charge simulation method

OM INSTITUTE OF TECHNOLOGYVanta Vachhoda

Branch : Electrical 6th sem

Subject : HVE

Name Enrollment No. 1. Parmar Dharmendrasinh G. 1310301090292. Parmar Ajay R. 1310301090273. Parmar Jaydeep V. 131030109033

Prepared by :

Charge Simulation Method (CSM)

Contents

1. Abstract …………………………………………. 42. Introduction …………………………………... 6 3. Graphical simulation of charges ......... 7 4. Basic principle ………………………………… 105. Charge simulation method ……………... 126. Importance of CSM …………………………. 20

Abstract

• Knowledge of electric field and potential distribution along high voltage insulators is of great importance in the design, operation and performance of the equipment.

• Most of high voltage field problems are so complex that graphical, experimental or analytical method of solution is very difficult.

• Hence, numerical methods of field calculation have been developed.

• In view of innumerable possibilities of complex electrode geometry configurations in equipments, and the electric fields being complex in these regions, analytical solutions for Electric Field Intensity are extremely difficult.

• The charge simulation method (CSM), due to its favorable characteristics, is very commonly used for field analysis of HV insulation systems.

• it has been tried to implement the basic charge configuration that is point, line and ring charges to CSM for electric field calculations and the results have been validated with that obtained by the analytical method.

Introduction

• In the charge simulation method, the actual electric filed is simulated with a field formed by a number of discrete charges which are placed outside the region where the field solution is desired.

• Values of the discrete charges are determined by satisfying the boundary conditions at a selected number of contour points.

• Once the values and positions of simulation charges are known, the potential and field distribution anywhere in the region can be computed easily.

Graphical simulation of charges

Point charge :

(a) Optimal position of fictitious charges

(b) Electric Field comparison at contour points

Line charge :



Ring charge :



Basic principle

• The basic principle of the charge simulation method is very simple.

• If several discrete charges of any type (point, line, or ring, for instance) are present in a region, the electrostatic potential at any point C can be found by summation of the potentials resulting from the individual charges as long as the point C does not reside on any one of the charges.

• Let Qj be a number of n individual charges and Φi be the potential at any point C within the space. According to superposition principle

• Where are the potential coefficients which can be evaluated analytically for many types of charges by solving Laplace or Poisson’s equations, is the potential at contour (evaluation) points, is the charge at the point charges.

Charge Simulation Method (CSM)

• It describe the surface charge present at the boundary of an electrode by fictitious, discrete the charges in the interior of the electrode.

• Point, line or ring type charges are possible depending upon the geometry.

• The position and type of simulation charges are to be determined first and then the magnitude of the charges are calculated so that their combined effect satisfy the boundary conditions.

• The potential of the various type of the charges are ( )= P( ) Q where, P – is potential coefficient dependent on location and type of charge Q – the charge or charge per unit length. For a point charge,

P(r)=

• The potential is known at the contour points on the electrode. If the charge location is also specified, we obtain the potential at the contour point K.

• Which leads to a matrix equation when extended to all counter points. The unknown charge can be determined by the inversion of [P].

[Ø]=[P][Q]

• After solving above equation it is necessary to check weather the set of calculated charges produce the actual boundary conditions everywhere on the electrode surface.

Fig. 1: Illustration of the charge simulation technique

• The potential coefficients will be as in the following equation :

• where, is the distance between contour point i and charge point j and is the distance between the contour point i and image charge point j’ as shown in Figure 1.

• As in Figure 1, the fictitious charges are taken into account in the simulation as point charges.

• The position of each point charges and each contour point are determined in X, Y and Z coordinates where the distance between the contour (evaluation) points are calculated as the following :

• where, Xj, Yj and Zj are the dimensions of the point charge and Xi, Yi and Zi are the dimensions of the contour point.

• Charge simulation for multi dielectric medium is more complicated than a single dielectric as under the influence of applied voltage the dipoles are realigned in a dielectric and it has the effect of producing a net surface charge on the dielectric.

• Therefore in addition to the electrodes each dielectric surface needs to be simulated by the discrete charges.

• The accuracy of simulation of multielectric boundaries deteriorates when the electric boundary has a complex profile.

• The error of this method depends upon type, number as well as the location of the simulation charges, the location of counter points and complexity of the profile of electrodes and the dielectrics.

Importance of the CSM

• The successful application of the CSM requires a proper choice of the types of fictitious charges.

• Point and line charges of finite length and ring charges have been used .

• In general, the choice of type of fictitious charge to be used depends upon the complexity of the physical system and the available computational facilities.

• In practice, most of the HV systems can be successfully simulated by using point, line and ring charges or a suitable combination of these charges

• The correct choice of the type of fictitious charges is very important, especially with respect to the realized accuracy. Also, it is very important to determine the position of fictitious charges.

Engineering

charge simulation method