# 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 box-counting 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.

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**ABSTRACT:**In this paper, combined with the methods of real-time microscopic digital imaging and partial discharge (PD) continuous measurements, the effect of temperature on electrical tree propagation and PDs characteristics in XLPE cable insulation was investigated using an embedded needle electrode arrangement over a range of applied voltages from 9 to 15 kV rms. The temperature of the experiments varied from 10 °C up to 70 °C, which lay within the rated operating temperature range of XLPE cables. The results obtained show that temperature has dominant effect on electrical tree shapes and growth time. As the electrical tree shapes at lower voltages are influenced by the change of tree channel conductivity, this process appeared to be accelerated greatly by increase of experimental temperature. The tree growth time at higher voltages was decreased at higher temperatures due to the change of material morphology and it was accompanied by intensive PD activity.Electrical Insulation and Dielectric Phenomena (CEIDP), 2012 Annual Report Conference on; 01/2012 -
##### Conference Paper: Characteristics of electrical treeing in extruded polypropylene and cross-linked polyethylene cable insulation

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**ABSTRACT:**This paper presents results from experimental investigations performed in order to characterize and compare electrical tree formation in extruded syndiotactic polypropylene (s-PP) and cross-linked polyethylene (XLPE) cable insulation. All tests were performed using molded needle-plate samples with an insulation distance of 1.05 mm. Initiation and formation of electrical trees from the needle tips were studied using partial discharge measurements and optical microscopy video techniques. The tree growth was characterized by measuring length and width of the trees, the time needed for the first branch to reach the opposite ground electrode and time to electric breakdown. The effect of different AC voltages, with magnitudes up to 12 kV and frequencies in the range of 50 - 1000 Hz, were examined.High Voltage Engineering and Application (ICHVE), 2012 International Conference on; 01/2012 - 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

1070-9878/09/$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 box-counting 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, box-counting, 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

long-term 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 time-to-breakdown (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 two-dimensional 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 bush-type to

branch-type trees with higher voltage [4]. Smaller pin-plane

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 pin-plane 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 cross-linking. It was observed that the post-curing

temperature of the resin influences the treeing behavior and

the fractal dimension increases with increasing post-curing

temperature and degree of cross-linking. 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 branch-type to dense

bush-type 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. 3-D 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 non-conductive 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 single-cast 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 earth-plane electrode separation of

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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 1; February 2009

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2mm± 0.2mm at elevated temperature of between 120-140

°C. The sample was then annealed for approximately 5

minutes to minimize any mechanical stress build up around

the pin-plane 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 needle-plane 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 pre-initiated

using a 2kHz, 7kV AC voltage until a small (50-80μm) 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 pre-initiation 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

pin-plane 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 box-counting 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 border-only 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 software-based imaging

system KS400 was used. KS400 allows the development of

application-specific 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 box-counting fractal dimension, Db, the 2-D

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

Lamp-house

Sample localization system

Function generator

Wide-band 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 log-log 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 self-similarity 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 R-squared 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 R-squared 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 earth-plane 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:

1Time-2Time

1 ExtentMax.-2 ExtentMax.

(mm/min)rateGrowth

?

(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 pin-plane

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 pin-plane 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 pin-plane 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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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 1; February 2009

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

00.511.52

PIN PLANE DISTANCE (MM)

GROWTH RATE (MM/MINUTES)

A

BC

20Hz AT 1200 MINUTES

0

5000

10000

15000

20000

25000

30000

35000

40000

00.511.52

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 pin-plane distance at 50 Hz. Samples

stressed continuously with frequency at 50Hz revealed that

tree shape remains branch-type 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 pre-dominant within

the side-branches 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 A-C 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

00.511.52

PIN PLANE DISTANCE (MM)

GROWTH RATE (MM/MINUTES)

ABC

50Hz AT 452 MINUTES

0

5000

10000

15000

20000

25000

00.51 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

00.511.52

PIN PLANE DISTANCE (MM)

GROWTH RATE (MM/MINUTES)

AC

500Hz AT 40 MINUTES

4000

6000

8000

10000

12000

14000

16000

18000

00.511.52

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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