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
HIGH VOLTAGE TECHNIQUESelectrostatic field analysis methods
Assistant Professor Suna BOLAT
Eastern Mediterranean UniversityDepartment of Electric & Electronic Engineering
Electrostatic field analysis methods
1. Analytical calculations2. Analog methods3. Numerical methods
Analytical calculations
• Analytical solution of differential equations (Laplace, Poisson)• Conform transform• Schwarz – Christoffel transform• ...
Analog methods
• Graphical methods• Experimental methods
– On the model– On a real system
Numerical methods
• Finite difference method• Finite element method• Boundary element method• Charge simulation method• Monte – Carlo method• Moment method
Experimental methods
• Electrolytic tank experiment• Semi-conductor paper method• Resistance simulation method• Grass seed method
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
Current lines Flux linesanalogy
Model electrodes
Electrolitic liquid (?)
To voltage source
Experimental setup
Measurement bridge
Numerical methods
• Finite difference method
Principle: it leans on finite difference operations
All the derivatives are substituted by numerical representations.
Letting k = h, (square grids)
Example
Numerical methods
• Charge Simulation method
Principle: simulating the field between condutors by using simulation charges
- - - - - -
+ +
+ ++ + +
+
- V2
V1
�V
Q1
Q2
Q4
Q3X X
XXB1
B2 B3B4
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
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
Types of simulation charges
• Point charge• Line charge• ...
Point charge
For spherical systems
potential factor:
q P ()
()
B1B1
B2X
XX
q1
q3q2
VBoundary points
electrode
Voltages at the boundaries
In general...
[P] [q] = [V]
Potential factor matrix
Simulation charges vector
Potential vector
• After finding simulation charges, the value of the charges should be controlled
• Choose control points on known potentials&
Potential of any point
Potential of any K point in the region:
Electric field at any point
𝐸=𝑞
4𝜋 ε 𝑟 .1𝑟2
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
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
Chapter 1 is over...