Application on Electric Field Distribution in Power Apparatus by FEM Correct1

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Application on Electric Field

Distribution

in Power Apparatus by FEM

By

Mr. Yongyuth Vachiratarapadorn

Chief, Transmission Equipment Technology

Center of Excellence for Transmission System Technology

Electricity Generating Authority of Thailand



Electric Field Calculation

Method of electric field calculation

1. Using mathematical analysis to

determine the values. 2. Using Finite Difference Method

3.Using Finite Element Method

4.Using Space Charge Simulation Method



Objective

To present application of Finite

Element Method in electric field

calculation in electrical apparatus

Determine highest electric field stresson electrical apparatus (Critical points).



Content

1. Review Finite Element Method

2. Electric Field on Electrical Apparatus

- HVAC Cable- Insulator in HVAC Transformer

- Insulator in HVDC Transformer

- Disconnecting Switch

3. Conclusion



FINITE ELEMENT METHOD EQUATION

Formulation of Finite ElementEquations has three methods as follows:1. Direct Method : using mathematical

equations to determine the values 2. Variational Approach: using minimization of energy principle

3. Method of Weighted Residuals: using minimize the guest solution of differential equations



Step 3: formulate FM equations using

1.Direct Method

2. Variational Approach

3. Method of Weighted Residuals

Which one of these will result in a matrix equation:

? A { } { }e ee

K F J !

FINITE ELEMENT METHOD

FEM is a tools to apply to varies problems such as solid,fluid and electric field calculations.

Step 1: divide boundary of the problem into partial triangle.

Step 2: Select linear interpolation for approximation function.



FINITE ELEMENT METHOD ( )

Step 4: Formulate Global Matrix fromequations of the partial triangles

? A { } { } syst em syst em syst em K F J !

Step 5: Apply Boundary Conditions anddetermine the Nodal Unknowns{ } syst emJ

Step 6: Determine electric potential and

use electric potential to calculateelectric field and so on.



50mm

20mm

10mm

150 mm

I!

AC

100

V

V= 0 V=0

V=0

6.66 13.32 20 26.66 33.33 40 46.66 53.33 60 66.66 73.33 80 86.66 93.33 100

5 10 15 20 25 30 35 40 45 50 55 60 65 69 72

10 v20 v30 v40 v

50 v60 v70 v80 v90 v

FIGURE 1 SHOW THE APPLIC ATION ON C ABLE WHICH THE INSULATION

HAVE RELATIVE PERMITTIVITY I = 2)



50

mm20

mm10

mm

150 mm

I!

I!

AC

V=0

100

V

V=0

V=06.66 13.32 20 26.66 33.33 40 46.66 53.33 60 66.66 73.33 80 86.66 93.33 100

2.87 5.74 8.6 11.5 14.36 17.23 20.11 23 25.85 28.72 31.58 34.41 37.14 39.56 41

10 V

20 V3

0 V

40 V50 V70 V90 V

FIGURE2 S

HOWTHE

APPLI

C A

TION

ON

C ABLE

WHI

CH

THE

IN

SULA

TION

HAVE RELATIVE PERMITT IVITY I = 0.5 & 2)



Application of FEM

1. Calculate electric field inside HV transformer 2. Calculate electricfield inside HV cable 3. Study electric field

distribution betweenelectrodes 4. Calculate electricfield stress of bushingColor code

Equipotential is presented as a line.

Red is conductor.

Green is insulator.

Black is air or oil .



SHOW AC ELECTRIC FIELD DISTRIBUTION IN AC- TRANSFORMER INSULATION



SHOW DC ELECTRIC FIELD DISTRIBUTION IN HVDC- TRANSFORMER INSULATION



SHOW AC ELECTRIC FIELD DISTRIBUTION OF CYLINDER OVER PLAIN



SHOW AC ELECTRIC FIELD DISTRIBUTION OF CONDUCTOR OVER PLAIN



SHOW AC ELECTRIC FIELD DISTRIBUTION IN CABLE INSULATION WITH GROUND AT ONE END



SHOW AC ELECTRIC FIELD DISTRIBUTION IN PARALLEL PLATE



SHOW AC ELECTRIC FIELD DISTRIBUTION IN VOLTAGE TRANSFORMER INSULATION



SHOW AC ELECTRIC FIELD DISTRIBUTION IN CAVITY IN INSULATION



SHOW NON - UNIFORM FIELD BETWEEN ROD - PLAIN

ROD

E

Emax

Emin

0 d

U

Eav



NON ² UNIFORM ELECTRICFIELD

max

Eav E

L !

: Field U t ilizat ion F act or L

U Eav

d !

:U Vol t ag e S t re ss between E lect rode s

: Eav Aver ag e orUniform E lect ric field S t re ss

max : E Maximum E lect ric field S t re ss

d: Gap di st ance between E lect rode s



SHOW AC ELECTRIC FIELD DISTRIBUTION OF ROD OVER PLAIN



SHOW AC ELECTRIC FIELD DISTRIBUTION OF CYLINDER CONDUCTOR OVER PLAIN



SHOW AC ELECTRIC FIELD DISTRIBUTION OF CYLINDER CONDUCTOR WITH SHIELD



ELECTRODES FOR TRANSFORMER OIL TESTER

ASTM D877

DISC GAP 25.4 mm. DIAMETER GAP 2.5 mm. ( 30 KVmin BREAKDOWN VOLTAGE)

0.8L !

IEC 156

SPHERE GAP 12.5 mm. DIAMETER GAP 2.5 mm. (60 KVmin BREAKDOWN VOLTAGE)

0.95L !

ASTM D1816

MUSHROOM GAP 35 mm. DIAMETER GAP 1 mm. (30 KVmin BREAKDOWN VOLTAGE)

GAP 2 mm. (60 KVmin BREAKDOWN VOLTAGE)

0.97 2 . for mm gapL !

0.98 1 . for mmgapL !



SHOW AC ELECTRIC FIELD DISTRIBUTION OF DISC GAP



SHOW AC ELECTRIC FIELD DISTRIBUTION OF SPHERE GAP



SHOW AC ELECTRIC FIELD DISTRIBUTION IN MUSHROOM GAP



SHOW AC ELECTRIC FIELD DISTRIBUTION ON POST TYPE INSULATOR



SHOW DC ELECTRIC FIELD DISTRIBUTION ON POST TYPE INSULATOR



SHOW AC ELECTRIC FIELD DISTRIBUTION ON POST TYPE INSULATOR WITHOUT SHED



SHOW DC ELECTRIC FIELD DISTRIBUTION ON POST TYPE INSULATOR WITHOUT SHED



SHOW AC ELECTRIC FIELD DISTRIBUTION ON PIN POST TYPE INSULATOR



SHOW DC ELECTRIC FIELD DISTRIBUTION ON PIN POST TYPE INSULATOR



SHOW AC ELECTRIC FIELD DISTRIBUTION ON SUSPENSION TYPE INSULATOR



SHOW DC ELECTRIC FIELD DISTRIBUTION ON SUSPENTION TYPE INSULATOR



SHOW AC ELECTRIC FIELD DISTRIBUTION ON LEAD ENTRANCE OF TRANSFORMER



SHOW AC ELECTRIC FIELD DISTRIBUTION IN OIL TYPE BUSHING



SHOW AC ELECTRIC FIELD DISTRIBUTION IN CONDENSER TYPE BUSHING



SHOW AC ELECTRIC FIELD DISTRIBUTION IN OIL& CONDENSER TYPE BUSHING



SHOW AC ELECTRIC FIELD DISTRIBUTION IN OIL& CONDENSER TYPE BUSHING WITH SHIELD RING




WITH SHIELD RING & BARRIERS



SHOW AC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF OIL TYPE BUSHING



SHOW AC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF CONDENSER TYPE BUSHING



SHOW AC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF CONDENSER TYPE BUSHING

WITH SHIELD RING & BARRIERS



SHOW DC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF AC CONDENSER TYPE BUSHING



SHOW DC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF DC CONDENSER TYPE BUSHING



Show AC Electric Field Distribution on Disconnecting S witch Finger Old Design



Show AC Electric Field Distribution on Disconnecting S witch Finger New Design



Show AC Electric Field Distribution on Disconnecting S witch Finger New Design wit h Shield Ring



Conclusion

Finite Element Method (FEM) is used to

determine cr itical point of power system

apparatus.

FEM is applied to calculate electr ic f ield

and potential distr ibutions of the newdesign of disconnected switches.

Application on Electric Field Distribution in Power Apparatus by FEM Correct1

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