1. HIGH VOLTAGE TECHNIQUES electrostatic field analysis methods Assistant Professor Suna BOLAT Eastern Mediterranean University Department of Electric & Electronic Engineering

2. Electrostatic field analysis methods 1.Analytical calculations 2.Analog methods 3.Numerical methods

3. Analytical calculations Analytical solution of differential equations (Laplace, Poisson) Conform transform Schwarz – Christoffel transform...

4. Analog methods Graphical methods Experimental methods – On the model – On a real system

5. Numerical methods Finite difference method Finite element method Boundary element method Charge simulation method Monte – Carlo method Moment method

6. Experimental methods Electrolytic tank experiment Semi-conductor paper method Resistance simulation method Grass seed method

7. 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

8. Current lines Flux lines analogy

9. Model electrodes Electrolitic liquid (?) To voltage source

10. Experimental setup

11. Measurement bridge

13. Numerical methods Finite difference method Principle: it leans on finite difference operations All the derivatives are substituted by numerical representations.

16. Example

17. Numerical methods Charge Simulation method Principle: simulating the field between condutors by using simulation charges

18. - - - - - - + + + + + + + + - V2 V1 ̃ V Q1 Q2 Q4 Q3 X X X X B1 B2 B3 B4

19. 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

20. Accuracy of this method depends on 1.Type of the simulation charges 2.Number of simulation charges 3.Location of simulation charges 4.Number of boundary points 5.Location of boundary points

21. Types of simulation charges Point charge Line charge...

22. Point charge q

23. B1 B2 X X X q1q1 q3q3 q2q2 V Boundary points electrode

24. Voltages at the boundaries

25. In general... [P] [q] = [V] Potential factor matrix Simulation charges vector Potential vector

26. After finding simulation charges, the value of the charges should be controlled Choose control points on known potentials&

27. Potential of any point

28. Electric field at any point

29. Infinite line charge For cylindrical systems P r0r0 l r 0 : the distance between line charge and the point with 0 potential r: the distance between charge and the point P V = 0

30. Potential at my heart if I stand under a high voltage line q r HP h Conductor (line) VLVL Ground (earth) Line simulation charge V = 0 r Suna

31. Chapter 1 is over...