HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods
description
Transcript of HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods
![Page 1: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/1.jpg)
HIGH VOLTAGE TECHNIQUESelectrostatic field analysis methods
Assistant Professor Suna BOLAT
Eastern Mediterranean UniversityDepartment of Electric & Electronic Engineering
![Page 2: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/2.jpg)
Electrostatic field analysis methods
1. Analytical calculations2. Analog methods3. Numerical methods
![Page 3: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/3.jpg)
Analytical calculations
• Analytical solution of differential equations (Laplace, Poisson)• Conform transform• Schwarz – Christoffel transform• ...
![Page 4: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/4.jpg)
Analog methods
• Graphical methods• Experimental methods
– On the model– On a real system
![Page 5: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/5.jpg)
Numerical methods
• Finite difference method• Finite element method• Boundary element method• Charge simulation method• Monte – Carlo method• Moment method
![Page 6: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/6.jpg)
Experimental methods
• Electrolytic tank experiment• Semi-conductor paper method• Resistance simulation method• Grass seed method
![Page 7: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/7.jpg)
Electrolytic tank experiment
Principle: static electric field has an analogy with current field. Application: • Create a scaled model of electrode system• Replace the dielectric with a conductive material • Determine the current field lines on conductive media• Draw the electric field lines perdendicular to them
![Page 8: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/8.jpg)
Current lines Flux linesanalogy
![Page 9: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/9.jpg)
Model electrodes
Electrolitic liquid (?)
To voltage source
![Page 10: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/10.jpg)
Experimental setup
![Page 11: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/11.jpg)
Measurement bridge
![Page 12: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/12.jpg)
![Page 13: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/13.jpg)
Numerical methods
• Finite difference method
Principle: it leans on finite difference operations
All the derivatives are substituted by numerical representations.
![Page 14: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/14.jpg)
Letting k = h, (square grids)
![Page 15: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/15.jpg)
![Page 16: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/16.jpg)
Example
![Page 17: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/17.jpg)
Numerical methods
• Charge Simulation method
Principle: simulating the field between condutors by using simulation charges
![Page 18: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/18.jpg)
- - - - - -
+ +
+ ++ + +
+
- V2
V1
�V
Q1
Q2
Q4
Q3X X
XXB1
B2 B3B4
![Page 19: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/19.jpg)
Steps
• Place simulation charges outside of the region to be analyzed• Determine boundary points• Solve potential equation to calculate simulation charges for
boundary points• Control the value of charges• Calculate potential and electric field values for the desired
point using determined simulation charges
![Page 20: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/20.jpg)
Accuracy of this method depends on
1. Type of the simulation charges2. Number of simulation charges3. Location of simulation charges4. Number of boundary points5. Location of boundary points
![Page 21: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/21.jpg)
Types of simulation charges
• Point charge• Line charge• ...
![Page 22: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/22.jpg)
Point charge
For spherical systems
potential factor:
q P ()
()
![Page 23: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/23.jpg)
B1B1
B2X
XX
q1
q3q2
VBoundary points
electrode
![Page 24: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/24.jpg)
Voltages at the boundaries
![Page 25: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/25.jpg)
In general...
[P] [q] = [V]
Potential factor matrix
Simulation charges vector
Potential vector
![Page 26: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/26.jpg)
• After finding simulation charges, the value of the charges should be controlled
• Choose control points on known potentials&
![Page 27: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/27.jpg)
Potential of any point
Potential of any K point in the region:
![Page 28: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/28.jpg)
Electric field at any point
𝐸=𝑞
4𝜋 ε 𝑟 .1𝑟2
![Page 29: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/29.jpg)
Infinite line charge
For cylindrical systems
Pr0
𝜆=𝑄𝑙
l 𝑉 𝑃=𝜆2𝜋𝜀 ln
𝑟0𝑟
r0: the distance between line charge and the point with 0 potentialr: the distance between charge and the point P
V = 0
![Page 30: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/30.jpg)
Potential at my heart if I stand under a high voltage line
q
rHP
h
Conductor (line)
VL
Ground (earth)
Line simulation charge
V = 0
r
Suna
![Page 31: HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods](https://reader035.fdocuments.in/reader035/viewer/2022070421/5681632c550346895dd3a69d/html5/thumbnails/31.jpg)
Chapter 1 is over...