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 linesCurrent lines Flux linesFlux linesanalogyanalogy

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

X

X

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.1

𝑟2

Infinite line charge

For cylindrical systems

Pr0

𝜆=𝑄𝑙

l 𝑉 𝑃=𝜆2𝜋𝜀

ln𝑟0𝑟

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...