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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 TECHNIQUESelectrostatic fieldanalysis methods Assistant Professor Suna BOLAT Eastern Mediterranean University Department of Electric & ElectronicEngineering
Electrostatic fieldanalysis methods • Analytical calculations • Analog methods • 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 lines analogy
To voltage source Model electrodes Electrolitic liquid (?)
Numerical methods • Finite difference method Principle: it leans on finite difference operations All the derivatives are substituted by numerical representations.
Numerical methods • Charge Simulationmethod Principle: simulating the field between condutors by using simulation charges
Q1 Q4 Q3 + + V1 X Q2 X B4 B1 + + X X B3 B2 + + + + ̃ V - - - - - V2 - -
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 • Type of the simulation charges • Number of simulation charges • Location of simulation charges • Number of boundary points • Location of boundary points
Types of simulation charges • Point charge • Line charge • ...
Point charge For spherical systems potential factor: () q P ()
q1 q2 q3 electrode X B1 X Boundary points X B1 B2 V
In general... [P] [q] = [V] Simulation charges vector Potential factor matrix 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:
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
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)