittivity varies linearly from
high voltage electrode to enclosure (εr=9 to 3), the corresponding
electric field plots fig (3.10) and graphs are given in figs (3.10(a) to
3.10(f))
3.3.3 TYPE-C SPACER FOR BULB SHAPE INSULATOR
3.3.3(a) ELECTRIC FIELD GRAPHS FOR TYPE C SPACER
Radial Co-ordinate in mm
Fig.3.10(a) Electric Field Distribution of type-C Spacer for conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig.3.10 Electric field plot with εr=9 to εr=3 (linear variation) for type C
Bulb Shape spacer
Surface: Electrical Potential (V)
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Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig.3.10(b) Electric Field Distribution of type-C Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig.3.10(c) Electric Field Distribution of type-C Spacer
for conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig.3.10(d) Electric Field Distribution of type-C Spacer
for conductor-2 along Y-axis
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Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig.3.10(e) Electric Field Distribution of type-C Spacer
for conductor-3 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig.3.10(f) Electric Field Distribution of type-C spacer
for conductor-3 along Y-axis
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In type D spacer, the value of relative permittivity varies (high voltage
electrode to enclosure) linearly from 9 to 3 (50% of the radial co-
ordinate) and then it becomes constant thereafter, the corresponding
electric field plots fig (3.11) and graphs are given in figs (3.11(a) to
3.11(f)).
3.3.4 TYPE-D SPACER FOR BULB SHAPE INSULATOR
3.3.4(a) ELECTRIC FIELD GRAPHS FOR TYPE D SPACER
Fig-3.11 Electric field plot with εr=9 to εr=3(variation up to 50% and
remains constant) for Type-D Bulb Shape spacer
Surface: Electrical Potential (V)
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig.3.11(a) Electric Field Distribution of type-D Spacer for
conductor-1 along X-axis
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Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig.3.11(b) Electric Field Distribution of type-D Spacer
for conductor-1 along Y-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig.3.11(c) Electric Field Distribution of type-D Spacer
for conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig.3.11(d) Electric Field Distribution of type-D Spacer
for conductor-2 along Y-axis
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Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig.3.11(e) Electric Field Distribution of type-D Spacer
for conductor-3 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig.3.11(f) Electric Field Distribution of type-D Spacer
for conductor-3 along Y-axis
Radial Co-ordinate in mm
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Table- 3.1 Comparative values of bulb shape Insulator for Conductor-1 along X and Y axis
Radial
Co-Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1
X (106) Y (106) X (107) Y (106) X (104) Y (104) X (107) Y (106)
0 -5 -3.5 0.8 -3.9 -0.7 -0.4 -0.8 -3.8
50 -9 -5 -0.83 -6 -0.8 -0.5 -0.85 -4
100 -5 3 -0.6 2 -0.4 0.3 -0.7 3
150 -2 7 -0.2 6 -0.3 0.7 -0.2 6
200 3 7 0.3 7 0.5 0.9 0.4 7
250 8 3 0.7 3 0.8 0.4 0.8 4
300 7 -3 0.6 -2.7 0.5 -0.28 0.7 -2
350 3 -6 0.2 -6 0.3 -0.6 0.3 -6
400 -4 -7 -0.4 -7 -0.4 -0.25 -0.4 -7
450 -7 -5 -0.7 -4 -0.7 -0.5 -0.7 -5
Table-3.2 Comparative values of bulb shape Insulator for Conductor-2 along X and Y axis
Radial Co-Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B
TYPE-C TYPE-D
CONDUCTOR-2 CONDUCTOR-2 CONDUCTOR-2 CONDUCTOR-2
X (106) Y (106) X (106) Y (107) X Y (104) X (106) Y (106)
0 0.3 -4 -0.8 -3.9 1000 -0.4 -0.8 -3.8
50 -0.5 -5 -0.83 -6 -
3000 -0.5 -0.85 -4
100 3 -2 -0.6 2 5500 0.3 -0.7 3
150 4.5 1 -0.2 6 7000 0.7 -0.2 6
200 3.5 5 0.3 7 5500 0.9 0.4 7
250 0.3 3 0.7 3 0 0.4 0.8 4
300 -1.5 1 0.6 -2.7 -
3000 -0.28 0.7 -2
350 -2.5 -1 0.2 -6 -
5000 0.6 0.3 -6
400 -2.5 -3 -0.4 -7 -
4000 -0.25 -0.4 -7
450 -0.5 -4 -0.7 -4 -
1000 -0.5 -0.7 -5
3.3.5 COMPARATIVE TABLES FOR BULB SHAPE SPACER
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From graphs the comparative values of maximum field strength
(V/mm) in various types of spacers are shown in tables (3.1 to 3.3).
Comparative values of electric field stress (kV/mm) in various types of
spacer in fig (3.12 to 3.17).
Table-3.3 Comparative values of bulb shape Insulator for Conductor-3 along X and Y axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3
X (106) Y (106) X
(106) Y (106) X Y X
(106) Y (106)
0 -3 2.3 -3 2.5 -4000 3000 -3.8 2.5
50 -4 2.3 -4 2 -4000 2000 -4 3
100 -1 3.8 0 3.5 0 4000 0 4
150 3 3.2 3 3 3500 3500 -3 3.5
200 6 1.5 6 1 6500 1000 7 1
250 3 -1.5 3 -1.5 2000 -1000 4 -1.5
300 0 -1.7 0 -1.7 0 -500 0 -1.5
350 -2 -1.9 -2 -1.9 -2000 -1500 -2 -2
400 -3 0 -3 0 -4000 0 -4 0
450 -3.8 2 -4 2 -4000 1500 -4 1.9
3.3.6 COMPARATIVE ELECTRIC FIELD STRESS GRAPHS
FOR BULB SHAPE SPACER
Fig-3.12 Electric field stress distribution for conductor-1 along X-axis
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Fig-3.14 Electric field stress distribution for conductor-2 along X-axis
Fig-3.13 Electric field stress distribution for conductor-1 along Y-axis
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Fig- 3.15 Electric field stress distribution for conductor-2 along Y-axis
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� In the proposed work, various types of FGM spacers have been
considered. In type A spacer, the value of the relative
permittivity εr = 3 is constant the corresponding electric field
plots and graphs are shown in figs (3.8 to 3.8(f)), where as for
type B spacer, the corresponding value of the permittivity εr = 6
right from high voltage electrode to enclosure, the corresponding
electric field plots and graphs are shown in figs (3.9 to 3.9(f)). In
type C spacer, the value of relative permittivity varies linearly
from 9 to 3, the corresponding electric field plots and graphs
are shown in figs(3.10 to 3.10(f)). In type D spacer, the value of
relative permittivity varies linearly from 9 to 3 (50% of the radial
3.3.7 RESULTS AND DISCUSSIONS FOR BULB SHAPE SPACER
Fig-3.16 Electric field stress distribution for conductor-3 along X-axis
Fig-3.17 Electric field stress distribution for conductor-3 along Y-axis
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206
co-ordinate) and then it becomes constant thereafter, the
corresponding electric field plots and graphs are shown in figs
(3.11 to 3.11(f)).
� The comparative values of maximum field strength in various
types of spacers are shown in table (3.1 to 3.3).
� From fig (3.12), for Conductor-1 along X-axis, in type-A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -180kV/mm to -15kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -166kV/mm to -15kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -0.1kV/mm to 0kV/mm under
the radial co-ordinate of 50 to 450 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -170kV/mm to -15kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From fig (3.13), for conductor 1 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -100kV/mm to -11kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -120kV/mm to -8.88kV/mm
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207
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -0.1kV/mm to -
0.01kV/mm under the radial co-ordinate of 50 to 450 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -80kV/mm to -
11.1kV/mm under the radial co-ordinate of 50 to 450 mm.
� From fig (3.14), for conductor 2 along X-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -10kV/mm to -1.1kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -16kV/mm to -1.5kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -0.06kV/mm to -
2222kV/mm under the radial co-ordinate of 50 to 450 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -17kV/mm to -
1.5kV/mm under the radial co-ordinate of 50 to 450 mm.
� From fig (3.15), for conductor 2 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -100kV/mm to -8.8kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
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208
the electric field stress value varies from the surface of the
conductor to the enclosure with -1200kV/mm to -8.8kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -0.1kV/mm to -
0.01kV/mm under the radial co-ordinate of 50 to 450 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -80kV/mm to -
11.1kV/mm under the radial co-ordinate of 50 to 450 mm.
� From fig (3.16), for conductor 3 along X-axis type–A spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -80kV/mm to -8.4kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 920kV/mm to 9.87kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 0kV/mm to 0kV/mm under the
radial co-ordinate of 50 to 450 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -80kV/mm to -8.8kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From fig (3.17), for conductor 3 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
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209
conductor to the enclosure with 46kV/mm to 4.44kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 40kV/mm to 4.44kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 0.04kV/mm to 0kV/mm under
the radial co-ordinate of 50 to 450 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 60kV/mm to 4.22kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From the above results, the electric field stress on surface on
the conductor of Type-C spacer is reduced when compared to
Type-A, Type-B and Type-D.
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210
In type A spacer, the value of the relative permittivity, εr = 3 is
constant right from high voltage electrode to enclosure and the
corresponding electric field plots fig(3.18) and graphs are given in figs
(3.18(a) to 3.18(f))
3.4 MODEL 2: DETAILED ANALYSIS OF POST TYPE
INSULATOR
3.4.1 TYPE-A SPACER FOR POST TYPE INSULATOR
Fig-3.18 Electric field plot with εr=3(constant) for Type-A Post
Type spacer
Surface: Electrical Potential (V)
3.4.1(a) ELECTRIC FIELD GRAPHS FOR TYPE A SPACER
Fig-3.18(a) Electric Field Distribution of type-A Spacer for conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
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211
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.18(b) Electric Field Distribution of type-A Spacer for
conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.18(c) Electric Field Distribution of type-A Spacer
for conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.18(d) Electric Field Distribution of type-A Spacer for conductor-2 along Y-axis
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212
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.18(e) Electric Field Distribution of type-A Spacer
for conductor-3 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.18(f) Electric Field Distribution of type-A Spacer
for conductor-3 along Y-axis
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213
In type B spacer, the corresponding value of the relative permittivity,
εr = 6 right from high voltage electrode to enclosure, the corresponding
electric field plots figs(3.19) and graphs are given in figs (3.19(a) to
3.19(f))
3.4.2(a) ELECTRIC FIELD GRAPHS FOR TYPE-B SPACER
3.4.2 TYPE-B SPACER FOR POST TYPE INSULATOR
Fig-3.19 Electric field plot with εr=6(constant) for Type-B
Post Type spacer
Surface: Electrical Potential (V)
Fig-3.19(a) Electric Field Distribution of type-B Spacer for
conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
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214
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.19(b) Electric Field Distribution of type-B Spacer
for conductor-1 along Y-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.19(c) Electric Field Distribution of type-B Spacer for
conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.19(d) Electric Field Distribution of type-B Spacer for
conductor-2 along Y-axis
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215
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.19(e) Electric Field Distribution of type-B Spacer for
conductor-3 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.19(f) Electric Field Distribution of type-B Spacer for
conductor-3 along Y-axis
Radial Co-ordinate in mm
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216
In type C spacer, the value of relative permittivity varies linearly from
high voltage electrode to enclosure (εr=9 to 3), the corresponding
electric field plots fig (3.20) and graphs are given in figs (3.20(a) to
3.20(f))
3.4.3(a) ELECTRIC FIELD GRAPHS FOR TYPE-C SPACER
3.4.3 TYPE-C SPACER FOR POST TYPE INSULATOR
Fig-3.20(a) Electric Field Distribution of type-C Spacer for conductor-1 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.20 Electric field plot with εr=9 to εr=3 (linear
variation) for type C Post Type spacer
Surface: Electrical Potential (V)
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217
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.20(b) Electric Field Distribution of type-C Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.21(c) Electric Field Distribution of type-C Spacer
for conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.20(d) Electric Field Distribution of type-C Spacer for conductor-2 along Y-axis
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218
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.20(e) Electric Field Distribution of type-C Spacer for
conductor-3 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.20(f) Electric Field Distribution of type-C Spacer
for conductor-3 along Y-axis
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219
In type D spacer, the value of relative permittivity varies (high voltage
electrode to enclosure) linearly from 9 to 3 (50% of the radial co-
ordinate) and then it becomes constant thereafter, the corresponding
electric field plots fig (3.21) and graphs are given in figs (3.21(a) to
3.21(f)).
3.4.4(a) ELECTRIC FIELD GRAPHS FOR TYPE-D SPACER
3.4.4 TYPE-D SPACER FOR POST TYPE INSULATOR
Fig-3.21 Electric field plot with εr=9 to εr=3(variation up to 50%
and remains constant) for Type-D Post Type spacer
Surface: Electrical Potential (V)
Fig-3.21(a) Electric Field Distribution of type-D Spacer
for conductor-1 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
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220
Radial Co-ordinate in mm
Fig-3.21(c) Electric Field Distribution of type-D Spacer for
conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.21(b) Electric Field Distribution of type-D Spacer for
conductor-1 along Y-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.21(d) Electric Field Distribution of type-D Spacer for
conductor-2 along Y-axis
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221
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.21(e) Electric Field Distribution of type-D Spacer for
conductor-3 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.21(f) Electric Field Distribution of type-D Spacer
for conductor-3 along Y-axis
Radial Co-ordinate in mm
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222
Table.3.4 Comparative values of post type insulators for Conductor-1 along X and Y axis
Radial Co-Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1
X (107) Y(106) X (107) Y(106) X (107) Y (106) X (104) Y(106)
0 0 -5 0 -6 0 -5.8 0 -5
100 -0.4 -6.5 -0.5 -6 -0.4 -6.4 -0.5 -7
200 -0.6 4 -0.5 4 -0.5 3.8 -0.7 4
300 0.6 7 0.5 7 0.5 7 0.3 8
400 0.8 -4 0.55 -4 0.8 -3.4 0.8 -5
500 0.1 -6 0.2 -6 0.1 -6.2 0.1 -6
Table.3.5 Comparative values of post type insulators for Conductor-2 along X and Y axis
Radial Co-Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-2 CONDUCTOR-2 CONDUCTOR-2 CONDUCTOR-2
X (107) Y(106) X(107) Y(106) X (106) Y(106) X (107) Y(106)
0 0 -1.5 0 -1 0 -1.02 0 -1.5
100 0.6 -1 0.8 -0.5 6.4 -0.08 0.8 -1
200 0.5 3 0.6 3 6 3.0 0.6 3
300 0.4 4 0.4 4 5.6 3.80 0.4 4
400 0.3 -3 0.3 -2 2.4 -2.5 0.3 -3
500 -0.2 -3 -0.2 -3 -2.06 -2.5 -0.3 -3
600 -0.1 1 -0.1 1 -1.00 1.00 -0.1 1
700 0.4 2 0.3 2 2.6 2.00 0.1 2
800 0.5 0.5 0.5 0.5 4.8 0.5 0.5 0.5
900 0 -0.5 0 -0.5 0 -0.5 0 -0.5
3.4.5 COMPARATIVE TABLES FOR POST TYPE SPACER
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223
From graphs the comparative values of maximum field strength
(V/mm) in various types of spacers are shown in tables (3.4 to 3.6).
Comparative values of electric field stress (kV/mm) in various types of
spacer in fig (3.22 to 3.27).
Table.3.6 Comparative values of post type insulators for Conductor-3 along X and Y axis
Radial
Co-Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B
TYPE-C TYPE-D
CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3
X(106) Y(106) X(106) Y(106) X(106) Y(106) X(106) Y(106)
0 0 2.5 0 3 0 2.9 0 3
100 2 3.5 2 3.5 2 3.5 2 3.5
200 4 -1.5 4 -1.5 3.6 -1.5 4 -1.8
300 -2 -2 -1 -1.8 -1.4 -1.6 -2 -2
400 -3.5 2 -4 2 -3.4 2.04 -3 2.5
500 -0.5 3 -1.5 3 -0.08 3.00 -1 3
3.4.6 COMPARATIVE ELECTRIC FIELD STRESS GRAPHS FOR
POST TYPE SPACER
Fig-3.22 Electric field stress distribution for conductor-1 along X-axis
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224
Fig-3.23 Electric field stress distribution for conductor-1 along Y-axis
Fig-3.24 Electric field stress distribution for conductor-2 along X-axis
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225
Fig-3.26 Electric field stress distribution for conductor-3 along X-axis
Fig-3.25 Electric field stress distribution for conductor-2 along Y-axis
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226
� In the proposed work, various types of FGM spacers have been
considered. In type A spacer, the value of the relative
permittivity εr = 3 is constant the corresponding electric field
plots and graphs are shown in figs (3.18 to 3.18(f)), where as for
type B spacer, the corresponding value of the permittivity εr = 6
right from high voltage electrode to enclosure, the corresponding
electric field plots and graphs are shown in figs (3.19 to 3.19(f)).
In type C spacer, the value of relative permittivity varies linearly
from 9 to 3, the corresponding electric field plots and graphs
are shown in figs(3.20 to 3.20(f)). In type D spacer, the value of
relative permittivity varies linearly from 9 to 3 (50% of the radial
co-ordinate) and then it becomes constant thereafter, the
3.4.7 RESULTS AND DISCUSSIONS FOR POST TYPE SPACER
Fig-3.27 Electric field stress distribution for conductor-3 along Y-axis
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227
corresponding electric field plots and graphs are shown in figs
(3.21 to 3.21(f)).
� The comparative values of maximum field strength in various
types of spacers are shown in table (3.4 to 3.6).
� From fig (3.22), for conductor-1 along X-axis, in type-A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -40kV/mm to 2kV/mm under
the radial co-ordinate of 100 to 500 mm. In type-B spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -50kV/mm to 4kV/mm under
the radial co-ordinate of 100 to 500 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -40kV/mm to 2kV/mm under
the radial co-ordinate of 50 to 450 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -0.05kV/mm to 0.002kV/mm
under the radial co-ordinate of 50 to 450mm.
� From fig (3.23), for conductor-1 along Y-axis, in the type–A
spacer, the electric field stress value varies from the surface of
the conductor to the enclosure with -65kV/mm to -12kV/mm
under the radial co-ordinate of 100 to 500mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -60kV/mm to -12kV/mm under
the radial co-ordinate of 100 to 500 mm. In type-C spacer, the
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228
electric field stress value varies from the surface of the
conductor to the enclosure with -64kV/mm to 12.4kV/mm
under the radial co-ordinate of 100 to 500mm. In type-D spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -70kV/mm to -12kV/mm under
the radial co-ordinate of 100 to 500 mm.
� From fig (3.24), for conductor 2 along X-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -60kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-B spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 80kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 64kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 80kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm.
� From fig (3.25), for conductor 2 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -10kV/mm to -0.55kV/mm
under the radial co-ordinate of 100 to 900 mm. In type-B
spacer, the electric field stress value varies from the surface of
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229
the conductor to the enclosure with -5kV/mm to -0.55kV/mm
under the radial co-ordinate of 100 to 900 mm. In type-C
spacer, the electric field stress value varies from the surface of
the conductor to the enclosure with -0.8 kV/mm to -
0.55kV/mm under the radial co-ordinate of 100 to 500 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -10kV/mm to
-0.55kV/mm under the radial co-ordinate of 100 to 500 mm.
� From fig (3.26), for conductor 3 along X-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -20kV/mm to -1kV/mm under
the radial co-ordinate of 100 to 500 mm. In type-B spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -20kV/mm to -3kV/mm under
the radial co-ordinate of 100 to 500 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 20kV/mm to –0.16kV/mm
under the radial co-ordinate of 100 to 500 mm. In type-D
spacer, the electric field stress value varies from the surface of
the conductor to the enclosure with 20kV/mm to -2kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From fig (3.27), for conductor 3 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 35kV/mm to 6kV/mm under
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230
the radial co-ordinate of 100 to 500 mm. In type-B spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 35kV/mm to 6kV/mm under
the radial co-ordinate of 100 to 500 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 35kV/mm to 6kV/mm under
the radial co-ordinate of 100 to 500 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 35kV/mm to 6kV/mm under
the radial co-ordinate of 100 to 500 mm.
� From the above results, the electric field stress on surface on
the conductor of Type-D spacer is reduced when compared to
Type-A, Type-B and Type-C.
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231
In type A spacer, the value of the relative permittivity, εr = 3 is
constant right from high voltage electrode to enclosure and the
corresponding electric field plots fig(3.28) and graphs are given in figs
(3.28(a) to 3.28(f))
3.5 MODEL 3: DETAILED ANALYSIS OF RIB TYPE
INSULATOR
3.5.1 TYPE-A SPACER FOR RIB TYPE INSULATOR
3.5.1(a) ELECTRIC FIELD GRAPHS FOR TYPE-A SPACER
Radial Co-ordinate in mm
Fig-3.28(a) Electric Field Distribution of type-A Spacer for conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.28 Electric field plot with εr=3(constant) for
Type-A Rib Shape spacer
Surface: Electrical Potential
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232
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.28(b) Electric Field Distribution of type-A Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.28(c) Electric Field Distribution of type-A Spacer
for conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.28(d) Electric Field Distribution of type-A Spacer for conductor-2 along Y-axis
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233
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.28(e) Electric Field Distribution of type-A Spacer
for conductor-3 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.28(f) Electric Field Distribution of type-A Spacer
for conductor-3 along Y-axis
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234
In type B spacer, the corresponding value of the relative permittivity,
εr = 6 right from high voltage electrode to enclosure, the corresponding
electric field plots figs(3.29) and graphs are given in figs (3.29(a) to
3.29(f))
3.5.2(a) ELECTRIC FIELD GRAPHS FOR TYPE-B SPACER
3.5.2 TYPE-B SPACER FOR RIB TYPE INSULATOR
Fig-3.29 Electric field plot with εr=6(constant) for Type-B Rib
Shape spacer
Surface: Electrical Potential (V)
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.29(a) Electric Field Distribution of type-B Spacer
for conductor-1 along X-axis
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235
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.29(b) Electric Field Distribution of type-B Spacer
for conductor-1 along Y-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.29(c) Electric Field Distribution of type-B Spacer
for conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.29(d) Electric Field Distribution of type-B Spacer
for conductor-2 along Y-axis
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236
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.29(e) Electric Field Distribution of type-B Spacer for
conductor-3 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.29(f) Electric Field Distribution of type-B Spacer for
conductor-3 along Y-axis
Radial Co-ordinate in mm
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237
In type C spacer, the value of relative permittivity varies linearly from
high voltage electrode to enclosure (εr=9 to 3), the corresponding
electric field plots fig (3.30) and graphs are given in figs (3.30(a) to
3.30(f))
3.5.3 TYPE-C SPACER FOR RIB TYPE INSULATOR
3.5.3(a) ELECTRIC FIELD GRAPHS FOR TYPE-C SPACER
Fig-3.30 Electric field plot with εr=9 to εr=3 (linear variation) for
type C Rib Shape spacer
Surface: Electrical Potential (V)
Radial Co-ordinate in mm
Fig-3.30(a) Electric Field Distribution of type-C Spacer for conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
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238
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.30(b) Electric Field Distribution of type-C Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.30(c) Electric Field Distribution of type-C Spacer
for conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.30(d) Electric Field Distribution of type-C Spacer for conductor-2 along Y-axis
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239
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.30(f) Electric Field Distribution of type-C Spacer for
conductor-3 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.30(e) Electric Field Distribution of type-C Spacer for
conductor-3 along X-axis
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240
In type D spacer, the value of relative permittivity varies (high voltage
electrode to enclosure) linearly from 9 to 3 (50% of the radial co-
ordinate) and then it becomes constant thereafter, the corresponding
electric field plots fig (3.31) and graphs are given in figs (3.31(a) to
3.31(f)).
3.5.4 TYPE-D SPACER FOR RIB TYPE INSULATOR
3.5.4(a) ELECTRIC FIELD GRAPHS FOR TYPE-D SPACER
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.31(a) Electric Field Distribution of type-D Spacer
for conductor-1 along X-axis
Fig-3.31 Electric field plot with εr=9 to εr=3(variation up to 50%
and remains constant) for Type-D Rib Shape spacer
Surface: Electrical Potential (V)
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241
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.31(b) Electric Field Distribution of type-D Spacer
for conductor-1 along Y-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.31(c) Electric Field Distribution of type-D Spacer for
conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.31(d) Electric Field Distribution of type-D Spacer for
conductor-2 along Y-axis
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242
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.31(f) Electric Field Distribution of type-D Spacer for
conductor-3 along Y-axis
Radial Co-ordinate in mm
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.31(e) Electric Field Distribution of type-D Spacer for
conductor-3 along X-axis
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243
Table-3.7 Comparative values of Rib type Insulator for Conductor-1 along X and Y axis
Radial Co-Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-1 CONDUCTOR-
1 CONDUCTOR-
1 CONDUCTOR-
1
X (106) Y (106) X
(106) Y (106) X
(107) Y (106) X
(106) Y (106)
0 0 -3 0 -3 0 -4 -1 -0.5
100 -4 -4 -4 -4 -0.4 -8 -4 -5
200 -6 5 -6 -6 -0.7 6 -7 5
300 1 6 1 4 0.1 6 2 6
400 1 1 1.5 2 0.1 2 1.5 1.5
500 4 3 4 3 0.5 3 4.5 3.5
600 8.5 -2 8 -2 0.9 -2 8.5 -2
700 -3 -7 -4 -6 -0.6 -4 -6 -6
800 -1 -3 -1 -4 -0.1 -4 -1 -3
900 0 -2 0 -2 0 -2 0 -1
Table-3.8 Comparative values of Rib type Insulator for Conductor-2 along X and Y axis
Radial Co-Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-2 CONDUCTOR-
2 CONDUCTOR-
2 CONDUCTOR-
2
X (106) Y
(106) X
(106) Y
(106) X
(107) Y
(107) X
(106) Y
(106)
0 0 0.5 0 0 0 0 0 0.5
100 3 -3 2 -3 0.4 -0.2 4.3 -2
200 4 1.5 3 1.5 0.4 0.2 4 1.58
300 -1 2 -1.5 2 -0.3 -0.3 -1 2.3
400 -1.5 1 -1 1 0 0 -1.2 1.3
500 -2 1.8 -1.5 2 0 0.2 -2 1.7
600 -4 -1 -3.5 -1 -0.4 0 -4 -0.5
700 2 -3.5 2 -3 0.3 -0.2 4 -2.5
800 1 -1 1 -1.5 0.1 -0.15 1 -1.5
900 0 0 0 0 0 0 0 0
3.5.5 COMPARATIVE TABLES FOR RIB TYPE SPACER
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244
From graphs the comparative values of maximum field strength
(V/mm) in various types of spacers are shown in tables (3.7 to 3.9).
Comparative values of electric field stress (kV/mm) in various types of
spacer in fig (3.32 to 3.37).
Table-3.9 Comparative values of Rib type Insulator for Conductor-3 along X and Y axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3
X (106) Y (106) X (106) Y (106) X (106) Y (106) X (106) Y (106)
0 0 0 0 0 1 -0.1 0.5 -1
100 2 0.2 2.3 0.5 3.5 0.1 3.5 0
200 2 3 2 3 0 5 0 4.5
300 -2.5 2 -2.5 1 3 1 -2.75 1
400 -2.3 0.5 -2.6 0.5 -1.5 0 -1.5 0
500 -2.5 1 -2.7 1 -2.5 0.3 -2.5 0.5
600 -2 -1 -2 -1 -1 -3.5 -0.5 -3
700 4 -5 3 -5 5 1 5 -0.5
800 2 -2.5 2.5 -2.5 1.5 -2 1 -1.5
900 0 0 0 0 0 0 0 0
3.5.6 COMPARATIVE ELECTRIC FIELD STRESS GRAPHS
FOR RIB TYPE SPACER
Fig-3.32 Electric field stress distribution for conductor-1 along X-axis
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245
Fig-3.33 Electric field stress distribution for conductor-1 along Y-axis
Fig-3.34 Electric field stress distribution for conductor-2 along X-axis
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246
Fig-3.35 Electric field stress distribution for conductor-2 along Y-axis
Fig-3.36 Electric field stress distribution for conductor-3 along X-axis
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247
� In the proposed work, various types of FGM spacers have been
considered. In type A spacer, the value of the relative
permittivity εr = 3 is constant the corresponding electric field
plots and graphs are shown in figs (3.28 to 3.28(f)), where as for
type B spacer, the corresponding value of the permittivity εr = 6
right from high voltage electrode to enclosure, the corresponding
electric field plots and graphs are shown in figs (3.29 to 3.29(f)).
In type C spacer, the value of relative permittivity varies linearly
from 9 to 3, the corresponding electric field plots and graphs
are shown in figs(3.30 to 3.30(f)). In type D spacer, the value of
relative permittivity varies linearly from 9 to 3 (up to 50% of the
radial co-ordinate) and then it becomes constant thereafter, the
3.5.7 RESULTS AND DISCUSSIONS FOR RIB TYPE SPACER
Fig-3.37 Electric field stress distribution for conductor-3 along Y-axis
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248
corresponding electric field plots and graphs are shown in
figs(3.31 to 3.31(f)).
� The comparative values of maximum field strength in various
types of spacers are shown in table (3.7 to 3.9).
� From fig (3.32), for conductor 1 along X-axis, in type-A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -40kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-B spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -40kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -40kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -40kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm.
� From fig (3.33), for conductor 1 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -40kV/mm to -2.22kV/mm
under the radial co-ordinate of 100 to 900 mm. In type-B
spacer, the electric field stress value varies from the surface of
the conductor to the enclosure with -40kV/mm to -2.22kV/mm
under the radial co-ordinate of 100 to 900 mm. In type-C
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249
spacer, the electric field stress value varies from the surface of
the conductor to the enclosure with -80kV/mm to -2.22kV/mm
under the radial co-ordinate of 100 to 900 mm. In type-D
spacer, the electric field stress value varies from the surface of
the conductor to the enclosure with -50kV/mm to -1.11kV/mm
under the radial co-ordinate of 100 to 900 mm.
� From fig (3.34), for conductor 2 along X-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 30kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-B spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 20kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 40kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 43kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm.
� From fig (3.35), for conductor 2 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -30kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-B spacer, the
electric field stress value varies from the surface of the
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250
conductor to the enclosure with -30kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -20kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -20kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm.
� From fig (3.36), for conductor 3 along X-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 20kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-B spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 23kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 35kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 35kV/mm to 0kV/mm under
the radial co-ordinate of 100 to 900 mm.
� From fig (3.37), for conductor 3 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 2kV/mm to 0kV/mm under the
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251
radial co-ordinate of 100 to 900 mm. In type-B spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 5kV/mm to 0kV/mm under the
radial co-ordinate of 100 to 900 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 1kV/mm to 0kV/mm under the
radial co-ordinate of 100 to 900 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 0kV/mm to 0kV/mm under the
radial co-ordinate of 100 to 900 mm.
� From the above results, the electric field stress on surface on
the conductor of Type-D spacer is reduced when compared to
Type-A, Type-B and Type-C.
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252
In type A spacer, the value of the relative permittivity, εr = 3 is
constant right from high voltage electrode to enclosure and the
corresponding electric field plots fig(3.38) and graphs are given in figs
(3.38(a) to 3.38(f))
3.6 MODEL4: DETAILED ANALYSIS OF V-SHAPE
INSULATOR
3.6.1 TYPE A SPACER FOR V-SHAPE INSULATOR
3.6.1(a) ELECTRIC FIELD GRAPHS FOR TYPE-A SPACER
Radial Co-ordinate in mm
Fig-3.38(a) Electric Field Distribution of type-A spacer for Insulator 1 conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.38 Electric field plot with εr=3(constant) for Type-A V-shape
spacer
Surface: Electrical Potential (V)
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253
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.38(c) Electric Field Distribution of type-A spacer
for Insulator 1 conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.38(b) Electric Field Distribution of type-A spacer
for Insulator 1 conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.38(d) Electric Field Distribution of type-A spacer
for Insulator 1 conductor-2 along Y-axis
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254
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.38(e) Electric Field Distribution of type-A spacer
for Insulator 1 conductor-3 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.38(f) Electric Field Distribution of type-A spacer
for Insulator 1 conductor-3 along Y-axis
Fig-3.38(g) Electric Field Distribution of type-A spacer
for Insulator 2 conductor-1 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
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255
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.38(h) Electric Field Distribution of type-A spacer for Insulator 2 conductor-1 along Y-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.38(i) Electric Field Distribution of type-A spacer
for Insulator 2 conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.38(j) Electric Field Distribution of type-A spacer
for Insulator 2 conductor-2 along Y-axis
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256
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.38(l) Electric Field Distribution of type-A spacer
for Insulator 2 conductor-3 along Y-axis
Radial Co-ordinate in mm
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.38(k) Electric Field Distribution of type-A spacer
for Insulator 2 conductor-3 along X-axis
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257
In type B spacer, the corresponding value of the relative permittivity,
εr = 6 right from high voltage electrode to enclosure, the corresponding
electric field plots figs(3.9) and graphs are given in figs (3.9(a) to 3.9(l))
3.6.2 TYPE B SPACER FOR V-SHAPE INSULATOR
3.6.2(a) ELECTRIC FIELD GRAPHS FOR TYPE-B SPACER
Radial Co-ordinate in mm
Fig-3.39(a) Electric Field Distribution of type-B spacer for Insulator 1 conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39 Electric field plot with εr=6(constant) for Type-B V-Shape spacer
Surface: Electrical Potential (V)
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258
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(b) Electric Field Distribution of type-B spacer for Insulator 1 conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(c) Electric Field Distribution of type-B spacer for
Insulator 1 conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(d) Electric Field Distribution of type-B spacer for Insulator 1 conductor-2 along Y-axis
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259
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(e) Electric Field Distribution of type-B spacer for Insulator 1 conductor-3 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(f) Electric Field Distribution of type-B spacer for Insulator 1 conductor-3 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(g) Electric Field Distribution of type-B spacer for Insulator 2 conductor-1 along X-axis
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260
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(h) Electric Field Distribution of type-B spacer for Insulator 2 conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(i) Electric Field Distribution of type-B spacer for
Insulator 2 conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(j) Electric Field Distribution of type-B spacer
for Insulator 2 conductor-2 along Y-axis
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261
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(k) Electric Field Distribution of type-B
spacer for Insulator 2 conductor-3 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.39(l) Electric Field Distribution of type-B
spacer for Insulator 2 conductor-3 along Y-axis
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262
In type C spacer, the value of relative permittivity varies linearly from
high voltage electrode to enclosure (εr=9 to 3), the corresponding
electric field plots fig (3.40) and graphs are given in figs (3.40(a) to
3.40(l))
3.6.3 TYPE C SPACER FOR V- SHAPE INSULATOR
3.6.3(a) ELECTRIC FIELD GRAPHS FOR TYPE-C SPACER
Fig-3.40(a) Electric Field Distribution of type-C spacer for Insulator 1 conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Surface: Electrical Potential (V)
Fig-3.40 Electric field plot with εr=9 to εr=3 (linear variation) for type C V-Shape spacer
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263
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.40(c) Electric Field Distribution of type-C spacer
for Insulator 1 conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.40(d) Electric Field Distribution of type-C spacer
for Insulator 1 conductor-2 along Y-axis
Fig-3.40(b) Electric Field Distribution of type-C spacer for
Insulator 1 conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
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264
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.40(e) Electric Field Distribution of type-C spacer
for Insulator 1 conductor-3 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.40(f) Electric Field Distribution of type-C spacer
for Insulator 1 conductor-3 along Y-axis
Radial Co-ordinate in mm
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.40(g) Electric Field Distribution of type-C spacer
for Insulator 2 conductor-1 along X-axis
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265
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.40(i) Electric Field Distribution of type-C spacer
for Insulator 2 conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.40(j) Electric Field Distribution of type-C spacer
for Insulator 2 conductor-2 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.40(h) Electric Field Distribution of type-C spacer for Insulator 2 conductor-1 along Y-axis
Radial Co-ordinate in mm
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266
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.40(l) Electric Field Distribution of type-C spacer
for Insulator 2 conductor-3 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.40(k) Electric Field Distribution of type-C spacer
for Insulator 2 conductor-3 along X-axis
Radial Co-ordinate in mm
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267
In type D spacer, the value of relative permittivity varies (high voltage
electrode to enclosure) linearly from 9 to 3 (50% of the radial co-
ordinate) and then it becomes constant thereafter, the corresponding
electric field plots fig (3.41) and graphs are given in figs (3.41(a) to
3.41(l)).
3.6.4 TYPE D SPACER FOR V-SHAPE INSULATOR
3.6.4(a) ELECTRIC FIELD GRAPHS FOR TYPE-D SPACER
Radial Co-ordinate in mm
Fig-3.41(a) Electric Field Distribution of type-D spacer for Insulator 1 conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.41 Electric field plot with εr=9 to εr=3(variation up to
50% and remains constant) for Type-D V Shape spacer
Surface: Electrical Potential (V)
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268
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.41(b) Electric Field Distribution of type-D
spacer for Insulator 1 conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.41(c) Electric Field Distribution of type-D spacer
for Insulator 1 conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.41(d) Electric Field Distribution of type-D spacer
for Insulator 1 conductor-2 along Y-axis
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269
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.41(e) Electric Field Distribution of type-D spacer
for Insulator 1 conductor-3 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.41(f) Electric Field Distribution of type-D spacer
for Insulator 1 conductor-3 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.41(g) Electric Field Distribution of type-D spacer
for Insulator 2 conductor-1 along X-axis
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270
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.41(h) Electric Field Distribution of type-D spacer for Insulator 2 conductor-1 along Y-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
Fig-3.41(i) Electric Field Distribution of type-D spacer
for Insulator 2 conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
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271
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.41(l) Electric Field Distribution of type-D spacer
for Insulator 2 conductor-3 along Y-axis
Radial Co-ordinate in mm
Fig-3.41(j) Electric Field Distribution of type-D spacer for
Insulator 2 conductor-2 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.41(k) Electric Field Distribution of type-D spacer for
Insulator 2 conductor-3 along X-axis
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Table-3.10 Comparative Values of V-shape Insulator for Insulator-1 Conductor-1 along X and Y axis
Radial
Co-Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1
X (108) Y (108) X (108) Y (108) X (108) Y (108) X
(108) Y (108)
0 -0.12 -0.1 -0.25 -0.25 -0.2 -0.2 -0.12 -0.1
20 -0.06 -0.04 -0.1 -0.1 -0.1 -0.06 -0.08 -0.04
40 -0.08 -0.04 -0.1 -0.1 -0.08 -0.06 -0.08 -0.04
60 -0.06 -0.06 -0.1 -0.1 -0.06 -0.06 -0.08 -0.04
80 -1.3 -1.7 -3 -4 -1.16 -1.3 -1.2 -1.7
100 -0.04 -0.08 -0.1 -0.1 -0.05 -0.04 -0.08 -0.08
120 -0.04 -0.06 -0.1 -0.1 -0.05 -0.1 -0.08 -0.06
140 -0.04 -0.04 -0.1 -0.1 -0.05 -0.1 -0.08 -0.02
160 -0.04 -0.02 -0.1 -0.1 -0.05 -0.1 -0.08 -0.02
180 -0.06 -0.02 -0.1 -0.1 -0.1 -0.1 -0.08 -0.02
Table-3.11 Comparative Values of V-shape Insulator for Insulator-1 Conductor-2 along X and Y axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-2 CONDUCTOR-2 CONDUCTOR-2 CONDUCTOR-2
X (106) Y (107) X (107) Y (107) X (107) Y (107) X (106) Y (107)
0 1.4 -0.8 0.36 -1.5 0.28 -1.25 1.6 -0.8
20 1.2 -0.3 0.14 -0.25 0.2 -0.3 1.2 -0.3
40 1.8 -0.32 0.19 -0.3 0.21 -0.25 1.8 -0.32
60 2.4 -0.38 0.22 -0.3 0.2 -0.25 2.2 -0.38
80 2.8 -0.39 0.2 -0.25 0.2 -0.2 2.8 -0.4
100 4.8 -1.6 0.8 -4 0.8 -2.75 4 -1.7
120 1 -0.46 0.1 -0.4 0.05 -0.25 1 -0.44
140 0.9 -0.38 0.1 -0.35 0.08 -0.3 0.9 -0.39
160 0.8 -0.36 0.08 -0.3 0 -0.5 0.8 -0.34
180 0.5 -0.5 0.02 -0.5 0.1 -0.75 0.6 -0.4
3.6.5 COMPARATIVE TABLES FOR V-SHAPE SPACER
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Table-3.12 Comparative Values of V-shape Insulator for Insulator-1 Conductor-3 along X and Y axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3
X (107) Y (107) X (108) Y (107) X (108) Y (107) X (107) Y (107)
0 -1 0.25 -0.2 0.5 -0.12 0.5 -1 0.25
20 -0.04 0.15 -0.05 0.1 -0.06 0.25 -0.05 0.2
40 -0.04 0.15 -0.05 0.1 -0.06 0.2 -0.05 0.2
60 -0.04 0.2 -0.05 0.15 -0.06 0.2 -0.05 0.2
80 7.4 1.04 1.75 2.55 -1.1 1.85 7.8 1.2
100 -0.04 0 -0.05 0 -0.04 0 -0.05 0
120 -0.04 0 -0.05 0 -0.06 -0.1 -0.05 0
140 -0.04 0.04 -0.05 0 -0.06 -0.04 -0.05 0.1
160 -0.02 0.08 -0.05 0.02 -0.06 0 -0.05 0.1
180 -0.02 0.2 -0.05 0.02 -0.08 0.25 -0.05 0.2
Table-3.13 Comparative Values of V-shape Insulator for Insulator 2 Conductor-1 along X and Y axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1
X (107) Y(107) X (107) Y (107) X (107) Y (108) X (107) Y (107)
0 -1.5 -0.5 -3 -1 -2.5 -0.8 -1.5 -0.5
20 -0.6 -0.1 -0.6 -0.15 -0.08 0 -0.7 -0.1
40 -0.75 -0.04 -0.8 -0.02 -0.08 0.25 -0.75 -0.05
60 -0.8 0 -0.8 0 -0.06 0.25 -0.8 0
80 -0.9 0.08 -0.8 0 -0.5 0 -0.9 0.04
100 0 0.35 -8 -2 -7.4 -2.2 -4 -1
120 -0.8 -0.28 -0.8 -0.25 -0.06 -0.25 -0.8 -0.3
140 -0.75 -0.22 -0.75 -0.25 -0.06 -0.3 -0.7 -0.22
160 -0.6 -0.21 -0.7 -0.25 -0.09 -0.4 -0.6 -0.22
180 -1 -0.4 -1 -0.5 -2 -0.6 -1 -0.4
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Table-3.14 Comparative Values of V-shape Insulator for Insulator-2 Conductor-2 along X and Y axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-2 CONDUCTOR-2 CONDUCTOR-2 CONDUCTOR-2
X (106) Y (107) X (107) Y (107) X (107) Y (107) X (107) Y (107)
0 -1.9 -1 -0.38 -2 -0.3 -1.5 -2 -1
20 -0.08 -0.3 -0.08 -0.35 -0.04 -0.5 -0.8 -0.35
40 -0.09 -0.32 -0.08 -0.35 -0.02 -0.4 -0.9 -0.4
60 -1 -0.4 -0.08 -0.45 -0.02 -0.35 -1 -0.45
80 0.5 0.06 -1.36 -4.08 -0.2 -3.5 -7.2 -2.25
100 -2 -0.35 -0.1 -0.3 -1.1 -0.25 -2 -0.35
120 -2.1 -0.35 -0.2 -0.4 -0.24 -0.25 -2 -0.3
140 -1.5 -0.3 -0.18 -0.4 -0.22 -0.3 -1.5 -0.3
160 -1.1 -0.25 -0.1 -0.35 -0.2 -0.35 -1.1 -0.25
180 -1.1 -0.3 -0.2 -0.5 -0.2 -0.5 -1.1 -0.5
Table-3.15 Comparative Values of V-shape Insulator for Insulator 2
Conductor-3 along X and Y axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3
X (107) Y (107) X (107) Y (107) X (107) Y (107) X (107) Y (107)
0 -0.6 0.58 -1.25 1 -1 0.8 -0.6 0.58
20 -0.2 0.24 -0.25 0.25 -0.25 0.35 -0.2 0.24
40 -0.2 0.32 -0.25 0.4 -0.2 0.35 -0.2 0.34
60 -0.2 0.38 -0.2 0.45 -0.2 0.35 -0.2 0.39
80 -0.2 0.4 -0.15 0.4 -0.1 0.25 -0.2 0.4
100 0.2 1.52 -2.75 3 -2.75 2.5 -1.4 1.5
120 -0.34 0.3 -0.3 0.25 -0.25 0.25 -035 0.3
140 -0.28 0.28 -0.25 0.25 -0.25 0.25 -0.25 0.2
160 -0.24 0.22 -0.25 0.25 -0.5 0.25 -0.2 0.1
180 -0.4 0.21 -0.5 0.35 -0.75 0.4 -0.4 0.28
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3.6.6 COMPARATIVE ELECTRIC FIELD STRESS GRAPH FOR V-
SHAPE SPACER
Fig-3.42 Electric Field Stress distribution for Insulator-1
Conductor-1 along X-axis
Fig-3.43 Electric Field Stress distribution for Insulator-1
Conductor-1 along Y-axis
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Fig-3.44 Electric Field Stress distribution for Insulator-1
Conductor-2 along X-axis
Fig-3.45 Electric Field Stress distribution for Insulator-1
Conductor-2 along Y-axis
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Fig-3.46 Electric Field Stress distribution for Insulator-1
Conductor-3 along X-axis
Fig-3.47 Electric Field Stress distribution for Insulator-1 Conductor-3
along Y-axis
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Fig-3.48 Electric Field Stress distribution for Insulator-2
Conductor-1 along X-axis
Fig-3.49 Electric Field Stress distribution for Insulator-2
Conductor-1 along Y-axis
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Fig-3.50 Electric Field Stress distribution for Insulator-2 Conductor-2
along X-axis
Fig-3.51 Electric Field Stress distribution for Insulator-2 Conductor-
2 along Y-axis
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From graphs the comparative values of maximum field strength
(V/mm) in various types of spacers are shown in tables (3.10 to 3.15).
Comparative values of electric field stress (kV/mm) in various types of
spacer in fig (3.42 to 3.53).
Fig-3.52 Electric Field Stress distribution for Insulator-2
Conductor-3 along X-axis
Fig-3.53 Electric Field Stress distribution for Insulator-2
Conductor-3 along Y-axis
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� In the proposed work, various types of FGM spacers have been
considered. In type A spacer, the value of the relative
permittivity εr = 3 is constant the corresponding electric field
plots and graphs are shown in figs (3.38 to 3.38(i)), where as for
type B spacer, the corresponding value of the permittivity εr = 6
right from high voltage electrode to enclosure, the corresponding
electric field plots and graphs are shown in figs (3.39 to 3.39(i)).
In type C spacer, the value of relative permittivity varies linearly
from 9 to 3, the corresponding electric field plots and graphs
are shown in figs(3.40 to 3.40(i)). In type D spacer, the value of
relative permittivity varies linearly from 9 to 3 (up to 50% of the
radial co-ordinate) and then it becomes constant thereafter, the
corresponding electric field plots and graphs are shown in
figs(3.41 to 3.41(i)).
� The comparative values of maximum field strength in various
types of spacers are shown in table (3.10 to 3.15).
� From fig (3.42), for insulator-1 conductor-1 along X-axis, in
type-A spacer, the electric field stress value from the surface of
the conductor is -300kV/mm and it increases to -33kV/mm
under the radial co-ordinate of 20 to 180 mm. In type-B spacer,
the electric field stress value from the surface of the conductor
is -500kV/mm and it increases to -55kV/mm under the radial
co-ordinate of 20 to 180 mm. In type-C spacer, the electric field
3.6.7 RESULTS AND DISCUSSIONS FOR V-SHAPE SPACER
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stress value from the surface of the conductor is -500kV/mm
and it increases to -55kV/mm under the radial co-ordinate of
20 to 180 mm. In type-D spacer, the electric field stress value
from the surface of the conductor is -400kV/mm and it
increases to -44kV/mm under the radial co-ordinate of 20 to
180 mm.
� From fig (3.43), for insulator-1 conductor-1 along Y-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -200kV/mm to -
11kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -500kV/mm to -
55kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -300kV/mm to
-55kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -200kV/mm to
-11kv/mm under the radial co-ordinate of 20 to 180 mm.
� From fig (3.44), for insulator-1 conductor-2 along X-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 60kV/mm to
2.77kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
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surface of the conductor to the enclosure with 70kV/mm to
1.11kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 100kV/mm to
5.55kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 60kV/mm to
3.33kV/mm under the radial co-ordinate of 20 to 180 mm.
� From fig (3.45), for insulator-1 conductor-2 along Y-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -150kV/mm to -
27kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -125kV/mm to -
27kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -150kV/mm to
-41kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -150kV/mm to
-22kV/mm under the radial co-ordinate of 20 to 180 mm.
� From fig (3.46), for insulator-1 conductor-3 along X-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -20kV/mm to -
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1.1kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -250kV/mm to -
27kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -300kV/mm to
-44kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -25kV/mm to -
2.7kV/mm under the radial co-ordinate of 20 to 180 mm.
� From fig (3.47), for insulator-1 conductor-3 along Y-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 75kV/mm to
11.1kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 50kV/mm to
1.11kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 125kV/mm to
13.8kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 100kV/mm to
11.1kV/mm under the radial co-ordinate of 20 to 180 mm.
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� From fig (3.48), for insulator-2 conductor-1 along X-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -300kV/mm to -
55kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -300kV/mm to -
55kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -40kV/mm to
-111kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -350kV/mm to -
55kV/mm under the radial co-ordinate of 20 to 180 mm.
� From fig (3.49), for insulator-2 conductor-1 along Y-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -50kV/mm to -
22kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -75kV/mm to -
27kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 0kV/mm to
-333kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
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surface of the conductor to the enclosure with -50kV/mm to -
22kV/mm under the radial co-ordinate of 20 to 180 mm.
� From fig (3.50), for insulator-2 conductor-2 along X-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -4kV/mm to -
6.1kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -40kV/mm to -
11kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -20kV/mm to
-11kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -400kV/mm to -
61kV/mm under the radial co-ordinate of 20 to 180 mm.
� From fig (3.51), for insulator-2 conductor-2 along Y-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -150kV/mm to -
16kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -175kV/mm to -
27kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -250kV/mm to -
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27kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -175kV/mm to
-27kV/mm under the radial co-ordinate of 20 to 180 mm.
� From fig (3.52), for insulator-2 conductor-3 along X-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -100kV/mm to -
22kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -125kV/mm to -
27kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -125kV/mm to
-41kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with -100kV/mm to
-22kV/mm under the radial co-ordinate of 20 to 180 mm.
� From fig (3.53), for insulator-2 conductor-3 along Y-axis, in
type–A spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 120 kV/mm to
11.6kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-B spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 125 kV/mm to
19.4kV/mm under the radial co-ordinate of 20 to 180 mm. In
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288
type-C spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 175kV/mm to
22.2kV/mm under the radial co-ordinate of 20 to 180 mm. In
type-D spacer, the electric field stress value varies from the
surface of the conductor to the enclosure with 120kV/mm to
15.5kV/mm under the radial co-ordinate of 20 to 180 mm.
� From the above results, the electric field stress on surface on
the conductor of Type-D spacer is reduced when compared to
Type-A, Type-B and Type-C.
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289
In type A spacer, the value of the relative permittivity, εr = 3 is
constant right from high voltage electrode to enclosure and the
corresponding electric field plots fig(3.54) and graphs are given in figs
(3.54(a) to 3.54(f))
3.7 MODEL-5: DETAILED ANALYSIS OF DELTA-SHAPE
INSULATOR
3.7.1 TYPE A SPACER FOR DELTA SHAPE INSULATOR
Fig-3.54 Electric field plot with εr=3(constant) for Type-A Delta
shape spacer
Surface: Electrical Potential (V)
3.7.1(a) ELECTRIC FIELD GRAPHS FOR TYPE-A SPACER
Fig-3.54(a) Electric Field Distribution of type-A Spacer for conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
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290
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.54(c) Electric Field Distribution of type-A Spacer
for conductor-2 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.54(d) Electric Field Distribution of type-A Spacer for conductor-2 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.54(b) Electric Field Distribution of type-A Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
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291
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.54(f) Electric Field Distribution of type-A Spacer
for conductor-3 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.54(e) Electric Field Distribution of type-A Spacer
for conductor-3 along X-axis
Radial Co-ordinate in mm
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292
In type B spacer, the corresponding value of the relative permittivity,
εr = 6 right from high voltage electrode to enclosure, the corresponding
electric field plots figs(3.55) and graphs are given in figs (3.55(a) to
3.55(f))
3.7.2 TYPE B SPACER FOR DELTA SHAPE INSULATOR
3.7.2(a) ELECTRIC FIELD GRAPHS FOR TYPE-B SPACER
Fig-3.55 Electric field plot with εr=6(constant) for Type-B
Delta shape spacer
Surface: Electrical Potential (V)
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.55(a) Electric Field Distribution of type-B Spacer
for conductor-1 along X-axis
Radial Co-ordinate in mm
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293
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.55(b) Electric Field Distribution of type-B Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.55(c) Electric Field Distribution of type-B Spacer
for conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.55(d) Electric Field Distribution of type-B Spacer
for conductor-2 along Y-axis
Radial Co-ordinate in mm
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294
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.55(f) Electric Field Distribution of type-B Spacer
for conductor-3 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.55(e) Electric Field Distribution of type-B Spacer
for conductor-3 along X-axis
Radial Co-ordinate in mm
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295
In type C spacer, the value of relative permittivity varies linearly from
high voltage electrode to enclosure (εr=9 to 3), the corresponding
electric field plots fig (3.56) and graphs are given in figs (3.56(a) to
3.56(f))
3.7.3(a) ELECTRIC FIELD GRAPHS FOR TYPE-C SPACER
3.7.3 TYPE C SPACER FOR DELTA SHAPE INSULATOR
Fig-3.56 Electric field plot with εr=9 to εr=3 (linear
variation) for type C Delta shape spacer
Surface: Electrical Potential (V)
Fig-3.56(a) Electric Field Distribution of type-C Spacer for conductor-1 along X-axis
along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
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296
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.56(d) Electric Field Distribution of type-C Spacer for conductor-2 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.56(b) Electric Field Distribution of type-C Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.56(c) Electric Field Distribution of type-C Spacer
for conductor-2 along X-axis
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297
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.56(e) Electric Field Distribution of type-C Spacer
for conductor-3 along X-axis
Radial Co-ordinate in mm
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.56(f) Electric Field Distribution of type-C Spacer
for conductor-3 along Y-axis
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298
3.7.4(a) ELECTRIC FIELD GRAPHS FOR TYPE-D SPACER
3.7.4 TYPE D SPACER FOR DELTA SHAPE INSULATOR
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.57(a) Electric Field Distribution of type-D Spacer
for conductor-1 along X-axis
Radial Co-ordinate in mm
Surface: Electrical Potential (V)
Fig-3.57 Electric field plot with εr=9 to εr=3(variation up to
50% and remains constant) for Type-D Delta shape spacer
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299
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.57(b) Electric Field Distribution of type-D Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.57(c) Electric Field Distribution of type-D Spacer
for conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.57(d) Electric Field Distribution of type-D Spacer
for conductor-2 along Y-axis
Radial Co-ordinate in mm
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300
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.57(e) Electric Field Distribution of type-D Spacer
for conductor-3 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.57(f) Electric Field Distribution of type-D Spacer
for conductor-3 along Y-axis
Radial Co-ordinate in mm
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301
Table-3.16 Comparative values of Delta shape Insulator for Conductor-1 along X and Y axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1
X (107) Y (107) X (107) Y (107) X (107) Y (107) X (107) Y (107)
0 0 0.5 0.7 0.3 -0.8 0.4 -0.8 -0.3
50 -4.5 -2.7 -3.5 -2.3 -0.9 -0.5 -0.6 -2
100 -0.5 0.5 -0.3 0.5 -2 -0.5 -2.5 -2
150 -0.5 -0.75 -0.5 -0.75 -0.5 -0.8 -0.5 -0.9
200 0.4 -0.5 0.25 -0.5 0.5 -0.5 0.4 -0.5
250 0.5 -2.5 0.5 -0.25 0.6 -0.25 0.6 -0.4
300 0.8 2.5 0.75 0.25 0.9 0.25 0.8 0.2
350 0.5 0.75 0.5 0.75 0.5 0.75 0.5 0.4
400 -0.2 0.7 0 0.6 0 0.4 0 0.25
450 -0.5 0.5 -0.5 0.5 -0.5 0.3 -0.5 0.25
Table-3.17 Comparative values of Delta shape Insulator for Conductor-2 along X and Y axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1
X (106) Y (106) X (106) Y (106) X (107) Y (107) X (107) Y (107)
0 3.5 0.1 3.5 0.9 0.4 0.2 0.4 0.2
50 4.5 2 4.5 3 0.5 0.4 0.5 0.4
100 2 4.5 2 5 0.2 0.6 0.3 0.5
150 -0.5 2 -0.5 1.5 -0.1 0.3 -0.1 0.3
200 -2 0 -1.5 0.2 -0.19 0 -0.2 0.2
250 -2.5 0.5 -2.8 1 -0.3 -0.2 -0.3 -0.2
300 -1 -4 -1 -4.5 -0.1 -0.5 0 -0.6
350 0 -4.5 0 -4.5 0 -0.3 0 -1.4
400 1 -4 1 -4.2 0.1 -0.5 0 -0.7
450 3.2 -1 3.5 -1 0.4 -0.1 0.4 -0.2
3.7.5 COMPARATIVE TABLES FOR DELTA SHAPE SPACER
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302
From graphs the comparative values of maximum field strength
(V/mm) in various types of spacers are shown in tables (3.16 to 3.18).
Comparative values of electric field stress (kV/mm) in various types of
spacer in fig (3.58 to 3.63).
Table-3.18 Comparative values of Delta shape Insulator for Conductor-3 along X and Y axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3
X (107) Y (107) X (107) Y (107) X (107) Y (107) X (107) Y (107)
0 0.5 0.2 0.4 0.25 0.5 0.28 0.5 0.25
50 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
100 -0.2 0.4 -0.2 0.4 -0.2 0.45 -0.2 0.45
150 -0.9 0 -0.7 0 -1.4 -0.3 -2 3.5
200 -0.5 0.2 -0.5 0 -0.4 0.4 -0.3 1.5
250 -0.4 -0.1 0 -0.1 -0.4 -0.2 -0.5 -0.1
300 -0.2 -0.3 -0.2 -0.19 -0.1 -0.19 -0.1 -0.2
350 0 -0.4 0 -0.1 0 -0.1 0 -0.2
400 0.4 -0.3 0.4 -0.19 0.4 -0.19 0.5 -0.2
450 0.7 0.2 0.7 0.1 0.7 0.1 0.7 0.2
3.7.6 COMPARATIVE ELECTRIC FIELD STRESS GRAPHS
FOR DELTA SHAPE SPACER
Fig-3.58 Electric Field Stress Distribution for Conductor-1 along X-axis
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303
Fig-3.59 Electric Field stress Distribution for Conductor-1 along Y-axis
Fig-3.60 Electric Field stress Distribution for Conductor-2 along X-axis
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304
Fig-3.61 Electric Field stress Distribution for Conductor-2 along Y-axis
Fig-3.62 Electric Field stress Distribution for Conductor-3
along X-axis
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305
� In the proposed work, various types of FGM spacers have been
considered. In type A spacer, the value of the relative
permittivity εr = 3 is constant the corresponding electric field
plots and graphs are shown in figs (3.54 to 3.54(f)), where as for
type B spacer, the corresponding value of the permittivity εr = 6
right from high voltage electrode to enclosure, the corresponding
electric field plots and graphs are shown in figs (3.55 to 3.55(f)).
In type C spacer, the value of relative permittivity varies linearly
from 9 to 3, the corresponding electric field plots and graphs
are shown in figs(3.56 to 3.56(f)). In type D spacer, the value of
relative permittivity varies linearly from 9 to 3 (up to 50% of the
radial co-ordinate) and then it becomes constant thereafter, the
3.7.7 RESULTS AND DISCUSSIONS FOR DELTA SHAPE SPACER
Fig-3.63 Electric Field stress Distribution for Conductor-3 along Y-axis
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306
corresponding electric field plots and graphs are shown in
figs(3.57 to 3.57(f)).
� The comparative values of maximum field strength in various
types of spacers are shown in table (3.16 to 3.18).
� From fig (3.58), for conductor 1 along X-axis, in type-A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -900kV/mm to -11kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -700kV/mm to -11kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -180kV/mm to -11kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-D spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -120kV/mm to -11kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From fig (3.59), for conductor 1 along Y-axis, in the type–A
spacer, the electric field stress value varies from the surface of
the conductor to the enclosure with -540kV/mm to 11.1kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -460kV/mm to 11.1kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
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307
the electric field stress value varies from the surface of the
conductor to the enclosure with -100kV/mm to 6.66kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-D spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -400kV/mm to 5.55kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From fig (3.60), for conductor 2 along X-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 90kV/mm to 7.11kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 90kV/mm to 7.77kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 10kV/mm to 0.88kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-D spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 10kV/mm to 0.88kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From fig (3.61), for conductor 2 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 40kV/mm to -2.2kV/mm under
the radial co-ordinate of 50 to 450 mm. In type-B spacer, the
electric field stress value varies from the surface of the
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308
conductor to the enclosure with 60kV/mm to -2.2kV/mm under
the radial co-ordinate of 50 to 450 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 8kV/mm to -0.2kV/mm under
the radial co-ordinate of 50 to 450 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 8kV/mm to -0.4kV/mm under
the radial co-ordinate of 50 to 450 mm.
� From fig(3.62), for conductor 3 along X-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 60kV/mm to 15.5kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 60kV/mm to 15.5kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 60kV/mm to 15.5kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-D spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 60kV/mm to 15.5kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From fig (3.63), for conductor 3 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 60kV/mm to 4.44kV/mm
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309
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 60kV/mm to 2.22kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 60kV/mm to 2.22kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-D spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 60kV/mm to 4.44kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From the above results, the electric field stress on surface on
the conductor of Type-D spacer is reduced when compared to
Type-A, Type-B and Type-C.
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310
In type A spacer, the value of the relative permittivity, εr = 3 is
constant right from high voltage electrode to enclosure and the
corresponding electric field plots fig(3.64) and graphs are given in figs
(3.64(a) to 3.64(f))
3.8.1(a) ELECTRIC FIELD GRAPHS FOR TYPE A SPACER
Fig-3.64(a) Electric Field Distribution of type-A Spacer for conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
3.8 MODEL-6: DETAILED ANALYSIS OF BULB-INSIDE
INSULATOR
3.8.1 TYPE A SPACER FOR BULB-INSIDE INSULATOR
Fig-3.64 Electric field plot with εr=3(constant) for Type-A
Bulb Inside Shape spacer
Surface: Electrical Potential (V)
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311
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.64(b) Electric Field Distribution of type-A Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.64(c) Electric Field Distribution of type-A Spacer
for conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.64(d) Electric Field Distribution of type-A Spacer for conductor-2 along Y-axis
Radial Co-ordinate in mm
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312
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.64(e) Electric Field Distribution of type-A Spacer
for conductor-3 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.64(f) Electric Field Distribution of type-A Spacer
for conductor-3 along Y-axis
Radial Co-ordinate in mm
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313
In type B spacer, the corresponding value of the relative permittivity,
εr = 6 right from high voltage electrode to enclosure, the corresponding
electric field plots figs(3.65) and graphs are given in figs (3.65(a) to
3.65(f))
3.8.2 TYPE B SPACER FOR BULB-INSIDE INSULATOR
3.8.2(a) ELECTRIC FIELD GRAPHS FOR TYPE B SPACER
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.65(a) Electric Field Distribution of type-B Spacer
for conductor-1 along X-axis
Radial Co-ordinate in mm
Fig-3.65 Electric field plot with εr=6(constant) for
Type-B Bulb Inside shape spacer
Surface: Electrical Potential
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314
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.65(b) Electric Field Distribution of type-B Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.65(c) Electric Field Distribution of type-B Spacer
for conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.65(d) Electric Field Distribution of type-B Spacer
for conductor-2 along Y-axis
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315
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.65(e) Electric Field Distribution of type-B Spacer
for conductor-3 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.65(f) Electric Field Distribution of type-B Spacer
for conductor-3 along Y-axis
Radial Co-ordinate in mm
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316
3.8.3(a) ELECTRIC FIELD GRAPHS FOR TYPE-C SPACER
3.8.3 TYPE C SPACER FOR POST INSIDE INSULATOR
Fig-3.66 Electric field plot with εr=9 to εr=3 (linear
variation) for type C Bulb inside shape spacer
Surface: Electrical Potential (V)
Fig-3.66(a) Electric Field Distribution of type-C Spacer for conductor-1 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Radial Co-ordinate in mm
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317
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.66(b) Electric Field Distribution of type-C Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.66(c) Electric Field Distribution of type-C Spacer
for conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.66(d) Electric Field Distribution of type-C Spacer for conductor-2 along Y-axis
Radial Co-ordinate in mm
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318
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.66(e) Electric Field Distribution of type-C Spacer
for conductor-3 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig 3.66(f) Electric Field Distribution of type-C Spacer
for conductor-3 along Y-axis
Radial Co-ordinate in mm
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319
In type D spacer, the value of relative permittivity varies (high voltage
electrode to enclosure) linearly from 9 to 3 (50% of the radial co-
ordinate) and then it becomes constant thereafter, the corresponding
electric field plots fig (3.67) and graphs are given in figs (3.67(a) to
3.67(f)).
3.8.4(a) ELECTRIC FIELD GRAPHS FOR TYPE-D SPACER
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.67(a) Electric Field Distribution of type-D Spacer
for conductor-1 along X-axis
Radial Co-ordinate in mm
3.8.4 TYPE D SPACER FOR BULB INSIDE INSULATOR
Fig-3.67 Electric field plot with εr=9 to εr=3(variation up to 50%
and remains constant) for Type-D Bulb inside shape spacer
Surface: Electrical Potential (V)
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320
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.67(c) Electric Field Distribution of type-D Spacer
for conductor-2 along X-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.67(d) Electric Field Distribution of type-D Spacer for
conductor-2 along Y-axis
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.67(b) Electric Field Distribution of type-D Spacer
for conductor-1 along Y-axis
Radial Co-ordinate in mm
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321
Radial Co-ordinate in mm
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.67(e) Electric Field Distribution of type-D Spacer
for conductor-3 along X-axis
Ele
ctri
c F
ield
Str
ength
in V
/ m
m
Fig-3.67(f) Electric Field Distribution of type-D Spacer
for conductor-3 along Y-axis
Radial Co-ordinate in mm
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322
Table-3.19 Comparative Values of Bulb inside shape insulator for Conductor-1 along X and Y-axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1 CONDUCTOR-1
X (107) Y (106) X (107) Y (106) X (107) Y (107) X (107) Y (107)
0 0.1 1 0.3 1.8 -0.2 0 -0.2 0
50 -0.8 -4 -0.8 -4 -0.8 -0.3 -0.8 -0.3
100 -0.7 2 -0.7 2 -0.7 0.3 -0.7 0.3
150 -0.3 6 -0.3 5 -0.3 -0.7 -0.3 0.6
200 0.3 7 0.2 7 0.3 0.8 0.3 0.7
250 0.7 4 0.7 4 0.7 0.5 0.8 0.4
300 0.6 -2 0.6 -2 0.6 -0.3 0.7 -0.3
350 0.3 -6 0.1 -5 0.3 -0.7 0.4 -0.6
400 -0.2 -7 -0.2 -7 -0.3 -0.8 -0.3 -0.7
450 -0.7 -5 -0.7 -5 -0.7 -0.6 -0.8 -0.5
Table-3.20 Comparative Values of Bulb inside shape insulator for Conductor-2 along X and Y-axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-2 CONDUCTOR-2 CONDUCTOR-2 CONDUCTOR-2
X (106) Y (106) X (106) Y (106) X (107) Y (106) X (106) Y (106)
0 0 0 -2 0 0 -0.25 0 0
50 1 -4.5 1 -4.5 0.15 -4.5 0.8 -4.5
100 3 -2.4 2.5 -2.4 0.3 -2.4 3 -3
150 4.5 0.6 4 0.3 0.45 0 4.5 0
200 4 4.5 4 4.2 0.4 5 4 5
250 0.5 4 0 4 0 4 0.5 4
300 -1 1 -1 1 -0.1 1.6 -1 1
350 -2.3 0 -2 0 -0.23 0 -2.5 0
400 -2 -3 -2 -2.5 -0.23 -2.5 -2.3 -3
450 -1 -4 -1 -4 -0.1 -4.2 -0.5 -4
3.8.5 COMPARATIVE TABLES FOR BULB INSIDE SPACER
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323
From graphs the comparative values of maximum field strength
(V/mm) in various types of spacers are shown in tables (3.19 to 3.21).
Comparative values of electric field stress (kV/mm) in various types of
spacer in fig (3.68 to 3.73).
Table-3.21 Comparative Values of Bulb inside shape insulator for Conductor-3 along X and Y-axis
Radial Co-
Ordinate
(mm)
ELECTRIC FIELD STRENGTH ON 3-Ф CONDUCTORS (V / mm)
TYPE-A TYPE-B TYPE-C TYPE-D
CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3 CONDUCTOR-3
X (106) Y (106) X (106) Y (106) X (106) Y (106) X (107) Y (106)
0 0.3 0 0.3 0.2 0 0.2 0 0.2
50 -3.5 2.5 -4 2.5 -3.8 2.9 -0.37 3
100 -0.9 3.5 -1 3.5 -1 4 -0.15 4
150 2 3.25 2 3.25 2.5 3.7 0.2 3.9
200 6 1 6 1 6.4 1 0.65 1
250 4 -1.5 3 -1.5 4 -2 0.4 -1.9
300 0.3 -1.75 0.4 -1.75 0 -1.5 0.2 -1.8
350 0.9 -2 -1.5 -1.3 -1.9 -2.3 -0.9 -2
400 -3.8 -0.5 -3.6 0 -4 -1 -0.4 -0.7
450 -3.9 2 -4 2 -4 1.5 -0.4 1.8
3.8.6 COMPARATIVE ELECTRIC FIELD STRESS FOR BULB
INSIDE SPACER
Fig-3.68 Electric Field Stress Distribution for Conductor-1 along X-axis
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324
Fig-3.69 Electric Field Stress Distribution for Conductor-1 along Y-axis
Fig-3.70 Electric Field Stress Distribution for Conductor-2 along X-axis
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325
Fig-3.71 Electric Field Stress Distribution for Conductor-2 along Y-axis
Fig-3.72 Electric Field Stress Distribution for Conductor-3 along X-axis
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326
� In the proposed work, various types of FGM spacers have been
considered. In type A spacer, the value of the relative
permittivity εr = 3 is constant the corresponding electric field
plots and graphs are shown in figs (3.64 to 3.64(f)), where as for
type B spacer, the corresponding value of the permittivity εr = 6
right from high voltage electrode to enclosure, the corresponding
electric field plots and graphs are shown in figs (3.65 to 3.65(f)).
In type C spacer, the value of relative permittivity varies linearly
from 9 to 3, the corresponding electric field plots and graphs
are shown in figs(3.66 to 3.66(f)). In type D spacer, the value of
3.8.7 RESULTS AND DISCUSSIONS FOR BULB INSIDE SPACER
Fig-3.73 Electric Field Stress Distribution for Conductor-3 along Y-axis
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327
relative permittivity varies linearly from 9 to 3 (50% of the radial
co-ordinate) and then it becomes constant thereafter, the
corresponding electric field plots and graphs are shown in figs
(3.67 to 3.67(f)).
� The comparative values of maximum field strength in various
types of spacers are shown in table (3.19 to 3.21).
� From fig (3.68), for conductor 1 along X-axis, in type-A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -160kV/mm to -15kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -160kV/mm to -15kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -160kV/mm to -15kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-D spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -160kV/mm to -17kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From fig (3.69), for conductor 1 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -80kV/mm to -11kV/mm under
the radial co-ordinate of 50 to 450 mm. In type-B spacer, the
electric field stress value varies from the surface of the
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328
conductor to the enclosure with -80kV/mm to -11kV/mm under
the radial co-ordinate of 50 to 450 mm. In type-C spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -60kV/mm to -13kV/mm under
the radial co-ordinate of 50 to 450 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with -60kV/mm to -11kV/mm under
the radial co-ordinate of 50 to 450 mm.
� From fig (3.70), for conductor 2 along X-axis, in type-A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 20kV/mm to -2.22kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 20kV/mm to -2.22kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 3kV/mm to -0.22kV/mm under
the radial co-ordinate of 50 to 450 mm. In type-D spacer, the
electric field stress value varies from the surface of the
conductor to the enclosure with 16kV/mm to -1.11kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From fig (3.71), for conductor 2 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -90kV/mm to -8.8kV/mm
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329
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -90kV/mm to -8.8kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -90kV/mm to -9.3kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-D spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -90kV/mm to -8.8kV/mm
under the radial co-ordinate of 50 to 450 mm.
� From fig (3.72), for conductor 3 along X-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -70kV/mm to -8.6kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -80kV/mm to -8.8kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -76kV/mm to -8.8kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-D spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with -74kV/mm to -8.8kV/mm
under the radial co-ordinate of 50 to 450 mm.
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� From fig (3.73), for conductor 3 along Y-axis, in type–A spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 50kV/mm to 4.44kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-B spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 50kV/mm to 4.44kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-C spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 58kV/mm to 3.33kV/mm
under the radial co-ordinate of 50 to 450 mm. In type-D spacer,
the electric field stress value varies from the surface of the
conductor to the enclosure with 600kV/mm to 40kV/mm under
the radial co-ordinate of 50 to 450 mm.
� From the above results, the electric field stress on surface on
the conductor of Type-C spacer is reduced when compared to
Type-A, Type-B and Type-D.
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In table 3.22 shows comparision of different three phase models
Note: Materials used for all three phase Insulators are:
� Conductor and Enclosure is Aluminum � Insulator is Epoxy Resin
� In reference to the above table,
dC = Diameter of the Conductor
dE = Diameter of the Enclosure
TE = Thickness of the Enclosure
TC = Thickness of the Conductor
X1C = Path-1 Conductor-1 X-axis
X1CI1 = Path-1 Conductor-1 Insulator-1 X-axis
X1CI2 = Path-1 Conductor-1 Insulator-2 X-axis
Table-3.22 Comparative models in three phase GIS
Features Bulb Shape Insulator
Post Shape Insulator
Rib Shape Insulator
V-Shape Insulator
Delta Shape Insulator
Bulb Inside Shape
Insulator
Design
Modeling
dC = 89mm dE = 508mm TE =6.4mm TC = 12.7mm Gas = SF6
dC = 89mm dE = 508mm TE =6.4mm TC = 12.7mm Gas = SF6
dC = 89mm dE = 508mm TE =6.4mm TC = 12.7mm Gas = SF6
dC = 89mm dE = 508mm TE =6.4mm TC = 12.7mm Gas = SF6
dC = 89mm dE = 508mm TE =6.4mm TC = 12.7mm Gas = SF6
dC = 89mm dE = 508mm TE =6.4mm TC = 12.7mm Gas = SF6
Electric Field Stress for TYPE-D Spacer
X1C Axis = -70kV/mm
X1C Axis = 0.01kV/mm
X1 Axis = -35kV/mm
X1CI1 Axis = -80kV/mm X1CI2-Axis = -400kV/mm
X1C Axis = -250kV/mm
X1C Axis = -7.5kV/mm
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3.9 SUMMARY
In this chapter, a complex three phase common enclosure
system is considered for insulation studies. The critical electrical
stress on surface of three phase have been estimated by using
different shapes of insulators. The estimation and reduction of Electric
Stress in Gas Insulated Systems is one of the important factors to
maintain insulating properties of spacers. In the proposed work, the
estimation and reduction of Electric stress on the surface of electrode
has been verified. In order to verify the effect of shape of spacer on
surface field, various insulator shapes like Bulb shape Insulator, Post
shape Insulator, Rib shape insulator, V shape Insulator, Delta shape
Insulator and Bulb inside shape Insulator have been considered for
numerical simulation. In order to verify the effect of Functionally
Graded Insulating material, the surface field was estimated for various
materials.
From the results, the following conclusions have been drawn.
A typical three phase GIS models have considered for numerical
simulation. The results obtained from the single phase GIS model are
summarized as follows:
� BULB SHAPE INSULATOR
� From Fig-3.12, it is concluded that the electric field stress on
the surface of conductor for conventional spacer along
conductor-1 along X-axis is -50kV/mm and it gradually
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decreases to -70kV/mm, when using the functionally Graded
material.
� The electric field stress on surface of conductor along X-axis is
reduced by 28.57%.
� POST TYPE INSULATOR
� From Fig-3.22, it is concluded that the electric field stress on
the surface of conductor for conventional spacer along
conductor-1 along X-axis is 20kV/mm and it gradually
decreases to 0.01kV/mm, when using the functionally Graded
material.
� The electric field stress on surface of conductor along X-axis is
reduced by 99.95%.
� RIB TYPE INSULATOR
� From Fig-3.32, it is concluded that the electric field stress on
the surface of conductor for conventional spacer along
conductor-1 along X-axis is -30kV/mm and it gradually
decreases to -35kV/mm, when using the functionally Graded
material.
� The electric field stress on surface of conductor along X-axis is
reduced by 14.28%.
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� V SHAPE INSULATOR
� From Fig-3.42, it is concluded that the electric field stress on
the surface of conductor for conventional spacer along
Insulator-1 conductor-1 along X-axis for Insulator-1 Conductor-
1 is -40kV/mm and it gradually decreases to -80kV/mm, when
using the functionally Graded material.
� The electric field stress on surface of conductor along X-axis is
reduced by 50%.
� From Fig-3.48, it is concluded that the electric field stress on
the surface of conductor for conventional spacer along
insulator-2 conductor-1 along X-axis for Insulator-2 Conductor-
1 is -100kV/mm and it gradually decreases to -400kV/mm,
when using the functionally Graded material.
� The electric field stress on surface of conductor along X-axis is
reduced by 75%.
� DELTA SHAPE INSULATOR
� From Fig-3.58, it is concluded that the electric field stress on
the surface of conductor for conventional spacer along
condeuctor-1 along X-axis is -50kV/mm and it gradually
decreases to -250kV/mm, when using the functionally Graded
material.
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� The electric field stress on surface of conductor along X-axis is
reduced by 80%.
� BULB INSIDE SHAPE INSULATOR
� From Fig-3.68, it is concluded that the electric field stress on
the surface of conductor for conventional spacer along
conductor-1 along X-axis is -5kV/mm gradually decreases to
-7.5kV/mm, when using the functionally Graded material.
� The electric field stress on surface of conductor along X-axis is
reduced by 33.33%.
For three phase GIS system, from the results it can be concluded
that Post type spacer resulted in minimum electric field stress when
compared to Rib shape, Bulb inside, Bulb shape, V-shape and Delta
shape Insulators.