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HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods

HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods. Assistant Professor Suna BOLAT Eastern Mediterranean U niversity Department of Electric & E lectronic Engineering. Electrostat i c f i eld analys i s methods. Analytical calculations Analog methods

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HIGH VOLTAGE TECHNIQUES electrostat i c f i eld analys i s methods

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  1. HIGH VOLTAGE TECHNIQUESelectrostatic fieldanalysis methods Assistant Professor Suna BOLAT Eastern Mediterranean University Department of Electric & ElectronicEngineering

  2. Electrostatic fieldanalysis methods • Analytical calculations • Analog methods • 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. To voltage source Model electrodes Electrolitic liquid (?)

  10. Experimental setup

  11. Measurement bridge

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

  13. Letting k = h, (square grids)

  14. Example

  15. Numerical methods • Charge Simulationmethod Principle: simulating the field between condutors by using simulation charges

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

  17. 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

  18. Accuracy of this method depends on • Type of the simulation charges • Number of simulation charges • Location of simulation charges • Number of boundary points • Location of boundary points

  19. Types of simulation charges • Point charge • Line charge • ...

  20. Point charge For spherical systems potential factor: () q P ()

  21. q1 q2 q3 electrode X B1 X Boundary points X B1 B2 V

  22. Voltages at the boundaries

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

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

  25. Potential of any point Potential of any K point in the region:

  26. Electric field at any point

  27. Infinite line charge For cylindrical systems l r0: the distance between line charge and the point with 0 potential r: the distance between charge and the point P r0 P V = 0

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

  29. Chapter 1 is over...

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