H. M. HU ET AL.

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ciated with the development probability:

''

''

,

''

,

()

(,, )()

ik

ik

piki k

(2)

The essence of the model is that the probability of

electrical tree growth depend on local field determined

by discharge pattern, the key part is to solve Laplace eq-

uation in each process step by step growth at a time,

which reflects the impact of the new unit potential[5].

3. Self-Organization Criticality

The growth of electrical tree has the characteristics of

self-organization critical phenomenon and self organiza-

tion critical problem was put forward by Bake [3, 4] in

the research of sand of cellular automata model. The

state consisting of a square piece of sand is imagined that

slope distribution decision. Slope of random point in the

area is of increased to simulate the increasing number of

grains of sand. This will lead to ch ange around a few points

of the slope when it is more than the threshold value of

grains of sand can slide to a lower position. However, the

redistribution of the slope is caused by the sand move-

ment and further collapse of sand. As the grains of sand

sliding, sand pile will tend to a dormant state at this time

of infinite slope near threshold .Gradually increasing

number of grains of sand will lead to different scale of

sand pile collapse. But th e system is still in the stationary

state near collapse because size cannot be thought of system

is in critical state. Main characteristic of self-organiza-

tion critical system is developing to a critical state spon-

taneously under the influence of external factors. In this

state there is no specific measurement, space or time and

constant input produced the intermittent output as well as

conforming to no specific proportion of the power law

distribution.

From the perspective of self-organized criticality,

along the electrical tree distribution channel of the charge

is a spatial extension of dynamic system and presents a

spatial extension of dynamic systems. Partial discharge is

the output of the whole system as well as external factors

as the applied voltage. It is necessary to consider about

non-locality, nonlinear contact of space charge and re-

striction of electrical tree in charge movement and so on.

4. The Simulation Principle

For any kind of insulation degradation mechanism, the

dielectric damage is caused by partial discharge the en-

ergy released and the local field strength. Therefore the

degradation mechanism of rules need to consider the

above two aspects. Discharge channel formation rules of

the judge need to consider medium damage accumulation

and random electrical tree growth. Probability distribu-

tion is used to describe the random growth, and then it

based on the experimental data analysis of physical me-

chanism of insulation damage, it calculates the probabil-

ity of discharge channel development and discharge en-

ergy, the relationship between electric field strength.

When local damage energy or local field strength is low-

er than the critical value, the development of the prob-

ability is zero. And when the damage energy reaches

critical value and the local field strength more than the

critical value, the existin g electrical p oints in the tree will

form a new discharge channel. Many a branching pattern

of one dimensional point is used to simulate electrical

tree and point d of the connection between the distances

determines the minimum space simulation ratio. Discrete

time constant t

is used to describe the transient proc-

ess of electrical tree growth as well as time step n corre-

sponding to instantaneous time n. The point i

corresponds to the charge and specific energy

and at each discrete time points in the electrode potential

will change. Existing electrical tree structure or the in-

crease of the electrode tip point is the simulation of elec-

trical tree growth which depends on the electric field

strength and the energy distribution of the damage.

However, partial discharge will lead to field strength,

failure energy, and charge distribution of change. The

process time lasted until the electrical tree structure come

into contact with the other electrode.

tnt

n

i

qn

i

W

Every point of the electric potential is equal to all the

charge voltage superposition，the i-th point on the po-

tential of a discrete time step n can be expressed as fol-

lowing[6]:

0

*

0

4rr

4rr

n

j

nn

ij

ji ij

n

j

jij

q

q

π

π

(3)

o

is the vacuum dielectric constant,

is the relative

dielectric constant, i

r

,

r

is the position vector, n

i

is

a part of point charge electric potential , relationship

lies on the size of the electric field distributed around

electrical tree channel, The minimum measure in space

adopts the size of space charge area,

n

i

q

n

i

is expressed in

Spherical charge formula:

0

2d

n

ni

i

q

π (4)

Specific damage energy of any i-th point at ex-

isting electrical trees reaches a critical value c, there is

a new point is attached to the structure. Several addi-

tional locations are randomly situated around i-th point,

the gaps between them and i-th point are not less than

bond length d, and the selection of lately add itional posi-

tion among certain number of impossible locations is in

n

i

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