82I8-IJAET0805823 COMPUTATION OF ELECTRIC - e … … · Fig -4c Electric Field Distribution of type-A Spacer PATH-1 PATH-2 PATH-3 . International Journal of Advances in Engineering

International Journal of Advances in Engineering & Technology, May 2012.

©IJAET ISSN: 2231-1963

775 Vol. 3, Issue 2, pp. 775-786

COMPUTATION OF ELECTRIC FIELD FOR FGM SPACER

USING TRI-POST INSULATOR IN GIS

Gopichand Naik. M1, Amarnath. J

2, Kamakshiah. S

3

1Dept. of Electrical Engg., Andhra University, Visakhapatnam, India

2,3Jawaharlal Nehru Technological University, Hyderabad, India

ABSTRACT

The Gas Insulated Substation (GIS) have various advantages like Compactness, immunity from environmental

conditions, high operational reliability, low maintenance cost. In a number of GIS installations, the main design

considerations involved in gas insulated equipment are at cone insulator, gas and metal interface. Hence there

is a need for control of electric stresses in order to reduce internal discharges, surface discharges to the

enclosure surface. In conventional approach, in order to reduce such distortion of electric field, many

techniques are applied like, control of the spacer shape, additional shielding of electrodes for relaxation of

electric field around spacer and low permittivity of spacer material. The new techniques of Functionally

Gradient Material (FGM) spacer has been proposed in this paper. In this paper the applicability of FGM

spacer for gas insulated power apparatus has been verified. In the FGM spacer, a spatial distribution of

permittivity for the control of the electric field distribution in and around the spacer is used. The electric field

calculations for several types of FGM spacers have been carried out using Finite Element Method (FEM). The

electric field distribution along the radial distance of the spacer insulator have been obtained for various FGM

materials and results are compared.

KEYWORDS: Electric Field distribution, FGM, FEM, Modelling of Tri-post insulator.

I. INTRODUCTION

The present and future trend in electric power equipment tends to be compact and be operated under

higher voltage. The modular design of GIS offers a high degree of flexibility to meet layout

requirements of both substations as well as power station switchgear, making efficient use of available

space. GIS technology has reached a stage of application where wide ranges of GIS equipment up to

highest voltage of 800kV are available with many unique features. With the rise in operating voltages

in the equipment, the solid insulators play the most critical role for electrical insulation. To improve

the insulation performance of the solid insulators, we need to control electric field distribution around

the solid insulators [3-5]. 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 with keeping their simple structure and configurations. With the

use of FGM application to the solid spacer the properties of the insulator can be changed to get the

required relative permittivity at required location[6-8]. In this paper, we propose a computer-aided

optimization and simulation technique for FGM application. In the optimization process, permittivity

distribution of the FGM insulator is sequentially modified for minimizing the electric field stress in

and around FGM insulators. Investigations have been carried out in applicability of a Functionally

Gradient Material (FGM) for the spacer for use in GIS. The electric field calculations in and around

the FGM spacer has been carried out, from the viewpoints of reduction of electric field distributions, a

number of spatial distributions of relative permittivity εr in spacer have been investigated. The results

are compared between optimized FGM spacer, with one of conventional spacer which has a uniform



776 Vol. 3, Issue 2, pp. 775-786

distribution of permittivity. From the calculation results, we confirmed that the proposed optimization

method could calculate novel field distributions for different permittivity’s, which have higher

performance of the field control effect. Confirmation on the significant effect of the FGM spacer for

the improvement of the electric field distribution and applicability for gas / solid composite insulation

system.

COMSOL Multiphysics brings an unprecedented level of clarity to simulation work by giving you

both an organized model overview and a streamlined model-building process, powerful solvers and

flexibility in physics[ 9]. It uses functional form, structure, and aesthetics as the means to achieve

simplicity for modeling complex realities.

The paper is organized as, section two explains the Finite Element Method(FEM) as applicable to the

problem under consideration mathematically. In section three, explains about concept of FGM.

Section four explains about modeling of TRI-Post insulator with conventional spacer and FGM

spacers, electric field graphs, comparison tables and electric field stress graphs.

Section five explains about results of various graphs and section six about conclusions.

II. CONCEPT OF FEM

The finite element technique is to derive nodal potential equations from the maximization of a

functional, constructed by integrating an appropriate combination of the electromagnetic variables

over the space of the finite element[ 10]. The basic grid mesh is usually formed from sets of

interconnected triangles whose vertex co-ordinates may be conventionally varied if optimization of a

particular problem with respect to geometry required. The method may be applied to electrostatic and

time varying situations.

The Finite element method allows us to solve large scale, complex, electromagnetic field problems,

posed through simple and general data structures. For this reason, it is one of today’s best accepted

methods.

The static electric field E, is described by means of the electric scalar potential, V as

E = -grad V

Satisfying the differential equation

-div (ε grad V) = 0 in Ω

Where Ω is the problem region and ε is the permittivity. The boundary conditions are of dirichlet type

on electrodes with given potentials, that is on the surface ΓE.

V=V0 on ΓE and Neumen type on the surface ΓD where the normal component of the electric flux

density vanishes as on symmetry planes.

)1(0 donn

VΓ=

∂

∂ε

The problem region Ω is subdivided into finite elements that are sub regions in which the scalar

potential is interpolated from the nodal potential values by polynomials of low order. Hence the

potential approximated as

)2(11

)(

j

n

j

jDj

nn

j

j

nNVVNVVV

dd

∑∑=

+

=

+==≈

Where n=nD is the total number of nodes in the finite element mesh, Vj is the approximate value of

the potential in the Jth node and ni is the shape function associated with this node [1]. In the nD nodes

(j=n+1, n+2, ........n+nD) lying on the surface ΓE the potential is given, so the function VD is known and

satisfies the dirichlet boundary condition [2] by setting the approximation in the differential equations

multiplying it by the shape functions associated with the nodes not on ΓE (weighing functions) and

integrating over the problem region Ω. Taking account of the Neumann boundary condition [2] the

following set of algebraic equations is obtained.

)3(.1

Ω−=Ω ∫∫∑ΩΩ=

dNgradVgraddNgradV idj

n

j

j εε

Since the shape functions are only non zero in the few finite elements containing the node associated

with them, matrix of this equations system is extremely sparse, it can be advantageously solved by the



777 Vol. 3, Issue 2, pp. 775-786

method of conjugate gradients to yield the nodal potential values and hence the electric field

distribution[11].

III. CONCEPT OF FGM

GIS designs often use gas tight spacers to separate different bus compartments. It is preferable to limit

the bulk field to below 4kV/mm (rms). Most spacers are cast, filled epoxy resin systems. Resins are

usually bisphenol A, cycloaliphatic or hydantoin. Fillers are necessary for good thermal and tracking

properties and minimal shrinkage during casting. Although silica and quartz have been used. The

epoxy formulations are, however, proprietary. Silica/quartz fillers are subject to corrosion damage

when SF6 arcing by-products are present[12]. In the FGM solid insulators, spatial distributions of

permittivity are given for the control of the electric field distribution in and around the solid

insulators. Conventional materials have constant permittivity distribution on the contrary, FGMs have

continuously graded permittivity distribution by the arrangement of filler particles. Material A as a

matrix is considered to be epoxy for example. As a filler, Al2O3, SiO2 or TiO2 particles are applied

with several 10 µm diameter. In order to relax the stress concentration, the application of FGM is

expected to be effective by giving the suitable permittivity (εr) distribution inside the insulators.

Fig. 1 shows the concept of FGM. Around the interface of two different materials, the content rate of

material-A to material-B is spatially changed. This may be possible to relax the stress concentration at

the interface[14]. In the gas-solid insulation system, Electric field stress under an AC or an impulse

voltage application is generally intensified in a gas region because the dielectric permittivity of the

gas is lower than the solid material. In order to relax the stress intensification, the application of the

FGM is expected to be effective by giving the suitable permittivity distribution inside the spacer[14].

Fig.1. Concept of FGM

IV. MODELLING OF FGM SPACER

In this paper Electric Field is obtained by applying FEM on FGM tri-post type spacer for GIS under

650kV impulse voltage. A single phase bus duct with aluminum enclosure, aluminum conductor and

tri-post insulator is modeled as shown in Fig. 1 in a two dimensional axis. Diameter of the enclosure

is 226mm, conductor diameter 89mm and insulation thickness is taken as 30mm from the conductor.

The void is been filled with SF6 gas. The analysis is done with the tri-post type spacer for 4 types [15]

as shown from Fig-2.



778 Vol. 3, Issue 2, pp. 775-786

Fig-2 Geometry for the Tri-post type spacer

Fig-4 Electric field plot with εr=3 for Tri-post

type Insulator for Type-A spacer

Ele

ctri

c F

ield

Str

ength

in

V /

mm

Radial Co-ordinate in mm

Fig-4a Electric Field Distribution of type-A

Spacer for Path-1 along X-axis

B

A

C

D

0

3

6

9

Radial Co-ordinate (mm)

Rel

ativ

e P

erm

itti

vit

y (ε r

)

Fig-3. Distribution of relative permittivity in spacer

Ele

ctri

c F

ield

Str

ength

in

V /

mm


Fig-4b Electric Field Distribution of type-A

Spacer for Path-1 along Y-axis

Ele

ctri

c F

ield

Str

ength

in

V /

mm


Fig-4c Electric Field Distribution of type-A Spacer

for Path-2 along X-axis

PATH-1

PATH-2

PATH-3



779 Vol. 3, Issue 2, pp. 775-786

Ele

ctri

c F

ield

Str

ength

in

V /

mm


Fig-4d Electric Field Distribution of type-A


Ele

ctri

c F

ield

Str

ength

in

V /

mm


Fig-4e Electric Field Distribution of type-A Spacer


Ele

ctri

c F

ield

Str

ength

in

V /

mm


Fig-4f Electric Field Distribution of type-A


Fig-5 Electric field plot with εr=6 for Tri-

post type Insulator for Type-B spacer

Fig-5a Electric Field Distribution of

type-B Spacer for Path-1 along X-axis


Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-5b Electric Field Distribution of type-B



Ele

ctri

c F

ield

Str

ength

in

V /

mm



780 Vol. 3, Issue 2, pp. 775-786

Fig-5c Electric Field Distribution of type-B


Ele

ctri

c F

ield

Str

ength

in

V /

mm

Radial Co-ordinate in mm Fig-5d Electric Field Distribution of type-B



Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-5e Electric Field Distribution of type-B Spacer



Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-5f Electric Field Distribution of type-B



Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-6 Electric field plot with εr=9 to εr=3 for

Tri-post type Insulator for Type-C spacer Fig-6a Electric Field Distribution of type-C



Ele

ctri

c F

ield

Str

ength

in

V /

mm



781 Vol. 3, Issue 2, pp. 775-786

Ele

ctri

c F

ield

Str

ength

in

V /

mm


Fig-6b Electric Field Distribution of type-

C Spacer for Path-1 along Y-axis Fig-6c Electric Field Distribution of type-C



Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-6d Electric Field Distribution of type-

C Spacer for Path-2 along Y-axis


Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-6e Electric Field Distribution of type-C



Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-6f Electric Field Distribution of type-C


Ele

ctri

c F

ield

Str

ength

in

V /

mm


Fig-7 Electric field plot with εr=9 to εr=3(upto

50% and remains constant) for Tri-post type

Insulator for Type-D spacer



782 Vol. 3, Issue 2, pp. 775-786

Fig-7a Electric Field Distribution of type-D


Ele

ctri

c F

ield

Str

ength

in

V /

mm


Fig-7b Electric Field Distribution of type-D



Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-7c Electric Field Distribution of type-D



Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-7d Electric Field Distribution of type-D



Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-7e Electric Field Distribution of type-D



Ele

ctri

c F

ield

Str

ength

in

V /

mm

Fig-7f Electric Field Distribution of type-D Spacer

for Path-3 along Y-axis



783 Vol. 3, Issue 2, pp. 775-786

RADIAL CO-

ORDINATE

(mm)

ELECTRIC FIELD STRENGTH ON TRI-

POST INSULATOR ABOVE PATH-1

ALONG X-AXIS (V / mm)

TYPE-A TYPE-B TYPE-C TYPE-D

X (* 106) X(* 106) X (* 106) X (* 106)

0 -0.24 -0.24 -0.2 -0.22

20 -0.9 -0.9 -1.1 -1.0

40 -1.04 -1.08 -1.3 -1.18

60 -1.11 -1.1 -1.26 -1.19

80 -0.92 -0.98 -1.12 -1.04

100 -0.7 -0.7 -0.82 -0.8

120 -0.2 0 -0.3 -0.2

140 0.16 0.38 -0.02 -0.1

160 0 0 0.04 0

RADIAL CO-

ORDINATE

(mm)



ALONG Y-AXIS (V / mm)


Y (* 106) Y (* 106) Y (* 106) Y (* 106)

0 -0.25 -0.2 -0.18 -0.2

20 -0.55 -0.7 -0.6 -0.7

40 -0.5 -0.7 -0.5 -0.5

60 0.2 0.1 0.3 0.2

80 0.5 0.5 0.6 0.6

100 0.8 0.8 1 0.9

120 1 1.15 1.4 1.3

140 1.2 1.25 1.3 1.25

160 0.5 0.5 0.5 0.5

RADIAL CO-

ORDINATE

(mm)





X (* 106) X(* 106) X(* 106) X (* 106)

0 -0.35 -1.2 -0.2 0.25

20 -1.15 -4 -0.9 -0.8

40 -0.8 -5.2 -1.3 -1.3

60 -0.4 -2.2 -0.55 -0.55

80 0 -0.04 -0.2 -0.2

100 0.4 2 0.25 0.2

120 0.7 5.2 0.6 0.6

140 1 4 1.2 1.3

160 0.4 3.6 0.9 0.8

180 0 0 0 0

RADIAL

CO-

ORDINATE

(mm)





Y (* 106) Y (* 106) Y (* 106) Y (* 106)

0 -0.1 -0.1 -0.08 -0.09

20 -0.3 -0.52 -0.49 -0.59

40 -0.62 -0.46 -0.8 -0.6

60 -1.01 -0.56 -1.2 -0.92

80 -1.05 -0.98 -1.3 -1.04

100 -1.01 -0.96 -1.2 -1.02

120 -0.65 -0.7 -0.8 -0.9

140 -0.57 -0.36 -0.6 -0.58

160 -0.2 -.048 -0.2 -0.6

180 0 -0.1 0 -0.05

Table.1 Comparative Values for Tri-post Insulator

along X-axis for Path-1


along Y-axis for Path-1







784 Vol. 3, Issue 2, pp. 775-786

RADIAL CO-

ORDINATE

(mm)





X (* 106) X (* 106) X (* 106) X (* 106)

0 -0.08 -0.4 -0.08 -0.25

20 -0.2 -1.3 0.16 -1

40 0.08 -1.1 0 -1

60 0.64 -0.5 0.8 -0.48

80 0.9 0 1.1 0

100 1.04 0.4 1.26 0.45

120 1.02 1 1.2 0.75

140 0.84 1.1 1.1 1

160 0.4 0.5 0.4 0.5

180 0 0 0 0

RADIAL CO-

ORDINATE

(mm)





Y (* 106) Y (* 106) Y (* 106) Y (* 106)

0 0.35 -0.1 0.25 -0.1

20 1.15 -0.1 1.25 -0.5

40 1.15 -0.52 1.1 -0.7

60 0.8 -1 1 -1.1

80 0.6 -1.1 0.6 -1.2

100 0.25 -1.04 0.3 -1.1

120 -0.35 -0.58 -0.4 -0.6

140 -0.65 -0.54 -0.6 -0.8

160 -0.35 -0.3 -0.4 0





Fig-8 Comparative Values of Electric field stress for

Tri-post Insulator along X-axis for Path-1


Tri-post Insulator along Y-axis for Path-1







785 Vol. 3, Issue 2, pp. 775-786

V. RESULTS AND DISCUSSIONS

In the present work, various types of FGM spacers as shown in Fig.3 to Fig.6 has been considered. In

type A spacer, the value of the relative permittivity Єr = 3 is constant, where as for type B spacer, the

corresponding value of the permittivity Єr = 6 right from high voltage electrode to enclosure. In 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 and then it becomes constant thereafter. The electric

field graphs for various types of FGM spacer along the spacer surface have been presented in the Fig.

4a to Fig. 7f.The comparative values of maximum field strength in various types of spacers are

shown in table 1 to table 6.From the fig.8 the electric field stress of type D spacer is reduced from

radial co-ordinate 20mm to 160mm when compared to conventional spacer for path 1 along X-axis.

From the fig.9 the electric field stress of type D spacer is reduced from radial co-ordinate 20mm to

40mm when compared to conventional spacer for path 1 along Y-axis. From the fig.10 the electric

field stress of type D spacer is reduced from radial co-ordinate 60mm to 120mm when compared to

conventional spacer for path 2 along X-axis. From the fig.11 the electric field stress of type D spacer

is reduced from radial co-ordinate 20mm to 180mm when compared to conventional spacer for path 2

along Y-axis. From the fig.12 the electric field stress of type D spacer is reduced from radial co-

ordinate 20mm to 180mm when compared to conventional spacer for path 3 along X-axis. From the

fig.13 the electric field stress of type D spacer is reduced from radial co-ordinate 20mm to 180mm

when compared to conventional spacer for path 3 along Y-axis.

VI. CONCLUSIONS

The improvements of electrical insulation performance of gas insulated apparatus propose the

application of FGM spacer. In the FGM spacer, we have given the spatial distribution of the

permittivity єr for the control of electric field distribution in around the spacer. From the viewpoint of

the electric field reduction and field distribution improvement, the applicability of the FGM spacer is

verified by the numerical electric field calculation. Conclusions from the computed results are as

follows. The application of the FGM spacer could reduce the maximum electric field around, even if

we apply very simple shape of spacer. The highly stressed electrode area and volume of gas space

could be reduced. With the application of FGM spacer it is clearly observed that the maximum field

strength is reduced when compared to other type’s of spacers. The FGM spacer makes the electric

field distribution more uniform and suitable for the improvement of the insulation performance of Gas

Insulated apparatus

REFERENCES

[1]. D.S.Kershaw, “The Incomplete Cholesky – Conjugate Gradient Method for Iterative solution of system of

Linear Equations”, J.Comput.phys, Vol.26, 1978, pp.43-65.

[2]. O.C.Tienkiewicz, “The Finite Element Method” PIC Graw Hill, New York, 1977.







786 Vol. 3, Issue 2, pp. 775-786

[3]. A. Haddad and D.Warne: “Advances in High Voltage Engineering”, The Institution of Electrical Engineers

,( pp. 37- 76, 2004).

[4]. J.Sato, T.Shioiri, M.Miyazawa, T.Yoshida and K.Yokokura:“ Composite Insulation Technology for New

Compact 72/84kV C-GIS”, IEEE Transaction on Dielectrics and Electrical Insulation, Vol.2, pp.489-494

(1999).

[5]. A. Sabot “Insulation Co-ordination procedure for 420kV Gas Insulated Line (GIL)”,11th

International

Symposium on High Voltage Engineering, Vol.3, pp.1-10 (1999).

[6]. H.Okubo, M. Kurimoto, H.Shumiya, K.Kato, H. Adachi and S.Sakuma: “Permittivity Gradient

Characteristics of GIS Solid Spacer”, 7th

International Conference on Properties and application of

Dielectrics Material, 1:23-26 Vol 1, 07/2003.

[7]. H.Shumiya, K.Kato and H.Okubo: “Feasibility Study on FGM(Functionally Gradient Material) Application

for Gas Insulated Equipment”, 2004 IEEE Conference on Electrical Insulation and Dielectrics Phenomena,

pp 362-363 (2004).

[8]. .H.Shumiya, K.Kato and H.Okubo: “Fabrication and Prediction Techniques for FGM (Functionally

Gradient Materials) Application to Solid Insulators”, 2005 IEEE Conference on Electrical Insulation and

Dielectric Phenomena, pp 673-676 (2005).

[9]. R.Brambilla, F.Grilli, Simulating Superconductors in AC Environment: Two Complementary COMSOL

Models COMSOL Conference 2009(2009).

[10] .O.C.Zienkiewicz, R. L. Taylor, "The Finite Element Method, Volume I: The Basics," Fifth Edition,

Butterworth Heinemann, 2000

[11].Tadasu Takuma, Boonchai Techaumnat, ”Electric Fields in Composite Dielectrics and their Applications”

Springer,2010.

[12].H.Okubo, K.Kato, M.Hikita, N.Hayakawa and Y.Kito; “The Development of Personal Computer Based

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[13]. H.Singer; “Computation of Optimie Optimized Electrode Geometrics”, 3rd

International Symposium on

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Authors Information

Gopi Chand Naik was born in Hyderabad, India in 1980. He graduated from RVR & JC

College of Engineering, Guntur in the year 2001 and pursed M. Tech from JNTU, Kakinada

in the year 2003. He is presently pursuing his Doctoral Degree from J.N.T. University,

Hyderabad. He is presently working as Assistant Professor in the Department of Electrical

Engineering, Andhra University College of Engineering, Visakhapatnam, India. His

research areas include Gas Insulated Substations, Power Systems, Fuzzy Logics and

Electrical Drives.

Amarnath graduated from Osmania University in the year 1982, M.E from Andhra

University in the year 1984 and Ph.D from J.N.T. University, Hyderabad in the year 2001.

He is presently Professor in the Department of Electrical and Electronics Engineering,

JNTU College of Engineering, Hyderabad, India. He presented more than 60 research

papers in various national and international conferences and journals. His research areas

include Gas Insulated Substations, High Voltage Engineering, Power Systems and

Electrical Drives.

S. Kamakshaiah graduated from Osmania University. He obtained. M.E(HV) from IIsc,

Bangalore. and Ph.D also from IIsc, Bangalore. He worked as former professor & Head of

Electrical & Electronics Engineering and chairman of Electrical science J.N.T. University

,Hyderabad. He is presently Professor in the Department of Electrical and Electronics

Engineering, Vignan college of Engineering, Hyderabad, India. He presented many

research papers in various national and international conferences and journals. His

research areas include Electrical Machines, High Voltage Engineering, Power Systems,

and Electromagnetic Fields.

Documents

82I8-IJAET0805823 COMPUTATION OF ELECTRIC - e … … · Fig -4c Electric Field Distribution of type-A Spacer PATH-1 PATH-2 PATH-3 . International Journal of Advances in Engineering