Ionization peocesses and It's types

• At normal temperature and pressure, a gas acts as good insulting materials.
• When high voltage applied between the two electrode immersed in gaseous medium, the gas becomes a conductor an electrical breakdown occurs.

• Ionization by collisions are two types :

1. Elastic collisions : Elastic or simple mechanical collisions in which the energy exchange is always kinetic.
2. Inelastic collisions : Inelastic collisions, in which some of the  kinetic energy of the colliding particles is transferred into potential energy of the struck particle or vice versa.

GASES AS INSULATING MEDIUM :

• Few years ago, most of the electrical apparatus are used air as a insulating medium.
• Now a days, various gases are used for insulating medium such as nitrogen (N2), freon (CCl2F2) and sulphur hexafluoride (SF6).
• During testing when applied voltage is low, small currents flow between the conducting electrodes and the insulation keep its electrical properties.
• Whereas, if applied voltage is high, the large amount of current flowing through the insulation between electrodes and an electrical breakdown occurs.
• The maximum voltage applied to the insulation at the moment of breakdown occur is known as breakdown voltage.
• Two types of electrical discharge in gases :

1. Non-sustaining discharge
2. Self-sustaining discharge

• There are the various physical conditions of gases, like pressure, temperature, electrode field configuration, nature of electrode surfaces and the availibility of initial conducting particles are called the ionization processes.

Advantages and Disadvantages of Various Numerical Methods :

• For Computing the electric fields, various methods have been used, viz. Finite Difference Method, Finite Element Method, Charge Stimulation Method.

• Each of these methods has its own advantages for solving a particular problem.

• With the FDM, the numerical evaluation of the difference equation is simple but time consuming. For treating a given field problem, it is necessary to sub-divide the finite plane of the field problem into a predominantly regular net of polygons which is supplemented with irregular elements at the boundaries. However, in this method, all difference equations are approximation to the field equation by neglecting the higher order terms. Thus, the resulting error can be large.

• On the other hand, Finite Element Method is a very general method and has been used for solving a variety of problems. Any non-linearity/inhomogeneity can be modelled and the solution will be available on the entire surface of the domain. Material interface conditions are automatically satisfied. However, it needs a powerful graphic user interface for processing.

• Open geometry does not pose any problem with the Charge Stimulaion Method since the surface of the conductor is the only one that is discretized. In addition, as the solution satisfies the Laplace's/Poisson's equation, it will be very smooth, and always gives a small due to the application of superposition principle, non-linearities and non-homogeneity cannot be modelled using this method.

• Of the above methods, the choice of a particular method depends on the specific problem on hand. In general, the construction of Finite Element model requires considerable effort. Since the entire field region should be meshed. While the Charge Stimulation method require only the outer surface of the electrode and the outer layer of the dielectric to be meshed. In practice, an important difference between the various numerical methods in that the Finite Element Method can be used only with fields which are bounded while the Charge Simulation method can also deal with unbounded fields.

Charge Simulation Method (CSM)

Charge Simulation Method :

• This method is introduced by kelvin in 1872.
• H. Steinbingler developed this method for digital computation of electric fields in this dissertation submitted to the technical university Munich in 1969.
• The charge simulation methods is an integral equation technique unlike Finite Element Method (FEM) which is based on differential technique.
• It makes use of mathematical linearity and expressed Laplaces equation as a summation of particular solution due to set of known discrete fictitious charges.
• In effect the actual E-field due to the charges present on the electrode and dielectric boundaries is simulated by the field formed by a number of fictitious charges, which are placed outside the region where the field solution is desired.
• Location of the fictitious charges are predetermined by the programmer, while the magnitudes of these charges are found by satisfying the boundary condition at the selected number of contour points on the boundaries.
• The unknown charges are computed from the equation

                                                                       ...(1)

          where, [P] is the potential coefficient matrix

                      [Q] is the column vector of unknown charges

          and      [V] is the potential of the contour points (Boundary conditions)

• On knowing these  charges the potential and electric field intensity at any point can be determined from the combined effect of these charges.
• These are two variations of this method :

1. CSM with descrete charges
2. CSM with area charges

• CSM with discrete charges is based on the principle that the real surface charges on the surface of electrodes or dielectic interfaces are replaced by a system of point and line charges located outside the field domain.
• The position and the type of simulation charges are to be determined first and then the magnitudes of the charges are calculated so that their combined effect satisfies the boundary conditions.
• After determining these magnitudes by using the method of solving a system of linear equations, it is to be verified whether the systems of simulation charges fulfills the boundary  conditions between the location points with sufficient accuracy.
• Then the voltage and field strength at any point within the field domain can be calculated analytically by the superposition of simple potential and gradient functions.