28-11-2012, 04:18 PM
Simulation of Electrical Tree Propagation in a Solid Insulating Material Containing Spherical Insulating Particle of a Different Permittivity with the Aid of Cellular Automata
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Abstract:
The electrical tree propagation inside a solid insulating material is simulated
in the present paper. The effect of a small insulating spherical particle inside
the solid insulating material is investigated as far as the electrical eld is concerned.
Laplace's equation is solved inside the solid insulating material setting the boundary
conditions around the spherical particle. An attempt for comparison between the
simulation results and experimental data from the technical literature is being made,
trying to shed light to the physical mechanisms that are involved in the phenomenon.
Introduction
The insulating capability of various insulating systems is affected by numerous
factors. Physical aging, chemical aging and electrical aging contribute to the deterioration
of the insulation performance and electrical trees are the visible result of
this deterioration [1]. Electrical trees are conducting channels, usually lled with
gas. They are strongly connected to the existence of air voids and are also correlated
with the space charge formation and partial discharge activity in the vicinity
of the electrical tree or near the injected electrode [2, 3]. The words tree and
dendrite are used interchangeably in the context of this paper.
Cellular Automata and the Related Algorithm
The process of the electrical tree propagation is simulated in the present paper
with the aid of Cellular Automata (CA) [30, 31] which is a well-known simulation
method covering various scientic elds and applications [32, 33]. The treeing
phenomena can be employed either as microscopic or as macroscopic phenomena,
which is very common for almost every physical dynamic system. The macroscopic
observation of the electrical tree patterns can be combined with the study of the
microscopic conditions that dene the tree propagation.
Denition of Boundary Conditions
The denition of the appropriate boundary conditions is crucial for the correct calculation
of the electric eld. Three simulations are presented in this paper. For
the rst case, the value of +80 kV is applied at the upper needle electrode. Fig.
2 shows the equipotential lines of the electrode arrangement with applied voltage
of +80 kV. The voltage of 0 kV is applied at the opposite plane electrode and the
boundary values around the dielectric sphere are calculated with the aid of the fol lowing equation [35, 36],
Discussion
The chemical bond breaking inside the solid insulating material is the mechanism
that is represented by the formation of one tree cell. The tree channel consists
of totally conducting material (gas) so the potential value applied at the needle
electrode is considered to be the same at every tree cell in contact with the electrode
cell.
As it is shown in Figs. 4-6, no tree inception is noticed from the insulating
particle. The physical meaning of this behavior is that the bound charges do not
have sufcient energy to break their chemical bonds. The case of electrical trees
emanating from insulating particles should not be excluded because from Eq. (2)
as is stated in the previous paragraph, it is clear that the position of the particle and
the potential values at the circumference of the particle are crucial factors for its
electrical behavior.
Conclusions
Treeing phenomena in the case of a small insulating spherical particle inside a
solid insulating material are simulated in the present paper. Using basic concepts
and equations of the Electromagnetic Field Theory, the appropriate boundary conditions
were applied at the insulating particle boundaries producing interesting results
in the simulation of dendrite propagation. The existence of the insulating
particle inside the dielectric material may be a a signicant factor for the electrical
tree propagation but not for its initiation.