Fields in multi-dielectric in isotropic system

Analysis of electric field intensity with multi dielectric in isotropic system :

• In every high voltage equipment, the insulation system form of more than one isotropic dielectric material.
• Example of dielectric material used for high voltage equipments like trabsformer oil (liquid), paper and ceramic dielectrics, compressed gas switch gears have ceramic and teflon (solid) and air, nitrogen or sulphur hexafluoride gaseous dielectrics.
• Different dielectric materials behaviour in an electrostatic field is divided by their primitive 'E' where

          E = E0Er

• In relative values variation of permittivity of dielectric materials in multi dielectric system extend to different potential and also field distribution in individual dielectrics.
• A multidielectric composite insulation system, shall have interfaces between any two dielectrics.
• In this system, interfaces are divided among themeselves by their direction with respect to the local field or current flow lines.
• The direction between an interface and electric field lines could be  longitude, perpendicular and diagonal.
• In recent years, several numerical methods for solving partial differential equations which include Laplace's and Poisson's equations have become available.
• There are inherent difficulties in solving these equations for two or three dimensional fields with complex boundary conditions, or for insulating materials with different permittivities and/or conductivities.
• Proper design of any high voltage apparatus requires a complete knowledge of the electric field distribution.
• For a simple physical system with some symmetry,it is possible to find an analytical solution. However, in many cases, the physical systems are very complex and therefore in such cases, numerical methods are employed for the calculation of electric fields.
• Essentially, four types of numerical methods are commonly employed in high voltage engineering applications. They are : Finite Difference Method (FDM), Finite Element Method (FEM), Charge Simulation Method (CSM) and Surface Charge Simulation Method (SSM) or Boundary Element Method (BEM).
• The first two methods are generally classified as domain methods and the last two are caterized as boundary methods.