Home Search Collections Journals About Contact us My IOPscience

The contribution of discharge area variation to partial discharge patterns in disc-voids

This article has been downloaded from IOPscience. Please scroll down to see the full text article.

2004 J. Phys. D: Appl. Phys. 37 1815

(http://iopscience.iop.org/0022-3727/37/13/013)

View the table of contents for this issue, or go to the journal homepage for more

Download details:
IP Address: 138.73.1.36
The article was downloaded on 20/04/2013 at 18:40

Please note that terms and conditions apply.

INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 37 (2004) 1815–1823 PII: S0022-3727(04)74461-7

The contribution of discharge area

variation to partial discharge patterns in
disc-voids
Kai Wu1,3 , Yasuo Suzuoki2 and L A Dissado3
1
Center for Integrated Research in Science and Engineering, Nagoya University,
Nagoya 464-8603, Japan
2
Department of Electrical Engineering, Nagoya University, Nagoya 464-8603, Japan
3
Department of Engineering, University of Leicester, Leicester LE1 7RH, UK

Received 5 January 2004

Published 16 June 2004
Online at stacks.iop.org/JPhysD/37/1815
doi:10.1088/0022-3727/37/13/013

Abstract
Experimental ac partial discharge (PD) patterns are presented for a disc-void
(area greater than length) with metal surfaces, one metal and one insulating
surface, and with both surfaces insulating. These patterns indicate that the
portion of the surface over which the charge is deposited (discharge area)
plays an important role in producing the fluctuations in discharge magnitude
commonly observed for such voids. A simulation model for PD patterns in
voids is presented, which expressly includes the effects of the charge
distribution left on the void surface by consecutive PDs. This model defines
two factors that control the PD propagation. These are: a minimum field
required to maintain the discharge within an existing surface path Ein and a
minimum peripheral field required to extend the discharge path Ep . There is
also one other factor, the occurrence probability that controls the incidence
of the PD. It is shown that the model gives a variation in PD magnitude
throughout the active region of phase without any stochastic factors, i.e.
when only variations in the discharge areas are allowed for, but that in order
to reproduce the typical (turtle-like) PD patterns observed for the disc-void
with insulating interfaces the occurrence probability and surface
conductivity have to be included. The current model is compared to
previous models and the relationship of the model factors to the change of
PD patterns with ageing is briefly discussed.

1. Introduction Monte Carlo simulation of the phase-resolved PD pattern

(i.e. φ-q–n pattern, φ: phase angle, q: PD charge, and
The manufacture of insulation systems almost always leads to n: PD number) is an effective approach to disclose the PD
the presence of air-filled voids of a range of sizes and shapes. mechanism. In conventional simulations [5–7], it is assumed
Electrical discharges (partial discharges (PDs)) may take place that the total field in a cavity after PD is reduced in proportion to
in such voids at service stresses that may cause degradation and the PD magnitude, and that the critical field for PD occurrence
eventual insulation failure. Consequently the identification and the residual field after the discharge mainly determine the
and analysis of such PDs is of importance as a diagnostic of subsequent PD magnitude. However, these kinds of models
the state of the insulation. Recently, some new techniques, cannot explain the large difference among PD magnitudes
e.g. a neural network and an expert system, have provided (even over 1000 times) in cavities in insulating materials, and
efficient methods for computer-aided automatic PD diagnosis the implicated phenomena of changes in the PD pattern with
[1–4]. However, a substantial improvement in the reliability of degradation. Changes in the PD pattern depend on many
diagnosis will only be achieved when the mechanisms whereby factors, such as gas condition, degradation products, change
the PD and PD pattern change with material ageing are known. of surface condition and the charge deposited on the surfaces

0022-3727/04/131815+09$30.00 © 2004 IOP Publishing Ltd Printed in the UK 1815

K Wu et al

due to former PDs [8–10]. For example, the charge left on the
channel wall due to former PDs is the most important factor
to determine the PD propagation range and the PD magnitude
[11, 12] in narrow channels in divergent field conditions. In
this case, the large variation in PD magnitude was found
to be mainly due to the different PD propagation lengths in
the narrow tree channels [11, 12]. Disc-voids have a length
that is much smaller than their surface area and hence charges
are unlikely to be deposited on the sidewalls, as occurs in tree
channels. The simulation models [5–7] therefore treat the
discharge as modifying the electric field strength uniformly Figure 1. Drawing of a sample with a void possessing two metal
throughout the volume of the void. However, some authors surfaces.
have shown that the luminous region of a PD pulse in a disc-
void is much smaller than the void radius (20 mm) and that it
changed with PD degradation [13, 14]. Therefore it is likely
that in a typical disc-void, the surface region to which the
charges can propagate in a PD process (the discharge area)
will not always be the same. Other work using point–plane
discharges [15] have shown that the area of surface covered by
the discharge is not uniform and may change with subsequent
discharges. It is therefore likely that similarly to the situation
in a narrow channel, the PD magnitude in disc-voids might be
closely related to field modification due to the non-uniformity
of void surface area charged by the previous discharge. In this
paper, this hypothesis is evaluated by means of both experiment
and computer simulation.
Figure 2. Experimental measurement system.
2. Experimental study
in the PD magnitude. Moreover, some PD pulses appeared as
The effect of discharge area upon the PD pattern has been dispersed groups (figures 3(b) and 4(b)–(d)), which imply a
investigated using three types of sample containing a disc-void: restriction of PD to specific regions of phase angle. Patterns
(a) a disc-void with both surfaces made of metal; (b) a disc- with several regular points, such as figure 3(b), were often
void with only one surface made of metal; and (c) a traditional observed, which indicate a strict periodicity of PD occurrence.
disc-void with dielectric surfaces. In case (a) we would expect Although the void diameters were different for the PD patterns
the metal surfaces to act as equi-potentials and hence for the shown in figures 3 and 4, very little difference in PD magnitude
field within the void to be uniform both before and after a was observed.
discharge. This would eliminate the effect of localization of
the deposited charge. The results from this sample will be 2.2. PD patterns from a void with insulating surfaces
compared to those from (b) and (c) where such localization
may occur on the dielectric surfaces. The PD patterns from a typical void with insulating surfaces are
shown in figure 5 for comparison with those obtained from the
2.1. PD patterns from a void with metal surfaces cavity with metal surfaces (figure 3). The sample was similar
to that of figure 1, but with the two aluminium foils removed.
The construction of this sample is shown in figure 1. Three In contrast to figures 3 and 4, the PD magnitude showed a
layers of low-density polyethylene with a hole in the middle considerable variation and dispersed groups of discharges were
layer were pressed together to form the specimen after they rarely observed.
were cleaned by acetone. On each side of the void, two We also measured the discharges in a cavity with single
aluminium foils with a diameter of 7.5 mm were sandwiched metal surface, when only the lower aluminium foil in the
to form the metal surfaces of the void. Because of the high sample as shown in figure 1 was removed. The experimental
conductivity of the metal, the fields between the two metal results shown in figure 6 were similar to those of a large
surfaces are kept uniform in the PD process, and the effect of void with insulating surfaces, and a large variation of the PD
charge distribution on the insulating surfaces of a typical void magnitude was observed.
can be excluded. In both cases where the disc-void had at least
Figure 2 shows the experimental system. The magnitudes one insulating surface, figures 5 and 6, the maximum PD
of consecutive PDs in 600 cycles (10 s) were recorded by a magnitude was found to be greatly decreased after 1 h of
computer-aided measuring system (the same as in [5]) every voltage application, and the phase at which PD inception
2 min, and the PD patterns shown in figures 3 and 4 were occurred increased in every cycle. This is different from
obtained. In the patterns, one point stands for one PD pulse. the results of previous experiments [14, 16] by other authors.
In figures 3 and 4, the PD pattern showed a narrow In these experiments, the samples were cleaned in acetone
horizontal band, which indicated only a very small variation by ultrasound and then were exposed to air for a time long

1816
 PD patterns in disc-voids

Figure 3. PD patterns from a 3 mm diameter void between two metal surfaces (the applied voltage: 10.2 kV). (a) 1 min; (b) 1 h;
(c) 4 h; (d) 16 h.

Figure 4. Typical PD patterns observed from a 1 mm diameter void between two metal surfaces (the applied voltage: 10.2 kV). (a) 1 min;
(b) 30 min; (c) 2 h; (d) 5 h.

P P

Figure 5. PD patterns observed from a 3 mm diameter void (the applied voltage: 4 kV). (a) 2 min; (b) 22 min.

enough to allow any residual acetone to disperse. In our acetone molecules might be left in the gas in the void. This
experiments, the three layers of polyethylene were pressed may lead to the differences in experimental results observed
together after they were cleaned by tissue soaked in acetone and over 1 h of discharging. However, in spite of these differences
exposed in air for only 10–20 min. Therefore, in our samples, experimental PD data from many sources [5, 10, 14, 16, 17]
the void surface might not be completely clean and also some show the considerable variation of PD magnitude observed

1817
K Wu et al

Figure 6. PD patterns from a 3 mm diameter void with single metal surface (the applied voltage: 10.2 kV). (a) 1 min; (b) 1 h.

here, which can therefore be taken to be typical of disc-voids surface would have a much shorter time lag than positive pulses
with insulating surfaces. which start from the insulating surface. However, very little
polarity difference was observed in the PD patterns (figure 6).
2.3. Discussion of experimental results Furthermore, although figures 3 and 4 suggest that the time lag
of PD starting from metal surfaces does not change much with
The PD magnitude in disc-voids with two metal surfaces can the duration of the discharging, the negative pulses starting
be expressed very well by the following equation: from the metal surface of the insulator/metal void show a
great reduction within 1 h of voltage application as shown in
Q = C(Ec − Er )d, (1)
figure 6.
where, Q is the PD magnitude, C is the capacitance between In summary, it can be deduced that the considerable
the metal surfaces, d is the length of the void, Ec is the field in fluctuation of PD magnitude in typical voids cannot be
void just before the PD occurrence and Er is the residual field explained by the effects of either by a variation in Ec or a larger
after PD. Because there may be a distribution in the time lag time lag just on their own. We suggest that an important role
between successive discharges or equivalently the probability is played by the variation of discharge area for the PDs, which
for PD occurrence (see, e.g. [18]) Ec and the over-voltage of would enter equation (1) through a variation in the effective
PD (i.e. the difference between the actual field at which the value of the capacitance C. Since the discharge area may, in
PD takes place and the minimum field for PD occurrence) can principle vary from a few tens of micrometres to that of the
vary over a certain range. whole void surface the range is enormous, and well able to
Because the area of the aluminium foil is constant, the give rise to the range of PD magnitudes measured.
capacitance between the two metals remains nearly the same
when the void diameter is reduced from 3 to 1 mm. Therefore, 3. Simulation model including discharge area effects
the PD magnitude in figures 3 and 4, does not change much
with the reduction of cavity size. We assume that in a disc-void with insulating surfaces, the
The small variation in PD magnitude in voids with metal propagation of a PD across the void surface is affected by the
surfaces suggests a small variation range of the field at which charge distribution left on the void surface by the previous
the PD occurs (Ec ) and a small time lag (high occurrence PDs. This can be expected to lead to a variation of discharge
probability) for the PD pulses with little variation. Thus, a area and thus of PD magnitude, in a sequence of discharges.
PD takes place when the field exceeds Ec , then after the PD We have therefore included the effect of discharge area in our
occurrence the field decreases to a lower value Er , and a PD proposed simulation model described later.
next occurs when the field again exceeds Ec with the increase
of the ac voltage. This periodicity of PDs may lead to the 3.1. Calculation method
dispersed-group PD pattern [11]. However, it is difficult to
use equation (1) to explain the considerable fluctuation of In the simulation the disc-void is embedded in the insulating
PD magnitude (over 1000 times) in typical disc-voids with material as shown in figure 7. The network used in the
dielectric surfaces if each PD is assumed to cover the same calculation is a three-dimensional one of size 24 × 24 × 5.
discharge area (i.e. C is a constant for each PD), even though The electrode separation is 5, and the void size is 18 × 18 × 1.
the variation range of Ec may be larger than in the voids with One unit in the network corresponds to 0.2 mm. The relative
metal surfaces and the PD occurrence probability may be lower. permittivity of the insulating material, ε1 , is 2.3, and that of
Since the minimum value of Ec is determined by the avalanche the gas in the void, ε2 , is 1. The applied voltage is sinusoidal
condition of the gases, it is impossible that Ec can range up to with a frequency of 50 Hz and a peak value, U0 , of 5 kV.
several times the minimum value as required by the variation When the field in the z direction between the two points
in PD magnitude. Therefore, the variation in PD magnitude (x1 , y1 , 0) and (x1 , y1 , 1) on the two opposite void surfaces
cannot be explained just in terms of a variation of Ec . If exceeds the critical field for PD occurrence, Ec , PD takes
the explanation were to be a lower occurrence probability in place, and a narrow streamer is formed between the two points
the dielectric voids due, for example, to a shortage of seed (figure 8). Once the streamer has made the connection the PD
electrons as compared to the metal-surfaced voids, we would is assumed to propagate along the void surfaces away from the
expect that in the case of a void with single metal surface contact points. The PD is terminated when the internal field
(figure 6), the negative pulses which start from the metal in the PD path becomes lower than a critical value Ein and the

1818
 PD patterns in disc-voids

process on the void surfaces. The PD is terminated when

all of the fields in the PD paths are lower than the minimum
field for maintaining the discharge (Ein ) and all of the fields
in the perimeter segments around the PD paths become less
than the minimum field for extending the discharge (Ep ).
This procedure produces branched structures for the charge
deposited upon the void surface shown in figure 8, similar to
those observed experimentally [15]. The magnitude of the PD
charge is equal to the difference between the induced charges
Figure 7. Void configuration for simulation.
on the electrode before and after the PD.
If the conductivities of the surface and in the body of the
insulating materials are neglected, the charge distribution on
the void surfaces after a PD does not change until the next
PD. The total field distribution changes with the ac voltage,
and the next PD occurs when the maximum field in the void
again exceeds the critical field for PD occurrence. The PD
pattern is simulated after the above calculations are repeated
for several decades of cycles.
The effect of surface conductivity on PD behaviour can
also be included in this model. In this case, the change of
charge density at a point (x, y, z) on the void surface in the
interval between PD pulses can be expressed as
γ t
ρx,y,z = 2 (ϕx+1,y,z + ϕx−1,y,z + ϕx,y+1,z
h
+ϕx,y−1,z − 4ϕx,y,z ), (3)
Figure 8. Sketch of discharge propagation along the void surfaces.
where γ is the surface conductivity, t is the time step in the
calculation, h is the length of one segment. Preliminary results
field in the perimeter segments on the two surfaces around the for this situation have been reported in [20]. The effect of bulk
PD paths becomes less than another critical value Ep . conductivity [7] may also be included in a similar way, but
The PD propagation is decided by the instantaneous field these calculations have not yet been carried out.
distribution, which is determined by the applied voltage and the
charge distribution on the void surfaces. It can be calculated
3.2. Simulation results
by Poisson’s equation
ρ 3.2.1. Variation of PD magnitude. Figure 9(a) shows the
∇ 2ϕ = − , (2) simulation result when no stochastic mechanisms are taken into
εε0
consideration, i.e. a discharge takes place in the void as soon as
where ϕ is the potential, ρ is the charge density and εε0 is the a critical field Ec0 is exceeded. Because of the charge deposited
permittivity (ε is the relative permittivity, and is 2.3 for the upon the void surface by one PD, the charge deposited by a
insulating materials and 1 for the gas in the void). subsequent PD extends to a different shape [15] and hence
The algorithm used to describe PD propagation on the different distribution, resulting in a range of PD magnitudes
void surface is one that has been previously used to simulate (up to ∼100 pC).
PD propagation in electrical trees [19]. First, the segment Figures 9(b)–(d) show the results when the effect of time
SEGm in which the field is the largest is chosen from the PD lag is considered. This effect can be expressed by assuming a
paths and all of the perimeter segments around the PD paths. probability for PD occurrence,
If SEGm is one of the perimeter segments and the field in it is

larger than Ep , the segment SEGm is changed to become part of f (E) (E
Ec0 ),
P (E) = (4)
a PD path. Otherwise it remains a non-discharging perimeter 0 (E < Ec0 ),
segment. If SEGm belongs to a PD path and the field in it
where P (E) is the average number of PD occurrences in a unit
exceeds Ein , amounts of charge −Q and Q are added to
time when the field is E, f (E) is a defined function and Ec0 is
the two end points of SEGm , respectively, in order to represent
the critical field above which PD can occur. In this simulation,
the continuation of the discharge process in the segment. This
we assume a simple linear expression for f (E),
has the effect of reducing the field in SEGm and eventually
terminating the discharge there. Here, the polarity of Q for f (E) = f0 (E − Ec0 ), (5)
one end point is determined by the polarity of the field along
SEGm . Q is a constant and its value does not influence the where f0 is a constant.
calculation result if it is small enough. As a result of this The reduction of PD occurrence probability allows
procedure the charge distribution is altered and hence the field the possibility that the field in the void will rise to a larger
distribution is changed, in the void and on its surfaces. The new value (Ec ) than the minimum required field Ec0 , before a
field distribution is now re-calculated by using equation (2). discharge takes place. This will result in larger range of
Repeating the above calculations simulates the PD propagation PD magnitude (figures 9(b)–(d)), than is derived when no

1819
K Wu et al

Figure 9. Simulated PD patterns (Ec0 = 5 kV mm−1 , Ep = 1.25 kV mm−1 ). (a) f (E) = ∞(E > Ec0 ), Ein = 0.063 kV mm−1 ;
(b) f (E) = 5.76(E − Ec0 ) , Ein = 0.063 kV mm−1 ; (c) f (E) = 1.14(E − Ec0 ), Ein = 0.063 kV mm−1 ; (d) f (E) = 0.114(E − Ec0 ) ,
Ein = 0.063 kV mm−1 ; (e) f (E) = 1.14(E − Ec0 ), Ein = 0.09 kV mm−1 .

(a) (b)

Figure 10. Typical turtle-like PD pattern and the simulated one. (a) Typical turtle-like PD pattern actually observed [17]. (b) Simulated
turtle-like PD pattern (the surface conductivity is 3.2 × 107 , Ec0 = 5 kV mm−1 , Ep = 1.25 kV mm−1 , Ein = 0.063 kV mm−1 ,
f (E) = 0.114(E − Ec0 )).

stochastic features were involved (figure 9(a)). The other a low PD occurrence probability is considered (figure 9(d)).
factors that influence the PD magnitude are the critical fields for However, in figure 9(d), PD may still occur when the phase is
discharge maintenance (Ein ) and extension (Ep ). Obviously, much larger than 90˚ or 270˚. PDs in these phase regions can be
increases of these two parameters lead to the reduction of the substantially removed when the effect of surface conductivity
PD propagation range on the void surface, and thus give a is included (see figure 10(b)). In this case the patterns produced
decrease of PD magnitude (comparing figures 9(c) and (e)). are very similar to a typical turtle-like pattern.
As Ein and Ep may change with the conditions of the surface In figure 9(d), because of the low probability for PD
and the gas in the void, these factors provide a means of relating occurrence, PD may not take place immediately in some
changes in PD pattern over time with quantifiable changes in region in the void even when the field in that region has
the surface and gas condition. The proposed model therefore greatly exceeded the critical field for PD occurrence (Ec0 ).
provides a new approach for analysing the effect of discharge Thus, PD may still occur after the phase angle has become
ageing via the transition of PD pattern. much larger than 90˚ or 270˚. However, when the surface
conductivity is taken into consideration, the charge migration
3.2.2. Effect of surface conductivity and turtle-like PD pattern. along the surface tends to make the field distribution in the void
In actual experiments, a typical PD pattern (as shown in more uniform. This effect leads to a fast reduction of the
figure 10(a) [17]), which has been called the turtle-like pattern, maximum field in local regions of the void, when the phase
is often observed [5, 21]. In figure 10(a), because of the becomes near or above 90˚ or 270˚. Thus the maximum field
limited measuring range when the multiplication factor of in the void becomes lower than Ec0 earlier in phase.
the equipment is fixed, the small PDs below about 200 pC
cannot be observed. In this typical pattern the PD magnitude 3.3. Comparison with other models
does not increase as sharply near the inception phase angle
in each cycle, as is calculated in the simulations shown in 3.3.1. PD pattern shapes. In conventional simulations [5, 6],
figures 9(a)–(c). Nor do the discharges continue beyond the each PD is assumed to cover the same discharge area. The
90˚ and 270˚ phase angles. In our simulation, the increase PD magnitude is determined by two parameters: the field for
in the head of PD pattern can be reduced in steepness when PD occurrence (or the probability for PD occurrence) and

1820
 PD patterns in disc-voids

equivalent to our model. If we use equation (1) to determine

the average field reduction (E) in the whole void equivalent
to that caused by a PD of discharge area S we find
S
E = (Ec − Er ), (7)
S0
where S is the discharge area and S0 is the area of the whole
void. Therefore, when the PD charge (or the discharge area)
decreases to zero, the equivalent field reduction E also tends
to zero and the average residual field in the void is effectively
equal to Ec as assumed in [5].
The shape of PD pattern in figure 11(a) shows no
difference in PD magnitude with phase angle and is similar
to the simulated PD pattern obtained in our model when none
of the parameters is allowed to vary stochastically (shown in
figure 9(a)). In principle, the PD magnitudes in our simulation
should have the same value at the different phases because
it is assumed that PD occurs as soon as the field reaches
the minimum level for PD occurrence (Ec0 ). However, because
of the discrete time-step in the numerical calculation, the
calculated field (Ec ) at which Ec0 is exceeded tends to be
higher when the rate of voltage increase is larger, leading
to the small variation of PD magnitude with phase angle in
figure 9(a). The difference between the results of our model
and the conventional one are however very small and this
indicates that the physical meaning behind the assumption of
the randomness of residual field (Er ) in conventional models is
in fact the variation of the charged area of the disc-void surface.
In our model, an exact replication of the turtle-like
Figure 11. Simulated PD patterns in a void with the diameter of
7.5 mm and length of 0.4 mm without consideration of the pattern (figure 10(a)) requires the inclusion of a stochastic
variation of discharge areas (the voltage on the void is 3 kVpeak , variation in the PD occurrence probability as well as the
Ec0 = 4.5 kV mm−1 ). (a) f (E) = ∞ (E > Ec0 ), field due to the surface charge, and a surface conductivity to
Er = 1 + 1.0Nr (kV mm−1 ); (b) f (E) = 8(E − Ec0 ), spread the charge across the void surface. The latter is most
Er = 2.5 kV mm−1 ; (c) f (E) = 8(E − Ec0 ), effective near the voltage peaks and troughs and inhibits PD
Er = 2 + 1.0Nr (kV mm−1 ).
occurrence when the voltage amplitude is dropping. Similar
features were suggested in [7] for the simulation of PDs in
the residual field Er in the void after a discharge has been narrow electrical tree channels, point to plane geometries,
completed. When only Er is considered to be a stochastic and electrode-bounded cavities. There the residual field was
variable the simulated pattern is as shown in figure 11(a). determined partly by the surface and space charges, much as
In this case Er is considered to lie uniformly in the range in our model, but these decayed exponentially in time with
Er0 ± A, i.e. a time constant depending upon charge dissipation into the
Er = Er0 ± A · Nr , (6) bulk insulation or recombination because of transport around
the cavity surface. The PD occurrence probability combined
where Er0 is a chosen mean value, A is a constant, and Nr is with the time dependent charge field to determine the field at
a random number distributed uniformly between 0 and 1. If which the discharge occurred and hence its magnitude as in
alternatively a stochastic mechanism is assumed only for the our model. However, in our model the total amount of surface
PD occurrence (as in equations (4) and (5)), the simulated charge does not vary in time but remains unchanged until the
pattern is as shown in figure 11(b). When both stochastic next discharge, when accumulation or (part) neutralization
factors are introduced, a turtle-like PD pattern can be simulated (if the discharge polarity has changed due to the ac cycle)
(figure 11(c)). Here, the PD magnitude shown in figure 11 is takes place as observed experimentally [15] (albeit not with
the induced PD charge on the void surfaces, which should be polymeric surfaces). A second difference is that the field is
much larger than the apparent charge observed experimentally. not assumed to be the same throughout the void but calculated
However, as the induced PD charge is proportional to the directly from the distribution of net charge on the large area of
apparent charge, the pattern shape should be the same. the void surface. We can however expect the bulk conductivity
In these simulations (figure 11) the ratio of the maximum of the insulating material to play a role in determining the
to minimum PD magnitudes is not greater than 3, in contrast magnitude of the surface charge, and hence the field in the
to the large fluctuations observed in actual PD patterns. In void. The strength of this effect will depend upon the ability
order to simulate the actual patterns, some authors [5] assume of the bulk conductivity to remove surface charge from the
that the residual field increased as the over-voltage (Ec − Ec0 ) vicinity of the void during a half-cycle, and it will act in a
reduced and became equal to the field for PD occurrence (Ec ) similar way to the surface conductivity already included in our
when the over-voltage is zero. This assumption is somewhat simulations.

1821
K Wu et al

3.3.2. Stochastic mechanisms. In principle, if no stochastic metal surface given in figure 6 show that a large reduction
mechanism is taken into consideration, symmetrical extensions in PD magnitude can occur without a significant increase in
of the discharges on the disc-void surfaces should be obtained the occurrence probability, which is already very high for the
(at least for the first PD). This is not the case in our model. metal surface as illustrated in figure 3. This suggests that an
Because of the inaccuracy associated with the numerical increase in PD occurrence probability, which was considered
calculation and the procedure that only one new segment to be the main reason for the transition to SPMD in [16], is not
can be added to the PD paths in one calculation step, the the only factor, an increase in the fields required for discharge
PD paths that we calculate are usually not of symmetrical continuation and extension, i.e. Ein or Ep may also play an
shape. In actual discharges, the distribution of charges in important role. These latter factors are much more clearly
the discharge in the gas and the microscopic disorders in related to changes in the void surface or gas condition known
material density on the void surface give rise to small but to occur during ageing [9, 22, 23] than alterations in the PD
unquantifiable spatial variations, any one of which may lead to occurrence probability, and hence may be able to correlate
an asymmetrical surface propagation. It is therefore reasonable physical ageing and transitions in the PD pattern much better.
to accept the rounding errors as representing these variations The reduction with time of the range of phase seen
without the inclusion of additional stochastic factors. Our in the PD patterns in figure 6 can be explained in terms
results (figure 9(a)) show that the deterministic variation of of an increase in surface conductivity. In the light of our
charge distribution on the void surface is sufficient to allow comments in section 2.2, it seems that some acetone molecules
a substantial variation of PD magnitude without recourse to and other impurities may remain in the void after cleaning,
stochastic factors such as utilized in determining the value and that during the discharging these molecules increase the
of residual field (Er ) in conventional models. However, a conductivity of the surface. This tends to make the field
stochastic PD occurrence probability is required to produce distribution more uniform and reduces the maximum field in
the typical turtle-like pattern. Therefore, for simplicity, when the large cavity, resulting in a larger inception phase angle of
the PD occurrence probability is considered in simulating the PD in each cycle.
actual PD patterns in our model, we suppose that no other
stochastic factor is necessary. Regardless of the stochastic 4. Conclusions
mechanism, however, the change in charge distribution by PDs
may be the main factor leading to the fluctuation of discharge The comparison of experimental PD patterns and disc-voids
areas and PD magnitudes. with insulating and metallic conducting surfaces shows that
variations in PD magnitude are associated with the area of
3.4. Discussion of PD pattern transition the void surface charged during the discharge. The proposed
simulation model shows that the region of void surface charged
Other than the stochastic mechanism for PD occurrence our during a discharge influences the magnitude of a subsequent
model is essentially based on physical concepts. We therefore discharge and is sufficient to produce variations of discharge
expect that it will be able to yield an insight into the mechanism magnitude during the active phase region for discharging
whereby the PD pattern changes with material degradation. If without the inclusion of any stochastic factors. This feature
we look at the changes of PD pattern with discharge duration of of discharge behaviour is the main physical origin of the
one hour found for voids with just one metal surface, figure 6, stochastic variation in residual field assumed in conventional
we see that the PDs are much reduced in magnitude. Since models. In order to reproduce exactly the turtle-like patterns
the time lag for the negative PDs starting from the single observed in the experiments, both a PD occurrence probability
metal surface is unlikely to change much with time because and surface conductivity had to be included in the model,
of the easy availability of seed electrons, the reduction of PD with the occurrence probability being the more important
magnitude in a void with single metal surface must be due to factor of the two. It was also speculated that the commonly
an increase in the fields required for discharge continuation observed transition on material ageing to SPMD could be
and extension, i.e. Ein and Ep , caused by a change in surface related to the condition of the void surface via the surface
or gas conditions. A similar effect, though not so marked, is propagation parameters of the model.
seen in the void with insulating surfaces (figure 5). Therefore
here too a reduction in Ein and/or Ep probably occurs.
The transition to swarming pulsive micro-discharges References
(SPMD) after long-time ageing in typical voids with insulating [1] Hozumi N, Okamoto T and Imajo T 1992 Discrimination of
surfaces [5, 16] can be explained by a reduction of discharge partial discharge patterns using a neural network IEEE
area. The reduction in area corresponds to a reduction in Trans. Electr. Insul. 27 550–6
PD magnitude. Also, as a PD only weakly influences the [2] Cachin C and Wiesmann H J 1995 PD recognition with
knowledge-based preprocessing and neural networks IEEE
field distribution far from its discharge area, a reduction of
Trans. Dielectr. Electr. Insul. 2 578–89
discharge area means that PDs with small discharge areas may [3] Krivda A 1995 Automated recognition of partial discharges
take place independently in various small regions of the entire IEEE Trans. Dielectr. Electr. Insul. 2 796–821
void surface, and hence that the number of PDs can increase [4] James R E and Phung B T 1995 Development of
drastically. Our model suggests that the reduction in discharge computer-based measurements and their application to PD
pattern analysis IEEE Trans. Dielectr. Electr. Insul. 2
area required for the onset of SPMD can be produced either
838–56
by a reduction of the time lag of PD or an increase in Ein [5] Hikita M, Yamada K, Nakamura A and Mizutani T 1990
or Ep . The experimental results for a disc-void with a single Measurements of partial discharges by computer and

1822
 PD patterns in disc-voids

analysis of partial discharge distribution by the Monte Carlo [15] Takada T 1999 Acoustic and optical methods for measuring
method IEEE Trans. Electr. Insul. 25 453–68 electric charge distributions in dielectrics IEEE Trans.
[6] Gutfleisch F and Nimeyer L 1995 Measurement and Dielectr. Electr. Insul. 6 519–47
simulation of PD in epoxy voids IEEE Trans. Dielectr. [16] Ishida T, Nagao M, Mizuno Y and Kosaki M 1993 Swarming
Electr. Insul. 2 729–43 pulsive microdischarge characteristics of internal void
[7] Patsch R and Hoof M 1998 Physical modeling of partial specimen and the factors affecting its occurrence Trans. IEE
discharge patterns Proc. 6th ICSD (IEEE Pub. 98CH36132) Japan 113-A 43–51 (in Japanese)
pp 114–18 [17] Ijichi T 2001 A study on the aging mechanisms of insulating
[8] Mason J H 1978 Discharges IEEE Trans. Electr. Insul. 13 materials by observing φ-q–n pattern and current form of
211–38 PD Master Thesis Nagoya University
[9] Mayoux C and Laurent C 1995 Contribution of partial [18] Okamoto T, Kato T, Yoshimizu Y, Suzuoki Y and Tanaka T
discharges to electrical breakdown of solid insulating 2001 PD characteristics as a stochastic process and its
materials IEEE Trans. Dielectr. Electr. Insul. 2 integral equation under sinusoidal voltage IEEE Trans.
641–52 Dielectr. Electr. Insul. 8 82–90
[10] Morshuis P H F 1995 Assessment of dielectric degradation by [19] Dodd S J 2003 A deterministic model for the growth of
ultrawide-band PD detection IEEE Trans. Dielectr. Electr. non-conducting electrical tree structures J. Phys. D: Appl.
Insul. 2 744–60 Phys. 36 129–41
[11] Wu K, Suzuoki Y, Mizutani T and Xie H K 1999 A novel [20] Wu K, Suzuoki Y and Dissado L A 2003 Improved simulation
physical model for partial discharge in narrow channels model for PD patterns in voids considering effects of
IEEE Trans. Dielectr. Electr. Insul. 6 181–90 discharge area Ann. Rep. CEIDP (IEEE Conf. Pub.
[12] Wu K, Suzuoki Y, Mizutani T and Xie H K 2000 Model 03CH37471) pp 32–5
for partial discharge associated with treeing [21] Suwaruno, Suzuoki Y and Mizutani T 1996 Pulse-sequence
breakdown-PDs in tree channels J. Phys. D: Appl. Phys. 33 analysis of partial discharges in a void and electrical treeing
1197–201 Conf. Record of IEEE International Symp. on Electrical
[13] Morshuis P H F and Kreuger F H 1990 Transition from Insulation vol 1, pp 130–3
streamer to Townsend mechanisms in dielectric voids [22] Tanaka T 1986 Internal partial discharge and material
J. Phys. D: Appl. Phys. 23 1562–8 degradation IEEE Trans. Electr. Insul. 21 899–905
[14] Mason J H 1995 Enhancing the significance of PD [23] Gamez-Garcia M, Bartnikas R and Wertheimer M R 1987
measurements IEEE Trans. Dielectr. Electr. Insul. 2 Synthesis reactions involving XLPE subjected to partial
876–88 discharges IEEE Trans. Electr. Insul. 22 199–205

1823