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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
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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
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Objective
To present application of Finite
Element Method in electric field
calculation in electrical apparatus
Determine highest electric field stresson electrical apparatus (Critical points).
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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
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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
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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.
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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.
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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)
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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)
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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 .
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN AC- TRANSFORMER INSULATION
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN AC- TRANSFORMER INSULATION
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN AC- TRANSFORMER INSULATION
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SHOW DC ELECTRIC FIELD DISTRIBUTION IN HVDC- TRANSFORMER INSULATION
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SHOW AC ELECTRIC FIELD DISTRIBUTION OF CYLINDER OVER PLAIN
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SHOW AC ELECTRIC FIELD DISTRIBUTION OF CONDUCTOR OVER PLAIN
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN CABLE INSULATION WITH GROUND AT ONE END
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN CABLE INSULATION WITH GROUND AT ONE END
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN PARALLEL PLATE
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN VOLTAGE TRANSFORMER INSULATION
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN CAVITY IN INSULATION
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SHOW NON - UNIFORM FIELD BETWEEN ROD - PLAIN
ROD
E
Emax
Emin
0 d
U
Eav
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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
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SHOW AC ELECTRIC FIELD DISTRIBUTION OF ROD OVER PLAIN
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SHOW AC ELECTRIC FIELD DISTRIBUTION OF CYLINDER CONDUCTOR OVER PLAIN
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SHOW AC ELECTRIC FIELD DISTRIBUTION OF CYLINDER CONDUCTOR WITH SHIELD
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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 !
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SHOW AC ELECTRIC FIELD DISTRIBUTION OF DISC GAP
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SHOW AC ELECTRIC FIELD DISTRIBUTION OF SPHERE GAP
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN MUSHROOM GAP
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SHOW AC ELECTRIC FIELD DISTRIBUTION ON POST TYPE INSULATOR
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SHOW DC ELECTRIC FIELD DISTRIBUTION ON POST TYPE INSULATOR
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SHOW AC ELECTRIC FIELD DISTRIBUTION ON POST TYPE INSULATOR WITHOUT SHED
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SHOW DC ELECTRIC FIELD DISTRIBUTION ON POST TYPE INSULATOR WITHOUT SHED
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SHOW AC ELECTRIC FIELD DISTRIBUTION ON PIN POST TYPE INSULATOR
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SHOW DC ELECTRIC FIELD DISTRIBUTION ON PIN POST TYPE INSULATOR
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SHOW AC ELECTRIC FIELD DISTRIBUTION ON SUSPENSION TYPE INSULATOR
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SHOW DC ELECTRIC FIELD DISTRIBUTION ON SUSPENTION TYPE INSULATOR
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SHOW AC ELECTRIC FIELD DISTRIBUTION ON LEAD ENTRANCE OF TRANSFORMER
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SHOW AC ELECTRIC FIELD DISTRIBUTION ON LEAD ENTRANCE OF TRANSFORMER
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SHOW AC ELECTRIC FIELD DISTRIBUTION ON LEAD ENTRANCE OF TRANSFORMER
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SHOW AC ELECTRIC FIELD DISTRIBUTION ON LEAD ENTRANCE OF TRANSFORMER
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN OIL TYPE BUSHING
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN CONDENSER TYPE BUSHING
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN OIL& CONDENSER TYPE BUSHING
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5/12/2018 Application on Electric Field Distribution in Power Apparatus by FEM Correct1 - slidepdf.com
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN OIL& CONDENSER TYPE BUSHING
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5/12/2018 Application on Electric Field Distribution in Power Apparatus by FEM Correct1 - slidepdf.com
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN OIL& CONDENSER TYPE BUSHING WITH SHIELD RING
![Page 48: Application on Electric Field Distribution in Power Apparatus by FEM Correct1](https://reader031.vdocuments.mx/reader031/viewer/2022020807/5571fe5e49795991699b3ce8/html5/thumbnails/48.jpg)
5/12/2018 Application on Electric Field Distribution in Power Apparatus by FEM Correct1 - slidepdf.com
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN OIL& CONDENSER TYPE BUSHING
WITH SHIELD RING & BARRIERS
![Page 49: Application on Electric Field Distribution in Power Apparatus by FEM Correct1](https://reader031.vdocuments.mx/reader031/viewer/2022020807/5571fe5e49795991699b3ce8/html5/thumbnails/49.jpg)
5/12/2018 Application on Electric Field Distribution in Power Apparatus by FEM Correct1 - slidepdf.com
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF OIL TYPE BUSHING
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF CONDENSER TYPE BUSHING
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5/12/2018 Application on Electric Field Distribution in Power Apparatus by FEM Correct1 - slidepdf.com
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SHOW AC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF CONDENSER TYPE BUSHING
WITH SHIELD RING & BARRIERS
![Page 52: Application on Electric Field Distribution in Power Apparatus by FEM Correct1](https://reader031.vdocuments.mx/reader031/viewer/2022020807/5571fe5e49795991699b3ce8/html5/thumbnails/52.jpg)
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SHOW DC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF AC CONDENSER TYPE BUSHING
![Page 53: Application on Electric Field Distribution in Power Apparatus by FEM Correct1](https://reader031.vdocuments.mx/reader031/viewer/2022020807/5571fe5e49795991699b3ce8/html5/thumbnails/53.jpg)
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SHOW DC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF DC CONDENSER TYPE BUSHING
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SHOW DC ELECTRIC FIELD DISTRIBUTION IN BOTTOM PART OF DC CONDENSER TYPE BUSHING
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Show AC Electric Field Distribution on Disconnecting S witch Finger Old Design
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Show AC Electric Field Distribution on Disconnecting S witch Finger New Design
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Show AC Electric Field Distribution on Disconnecting S witch Finger New Design wit h Shield Ring
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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.