modelling and analysis of functionally graded material...

183

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

184

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

185

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

186

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

187

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

188

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

189

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

190

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


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.8(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-3.8(d) Electric Field Distribution of type-A Spacer for conductor-2 along Y-axis

191


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.8(e) Electric Field Distribution of type-A Spacer for



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.8(f) Electric Field Distribution of type-A Spacer for


192

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


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



193

Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.9(b) Electric Field Distribution of type-B Spacer for



Fig-3.9(c) Electric Field Distribution of type-B Spacer for


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.9(d) Electric Field Distribution of type-B Spacer for


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

194


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.9(e) Electric Field Distribution of type-B Spacer for


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.9(f) Electric Field Distribution of type-B Spacer for



195

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


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


196


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


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


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig.3.10(d) Electric Field Distribution of type-C Spacer


197


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig.3.10(e) Electric Field Distribution of type-C Spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig.3.10(f) Electric Field Distribution of type-C spacer


198

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


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


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig.3.11(a) Electric Field Distribution of type-D Spacer for


199

Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig.3.11(b) Electric Field Distribution of type-D Spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig.3.11(c) Electric Field Distribution of type-D Spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig.3.11(d) Electric Field Distribution of type-D Spacer


200

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig.3.11(e) Electric Field Distribution of type-D Spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig.3.11(f) Electric Field Distribution of type-D Spacer



201

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)


TYPE-A TYPE-B

TYPE-C TYPE-D


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

202

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)




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

203


Fig-3.13 Electric field stress distribution for conductor-1 along Y-axis

204

Fig- 3.15 Electric field stress distribution for conductor-2 along Y-axis

205

� 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



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,



under the radial co-ordinate of 50 to 450 mm. In type-C spacer,


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


under the radial co-ordinate of 50 to 450 mm.

� From fig (3.13), for conductor 1 along Y-axis, in type–A spacer,





conductor to the enclosure with -120kV/mm to -8.88kV/mm

207



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,









2222kV/mm under the radial co-ordinate of 50 to 450 mm. In








208










� From fig (3.16), for conductor 3 along X-axis type–A spacer, the





conductor to the enclosure with 920kV/mm to 9.87kV/mm



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






209







conductor to the enclosure with 0.04kV/mm to 0kV/mm under





� 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.

210




(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


3.4.1(a) ELECTRIC FIELD GRAPHS FOR TYPE A SPACER


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


211


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.18(b) Electric Field Distribution of type-A Spacer for



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.18(c) Electric Field Distribution of type-A Spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m



212


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.18(e) Electric Field Distribution of type-A Spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.18(f) Electric Field Distribution of type-A Spacer


213



electric field plots figs(3.19) and graphs are given in figs (3.19(a) to

3.19(f))


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


Fig-3.19(a) Electric Field Distribution of type-B Spacer for


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


214

Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.19(b) Electric Field Distribution of type-B Spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.19(c) Electric Field Distribution of type-B Spacer for


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.19(d) Electric Field Distribution of type-B Spacer for


215


Ele

ctri

c F

ield

Str

ength

in V

/ m

m



Ele

ctri

c F

ield

Str

ength

in V

/ m

m




216




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


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


217


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.20(b) Electric Field Distribution of type-C Spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.21(c) Electric Field Distribution of type-C Spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.20(d) Electric Field Distribution of type-C Spacer for conductor-2 along Y-axis

218


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.20(e) Electric Field Distribution of type-C Spacer for


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.20(f) Electric Field Distribution of type-C Spacer


219





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


Fig-3.21(a) Electric Field Distribution of type-D Spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

220


Fig-3.21(c) Electric Field Distribution of type-D Spacer for


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.21(b) Electric Field Distribution of type-D Spacer for


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.21(d) Electric Field Distribution of type-D Spacer for


221


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.21(e) Electric Field Distribution of type-D Spacer for


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.21(f) Electric Field Distribution of type-D Spacer



222

Table.3.4 Comparative values of post type insulators for Conductor-1 along X and Y axis

Radial Co-Ordinate

(mm)




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


Radial Co-Ordinate

(mm)




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

223






Radial

Co-Ordinate

(mm)


TYPE-A TYPE-B

TYPE-C TYPE-D


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


224



225



226







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





3.4.7 RESULTS AND DISCUSSIONS FOR POST TYPE SPACER


227


(3.21 to 3.21(f)).



� From fig (3.22), for conductor-1 along X-axis, in type-A spacer,


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



the radial co-ordinate of 100 to 500 mm. In type-C spacer, 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,


conductor to the enclosure with -60kV/mm to -12kV/mm under


228


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 radial co-ordinate of 100 to 500 mm.






conductor to the enclosure with 80kV/mm to 0kV/mm under











under the radial co-ordinate of 100 to 900 mm. In type-B


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


the conductor to the enclosure with -0.8 kV/mm to -



surface of the conductor to the enclosure with -10kV/mm to

-0.55kV/mm under the radial co-ordinate of 100 to 500 mm.









conductor to the enclosure with 20kV/mm to –0.16kV/mm

under the radial co-ordinate of 100 to 500 mm. In type-D


the conductor to the enclosure with 20kV/mm to -2kV/mm





230












the conductor of Type-D spacer is reduced when compared to

Type-A, Type-B and Type-C.

231




(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




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

232


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.28(b) Electric Field Distribution of type-A Spacer


Radial Co-ordinate in

Ele

ctri

c F

ield

Str

ength

in V

/ m

m



Ele

ctri

c F

ield

Str

ength

in V

/ m

m



233


Ele

ctri

c F

ield

Str

ength

in V

/ m

m



Ele

ctri

c F

ield

Str

ength

in V

/ m

m




234




3.29(f))


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


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.29(a) Electric Field Distribution of type-B Spacer


235

Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.29(c) Electric Field Distribution of type-B Spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.29(d) Electric Field Distribution of type-B Spacer


236


Ele

ctri

c F

ield

Str

ength

in V

/ m

m



Ele

ctri

c F

ield

Str

ength

in V

/ m

m




237




3.30(f))

3.5.3 TYPE-C SPACER FOR RIB TYPE INSULATOR


Fig-3.30 Electric field plot with εr=9 to εr=3 (linear variation) for

type C Rib Shape spacer




Ele

ctri

c F

ield

Str

ength

in V

/ m

m

238


Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m



Ele

ctri

c F

ield

Str

ength

in V

/ m

m



239

Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.30(f) Electric Field Distribution of type-C Spacer for



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.30(e) Electric Field Distribution of type-C Spacer for


240





3.31(f)).

3.5.4 TYPE-D SPACER FOR RIB TYPE INSULATOR


Ele

ctri

c F

ield

Str

ength

in V

/ m

m





and remains constant) for Type-D Rib Shape spacer


241

Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.31(b) Electric Field Distribution of type-D Spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.31(c) Electric Field Distribution of type-D Spacer for


Ele

ctri

c F

ield

Str

ength

in V

/ m

m




242

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.31(f) Electric Field Distribution of type-D Spacer for




Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.31(e) Electric Field Distribution of type-D Spacer for


243

Table-3.7 Comparative values of Rib type Insulator for Conductor-1 along X and Y axis

Radial Co-Ordinate

(mm)



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


Radial Co-Ordinate

(mm)



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

244






Radial Co-

Ordinate

(mm)




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


FOR RIB TYPE SPACER


245



246



247











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


248

corresponding electric field plots and graphs are shown in

figs(3.31 to 3.31(f)).



� From fig (3.32), for conductor 1 along X-axis, in type-A spacer,
















under the radial co-ordinate of 100 to 900 mm. In type-B



under the radial co-ordinate of 100 to 900 mm. In type-C

249



under the radial co-ordinate of 100 to 900 mm. In type-D






















250

























251

radial co-ordinate of 100 to 900 mm. In type-B spacer, the



radial co-ordinate of 100 to 900 mm. In type-C spacer, the



radial co-ordinate of 100 to 900 mm. In type-D spacer, the



radial co-ordinate of 100 to 900 mm.




252




(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



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


253


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


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


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.38(d) Electric Field Distribution of type-A spacer


254

Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.38(e) Electric Field Distribution of type-A spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.38(f) Electric Field Distribution of type-A spacer


Fig-3.38(g) Electric Field Distribution of type-A spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

255


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


Fig-3.38(i) Electric Field Distribution of type-A spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.38(j) Electric Field Distribution of type-A spacer


256

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.38(l) Electric Field Distribution of type-A spacer




Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.38(k) Electric Field Distribution of type-A spacer


257



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



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


258


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


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


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

259


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


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


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

260


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


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.39(i) Electric Field Distribution of type-B spacer for



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.39(j) Electric Field Distribution of type-B spacer


261


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


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

262




3.40(l))

3.6.3 TYPE C SPACER FOR V- SHAPE INSULATOR


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



Fig-3.40 Electric field plot with εr=9 to εr=3 (linear variation) for type C V-Shape spacer

263


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.40(c) Electric Field Distribution of type-C spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.40(d) Electric Field Distribution of type-C spacer


Fig-3.40(b) Electric Field Distribution of type-C spacer for

Insulator 1 conductor-1 along Y-axis


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

264

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.40(e) Electric Field Distribution of type-C spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.40(f) Electric Field Distribution of type-C spacer




Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.40(g) Electric Field Distribution of type-C spacer


265

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.40(i) Electric Field Distribution of type-C spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.40(j) Electric Field Distribution of type-C spacer



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


266

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.40(l) Electric Field Distribution of type-C spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.40(k) Electric Field Distribution of type-C spacer



267





3.41(l)).

3.6.4 TYPE D SPACER FOR V-SHAPE INSULATOR



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


268


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


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.41(c) Electric Field Distribution of type-D spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.41(d) Electric Field Distribution of type-D spacer


269

Ele

ctri

c F

ield

Str

ength

in V

/ m

m


Fig-3.41(e) Electric Field Distribution of type-D spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.41(f) Electric Field Distribution of type-D spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.41(g) Electric Field Distribution of type-D spacer


270

Ele

ctri

c F

ield

Str

ength

in V

/ m

m


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


Fig-3.41(i) Electric Field Distribution of type-D spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


271

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.41(l) Electric Field Distribution of type-D spacer



Fig-3.41(j) Electric Field Distribution of type-D spacer for

Insulator 2 conductor-2 along Y-axis


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.41(k) Electric Field Distribution of type-D spacer for


272

Table-3.10 Comparative Values of V-shape Insulator for Insulator-1 Conductor-1 along X and Y axis

Radial

Co-Ordinate

(mm)




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


Radial Co-

Ordinate

(mm)




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

273


Radial Co-

Ordinate

(mm)




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)




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

274


Radial Co-

Ordinate

(mm)




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)




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

275

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


Conductor-1 along Y-axis

276





277



Fig-3.47 Electric Field Stress distribution for Insulator-1 Conductor-3

along Y-axis

278





279

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

280









281




plots and graphs are shown in figs (3.38 to 3.38(i)), where as for



electric field plots and graphs are shown in figs (3.39 to 3.39(i)).



are shown in figs(3.40 to 3.40(i)). In type D spacer, the value of




figs(3.41 to 3.41(i)).



� 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


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

282

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



type-B spacer, the electric field stress value varies from the



type-C spacer, the electric field stress value varies from the


-55kV/mm under the radial co-ordinate of 20 to 180 mm. In



-11kv/mm under the radial co-ordinate of 20 to 180 mm.



surface of the conductor to the enclosure with 60kV/mm to



283





















-22kV/mm under the radial co-ordinate of 20 to 180 mm.




284
























285













55kV/mm under the radial co-ordinate of 20 to 180 mm.












286

























287




















surface of the conductor to the enclosure with 120 kV/mm to



surface of the conductor to the enclosure with 125 kV/mm to


288










289




(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




Ele

ctri

c F

ield

Str

ength

in V

/ m

m


290


Ele

ctri

c F

ield

Str

ength

in V

/ m

m



Ele

ctri

c F

ield

Str

ength

in V

/ m

m



Ele

ctri

c F

ield

Str

ength

in V

/ m

m




291

Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m




292




3.55(f))

3.7.2 TYPE B SPACER FOR DELTA SHAPE INSULATOR


Fig-3.55 Electric field plot with εr=6(constant) for Type-B

Delta shape spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m




293

Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m




294

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.55(f) Electric Field Distribution of type-B Spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.55(e) Electric Field Distribution of type-B Spacer



295




3.56(f))


3.7.3 TYPE C SPACER FOR DELTA SHAPE INSULATOR


variation) for type C Delta shape spacer



along X-axis

Ele

ctri

c F

ield

Str

ength

in V

/ m

m


296

Ele

ctri

c F

ield

Str

ength

in V

/ m

m



Ele

ctri

c F

ield

Str

ength

in V

/ m

m





Ele

ctri

c F

ield

Str

ength

in V

/ m

m



297

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.56(e) Electric Field Distribution of type-C Spacer




Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.56(f) Electric Field Distribution of type-C Spacer


298


3.7.4 TYPE D SPACER FOR DELTA SHAPE INSULATOR

Ele

ctri

c F

ield

Str

ength

in V

/ m

m





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

299

Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.57(c) Electric Field Distribution of type-D Spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.57(d) Electric Field Distribution of type-D Spacer



300

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.57(e) Electric Field Distribution of type-D Spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m




301

Table-3.16 Comparative values of Delta shape Insulator for Conductor-1 along X and Y axis

Radial Co-

Ordinate

(mm)




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


Radial Co-

Ordinate

(mm)




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

302






Radial Co-

Ordinate

(mm)




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


FOR DELTA SHAPE SPACER

Fig-3.58 Electric Field Stress Distribution for Conductor-1 along X-axis

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

304


Fig-3.62 Electric Field stress Distribution for Conductor-3

along X-axis

305













3.7.7 RESULTS AND DISCUSSIONS FOR DELTA SHAPE SPACER


306


figs(3.57 to 3.57(f)).












under the radial co-ordinate of 50 to 450 mm. In type-D spacer,




� From fig (3.59), for conductor 1 along Y-axis, in the type–A


the conductor to the enclosure with -540kV/mm to 11.1kV/mm





307






















conductor to the enclosure with 40kV/mm to -2.2kV/mm under



308









� From fig(3.62), for conductor 3 along X-axis, in type–A spacer,
















309














310




(3.64(a) to 3.64(f))

3.8.1(a) ELECTRIC FIELD GRAPHS FOR TYPE A SPACER


Ele

ctri

c F

ield

Str

ength

in V

/ m

m


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


311

Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m



312

Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m




313




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 Electric field plot with εr=6(constant) for

Type-B Bulb Inside shape spacer

Surface: Electrical Potential

314

Ele

ctri

c F

ield

Str

ength

in V

/ m

m





Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m



315

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.65(e) Electric Field Distribution of type-B Spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.65(f) Electric Field Distribution of type-B Spacer



316


3.8.3 TYPE C SPACER FOR POST INSIDE INSULATOR


variation) for type C Bulb inside shape spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m


317

Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m



318

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.66(e) Electric Field Distribution of type-C Spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig 3.66(f) Electric Field Distribution of type-C Spacer



319





3.67(f)).


Ele

ctri

c F

ield

Str

ength

in V

/ m

m




3.8.4 TYPE D SPACER FOR BULB INSIDE INSULATOR


and remains constant) for Type-D Bulb inside shape spacer


320

Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.67(c) Electric Field Distribution of type-D Spacer



Ele

ctri

c F

ield

Str

ength

in V

/ m

m




Ele

ctri

c F

ield

Str

ength

in V

/ m

m




321


Ele

ctri

c F

ield

Str

ength

in V

/ m

m

Fig-3.67(e) Electric Field Distribution of type-D Spacer


Ele

ctri

c F

ield

Str

ength

in V

/ m

m




322

Table-3.19 Comparative Values of Bulb inside shape insulator for Conductor-1 along X and Y-axis

Radial Co-

Ordinate

(mm)




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


Radial Co-

Ordinate

(mm)




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

323






Radial Co-

Ordinate

(mm)




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


324

Fig-3.69 Electric Field Stress Distribution for Conductor-1 along Y-axis


325



326











3.8.7 RESULTS AND DISCUSSIONS FOR BULB INSIDE SPACER


327




(3.67 to 3.67(f)).





















328











conductor to the enclosure with 20kV/mm to -2.22kV/mm














329
























330















the conductor of Type-C spacer is reduced when compared to

Type-A, Type-B and Type-D.

331

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






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

332

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

333

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



conductor-1 along X-axis is 20kV/mm and it gradually

decreases to 0.01kV/mm, when using the functionally Graded

material.


reduced by 99.95%.

� RIB TYPE INSULATOR



conductor-1 along X-axis is -30kV/mm and it gradually


material.


reduced by 14.28%.

334

� V SHAPE INSULATOR



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.


reduced by 50%.



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.


reduced by 75%.

� DELTA SHAPE INSULATOR



condeuctor-1 along X-axis is -50kV/mm and it gradually


material.

335


reduced by 80%.

� BULB INSIDE SHAPE INSULATOR



conductor-1 along X-axis is -5kV/mm gradually decreases to

-7.5kV/mm, when using the functionally Graded material.


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.

modelling and analysis of functionally graded material...

Documents