Electrical treeing characteristics in XLPE power cable insulation in frequency range between 20 and 500 Hz
ABSTRACT Electrical treeing is one of the main reasons for long term degradation of polymeric materials used in high voltage AC applications. In this paper we report on an investigation of electrical tree growth characteristics in XLPE samples from a commercial XLPE power cable. Electrical trees have been grown over a frequency range from 20 Hz to 500 Hz and images of trees were taken using CCD camera without interrupting the application of voltage. The fractal dimension of electric tree is obtained using a simple boxcounting technique. Contrary to our expectation it has been found that the fractal dimension prior to the breakdown shows no significant change when frequency of the applied voltage increases. Instead, the frequency accelerates tree growth rate and reduces the time to breakdown. A new approach for investigating the frequency effect on trees has been devised. In addition to looking into the fractal analysis of tree as a whole, regions of growth are being sectioned to reveal differences in terms of growth rate, accumulated damage and fractal dimension.

Conference Paper: Effects of low temperature on treeing Phenomena of silicone rubber/SiO2 nanocomposites
[Show abstract] [Hide abstract]
ABSTRACT: Silicone rubber (SiR) has been widely used in XLPE cable accessories because of its excellent electrical and mechanical properties. The electrical tree is a serious threat to SiR insulation and it can even cause the insulation breakdown. Addition of nanoparticles into SiR can improve the insulating properties compared with undoped material. The effect of nanoparticles on tree characteristics at temperatures above 0 °C has been widely researched. However, the effect under low temperature has not been researched. In this paper, electrical treeing process in SiR/SiO2 nanocomposites was investigated over a range of low temperatures. The samples were prepared by mixing nanoSiO2 into room temperature vulcanized (RTV) SiR, with the content of 0, 0.5, 1.0, 1.5 and 2.0 wt% respectively. The experiment temperature ranges from 30 °C to 90 °C. AC voltage with a frequency of 50 Hz was applied between a pair of needleplate electrodes to initiate the electrical tree at different experiment temperatures. Both the tree structures and the growth characteristics were observed by using a digital microscope system. The experiment results indicated that low temperature is an important factors of the treeing process in SiR/SiO2 nanocomposites.2013 IEEE Conference on Electrical Insulation and Dielectric Phenomena  (CEIDP 2013); 10/2013 
Conference Paper: Electrical performance of silicone rubber / SiO2 nanocomposites under low temperature
[Show abstract] [Hide abstract]
ABSTRACT: This paper investigated the electrical tree growth process in SiR/SiO2 nanocomposites under the condition of low temperature. Samples were prepared by mixing nanoSiO2 into room temperature vulcanizing silicone rubber, with the content of 0, 0.5, 1, 1.5 and 2 wt% respectively. The experiment temperature ranged from  30 °C to 90 °C. AC voltage with a frequency of 50 Hz was applied between a pair of needleplate electrodes to investigate the electrical tree at different temperatures. The experimental results reveal that both nanoparticles and low temperature environment have a significant impact on the electrical tree growth characteristics of SiR/SiO2 composites. This paper studied electrical tree growth characteristics from the aspects such as the patterns of electrical tree, fractal dimension and the proportion of cumulative damage. It is suggested that there are both branch tree and bush tree when the temperature is 30 °C or 60 °C, but only pine tree when the temperature is 90 °C. It is also found that tree structure is closely related to the crystalline state.2014 International Symposium on Electrical Insulating Materials (ISEIM); 06/2014  SourceAvailable from: Mohd Hafizi AhmadTELKOMNIKA Indonesian Journal of Electrical Engineering. 08/2014; 12(8).
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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 1; February 2009
10709878/09/$25.00 © 2009 IEEE
179
Electrical Treeing Characteristics in XLPE Power Cable
Insulation in Frequency Range between 20 and 500 Hz
G. Chen
School of Electronics and Computer Science
University of Southampton, Southampton SO17 1BJ, UK
and C. H. Tham
SP Powergrid Ltd, Singapore
ABSTRACT
Electrical treeing is one of the main reasons for long term degradation of polymeric
materials used in high voltage ac applications. In this paper we report on an
investigation of electrical tree growth characteristics in XLPE samples from a
commercial XLPE power cable. Electrical trees have been grown over a frequency
range from 20 Hz to 500 Hz and images of trees were taken using CCD camera without
interrupting the application of voltage. The fractal dimension of electric tree is obtained
using a simple boxcounting technique. Contrary to our expectation it has been found
that the fractal dimension prior to the breakdown shows no significant change when
frequency of the applied voltage increases. Instead, the frequency accelerates tree
growth rate and reduces the time to breakdown. A new approach for investigating the
frequency effect on trees has been devised. In addition to looking into the fractal
analysis of tree as a whole, regions of growth are being sectioned to reveal differences in
terms of growth rate, accumulated damage and fractal dimension.
Index Terms — Electrical tree, fractal dimension, boxcounting, variable frequency,
growth rate, accumulated damage, partial discharge
1 INTRODUCTION
NOWADAYS, XLPE cables are widely chosen for power
distribution and transmission lines up to 500 kV owing to its
excellent electrical, mechanical and thermal characteristics.
Similar to any other insulating materials, its electrical
properties deteriorate over the time when it is subjected to
electrical stress. Electrical tree is one of the main reasons for
longterm degradation of polymeric materials used in high
voltage ac applications. Consequently, there have been
continuous efforts in last three decades to characterize
electrical treeing in XLPE and understand the mechanisms.
Electrical trees in solid insulation were firstly reported by
Mason [1]. Subsequent research reveals that treeing is
observed to originate at points where impurities, gas voids,
mechanical defects, or conducting projections cause
excessive electrical field stress within small regions of the
dielectric. The treeing process can be generally described by
the three stages, inception, propagation and runaway as
shown in Figure 1. However, the exact form may vary
depending on the mechanisms in operation.
Tree length
inception
runaway
Figure 1. Electrical treeing growing characteristics.
One of the detailed early studies on electrical tree was carried
out by Ieda and Nawata [2]. A few aspects were examined
and the experimental results concluded that tree extension
was induced by internal gas discharge in existing tree
channel. The gas discharge was pulsive, lasting less than
0.1μs and the electric potential of a needle electrode was
transferred to the tip of an existing tree channel through the
conductive plasma of a gas discharge. It was also suggested
that frequency only accelerates the growth process by
increasing the number of gas discharges but not the nature of
each discharge while the magnitude of local electric field at
the tip of discharge columns was determined by the applied
Manuscript received on 15 January 2008, in final form on 14 November 2008.
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G. Chen and C. H. Tham: Electrical Treeing Characteristics in XLPE Power Cable Insulation
180
voltage. Noto and Yoshimura [3] examined polyethylene
under various frequencies of ac electric stress. It was found
that tree does not follow a linear growth relationship with the
frequency. Under various applied voltages, tree exhibits
different growth characteristics with various frequencies. The
process of tree initiation decreased with increasing voltage
and frequency and was assumed to be due to the increase in
local electric field at the tip of the discharge column. Densley
[4] studied the effects of frequency, voltage, temperature and
mechanical stress on the timetobreakdown (TTB) of XLPE
cable insulation subjected to highly divergent field. It was
found that trees grow in different shapes and colors at various
frequencies and voltages. Tree shape changes at higher
frequency which in turn reduces the TTB. TTB are also
reduced significantly at higher temperatures and mechanical
stress. The measurement of partial discharges (PD) also
suggested the role of space charges were dominant in
determining TTB and the shape of the tree. A comprehensive
review of the developments made in the understanding of tree
mechanisms was attempted by Dissado [5].
The concept of fractal dimension was firstly introduced to
describe the geometrical characteristics of gas discharges by
Niemeyer et al [6]. A simple twodimensional stochastic
model producing structures similar to those observed in
experimental studies of branching gas discharges was
established. Barclay et al [7] later constructed a two
dimensional stochastic model of electrical treeing using a
statistical method and from which they performed fractal
analyses using a range of methods. It was found that trees of
low fractal dimension, D are the most dangerous as they grew
faster across the pin plane space while trees of high fractal
dimension grew slower but caused great amount of damages.
Factors which reduce the fractal dimension increases the risk
to the system. These include a crossover from bushtype to
branchtype trees with higher voltage [4]. Smaller pinplane
spacing was also found to increase the branch density of trees
formed [4], indicating that fractal dimension is determined by
the local electric field, which will depend on both the applied
voltage and the pinplane spacing. Cooper and Stevens [8]
studied the relationship between the fractal dimension of
trees in a polyester and its bulk properties for various degrees
of crosslinking. It was observed that the postcuring
temperature of the resin influences the treeing behavior and
the fractal dimension increases with increasing postcuring
temperature and degree of crosslinking. Maruyama et al [9]
revealed that a higher fractal dimension was resulted from a
higher gel content. In the same study, the relation between
the tree length and the fractal dimension was also made. It
was observed that trees changes from branchtype to dense
bushtype with increasing applied voltage and the fractal
dimension increases with
approximately 16 kV, after which it tends to saturate
regardless of the increase in tree length. Fuji et al [10]
examined the effect of the polarity of applied dc voltage on
tree patterns obtained in polymethylmethacrylate (PMMA)
samples. The studies pointed out that the fractal dimensions
obtained at the two polarities differ and the fractal behavior
depends on the local field or the space charge. A better
a stressing voltage of
understanding of fractal analysis and dimension applied on
tree with various methods, both experimental and
computational was done by Kudo [11]. The work estimated
the fractal dimension of tree using methods such as box
counting, fractal measure relations, correlation function,
distribution function and power spectrum. It was found that
there is a difference in fractal dimension obtained by the
different methods and is unclear of the best method for
estimating tree patterns. 3D fractal analysis of real electrical
trees had also been developed. It has been revealed in our
recent research [12] that a double structure of electrical tree
occurs when it grows at a submicroscopic structurally uneven
region of the material. A new parameter, the expansion
coefficient, was introduced to describe the electrical tree
propagation characteristics.
Several models have been developed to simulate electrical
tree growth. Stochastic model is popular due to its ease of
computation [7]. The model is based on diffusion limited
aggregation [13]. Simulated tree displays a remarkably
similar behavior to experiment [7]. To understand the
mechanism of electrical tree growth, physical process has
been introduced to the stochastic model [14]. The addition of
physical process helps to reproduce many of known
characteristics of tree growth [15]. A deterministic treeing
model has been proposed [16] and used successfully by Dodd
[17] to study the growth of nonconductive electrical tree
structures in epoxy resin. The model produces formation of
branched structure of tree without the need of random
variables. The more detailed description of these models can
be found in literature [17]. Recently, cellular automata (CA)
model has been reported to simulate tree growth [18]. Using
a very simple rule, the tree formation was successfully
reproduced in a dielectric with a point/plane electrode
arrangement in the presence of voids. In addition to the above
electrical models, the influence of mechanical stress on
electrical tree growth has also been reported [19]. It has been
demonstrated that the mechanical properties (specifically,
tensile strength, elastic modulus and fracture toughness) of
the dielectric material strongly affect the growth of electrical
trees in singlecast homogeneous polyester resin specimens.
Despite these efforts, a full understanding has not yet been
achieved due to complexity and various factors that may
affect tree initiation and growth. In this paper we intend to
investigate the influence of frequency on fractal dimension of
electrical trees in XLPE under a fixed applied voltage.
Methods for investigating the frequency effect on trees have
been devised. Besides looking into the fractal analysis of tree
as a whole, regions of growth are being sectioned to bring the
study further.
2 EXPERIMENTS
2.1 SAMPLE AND EXPERIMENTAL SETUP
Semiconducting layer and conductor of a commercial
XLPE cable, having an insulation thickness of 15 mm, were
removed, leaving only the insulation. Each cable specimen
measuring 5mm in lengths was then cut. The steel needle
with a tip radius of 5μm was inserted gradually into the
specimen to give a tip to earthplane electrode separation of
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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 1; February 2009
181
2mm± 0.2mm at elevated temperature of between 120140
°C. The sample was then annealed for approximately 5
minutes to minimize any mechanical stress build up around
the pinplane region before it was cooled down to room
temperature. A typical sample with an inserted needle is
schematically shown in Figure 2. All samples were inspected
for the presence of mechanical stress around the pin tip
region under polarized light. The samples with the presence
of mechanical stress were discarded. Detailed information of
preparing samples can be found in our research publications
[12].
Figure 2. A schematic diagram of XLPE sample for treeing experiment.
The needleplane specimen was kept in silicone oil cell to
control the temperature and to prevent external discharges or
flashover. They were subjected to continuous 7kV rms ac
electrical stress over a range of frequencies. An average of
six samples were tested at each frequency with testing
frequencies at 20, 50, 100, 300 and 500 Hz. Prior to
monitoring the growth of tree, all samples were preinitiated
using a 2kHz, 7kV AC voltage until a small (5080μm) tree
has formed at the tip. All the experiments were conducted at
room temperature (~20oC). Densley [4] considered that once
tree has initiated, it would have little or no effect on the
subsequent growth of tree. Therefore, the preinitiation will
have limited effect on the result. A CCD camera (JVC
TK1380) which is of sufficient spatial resolution to measure
the spatial distribution of tree channel was then used to
monitor electrical treeing optically during stressing. The
skeletal structure of the tree was monitored by back lighting
the sample with a projection lamp.
Images of evolving tree structures were captured
periodically until the tree spanned approximately 90% of the
pinplane spacing. At this point, the test was terminated to
protect both the external circuitry and the tree from damage
in the event of a breakdown. The optical bench microscope
was adjusted to a standard magnification level during all
stages of tree growth so as to minimize errors due to the
influence of magnification. The captured image was
processed on the KS400 system developed by Imaging
Associates Ltd. The experimental setup for treeing tests is
shown in Figure 3. After that, the fractal dimension was
computed with boxcounting method.
2.2 CALCULATION OF FRACTAL DIMENSION
2.2.1 Image Acquisition and Segmentation
A high quality original image is an essential condition for
accurate data analysis. The digitised image can be presented
as binary, skeletonized or borderonly image depending on
the fractal dimension method used. It must also allow a clear
distinction between the tree and the background, either by
greyscale or by colors; to allow a simple thresholding
operation. Thresholding provides an easy and convenient
way to perform simple segmentation, an operation
transforming digitized image into binary image required for
data extraction; on the basis of the different intensities or
colors in the foreground and background regions of an image.
In the simplest implementation, the output is a binary image
representing the segmentation. By looking at the image
intensity histogram, the appropriate segmentation technique
can be determined.
Figure 3. Experimental setup for treeing tests.
2.2.2 Image Analysis and Measurement of Fractal
Dimensions
For automatic image analysis, the softwarebased imaging
system KS400 was used. KS400 allows the development of
applicationspecific macros which enables one to include all
necessary functions in a single given application, i.e. image
acquisition, calibration, processing, measurement and data
output.
2.2.3 Box Counting Method
To estimate the boxcounting fractal dimension, Db, the 2D
Euclidean space containing the tree image was divided into a
grid of boxes of size ?, with the initial box size being 1.3
times of the tree. Box size ? was then made progressively
smaller and the corresponding number of boxes, N, covering
any part of the tree was counted. The sequence of box sizes
for grids was usually reduced by a factor of half from one
grid to the next. The count depends on box size ? and Db
according to eqnuation (1),
b
D
N
? ? ?
)(
(1)
Thus for a fractal structure a plot of log(N(?)) against log(?)
should yield a straight line whose gradient corresponds to Db,
cDN
b
??
)log()(log
??
(2)
where c is a constant.
Silicone oil
Sample
Earth electrode
Needle
HV electrode
Lamphouse
Sample localization system
Function generator
Wideband high voltage
amplifier
Microscope
CCD
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G. Chen and C. H. Tham: Electrical Treeing Characteristics in XLPE Power Cable Insulation
182
2.2.4 Data Processing
The fractal dimension, Db, may vary depending how it is
obtained from the loglog plot. In such a plot, Db is related
to the slope of the line, the number of data points being
related to the number of measuring steps. The actual data
points generally do not all lie on a straight line, thus
showing limited selfsimilarity or scale invariance which is
a characteristic of natural fractal object. Measured fractal
dimensions can only be compared if this influence is
excluded either by specifying a lower and upper limit for
the linear regression or by introducing other criteria, such
as defining a level of confidence in the Rsquared value. It
is an indicator from 0 (worst) to 1 (best) that reveals how
closely the estimated values for the trend line correspond to
the actual data. By applying the limits, certain data points
were selectively rejected as long as the linear regression of
the remaining data improved the Rsquared value. In the
present study, a program written as a macro for the KS400
system, has been used to obtain fractal dimension
automatically.
3 EXPERIMENTAL RESULTS
3.1 GROWTH RATE AND ACCUMULATED DAMAGE
Two methods were used to analyze tree growth from a
sequence of images captured periodically as tree grew from
the tip to the earthplane electrode. In the first method, arc of
radii from an origin at the tip was drawn and the maximum
tree extent from the tip was measured. The differences in tree
length and time between photographs were used to compute a
growth rate:
1 Time2 Time
1 ExtentMax.2 Extent Max.
(mm/min)rate Growth
?
(3)
The other method is to measure the effective
accumulated damages (area covered by tree structure in
pixels) computed using the KS400 after image processing
to obtain suitable binary images of tree structure. The area
was estimated by extracting the total number of pixels
covering the tree. Each pixel was to have an area of
4.255μm x 4.255μm. The two methods can effectively
describe the spatial and temporal development of tree
growth.
Images of the trees for various frequencies taken prior to
breakdown are shown in Figure 4. They were stressed
continuously at 7 kV rms and images were captured during
tree growth and each image was separately analyzed to
estimate the various parameters such as growth rate and
accumulated damage. Variation in tree growth rate did
exist within six samples tested for each frequency and data
are only presented from reproducible trees. The selected
results from 20 Hz, 50 Hz and 500 Hz are reported here to
limit the length of the paper as the results from 100 Hz and
300 Hz are similar to those from 50 Hz and 500 Hz,
respectively.
A radial zone method [20] has been used to analyze tree
growth at different frequencies. Figure 5 illustrates the
growth rate and accumulated damage versus the pinplane
distance at 20 Hz.
Figure 4. Captured photographs of tree growth for the XLPE cable samples
prior to breakdown (a) 20 Hz, (b) 50 Hz, (c) 100 Hz, (d) 300 Hz and (e) 500
Hz.
It can be seen that during the initial growth stage, the tree
displayed some rapid growth up to some 300μm from the pin
tip in 10 minutes. It exhibited a high growth rate during that
period but slowed down as tree extended away from the tip.
Branching was concentrated (highly branched), extending to
some 500μm and discernible damages were seen. The growth
rate has dropped significantly as growth continued. Slow
growth continues to be observed until the tree had advanced
past 50% of the pinplane distance followed by an increase in
growth rate. At around 1200 μm, growth rate increased
further and multiple branches were formed. It can be seen
from the increase in accumulated damage. This latter region
has often been identified as ‘runaway’ growth by many
authors.
The accumulated damage (number of pixels) versus the
tree length across the pinplane spacing shows a general
increase. Together with the growth rate, it suggests that
tree actually exhibits three distinct growth regions. In
region A, initial rapid filamentary tree growth occurs.
Here the rate of damage increases with distance, with
multiple branches being formed. Dense branching may
also occur near the pin tip. This is followed by an
intermediate region B, in which low growth rate is
observed. Finally, a region C occurs (the ‘runaway’
region), in which a large amount of damage per unit
radial extent reflects the large increase in tree branching
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183
that occurs. In this region, it is also observed that the
growth rate increases as leading branches extend towards
the earth plane.
20Hz AT 1200 MINUTES
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0 0.51 1.52
PIN PLANE DISTANCE (MM)
GROWTH RATE (MM/MINUTES)
A
BC
20Hz AT 1200 MINUTES
0
5000
10000
15000
20000
25000
30000
35000
40000
0 0.51 1.52
PIN PLANE DISTANCE (MM)
ACCUMULATED DAMAGE
(PIXELS)
ABC
Figure 5. Growth rate (a) and accumulated damage (b) as a function of pin
plane distance showing the three regions A, B and C of tree growth.
Figure 6 illustrates the growth rate and accumulated
damage versus the pinplane distance at 50 Hz. Samples
stressed continuously with frequency at 50Hz revealed that
tree shape remains branchtype without significant changes to
its shape. The tree exhibited a very rapid growth, extending
up to some 500μm in the first 12 minutes. It can be seen from
the high growth rate occurring in this region. After this initial
growth, there was a long period of quiescence where there
was very little or no significant growth from the leading
branches. Accumulated damage versus the distance shows
constant tree damage with length. During this period, partial
discharge activities were known to be predominant within
the sidebranches and channels which were lengthened and
thickened in size. This observation can be further reinforced
from Figure 6 that the tree had stopped extending but the
number of pixels actually shown an increment in value.
Subsequently, tree growth accelerated again after it had
spanned past the 50% spacing.
Tree formed near the origin with a rapid growth was
observed in the first 5 minutes at 500 Hz test as shown in
Figure 7. There was a lessening in growth after initial activity
with growth rate comparable to those observed at low
frequency. Large accumulated damage occurred near the
origin followed by one or two leading branches extending
outward till breakdown. Tree growth can be split into two
regions with AC transition occurs at 1400±100 μm. In
region C, the leading branch takes less than 10 minutes to
breakdown, influenced by the high growth rate.
50Hz AT 452 MINUTES
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 0.51 1.52
PIN PLANE DISTANCE (MM)
GROWTH RATE (MM/MINUTES)
ABC
50Hz AT 452 MINUTES
0
5000
10000
15000
20000
25000
0 0.51 1.52
PIN PLANE DISTANCE (MM)
ACCUMULATED DAMAGE
(PIXELS)
ABC
Figure 6. Growth rate (a) and accumulated damage (b) as a function of pin
plane distance showing the three regions A, B and C of tree growth.
500Hz AT 40 MINUTES
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 0.51 1.52
PIN PLANE DISTANCE (MM)
GROWTH RATE (MM/MINUTES)
AC
500Hz AT 40 MINUTES
4000
6000
8000
10000
12000
14000
16000
18000
0 0.511.52
PIN PLANE DISTANCE (MM)
ACCUMULATED DAMAGE
(PIXELS)
AC
Figure 7. Growth rate (a) and accumulated damage (b) as a function of pin
plane distance showing the two regions A and C of tree growth.
4 DISCUSSIONS
4.1 Growth Characteristics of Electrical Tree
While the success of the growth rate and accumulated
damage methods may have provided the study of tree growth
into regions, the methods are not easily incorporated into
other models found in the literature such as the field driven
tree growth (FDTG) model [20]. Growth rate computed by
taking the maximum radial extent of the tree is found that the
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G. Chen and C. H. Tham: Electrical Treeing Characteristics in XLPE Power Cable Insulation
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leading branch taken as the largest extent may stop growing
for some time while other side branches from the origin
continue to grow. This method may be ineffective in taking
account of growth occurring at other branches with shorter
radial extent. Therefore, the accumulated damage method
was devised to look into the spatial development of tree more
accurately.
From analyses, tree exhibits two or more regions of growth
and the fractal dimension in each region is dissimilar as
shown in Table 1. Thus the variation in local field EL may
have the effect of affecting the fractal dimension. It is
believed there are some variances in EL instead of equaling in
magnitude in both regions since the fractal dimensions are
different, which is thought to be affected by EL. The
difference in growth duration at each region can further
reinforce this analysis.
Table 1. Fractal dimension of tree growth in different regions.
Frequenc
y
(Hz)
20 1.79
50 1.69
100 1.70
300 1.68
500 1.66
Region A Region B Region C
1.71
1.71
1.63


1.70
1.64
1.66
1.59
1.54
It is also noted that tree exhibits same type of growth
characteristic with a high initial growth rate followed by a
period of quiescence (for tree with two growth regions),
then a ‘runaway’ region. The initial high growth may be
attributed by the field enhancement near the pin tip. With
tree approaching the earthplane electrode, field is once
again enhanced. Other explanations may be given for this
behavior such as image charges intensifying the local field
on approaching the plane electrode [14].
Analysis of six tested samples indicates some variation in
the positions of boundary between different growth regions.
The results shown in Figures 57 were taken from those
samples with positions sitting approximately in the middle.
The actual positions of the boundary can be affected by
several factors, including morphological features in
different samples and variation in local electric field during
tree growth.
4.2 FREQUENCYDEPENDENT TREE BREAKDOWN
Trees shown in Figures 4a to 4c are often known as
‘monkey puzzle’ (MP) tree [14]. It is in the last two regions
that tree takes on the appearance of a MP tree. This type of
structure is an open structure on the macroscopic level with
microscopic secondary branching existing along the length
of each main tree channel, the branch structure having a
hairy spider’s leg appearance. It is known to grow with
stressing voltage at low voltage [19]. At increasingly higher
stressing frequency, MP tree is not featured as branch
density dropped.
In Figure 8, it shows that tree radial extent follows quite a
linear relationship with frequency at the early stage. At
higher frequency, tree extends faster through fine
filamentary branches. This type of behavior has been
reported to occur [3]. Figure 9 shows TTB as a function of
the stressing frequency. TTB is seen to be faster at higher
frequency and comparing the accumulated damage at
different frequencies, it shows that TTB decreases with
lower accumulated damage. Therefore, TTB also depends
on the distribution of accumulated damage.
Figure 8. Tree radial extents as a function of frequency showing tree length
at various times.
4.3 FRACTAL DIMENSION REGIONS A, B AND C
The fractal nature of tree is demonstrated by the
consistency of the fractal dimension estimates obtained.
Disregarding the very small trees grew initially; value of 1.55
to 1.71 is always obtained for five frequencies tested without
a clear trend. It tends to saturate in this range as trees were of
branchtype. Thus, there is no significant change to the
fractal dimension. This branchtype characteristic has been
shown to produce under a stressing voltage of 7 kV [3]. Kudo
[11] performed a fractal analysis on the photographs of the
branch trees (Figure 9 of [3]), which were stressed at 7 kV,
has an estimated fractal dimension of around 1.6. This value
coincides closely with data here.
Figure 9. The time to breakdown against frequency.
As fractal dimension for different frequencies varies
randomly from 1.55 to 1.71, it is difficult to draw any
inference. On the other hand, there are different stages during
tree growth, it would be interesting to look at the fractal
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185
dimension in each region. Images were sectioned into three
regions using the approximated transition zone and the fractal
dimension of each region was computed using the KS400
system as shown in Table 1.
It can be seen that the value of fractal dimension in region
A is always higher than C for all the frequencies. In region C,
tree only constitutes of a few leading branches to form the
complete breakdown path, resulting in a lower fractal
dimension than in region A. At frequency of above 300Hz,
fewer branches were formed, leading to a lower fractal
dimension than at lower frequency. Dissado et al [14] show
that a bush tree with higher fractal dimension developed from
higher voltage (~1215 kV) takes a longer time to breakdown
than branch tree with lower fractal dimension at lower
voltage (~911 kV). The damage in region A at lower
frequency is more concentrated than at higher frequency.
Fine filamentary branches having a larger radial extent from
the tip were seen at higher frequency in region A, thus
resulting in lower fractal dimension.
Using the knowledge of higher fractal dimension resulting
in longer breakdown from Dissado’s work, it appears tree
growth in region A may actually control the TTB. Thus, a
regression line describing the empirical relationship relating
the fractal dimension and TTB is shown in Figure 10. It may
be possible to estimate the TTB by estimating the fractal
dimension of the growing tree in which the fractal dimension
in region A may be the controlling factor for TTB.
REGION A  FRACTAL DIMENSION
1.62
1.64
1.66
1.68
1.7
1.72
1.74
1.76
1.78
1.8
1.82
0 200400 600 8001000 1200
TTB TIME TO BREAKDOWN (MINUTES)
FRACTAL DIMENSION
300Hz
20Hz
50Hz
100Hz
500Hz
Figure 10. Correlation between the fractal dimension of region A and TTB.
4.4 ACCUMULATED DAMAGE – REGIONS A, B
AND C
The devised accumulated damage method was also applied
to the different regions similar to that of fractal analysis and
the results are shown in Table 2.
More accumulated damages appear to have been done to
region A at higher frequency. This is due to a larger region
exhibited from the tests and a higher branching density near
the tip. In the same region, the branch density is higher with
finer filamentary branches spreading at a wider arc angle
from the tip. At lower frequency, thicker branches were
densely packed together resulting in a solidly filled structure
and the branching is concentrated with only one or two such
branches present.
Table 2. Number of pixels accumulated in different growth regions.
Frequenc
y
(Hz)
20 3303
50 3625
100 5126
300 11842
500 17539
Region A Region B Region C
11230
6930
5148


23864
16925
13331
2073
1797
In region C, only a few runaway branches leading to
breakdown at higher frequency are formed, giving lower
damages. Tree growth occurs at all tree tips at low frequency
lead to tree structures in these region having a higher
branching density than in region B, resulting in higher
damages made. Like the regression line describing the
empirical relationship relating the fractal dimension and TTB
shown in Figure 10, a similar regression line in Figure 11 is
made to illustrate the possibility of calculating the TTB by
estimating the accumulated damage of the growing tree in
which the accumulated damage in region C may be the
controlling factor for TTB.
ACCUMULATED DAMAGE AT 20, 50, 100, 300 AND 500 Hz
0
5000
10000
15000
20000
25000
30000
0 200400600 80010001200
TTB TIME TO BREAKDOWN (MINUTES)
ACCMULATED DAMAGE
(PIXELS)
300Hz
20Hz
50Hz 100Hz
500Hz
Figure 11. Regression line describing the empirical relationship relating the
damage and TTB in region C.
4.5 NUMBER OF CYCLES
Partial discharges (PD) are typical measured and studied at
an operating frequency of the applied voltage, in general
50/60 Hz. However, there are many studies measuring PD at
other applied frequencies. A lower applied frequency reduces
the power and size needed for the voltage supply equipment.
Alternatively PD can also be studied at variable applied
frequencies to provide more information than measurements
at a single frequency as the variation in applied frequency
changes the local state at defects in the insulation [21]. It has
been stated that these changes can be used to better
characterize the defects, provided that the frequency
dependence of PD is interpreted physically.
An empirical relationship relating the number of cycles
experienced by the tree and the time to breakdown is
established by the regression line shown in Figure 12.
The relationship is determined using,
Cycle per Taken Time
seconds 60 TTB
?
Cycles ofNumber
?
(4)
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G. Chen and C. H. Tham: Electrical Treeing Characteristics in XLPE Power Cable Insulation
186
1050000
1100000
1150000
1200000
1250000
1300000
1350000
NO. OF C YC LES
1400000
1450000
1500000
0 200 400600800 10001200 1400
TTB  TIME TO BREAKDOWN (MINUTES)
100Hz
500Hz
300Hz
50Hz
20Hz
Figure 12. The number of cycles experienced by tree before breakdown.
It shows that tree does not experience the same number
of cycles before its breakdown. This may be due to the
time taken for charges to transport through tree branches
which are not affected by frequency. Other factors such
as morphology effect may play a role in the breakdown.
Using the same figure, it may also show the invalidity of
trying to correlate the data to partial discharge (PD)
monitoring at frequencies other than 50 Hz. From the
treeing study, the data may correlate the relationship
since tree extension is due to PD activities in the
channels. It is found that the concept of monitoring PD in
cable at lower frequency may not be fully consistent with
that at power frequency. Though, the number of
discharges occurring per cycle is lower at higher
frequency, the total number of discharges is actually
higher for a fixed period. Therefore, further experimental
and theoretical works are required.
Figure 13. Electrical tree growth as a function of the number of cycles.
To further validate the relationship between the tree growth
and number of field cycles, Figure 13 shows the tree radial
extent against the number of cycles at various frequencies. It
seems that the tree length increases linearly with the number
of cycles experienced. This linear relationship may suggest
that the mechanical fatigue is responsible for tree growth in
XLPE. Analysis carried on fractal dimension in regions A
and C as a function of the number of cycles also indicate that
there is a general increase in fractal dimension in both
regions. This further strengthens that the fatigue process is
related to the tree growth.
4.6 MATERIALDEPENDENT CRITICAL FIELD
The description of the propagation curves may be able to
provide some insight on tree growth affecting the fractal
dimension and the simple field driven tree growth (FDTG)
model [20] is being used and will be briefly described here.
The model is constructed by taking the assumption that the
incremental increase in accumulated damage occurs during
an ac stressing cycle is proportional to the magnitude of the
local electric field EL exceeding a materialdependent critical
field Ec. If the tree is conducting with the presence of PD
activity, it will modify EL by effectively reducing the pin
plane spacing and increasing the apparent pinplane radius.
As tree branches extend beyond the pin tip, EL can be related
to the new tree length, L by taking the tree to be effectively a
conducting hyperboloid extension of the point electrode. This
assumption gives the maximum field along the hyperboloid
axis as,
EL = EMAX =
??
2V
1+a
1a
L+r ln
?
?
?
?
?
?
(5)
where r is the radius of curvature of the pin tip, V is the peak
value of the applied voltage, and
L
?
with w the pinplane distance. This expression is equivalent
to that given by Mason [22]. From expression, E is a function
of L, thus the magnitude changes as tree grows. Initially E
will decrease as the equivalent hyperboloid radius increases,
leading to decelerating growth. When EL drops below Ec
(indicated by an arbitrary line in Figure 14) the growth will
slow to a stop. However, before this could happen, the field
may start to increase again as the earthplane electrode is
approached. As a result tree growth will start to accelerate
again. Such behavior is typical of many electrical trees [23].
a = 1 +
Lw
r
?
(6)
REGION A, B AND C
PINPLANE DISTANCE 2MM
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
27.5
30
32.5
35
0 0.2 0.40.6 0.811.2 1.41.6 1.82
PINPLANE SPACING (MM)
ELECTRIC FIELD AT TREE TIP (MV/M)
20Hz
50Hz
100Hz
7kV RMS
AB
C
ARBITRARY EC
ARBITRARY TRANSISTION ZONES
Figure 14. Local electric field at the damage perimeter as a function of
damage extent for tree growth with 2 transition zone. Dotted line shows the
ideal characteristic of the FDTG model.
Plots of EL against the hyperbolic radius using equation (5)
is shown in Figures 14 and 15 under 7 kV RMS with the pin
plane distance being 2 mm. Here, the curve shows how EL
varies as the tree grows across the pinplane gap. From the
figures, it demonstrates the different regions present without
a variation in EL. Comparing it with the ideal transition zones
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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 1; February 2009
187
from the model, it found limitations with the results. The
model fails to infer Ec graphically. In the literature, one
transition zone was found when a higher value of ELwas
applied. Since equation (5) does not take into consideration
of frequency when computing the local field, EL remains
constant with varying frequencies. One of the assumptions in
the FDTG model is that the tree can be considered as a
conducting hyperboloid extension of the pin tip. From Table
1, it is known that the fractal dimension of tree decreases
with frequency, this indicates that the assumption may not
hold for trees at high frequencies where a low fractal
dimension of tree has been observed. On the other hand, the
FDTG model assumes that there is no potential drop as the
tree is considered forming from conducting branches. Again,
this may not hold all the time, leading to an overestimation of
EL in magnitude. This will affect the tree growth
characteristics.
2 REGIONS
PINPLANE DISTANCE 2MM
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
27.5
30
32.5
35
0 0.2 0.4 0.60.81 1.21.41.61.82
PINPLANE DISTANCE (MM)
ELECTRIC FIELD AT TREE TIP (MV/M)
500Hz
300Hz
7kV RMS
AC
ARBITRARY TRANSISTION ZONE
14kV RMS
ARBITRARY EC
Figure 15. Local electric field at the damage perimeter as a function of
damage extent for tree growth with one transition zone. Dotted line shows
the ideal characteristic of the FDTG model when using the same sample, the
field will not drop below Ec with a higher stressing voltage.
In the literatures, two transition zones were found at low
stressing voltage and one at high stressing voltage. Thus, it is
interesting to see such similar behavior where there are also
two transition zones at low frequency and one at high
frequency. Therefore, the frequency has an effect of
modifying the number of growth regions even though EL
does not change. Despite the simplicity of the FDTG model,
it has been successfully applied to spatial and temporal
observations of electrical tree growth in synthetic resins [20].
5 CONCLUSIONS
Tree growth under the influence of frequency is not able to
infer much with fractal dimension due to the similar branch
type structure formed. Instead, it is found to have accelerated
the breakdown process with higher frequency leading to a
faster breakdown. This could be due to the higher number of
partial discharges at higher frequency. Fractal dimension is
thus thought to be influenced primarily by the magnitude of
stressing voltage as frequently discussed in the literature.
Further analyses were made and by using the devised
approaches, tree growth can be sectioned into two or three
regions depending on the frequency applied. At low
frequency, three regions are present in the growth process
while there are only two at higher frequency. The first is region
A, where high growth rate is exhibited in which filamentary
tree growth occurs at the pin tip. Next is region B in which tree
growth is slowed and the fractal dimension is lower than in
region A. Lastly in region C, growth rate picks up with an
increase in branch density and decrease in accumulated damage
as tree extends towards the earthplane electrode. Again, the
fractal dimension is lower than in region A. Therefore, the
regions analyses suggest that the timetobreakdown is
primarily influenced by the fractal dimension in region A and
the amount of tree damage in region C.
Tree is found not to have experienced the same number of
cycles, thus partial discharges before its breakdown at
various frequencies. It is thought that the time taken to
transport charges from the origin to the tree tip may have
affected the number of discharges occurring. It also shown
that the correlation of partial discharge activity at lower
frequency with power frequency through total number of
cycles tree experiences is not explicit and does not follow a
linear relationship. On the other hand, the tree growth shows
a nearly linear relationship with the number of field cycles.
This may suggest that the mechanical fatigue is responsible
for tree growth in XLPE.
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George Chen was born in China in 1961. He received the
B.Eng. and M.Sc. in 1983 and 1986, respectively in
electrical engineering from Xian Jiaotong University,
China. After he obtained the Ph.D. degree in 1990 in
electrical engineering from The University of Strathclyde,
UK, he joined the University of Southampton as a
postdoctoral research fellow and became a senior research
fellow subsequently. In 1997 he was appointed as a research Lecturer and
was promoted to a Reader in 2002. Over the years, he has developed a wide
range of interests in high voltage engineering and electrical properties of
materials and published over 150 papers.
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