1. The charge simulation method (CSM) simulates an actual electric field with a field formed by discrete charges placed outside the region where the field solution is desired. 2. CSM determines the values of discrete charges by satisfying boundary conditions at selected contour points on electrodes. Once charge values and positions are known, the potential and field distribution can be easily computed. 3. CSM describes surface charge on an electrode boundary using fictitious point, line, or ring charges in the electrode interior. Charge types and positions are determined first, then magnitudes are calculated to satisfy boundary conditions.

1. Vanta Vachhoda
Branch : Electrical 6th sem
Subject : HVE
Name Enrollment No.
1. Parmar Dharmendrasinh G. 131030109029
2. Parmar Ajay R. 131030109027
3. Parmar Jaydeep V. 131030109033
Prepared by :

2. Charge Simulation Method
(CSM)

3. Contents
1. Abstract …………………………………………. 4
2. Introduction …………………………………... 6
3. Graphical simulation of charges ......... 7
4. Basic principle ………………………………… 10
5. Charge simulation method ……………... 12
6. Importance of CSM …………………………. 20

4. 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.

5. • 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.

6. 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.

7. Graphical simulation of charges
Point charge :
(a) Optimal position of
fictitious charges
(b) Electric Field comparison
at contour points

8. Line charge :
(a) Optimal position of
fictitious charges
(b) Electric Field comparison at
contour points

9. Ring charge :
(a) Optimal position of
fictitious charges
(b) Electric Field comparison
at contour points

10. 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.

11. • 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.

12. 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.

13. • 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)=

14. • 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]

15. • 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

16. • 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.

17. • 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.

18. • 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.

19. • 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.

20. 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.

21. • 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.