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IEEE
Transactions on Dielectrics and Electrical Insulation
On
PD
Mechanisms at
Vol.
8
No.
4,
August
2001
High
Temperature
589
in
Voids Included in an
Epoxy
Resin
R.
Schifani,
R.
Candela
Department
of
Electrical Engineering of Palermo University, Italy
and
P.
Romano
CRES, Centro per la Ricerca Elettronica in Sicilia
Monreale
(PA),
Italy
ABSTRACT
In
this paper the effects of temperature
on
partial discharge
(PD)
activity taking place inside
a spherical void in epoxy resin system are studied. Indeed, some experimental tests previ-
ously performed
on
specimens, having different void shapes, under multi-stress condition of
temperature and voltage, have shown very different
PD
amplitude distributions at tempera-
tures higher than ambient. However, this phenomenon cannot be explained only by taking
into account the different thermobaric conditions of the enclosed
gas.
In
consequence of the
general physical inaccessibility of such voids, a study is here performed using a numerical
model based
on
an evolutionary optimization algorithm. This is used to evaluate the range
values for the physical parameters of the insulating system influencing the observed changes
in
PD
activity, Finally, comments are presented about the adopted criteria by which the com-
parison between the experimental data and the simulated ones is performed, and about the
interpretation of the dependence
on
temperature of the experimental
PD.
1
INTRODUCTION
HE
necessity of higher and higher voltage levels in
HV
power sys-
T
tems has driven to a stronger demand of insulating materials with
high electrical performances at affordable costs. Since synthetic poly-
mers partially meet these requirements, they have been studied quite
a bit in the most recent literature. However, they are affected by some
aging problems also due
to
internal
PD.
These discharges take place
in consequence
of
unavoidable local defects produced by the industrial
manufacturing process, and promote local erosion of the material that
may cause electric breakdown of the component in time. The difficulty
of
performing reliable life predictions and suitable evaluations
of
their
reliability in presence
of
such degradation phenomena, hindered a wide
diffusion of
HV
components made of epoxy materials.
Recently, computer aided techniques based on pulse height analysis
or phase distribution analysis, have largely improved the possibilities
of investigation in this field
[l-41,
thanks to their capability of recording
and processing a large amount of data. Even though the information on
the 'aging state'
of
a system or on the incoming breakdown can be ob-
tained now in many cases, the comparative analysis between materials
in terms of resistance to
PD
activity can be improved further.
An intensive research activity on the subject has been carried out,
covering many aspects of this phenomenon. In particular,
two
main re-
search areas can be identified. The first area
[5-91
uses modern digital
measuring techniques in order to have some reliable indication regard-
ing the kind of internal defects, which has been recognized by means
of neural networks, and suitable numerical algorithms applied to the
acquired data. The second ohe
[lo-121
develops a pioneering work on
the physics of discharge, thus letting us know the basis to understand
the discharge mechanisms and to improve the existing
PD
models.
Since many years, the authors have been studying the characteristics
of
PD
activity in enclosed cavities at temperatures higher than the am-
bient, because some dielectric materials
[13,14],
like the ones employed
in electrical machines, are subjected in service to a condition where
PD
are found to be active under multistress conditions. On this subject,
little information is available in the literature.
In
this paper a study
on
PD
activity into an embedded spherical void at different working
temperatures is presented. Starting from the current knowledge of
PD
physics; the temperature parameter
T
has been taken into account in
all the equations describing the phenomenon. This dielectric configu-
ration has been chosen because its electric field and
PD
activity is well
known at
ZOT,
and because it is frequently encountered in insulation
systems.
1070-9878/1/
$3.00
0
2001
IEEE
590
Schifani
et
al.:
PD
at
High
Temperature
in
Epoxy
Resins
2
SOME PHYSICAL REMARKS
of
N
1%.
Therefore, the following equations can be written
17)
ON THE SPECIMEN
P&,V&~
=
nRpT1
In order to characterize the insulating system dependence on the
environmental temperature, it is necessary to know the electric field in-
side the void, the pressure during the initial stage of discharge activity,
and the thermal characteristics of the epoxy resin.
2.1
ELECTRIC FIELD
Considering a spherical void of radius
R,
in the middle of a solid
dielectric material between a couple of plane electrodes, it is known
that the electric field distribution inside and outside the void can be
evaluated solving the Laplace equation
where V is the scalar potential function. Equation
(1)
can be rewritten
by spherical coordinates in a two-dimensional form
v2v
=
0
(1)
where V is referred to as'V(r,
e).
Inside the cavity the solution is
3E
Eor
cos
6'
v.
-
-~
Eo
+
2E
2-
r<R
(3)
where
E~
and
E
are respectively the absolute permittivity of the gas
inside the void and of the surrounding dielectric, and
EO
is the electric
field in absence of the void. The field inside the void along the main
diametral axis
(O=O)
is
(4)
As can be noted
in
Equation
(4),
the temperature acts on the electric
field through a function of the solid dielectric permittivity
E(T),
e.g.
through the
f
(T)
parameter.
2.2
MAKING
TEST SPECIMENS
Another parameter on which the related discharge activity depends
is the pressure
p
inside the void, which is linked
to
the adopted man-
ufacturing process for the specimen.
In
our case it is not possible to
perform an exact measurement of
p,
but only a theoretical evaluation
of it. The dielectric material used is an electrical graded epoxy resin
(Bakelite GmbH: EA330 KAtKB), which is subjected to the following
thermal cycle: curing at T1=353
K
for
6
h dnd a post-curing at T2=403
K
for 15 h. Spherical.defects have been produced artificially by injecting
a defined quantity of dry air into the resin during its curing phase. At
the beginning, the gas pressure in the void is considered to be
100
kPa
because this phase takes place in an open vessel. After curing, the resin
presented an estimated hardening shrinkage of
N
3%
(volume). There-
fore, the ordinary gas equation can be expressed as
with V+l and V&,
pbl
and
pg1
representing the volume and the
pressure before and after the resin curing phase, and where V:l
=
V;,
/1.03
from the above 3% shrinkage assumption. Therefore from
P;.lV&l
=
PklV&(1 (5)
Equation (5) it holds (in kPa)
p$l
=
1.03ph1
=
103
\'
f
pb2V4,
=
nRgT2
where
n
is the number
of
moles, R,=8.314510 Jmo1-lK-I is the univer-
sal gas constant, V&2
=
VQl
(1
+
3aAT)
and a=30~10-~
K
is the
thermal expansion coefficient of the resin. From the ratio between Equa-
tions
(7)
it follows that
p&,=118
kPa. The pressure value obtained at
the end of the post-curing phase
pg2,
evaluated by the ordinary gas
equations (written at constant temperature) and roughly considering
that V.-2
=
V&2/1.01,isp$2=119 kPa.
Bringing the cooling process down to 293
K
(To)
and considering
that
V;2
=
V~o(1
+
3aAT),
it
is possible to get
p~0=87
Wa.
In
a similar way at
TI,
it resulted in
p~1=104
kPa. Observe that, even if
the volume cavity may be considered constant between
TO
and
TI,
the
related pressure changes of only
10
to 15%.
Er
52
4.6
4.0
3.4
20
40
60
80
100
120
T,k
Figure
1.
E~
as
function
of
temperature
at
constant frequency
2.3
THERMAL CHARACTERISTICS
OF
THE RESIN
In order to set the thermal environmental conditions for the study
of
PD
activity and
to
obtain the
f
(T)
curve in Equation
(4),
the knowledge
of
E(T)
at 50
Hz
is required. But, the difficulty of obtaining experi-
mentally such curve is well known because the 50 Hz frequency is also
the power frequency and the results could be corrupted by an high in-
terference noise level coming from the feeding instrumentation used.
For this reason the resin permittivity dependence on temperature was
investigated in a set of five frequencies (from
400
Hz up to
1
MHz)
and
then the results were extrapolated at 50 Hz.
In
this aim a sheet speci-
men
(1
mm
thickness) has been put into a three-electrode holder where,
in order to avoid any influence of atmospheric moisture, a low pressure
(w
50 Pa) condition was induced. A computer controlled and auto-
matic precision bridge was used to get
E~
measurements in the above
frequency range and temperature going from the ambient up
to
120°C
with an heating specimen rate of
N
l"C/min. The results reported in
Figure
1
show a very negligible effect of temperature on permittivity,
so
that the
f(T)
function has been assumed constant in practice and
equal to 1.32 in the range of our interest.
2.4
SURFACE CONDUCTIVITY
OF
THE
RESIN
During the post-curing phase the temperature is raised to 403
K
and
has been kept constant for 15 h. As a result, the resin has a thermal ex-
pansion (from
TI
to
7'2)
which superimposes another shrinkage phase
Another parameter, on which
PD
depends, is the wall surface con-
ductivity of the enclosed void. Indeed the discharge activity produces
IEEE
Transactions
on
Dielectrics and Electrical Insulation
Vol.
8
No.
4,
August
2001
591
many gaseous byproducts that attack the resin surface in consequence
of their chemical nature. This consequently changes the surface conduc-
tivity of the resin.
A
virp epoxy specimen,
e.g.
not subjected to dis-
charges, generally presents a surface conductivity
k,
of about
10-l8
or
R
-I.
Bartnikas
et
al.
[12] have experimentally observed that
epoxy surfaces of plane shape directly exposed to
PD
in uniform elec-
tric field undergo important chemical and physical modifications; for
instance a strong increase of the surface conductivity from to
-
has been found. This important increase was observed to
happen during the first 100 h of exposure to
PD,
then
k,
appeared to
go
toward a saturation level. On the other hand Ku-Liepins [15] observed
that when the temperature of a resin increases from 20 to 150"C, the
surface conductivity goes up to
IOW4
R
(Equatorial area
of
the
void
not
directly exposed
to discharge activity)
iP:llr
area
of
the void
'
directly exposed to
discharge activity)
Figure
2.
Spherical void
in
a generic discharge condition.
However, in the case of a spherical void, some further useful aspects
should be pointed out. For instance not all the areas of surface cavity
are equally attacked by discharges,
e.g.
a more complex mechanism due
to surface conductivity should be observed. Actually, the void surface
sections parallel to the electric field are less, and differently, eroded than
the areas which are hit perpendicularly by the discharges, as shown in
Figure 2 where the evolution of a generic discharge is depicted. There-
fore, a surface conductivity causing a sensible
PD
charge decay would
be effective only if it is active along the equatorial area of the void,
e.g.
parallel to the
PD
current flow. This surface is not bombarded by charge
carriers and therefore can remain non-conducting during the tests. It is
this surface conductivity which we will refer to by the
k,
symbol. Con-
sidering that in this experimental work the tests have been performed
at 20 and at 80°C and that aging phenomena can be ignored during their
execution, a reasonable assumption for the related change of the resin
conductivity due to temperature increase has been set to
-
2 orders of
magnitude starting from
R
-1
that was assumed at 20°C from
the resin data sheet.
.
3
THEPDMODEL
The basic physical principles upon which the
PD
model is built, are
known from the literature [16,17]. Many types of discharge can gener-
ally occur in epoxy embedded voids [18]. They are streamer discharges,
Townsend discharges, swarming partial microdischarges, and glow dis-
charges.
They are distinguished by their charge magnitude and current shape
signals [19]. In this work the study is restricted only to the experimen-
tally detected pulsive discharges (streamer), which are associated with
higher pulsive-shape currents and detectable by conventional
PD
detec-
tor systems. Other discharges usually produce a much lower charge, or
are pulseless. Furthermore, in most cases, it has been found that they
are active during the aging progression of a void [20].
On the basis of Equation
(4)
the field inside the cavity of radius
R
is
(8)
4
E
=
fE0
f
-
7rry&O
where
fq
is the charge deposited on the cavity polar area (having
r1
mean radius, obviously lower than
R)
by previous
PD
activity in the ac
steady state, as shown in Figure 2.
It is accepted that the inception field
Ei
to produce a streamer dis-
charge within a spherical void has to exceed the value [21]
In the last equation, (E/p),,=24.2
(V
Pa-".')
e.g.
the value of
E/p
for which the effective coefficient of ionization
rj
is zero, B=8.6 (Pa
m)'
5,
n=0.5
(characteristic properties of the included air at constant
temperature), while the residual value of the electric field
E,
in the
cavity after a discharge is here assumed equal to
y
(E/p),,p
with y=0.2
[17]. Therefore, once the condition given by Equation (9) is fulfilled,
a starting electron is need for triggering the multiplication avalanche
mechanism. This electron availability has a random nature, thus the en-
suing
PD
phenomenon results in its classical statistical time evolution.
Our experience in the tests performed at 20°C was very similar to the
one of other authors [17]: when discharges were ignited by natural radi-
ation after a relatively long inception delay, then they continued involv-
ing a mechanism practically controlled by surface charge de-trapping
emission.
When the test temperature was elevated to 80°C (as a hypothetical
consequence of the real working condition for the dielectric material),
the enclosed void was subjected to a transformation at constant vol-
ume,
e.g.
the gas density remained constant while the inside pressure
increased as a consequence of the increased kinetic energy of the gas
molecules. In principle, this should give the same and identical dis-
charge mechanism as at
20"C,
but in the experiments carried out and
here presented, the inception discharge voltage resulted at 80°C
-
40%
higher than at 20°C and in all the specimens,
PD
presented a sort of
intermittency. This fact has been assumed as indicative of a different
phenomenon taking place at 80°C and, following the classical discharge
theory, the increase of pressure does not seem to be as the only impor-
tant cause. However, on the basis of the results obtained at the end of
Section 2.2.
(Elp),,
has been assumed constant in Equation (9) within
the examined temperatures, while the evaluated increase of
p
has been
reported on the
E,
value. Furthermore, the
PD
activity has been mea-
sured without an external X-ray source, that is in natural conditions,
and subjecting a virgin specimen to 20 kV, 50 Hz constant voltage until
discharges appeared. Then it was left under this voltage for a further
4
h to let discharging phenomenon
go
to the steady state condition, and
thus the discharge inception voltage was measured in agreement with
the IEC-Standard
No.
270,1981.
592
Schifani
et
al.:
PD
at
High
Temperature
in
Epoxy Resins
The charge
q
in Equation
(8)
is not a constant quantity, but it mainly
changes because of the transferred charge
Aq
due
to
the previous dis-
charge:
Secondly a further change, which
q(t)
is subjected to, can be due to
charge surface conduction along the equatorial area of wall cavity, ac-
cording to
Ohm's
law
Aq
=
E,.,TT;(E
-
ET)
(10)
--
dq
-
-
G(T)Ed
dt
where
G(T)
is the surface conductance of the resin as a function of
temperature.
In
particular,
G(T)
can be expressed approximately as
function of the specific surface conductivity
ks
where
d
is the mean distance, in the electric field direction, between the
two polar areas of the void where the discharge is taking place. It has
been assumed that the hypothetical conducting surface is the mantle of
the equivalent cylinder of
d
height as represented in Figure 2.
After the
PD
activity has been started, a main source of initial elec-
trons became the surface emission mechanism of the charges deployed
on the void surface. However, at the moment the surface emission phe-
nomenon in
PD
working conditions is not sufficiently understood in its
physical mechanism. Therefore, let us consider the number of trapped
electrons
(13)
q(t)
Ne
=
e
where
e
is the elementary charge. Part of the
Ne
electrons released
on the void surface diffuse into energetically deeper traps and/or into
depth of the insulating material from where they are no more ex-
tractable.
To
consider
tlus
loss from a phenomenological point of view,
the surviving electrons could be modeled roughly by an exponential
decay term
exp
-
(
t/qr)
with a time constant representing an effec-
tive lifetime of the electrons in an extractable trap. Furthermore, these
electrons are supposed to be thermally de-trapped and then emitted
from the surface on the basis of the
q5tr
function value, which is
where
q5
is the de-trapping work function
of
the material expressed in
eV. This should give a surface de-trapping rate
Ni
=
Ne
exp
(-
i)
vo
exp
(-
&)
(15)
where
WO
is the fundamental phonon frequency
of
the material,
K
the
Boltzmann constant
(8.617385~10-~
eV
K-')
and
T
the absolute tem-
perature. If one wishes also to consider the production of electrons
coming out from the natural radiation phenomenon, that is supposed
to
be always present, then the following should be taken into account
NT
=
c,~,
(E)
p(n~3)(1
-
p-0.5)
(16)
0
where
CTQT=2x106
kg-ls-',
(p/~)~=lo-~
kg
m-3 Pa-' is the pressure
reduced gas density and
p
is the ratio between the applied voltage and
the streamer inception voltage derived from Equation
(9).
Therefore,
the total rate production of electrons ready
to
trigger a discharge be-
comes
Nt
=
N,
+
NT
(17)
In order
to
consider the statistical aspect of
PD,
a new probability
function for the occurrence of a discharge has been defined here as
m
P(dt)
=
Cp,
[
1
-
exp
{-
( )"
}]
(18)
l=i
where
m
is the number of elementary Weibull functions fitting the ex-
perimental data and
a,
and
,Dz
their parameters. In our experimental
work, it resulted in m=2 for 20°C and
m=l
for 80°C.
This
probabil-
ity function has been chosen because it has better capability (by means
of
a
and
,D
parameters) to reproduce the observed different statisti-
cal aspects of
PD
at
20
and
80°C.
Therefore, in the time interval
dt,
if
the previous condition
of
Equation
(9)
is fulfilled, then Equation
(18)
is evaluated and compared with a random generator's output. If this
number is smaller than
P(dt),
then the electron is assumed to trigger
the discharge.
Direct comparisons between the simulated data and the experimen-
tal ones have been performed by evaluating the apparent charge
Aq'
induced at the electrodes by each true charge
Aq
givenby Equation
(10)
in agreement to the relation
[16]
where, for a spherical void of diameter
2R,
g
=
2~,/(1
+
2e,)
and
VXo
is the gradient
of
the dimensionless scalar field function
XO
[21],
which characterizes the coupling of the defect location to the measuring
electrodes.
Aq'
=
Aqg2RVXo
(19)
4
EXPERIMENTAL TEST
To
study the temperature effect on
PD
activity, many specimens have
been made with void diameters ranging from 1.3
to
2
mm,
but with
constant inter-electrode resin thickness equal
to
3.5
mm.
All
tests have been performed in agreement with a well defined pro-
cedure, either at
20°C
or at
80"C,
following the steps as below reported:
1.
select the temperature
to
use in
PD
tests,
20
or
80T,
2.
subject the specimen
to 50
Hz
sinusoidal voltage
of
20
kV
until dis-
3.
leave
the specimen under the second condition
for
4
h
to
be
sure
PD
4.
measure
PD
inception voltage,
5.
start
with
PD
measurements
after
the specimen has been left for
at
least
charge activity starts,
activity
is
in steady
state
conditions,
5
min
at
the
test
voltage, that
was
chosen
between
10
and
32
kV.
A
digital instrument
[8]
have been used in the experiments.
This
is
able to produce and store in computer memory
two
data vectors, the
first related to the amplitude discharges, the second to the correspond-
ing phase angles of the test voltage. The selected acquisition time was
30
s.
Thus, a suitable elaboration software outputs the following dia-
grams:
1.
H(q,
n)
amplitude
histogram,
as
number
of
discharges
n
us.
dis-
2.
H(p,
qm)
charge-phase histogram,
as
the mean charge value
qm
US.
3.
H(9,
n)
phase histogram, as number
of
discharges
n
us.
the ignition
charge amplitudes
q
(positive and negative);
the ignition phase
of
test voltage,
9%.
phase
of
test
voltage
9%.
IEEE
Transactions on Dielectrics and Electrical Insulation
Vol.
8
No.
4,
August
2001
593
300
350
400
450
503
Discharge
anylitude,
@q
Figure
3.
Amplitude histograms
of
positive discharges from
12
to
32
kV
of
a
2
mm
spherical void at 20°C.
-I
s
1.3
:I
200
a"
1,5
0
1
0
200
400
600
800
1000
Amplitude
discha%e,
(pQ
Figure
4.
Amplitude histograms
of
positive discharges at
20
kV
for
different
void
diameters
at
20°C.
279
1
Discharge number
(n)
I
'I
I
I
,
Eip
20'C
-90"
0"
SO'
180"
270"
Discharge phase.
(cp")
Figure
5.
An
experimental
3d
histogram
of
PD
in
a
1.8
mm
spherical
void at 28
kV
and
20°C.
However, a three-dimensional representation of the above data is
often required in terms
of
H(p,
q,
n)
distribution.
In Figures 3 and
4,
some measurements made at
20°C
are reported.
The tests have been performed either on a specimen having a 2
mm
diameter cavity with voltages ranging from
12
kV (discharge inception
voltage) to 32 kV, or on specimens with different cavity diameter, but
at constant voltage of 20
kV
In this case, only positive discharges have
been reported since the negative ones resulted almost symmetrical to
the former. The discharge activity can be considered as the combination
discharges having almost the same amplitude and the second one of a
small number
of
discharges with higher amplitudes. Their disposition
within the voltage period is clearly shown in Figure 5, where a three-
dimensional
PD
Pattern for a specimen subjected to 28 kV, having an
embedded void with
1.8
mm
diameter,
is
reported.
In
particular, the
second group of discharges (higher amplitude discharges with lower
repetition rate) is concentrated in the area of the sign inversion of the
electric field.
0
1000
2000
3000 4000
Discharge
ainplitudc,
(pC)
Figure
6.
Direct comparison between discharges at
20
and at
80°C
in
a
2
mm
void at
26
kV.
7
..:
Discharge number,
(n)
,/
!
,'
i
Ewp
80°C
-90"
0"
90"
180"
270'
Discharge phase,
((PO)
Figure
7.
An
experimental 3d histogram
of
PD
in
a
1.8
mm spherical
void
at
28
kV
and
80°C.
The tests performed at 80°C show a discharge mechanism quite dif-
ferent with respect to
20T,
as
is
seen in Figure
6
where
two
measure-
ments at
20
and
80°C
are reported for direct comparison purposes.
Fur-
thermore, the range between the minimum
(qmin)
and the maximum
value
(qmax)
of
detected discharges becomes at
80°C
much larger than
at
20"C,
and a lower and lower discharge repetition rate is observed.
The peak shaped histogram
of
the amplitude discharges is no more
present and the pulse charge magnitudes are randomly distributed
within the
qmin,
qmax
interval. The 3d
PD
pattern histogram has con-
sequently changed, as Figure
7
shows the case of a 1.8 mm diameter
of
two
groups of discharges, the first one made of a large number of void, and the dischargeshave now a completely different amplitude
594
Schifani
et
al.:
PD
at
High Temperature in
Epoxy
Resins
and phase distributions. Furthermore, the ratio between the discharge
number in a voltage period at 20 and at
80°C
became
w
10,
e.g.
one is
stressed to believe that at
80°C
the electron availability inside the void
becomes drastically reduced.
5
INTERPRETATION
OF
80°C
PD
DATA
BY
A NUMERICAL
MODEL
On the basis of what reported in the previous Section, a model of
PD
activity has been attempted first at 20T, and afterwards at 80°C
by a program written (Visual
Ctt)
in our laboratory. While the pres-
sure
p
inside the cavity and the resin surface conductivity
ks
are easily
identifiable either from a numerical point
of
view and from their de-
pendence on temperature (see Sections 2.2 and 2.4), the others parame-
ters entering the model via Equation
(15)
can be identified in
q,
and in
the exponential term
v,
exp(-q5/KT)
that as a whole can be called
The software used for evaluating
Ttr
and
C(T)
parameters was de-
rived from the differential evolution
(DE)
algorithm described in [22]. It
can be categorized into a class of evolutionary optimization algorithms,
comprising genetic algorithms and evolution strategies. Like any other
evolution process
in
nature,
DE
maintains a population of alternative
solutions for the optimization problem to be solved. These alternative
solutions are individuals of the population, from which the population
of the next generation is created using a specific reproduction scheme.
A cost function, used for evaluating individual solutions, is minimized
comparing the Weibull distribution obtained from the experimental test
with the same distribution output by the numerical
PD
model. Obvi-
ously,
individual solutions with a low cost function value have higher
probability to survive to the next generation than the individuals with a
highvalue. The parameters
found
by the program are
of
course not the
exact mathematical solution of the problem (which we
do
not know)
so
to get some rigorous physical interpretation
of
the phenomenon but,
knowing their related range values from the heuristic knowledge of
the phenomenon and following the idea of finding model parameters
that are physically reasonable in describing the experimental data, we
deemed they could be defined as good parameters for our purpose.
Furthermore, in consequence
of
the random nature of
PD,
a statistical
analysis has been performed on the solutions found by the numerical
model to check their compatibility with the experimental data. Once
the simulation was performed at 20T, the main authors goal in this re-
search was to find the change direction (increase or decrease) to which
the
T~
and
C(T)
parameters are
to
be submitted to in order to have
a
possible simulation
of
the
PD
activity occurring at
80°C.
Finally, a sen-
sitivity analysis on the parameters of the solutions here presented has
been added.
After [23] it has been found that for polymers, typical values for
v,
are
of
the order
of
10l2
to
1014
Hz,
while a range of
0.5
to
1.8
eV
has been assumed for the work function of the resin. Consequently,
C(T)
was defined in the range to be inspected. An oriented strategy
must be followed for the choice of the
nr
range. Actually,
nr
has been
supposed to be within
1
and
10
ms at
20°C
[16,17],
while at
80°C
an
higher and higher value,
to
1000
s,
has been hypothesized in agreement
to what showed in
[17]
for some experimental and simulated life tests
C(T).
performed on specimens similar to those ones here reported. Currently,
it is not possible
to
give a precise and physical explanation about this
very high value, since
Ttr
is essentially a phenomenological parameter,
but the related results here reported are quite in agreement with this
increase tendency.
The numerical model simulates a
PD
activity along 30
s
in a geomet-
rically and physically defined specimen giving as output
two
arrays,
the first one related to the pulse discharge amplitudes and the second
one related to the corresponding phase angles
of
the test voltage. As
already said, to each found solution a statistical filter has been applied.
On the basis of the results presented in literature
[24],
it can be ar-
gued that statistical analysis
of
PD
data
can
give
useful information
because thousand of data can be compressed into simple numbers eas-
ier to be manipulated. In particular, to represent the shape profile of a
discrete distribution
yz
=
f
(z2)
it is widely accepted the use of the
Skewness
(Sk)
and Kurtosis
(Ku)
parameters. More precisely, they are
the third and the fourth moments of
f(z,),
defined as
n
C
(z2
-
m')3f(zz)
(20)
Sk
=
z=1
u3
5
f(G)
cT4
i:
f
(xz)
z=1
n
C
(z2
-
m')4f(~z)
(21)
I(
-
a=l
u-
-3
2=1
where
m'
and are the average value and the standard deviation
of
f(z,)
respectively. Others parameters that have been taken into ac-
count are: the
PD
average discharge current, defined as [25]
I,,
=
-
with
AT
the acquisition time, and
the
voltage discharge phase range
for positive discharges
Ap"
(+)
and for negative ones
AV"(-),
and
the discharge number acquired in
30
s.
The above parameters have been evaluated for the
PD
patterns ob-
tained from measurements performed on a sample of five identical
specimens at
20
and
80°C
under different voltage levels and with void
diameters ranging from
1.7
to
1.9
mm,
optically checked.
In Table
1,
the scatter range experimentally found at 20°C for each
of the above parameters is reported in the second, fourth and sixth col-
umn.
In the third, fifth and seventh column the results obtained from
the one
of
the simulated tests which has the higher percentage
of
sta-
tistical parameters entering within the related experimental ranges are
reported. The hypothetical void diameter was 1.8
mm
and the simula-
tion has been performed for
30
s
under 28 kV.
In
Figure
8
the related
3d pattern together to the values of the parameters
Ttr
and
C
(20°C)
found by the
DE
algorithm are reported. It should be noted that
SI,
and
K,
parameters have been evaluated on three distributions,
e.g.
H(q,
n),
H(p,
qm)
and
H(p,
n).
A global analysis of the data puts
into evidence a fit of the simulation, that could be considered good since
N
70%
of the related parameters are falling into the corresponding scat-
ter range of the experimental data, and only a few of them are close to
the scatter range limit. In particular two of them,
e.g.
the kurtosis pa-
rameter applied to
H(p,
n)
for positive and negative discharges, are
(22)
'
c
14al
AT
IEEE
Transactions on Dielectrics and Electrical Insulation
Vol.
8
No.
4,
August
2001
595
-1
~
270
I
Oischarqenumber
(n)
4000
-90"
0"
so"
180"
2704
Discharge phase
(q9)
Figure
8.
An
example
of
simulated
3d
histogram
of
a
1.8
mm
spheri-
cal
void
at
28
kV
and
20°C.
Simulation
obtained
for:
C
(20"C)=4.50
E-
05
Hz,
~h=0.009
s.
The fixed parameters are
k,=1O-ls
R
-'
and
p=87
kPa.
out of range. However, it is well known that the skewness parameter
in most cases specifies better than what the kurtosis does, the charac-
teristic profile
of
a distribution shape.
Discharge number
(n)
/i
Simul
80°C
,
-90"
0"
SO"
180"
270"
Discharge phase.
(ve)
Figure
9.
An
example
of
simulated
3d
histogram
of
a
1.8
mm
spheri-
cal
void
at
28
kV
and
80°C.
Simulation
obtained
for:
C
(80"C)=2.30
E-
09
Hz,
rt,=600
s.
The fixed parameters are
ks=10-16
R
-'
and
p=104
kPa.
Following the same procedure, the next step has been to attempt an
evaluation of the previously described parameters in a
PD
test simu-
lated at
80°C.
In Figure
9
and in Table
2
the related results are reported
for a void with the same
1.8
mm diameter. Again, as at
20"C,
except for
the two kurtosis parameters applied to
H(p,
n)
distribution, the very
slight differences of some other ones are surely due to some approxi-
mations contained inside the model equations.
A sensitivity analysis of the
80°C
simulation on the single model
parameter values have been performed in order to study the incidence
of their values on the solution presented in Figure
9.
In particular, the
role of the charge decay time constant
p,
has been explored by changing
its value starting from the presented value of
-
600
s
and leaving the
other parameter unchanged. The results are reported in Figure
10
in
a bidimensional plot as the mean charge versus the voltage inception
phase.
It
is
possible to see that only a
qr
of the order of
30
ms produces
strong changes in the simulation, intermediate values have a little effect
except
for
the discharge number that shows a little decrease, thus giving
-4000
'
i
...........
__
......
.......,
(c)
-90
(I
90
1
so
27"
'&"(,U
...........................................
-100(1
-
(d)
-OU
0
90
180
270
l),\I
ti
*rg*
I'h
1\r,
ui"
Figure
10.
Effect
of
nTtr
value
on
the
simulation presented
in
Figure
9.
(a)
rk=600
s,
discharge number in 30
s
n=3214.
(b)
~h=lO
s,
discharge
number in
30
s
n=2986.
(c)
n,=l
s,
discharge number
in
30
s
n=2714.
(d)
.rb=O.O3
s,
discharge number
in
30
s
n=1234.
a range of acceptable
pr
value between
1
and
1000
s
and surely not
overlapping over the one related at
20°C.
On the contrary, starting again
from the conditions outlined in Figure 10(a) it is sufficient to change the
C
(80°C)
value from (2.30
E-09
Hz)
to
(2.30
E-07
Hz)
for having a very
strong different discharge activity as reported in Figure
11.
The first consideration that can be put forward concerns the decrease
of
C(T)
when the temperature goes from 20 to 80°C. It is not possible
to obtain from the
C(T)
value here found, an unique couple of
v,
and
$J
related values. This concept is shown in Figure 12 where
$J
is re-
ported
vs.
v,
for
C
(20T)=4.50
E-05
Hz
and
C
(80"C)=2.30
E-09
Hz.
In
every case it is clear that for the same range of
v,
values, different and
not overlapping ranges for
$J
values are shown.
In
particular higher
4
values than at
20°C
are present at
80°C.
Furthermore, a
slight
inter-
596
Sk(-)
K,(+)
Ku(-)
Ipo,(pA)
Avo(+)
Alp"(-)
Schifani et
al.:
PD
at
High Temperature in Epoxy Resins
-7.804--1.074 -2.7710 0.1420+0.5261
9.070-74.25 19.8450 0.044-0.987
4.130-+88.520 19.7620 -0.159-0.689
15.1+308.7 14.44-
140-161 145
149-162 153
Table
1.
Comparison
between
experimental and
the
simulated
PD
data
at
20°C
reported in Figure
8
0.1209-0.9904
-i.is53--i.i112
-1.1510+- 1.1407
Parameter
I
~(n,q)
I
SimuI.
1
H(An)
I
SimuI.
1
~(+,q,)
I
Simul.
'Sk(+)
1
1.434-8.112
1
2.7650 10.1150+0.6900( 0.2510)
0.0111-0.1092
I
0.0672
0.0789
-
1.1790
-1.1640
Disch.in30s
0.2389
-0.sos0
-0.7886
23200+38760 I29310
H(n,
4)
-0.0294-0.1920
~0.1910~-0.0033
-
1.8953+-0.0564
-1.7676+-0.1810
192.4+33.6
219-248
240-260
Simul.
ff(A
n)
Simul.
H(d,
qm)
0.0608 -0.971+-0.210 -0.7915 0.0093-0.1141
-0.0802 -0.941+-0.126 -0.8001 0.0153-0.1945
-0.9541
-
1.521-
-
1.026
-
0.2420
-
1.1931
--
1.0006
-0.9341 -1.891+-0.375 -0.1415 -1.2386--t-0.8170
126.2
210
236
Table
2.
Comparison
between
experimental and the simulated
PD
data
at
8093
reported in Figure
9
"
Simul.
0.1359
0.2257
-
1.0021
-0.8787
1745-3015 I3214
4
-3oon
i
-tono
'
-3000
2
j
-9U
n
90
180
270
Dischsrgc
phose,
Figure
11.
Effect
of
C(T)
value
on
the
simulation
presented
in
Fig-
ure
9.
C
(80"C)=2.30
E-07
Hz and discharge number
in
30
s
n=18134.
dependence of the above increase tendency in order to reproduce the
experimental
PD
data at
80T,
could appear sound, because the stronger
binding
(4
increase) of the electrons may also explain the increased de-
cay time to be assigned to
q,.
This fact should let
us
suppose that the
main difference of
PD
activity at temperature higher than the ambient
may be a higher discharge time lag and consequently a higher discharge
overvoltage, thus producing a strong decrease
of
the discharge number
and their spread over a larger and larger interval between
qmin
and
This interpretation of the results related to the effect of temperature
on
PD
activity could be very near to the evolution of the experimentally
observed phenomena, that was also present with similar characteristics
in different cavity shapes
[20].
Finally, the authors wish to point out that what was reported in
this paper concerns voids not subjected to
PD
aging phenomena.
In
fact, as already said in Section
2.4,
the protracted exposition
of
a resin
surface
to
the acid gaseous products
of
discharges changes the
PD
pulse
sequence during the aging in a way that is in general not known in
depth. However, we deemed it very interesting to have a good and
reasonable knowledge
of
the starting
PD
activity, especially when the
temperature is also present as a parameter conditioning the internal
Pmax
.
C
(8OOC)
1.4
I/-
0.8
4
O.OOE+@O
5.@0E+
13
1.WE+14
Vo, Hz
Figure
12.
Plot
of
the
function
voexp(-&)
=
C(T)
for
C
(20"C)=4.50
E-05
Hz and
for
C
(80"C)=2.30
E-09
Hz.
discharges.
6
CONCLUSIONS
N
this paper a study of
PD
activity at
20
and
8093
in
spherical voids is
I
pr esent 3d. Starting from the consideration that such voids are always
inaccessible, this study has been performed simulating the
PD
activity
and then extracting the proposed solution from the ones found by the
algorithm by means
of
an analysis based on the comparison of sixteen
statistical parameters. The interpretation of what happens at
80°C
in
PD
activity can be read through the changes which the model parameters
are subjected to for a good fit.
The following observations can therefore be made.
1.
From the experimental tests here performed on
PD
in an embedded
void
inside epoxy
material,
we
have
observed
that discharge
activity
strongly changes
from
20
to
80°C.
The range between
the
qmin
and
the
qmax
value
of
detected discharges becomes
at
80°C
much larger than
IEEE
Transactions on Dielectrics and Electrical Insulation
Vol.
8
No.
4,
August2001
597
the
one
at
20°C
and
the ratio between the discharge number
in
a
voltage
period
at
20
and
80°C
amounted
of
N
10.
Therefore,
one
is
stressed
to
believe that at
80°C
the
electron
availability inside the
void
becomes
drastically reduced.
2.
The
simulation
function
C,
depending
on
the
material
work
function
4
and
on
WO
value, decreases
from
20
to
SOT,
and
from
its
analysis
at
constant temperature
it
appears that within the expected range
of
values for
WO
it
is
likely
that
4
increases with temperature,
thus
giv-
ing
a lower first electron availability
for
the discharges.
This
fact
can
produce an increase
of
the discharge time lag and
a
strong
reduction
of
discharge rate.
3.
At
80°C
it
is
necessary
to
increase the time constant Tbvalue. This may
mean
a
higher lifetime
of
charges
deposited
on
the
void
polar
area
and
could be proposed as an effect
of
increase, e.g. a higher work
to
extract
an
electron
from
the material surface with a consequent lower
first
electron
availability
ACKNOWLEDGMENT
The
present
work
was
economically
supported
by
M.U.R.S.T.
ex-
40%.
The
authors
wish
to
thank
hg.
Eleonora
Riva
Sanseverino
for
her
effective
help
in
writing
the
paper.
Thanks
are
due
also to
Bakelite
Gmbh
for
having
supplied
the
epoxy
resin
here
tested.
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in
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