Transcript Title should be like this A P Robinson1, P L Lewin1, S Sutton2, S

Modelling of Partial Discharge Activity in Cavity within a Dielectric Insulation Material
Tianyu Bai, D.J.Swaffield and P.L.Lewin
University of Southampton, Southampton, UK
The Simulation Model
Introduction
PD activity in a cavity within a solid dielectric material depends on the cavity size and its
location within the material. This is because the electric field distribution in the cavity
depends on the conditions of the cavity.
The modelling of PD in a spherical cavity within dielectric material by using FEA method
enables users to predict some PD parameters that relate to electric field distribution under
different conditions of the cavity, such as PD repetition rate, maximum discharge amplitude
and the inception voltage. This may assist in the condition assessment of electrical
insulation systems through comparison of experimental data with simulation results
Fig.2 shows details of the two-dimensional (2D) model geometry that has been developed in
FEA software . The model consists of a homogenous dielectric material of 1mm thickness
and 10 mm diameter and a spherical cavity. The PD physical charge and apparent charge
are calculated by time integration of current through the cavity center and through the
ground electrode respectively. The horizontal line in the cavity center represents the area
used to calculate the current for the PD physical charge calculation. A 50Hz sinusoidal
voltage is applied at the upper electrode while the lower electrode is always grounded to
study the effect of cavity size on PD activity, the cavity diameter is varied but its position is
fixed in the middle of the material. To study the effect of cavity location within the dielectric
material on PD activity, the cavity diameter is fixed but its location is varied between the
upper and lower electrodes. This model has been reported in several publications [1,2]
The theory of PD behaviour in the void
PD frequency dependent behavior is mainly determined by three factors these are, the
surface charge decay rate after a PD occurrence, the initial electron generation rate, which
depends on the cavity surface time constant,  s and thirdly, the detrappable electron
effective lifetime, trap. The effect of surface charge decay on PD frequency dependent
activity is more significant if  s and  trap are smaller than the period of the applied voltage.
The temperature decay time constant,  Tdecay in the cavity also influences PD frequency
dependent behavior if its value is comparable with the period of the applied voltage.
A discharge in a void results in a deployment of charges on the surface S of the void. The
i
surface-charge density  will attain such values
that the field within the void will reduce
until the discharge is quenched. In view of the principle of superposition, it is evident that
the induced charge related to the charge distribution on S can be expressed, in the form
q    dS
(1)
s
In which  is a dimensionless scalar function which depends on the position of
The function  is given by Laplace’s equation
dS only.
FEA Method and Test Object
Fig.2. Complete 2D axial-symmetric model geometry
This paper is an extension from previous work by the Tony Devices High Voltage
Laboratory which has considered the modeling of PD activity in a spherical cavity within a
dielectric material by using Finite Element Analysis (FEA) to study the influence of applied
frequency.
The cavity inception field is calculated by
Einc
FEA EQUATIONS
The electric field and temperature distributions in the model are solved by FEA software.
The electric field distributions is solved by electric currents module of the FEA method,
where the governing equation is
  (V )    (V / t )  0
(2)
Where V is the electric potential,  is the conductivity and  is the permittivity. Whilst the
temperature distribution in the cavity is solved using a heat transfer module by using
 C p T / t    (k T )  Q
Where T is temperature,  is the mass density, C p
(3)
is the specific heat capacity, k is the
thermal conductivity and Q is the heat source density. Equations (2) and (3) are coupled
through the Q term, where Q is equal to the voltage across the cavity, U cav and current
through the cavity, I cav,which is calculated by (2).
TEST OBJECT

B 
 ( E / p)cr p 1 
n 
 (2 pr ) 
(4)
Where ( E / p)cr , B and n are parameters of ionization processes characterization in the
gas, p is the pressure in the cavity and r is the cavity radius . The corresponding cavity
inception voltage U inc and the applied inception voltage U 0inc can be obtained through the
FEA model.
U inc
and
field
Einc
U 0inc
are the voltage across the cavity and the applied voltage when the electric
in the cavity is equal to the inception field respectively.
When the voltage across the cavity, U cav (t ) , exceeds the inception voltage, U inc , PD
might occur with a condition that there is an initial free electron available. The total electron
generation rate due to surface emission, N et (t ) , is written as
Net (t )  Nes (t ) exp(U cav (t ) / U inc )  Nev
Where N es and
ionization
Nev
(5)
are the electron generation rate due to surface emission and volume
Conclusions
Current research is developing a sample of silicon rubber containing an artificial cavity.
Fig.1 shows the schematic diagram of the test object which consists of an artificial
spherical cavity of variable diameter placed in the middle of a dielectric material of 1 mm
thick and 38 mm diameter. Silicon Rubber and hardener (mixture ratio of 10:1) has a small
bubble injected into it during the cure process. The whole test object will be immersed in
mineral oil to prevent surface discharges. A 50 Hz sinusoidal voltage will be applied to the
test object. In order to study PD activity under different stresses and cavity conditions,
different experiments will be undertaken. The experiments will investigate the effect of
varying the applied voltage frequency and magnitude as well as investigate the effect of
different spherical cavity diameters on PD behavior.
 A Finite Element Analysis model describing a spherical cavity within a homogenous
dielectric material has been developed. The model has been used to dynamically
simulate PD activity as a function of frequency of the applied voltage.
 The model will be further adopted to account for degradation processes within the void.
 An experiment based on a single void in silicon rubber will be used to validate the
modified model.
References
[1] H.A.Illias,G.Chen, and P.L.Lewin “ Modelling of Partial Discharge Activity in Different
Spherical Cavity Sizes and locations within a Dielectric Insulation Material,” International
Conference on Properties and Applications of Dielectric Materials, pp. 485-488,2009.
[2] H.A.Illias,G.Chen, and P.L.Lewin “Modelling of surface charge decay in a spherical
cavity within a solid dielectric material using Finite Element Analysis,” International
Symposium on High Voltage Engineering,2009.
Figure 1. Schematic diagram of the test object
Contact details :
[email protected]
University of Southampton, Highfield, Southampton, SO17 1BJ, UK