Space Charge Formation and its Modified Electric Field
under Applied Voltage Reversal and Temperature Gradient
in XLPE Cable
M. Fu and L. A. Dissado
Department of Engineering
University of Leicester, Leicester, LE1 7RH, UK
G. Chen
School of Electronics and Computer Science
University of Southampton
Southampton, SO17 1BJ, UK
J. C. Fothergill
Department of Engineering
University of Leicester, Leicester, LE1 7RH, UK
ABSTRACT
The results of space charge evolution in cross-linked polyethylene power cables under dc
electrical field at a uniform temperature and during external voltage polarity reversal are
presented in the paper. A mirror image charge distribution was observed in the steady
state, but the pre-existing field altered the way in which the steady state charge
distribution was formed from that obtaining when the cable was first polarized. Polarity
reversing charge was generated in the middle of the insulation and moved towards the
appropriate electrodes under the influence of a field in excess of the maximum applied
field. Our results show that the mirror effect is a steady state effect that is due to cross-
interface currents that depend only on the interface field and not its polarity.
Measurements on cable sections with an elevated mean temperature and temperature
gradient show that the interface currents are temperature dependent, and that differences
between the activation energies of the interface and bulk currents can eliminate and
possibly even invert the polarity of the space charge distribution.
Index Terms - Space charge, PEA, XLPE insulated power cables, voltage polarity
reversal, temperature gradient, “mirror image effect”.
1 INTRODUCTION
THE renewed interest in high voltage direct current
(HVDC) transmission has led to many manufacturers
worldwide investing in polymer insulated dc power cables.
Cross-linked polyethylene (XLPE) is the most common form
of polymeric insulation, however the features that make it a
good insulator, may paradoxically lead to problems when it is
used in dc operation. Thus its low carrier mobility and high
trapping rates may, under certain conditions, give rise to space
charge in the body of the insulating material. This will result
in localised electric stress enhancement and even premature
failure of the cable insulation when the localised fields exceed
the design values [1-3]. This issue has stimulated the
investigation of space charge accumulation and retention, and
abundant data has been obtained from film and plaque
samples over the past two decades [4-11]. However, less
attention has been paid to space charge dynamics in full sized
cables presumably due to a limited range of experimental
systems suitable for examining cables. Such investigations
would however be more relevant to practical situations as all
the features specific to cable design, such as
insulator/semiconducting interfaces, insulating material
processing, and divergent electric field would be fully
reflected in the space charge behaviour. They would also
make it possible to investigate the effect of a temperature
gradient in radial insulation on the space charge accumulation,
and hence replicate the conditions experienced when the cable
is loaded in service.
In a dc transmission system, bi-directional power flow may
be achieved by exchanging the roles of rectifier (sending end)
and inverter (receiving end), i.e. through voltage polarity
reversal. The presence of space charge may result in an
enhanced electric field within the insulation as its spatial
Manuscript received on 3 November 2006, in final form 18 January 2008.
1070-9878/08/$25.00 © 2008 IEEE
IEEE Transactions on Dielectrics and Electrical Insulation Vol. 15, No. 3; June 2008
851
distribution may not be able to synchronously follow the
polarity reversal due to low charge carrier mobility, but the
magnitude and the location is unpredictable. This could pose a
vital threat to the cable insulation in service. The temperature
gradient existing across the insulation in a fully loaded cable
will make the space charge distribution, and consequently the
electric field more complex. The investigation of space charge
at elevated temperature in cable geometry is therefore of
importance for the electric field distribution and performance
of dc cable insulation.
Here we present results for the space charge evolution and
response to external voltage polarity reversal measured on full
size XLPE power cables using the pulsed electro-acoustic
(PEA) technique. The corresponding electric field
distributions along the radial direction are derived from the
space charge distribution, and the local field distribution is
discussed in terms of the evolution of mirror space charge
distributions in the steady state, and the basic physics behind
the formation of an inverted space charge distribution on
reversing the polarity of the conductor potential. The effect of
a temperature gradient on space charge in cable insulation is
also investigated, and it is argued that the reduction of space
charge observed is caused by differences in the temperature
dependence of the bulk conductivity and those applying to the
cross-interface currents.
2 EXPERIMENTAL
2.1 PEA FOR CABLE SAMPLES
The PEA system used for space charge distribution in cable
insulation measurement is schematically shown in figure 1. A
detailed description of the principle of PEA and the modified
system suitable for cable geometry has been given elsewhere
[1, 12, 13] and only a brief overview is given in this paper.
There have been several reports on the application of PEA
for space charge measurement in full size cables [13-16] in
most of which a curve-shaped ground electrode, transducer,
and acoustic absorber block were designed to fit around the
diameter of the cable sample. For different cable sizes,
modification is required to the above components in addition
to extra care in the sample assembly in order to ensure a good
acoustic contact between the cable and curved electrode. The
PEA system employed in this work adopts a flat ground
electrode which enables the system to be easily applied to
cables with different radii such as described in [17].
Tek644A Scope
Computer
R
Current transformer
C
Pulse
generator
DC
Supply
AC
PEA system
Cable sample
PVDF &
Amp
Figure 1. Schematic diagram of PEA system for cable geometry
2.2 CABLE SAMPLES AND TEMPERATURE
GRADIENT
Two types of cable sample were tested in the research. One
is a commercial XLPE ac power cable with an insulation
thickness of 3.6 mm, Cable A, which is tested to investigate
the space charge response to the voltage polarity reversal. The
other one is a prototype HVDC power cable with a 5.7 mm
thick insulation. This was received in both degassed and un-
degassed condition, but only results from the un-degassed
form (Cable B) are reported here. Due to its thicker insulation,
the latter cable was the one chosen for the temperature
gradient experiments. In order to allow sufficient clear
distance from the voltage-applying terminal to the ground
electrode the outer semiconductive screens at the two ends of
the cable were stripped, and the remaining section used as the
outer-earthed electrode. Stress relief rings were also built at
the screen cuts to reduce the likelihood of flashover along the
insulation surface.
A current transformer was set up in the testing rig, as
shown in Figure 1, to generate a radial temperature
distribution across the cable insulation by means of induction-
heating (joule heating I
2
R). It is assumed that the thermal
conductivity of the cable insulation remains constant over the
temperature range used in the present study (e.g. 30
o
C to 80
o
C). For a cable sample with a conductor radius of r
c
and outer
sheath radius of r
s
, the temperature distribution across the
insulation thickness can be calculated as a function of the
radius r [18] through:
()
()
⎟
⎠
⎞
⎜
⎝
⎛
−
+=
r
r
rr
TT
TrT
s
cs
sc
s
ln
ln
(1)
where T
s
and T
c
are the temperature of the outer screen and
the conductor respectively.
A typical induced ac current of 350 A was used to heat the
cable, which has a cross section of 78 mm
2
aluminium
conductor and 5.7 mm thick insulation. A temperature of 70
o
C at the conductor was obtained with a temperature
difference of 13
o
C across the insulation, when the outer
semiconductor was kept at ambient by natural convection
cooling.
2.3 VOLTAGE REVERSAL EXPERIMENTAL
PROCEDURES
In the voltage reversal test the sample was initially stressed
with a positive voltage at the centre conductor and the space
charge distribution was measured at different stressing times.
When the space charge distribution appeared to reach a steady
state the external dc voltage was switched off and the cable was
short-circuited for a short time to release the surface static
charge. Then the dc voltage was switched to the opposite
polarity and ramped up again. In order to make the voltage
reversal a more realistic representation of the operation of dc
transmission systems, the above implementation was finished
within about 90 s. The space charge distribution measurement
was then conducted over the following stressing period until a
steady state was again apparently obtained. The experimental
procedure and the voltage application are illustrated in Figure 2.
852
M. Fu et al.: Space Charge Formation and its Modified Electric Field under Applied Voltage Reversal
Figure 2. Voltage application procedure
2.4 DATA PROCESSING AND CHARGE DENSITY
CALIBRATION
2.4.1 GEOMETRICAL FACTOR AND CORRECTION
PEA measurements made on plaque samples can assume
that a uniform pulsed electric stress is applied and that the
acoustic wave propagation is without divergence
throughout the sample’s thickness. This does not apply to
cable geometry where the electric stress e
p
of the external
pulse voltage, v
p
(t),
is given by:
()
()
()
abr
tv
rte
p
p
ln
, =
(2)
with a and b being the inner and outer radii of the
insulation respectively. The PEA principle is based on the
measurement of the acoustic wave emitted as a result of the
interaction of the pulsed electric field and the space charge
layer, with the delay in reception by the transducer defining
the spatial location of the space charge emitting the
pressure wave. The divergence of the pulsed electric field
thus makes the intensity of the acoustic pressure wave
initiated dependent not only on the charge density but also
on its position.
It is generally assumed that the length of the cable
sample is much greater than the insulation thickness and
the material along the axial direction is homogeneous. The
space charge distribution in the coaxial geometry therefore
only varies in the radial direction and hence it can be
concluded that the acoustic pressure wave representing the
space charge density is also a function of the radial
position. The pressure wave per unit area at position r may
be expressed as [19],
()
()
()
turjk
sa
sa
e
r
Akuj
t
rt
rtp
−
−=
∂
∂
=
γ
φ
γ
,
,
(3)
where
γ
is the density of the medium in which the acoustic
wave is launched and travels through. This equation
describes the propagation of an acoustic wave in an elastic
(or lossless) medium in the radial direction within a
cylindrical coordinate system. It is noticeable that the
intensity of the pressure wave generated by the space
charge layer inside the cable insulation decreases along the
radial direction. This factor or ratio can be best described
by
()
()
()
2
1
,
,
br
rtp
bttp
=
Δ+
(4)
where p(t,r) and p(t+
Δ
t,b) are the acoustic pressure
wave intensities produced at radius r and detected at the
outer sheath b after transmission through the insulation,
Δ
t
is the time for the acoustic pulse travelling from position r
to b (i.e. the position of outer semiconducting layer).
The divergent effects due to coaxial geometry have been
taken into account for precise appraisal of the space charge
distribution in cable samples by applying the geometry
factor (b/r)
1/2
to the signal after the deconvolution, which is
the result of combination of divergences of pulsed field and
acoustic wave intensity in the radial direction [19].
2.4.2 ATTENUATION AND DISPERSION
COMPENSATION OF ACOUSTIC WAVE IN THICK
INSULATION
Apart from the divergence of the pulsed electric field and
acoustic pressure wave in cylindrical geometry, the
attenuation and dispersion caused by thick cable insulation to
acoustic wave pressure is another negative aspect to the PEA
technique which would introduce inaccuracy in the charge
density measurement and loss of spatial resolution. However,
this issue has been well discussed and a proper compensation
(or recovery) algorithm has been derived and deployed in [19,
20] to give an accurate space charge distribution
measurement, in particular, for thick samples. The reader is
referred to [19, 20] for details of the derivation and the
algorithm, which has been used here.
2.4.3 CHARGE DENSITY CALIBRATION
As the PEA technique is an indirect method of space
charge profile measurement, the correlation between the
acoustic wave and charge density needs to be determined by
calibration. In the process of calibration a voltage is applied
across the dielectric sample for a short period of time that is
sufficiently low enough to ensure that no space charge is
developed in the bulk sample, and only the capacitive charges
on two electrodes are present. In the case of cable samples, for
instance, the capacitive charge density induced at the inner
and outer electrodes is proportional to the field at the
interfaces, i.e.
(
)
(
)
aEa
r
ε
ε
σ
0
=
(5)
(
)
(
)
bEb
r
ε
ε
σ
0
=
(6)
where
ε
0
is the permittivity of free space,
ε
r
the relative
permittivity of the insulating material, E(a) and E(b) the
electric stresses at the two interfaces respectively. Knowing
the actual charge density at a given interface, the constant of
proportionality between the output of the PEA system and
charge density can be determined.
There has been a long-term interest in the determination of
the electric field distribution in dc cables. This is governed by
the conductivity of the insulating material. However the
conductivity is determined by temperature and the electric
stress, which it also determines. It is therefore difficult to
predict the electric field distribution throughout the cable
insulation under dc voltage with the accuracy of that under ac
voltage. The method used in the calculation of interface
IEEE Transactions on Dielectrics and Electrical Insulation Vol. 15, No. 3; June 2008
853
electric stress for charge density calibration was fully
explained in [19], where the electric stress at a distance r from
the centre of the conductor was shown to be given by,
()
()
δδ
δ
δ
ab
Ur
rE
−
=
−1
(7)
where
δ
is a constant that is determined by the material and
the temperature difference across the cable insulation. U is the
applied voltage. A value of 2/3 is given for the constant
δ
in
[21] and [22, 23], whereas a value of 1/2 is quoted in [24] for
XLPE without a temperature gradient. In view of the
complexity of the problem, the value of ½ for δ suggested in
[24] has been adopted in this paper for the calculation of the
electric stress needed for the purpose of charge density
calibration.
3 EXPERIMENTAL RESULTS
3.1 SPACE CHARGE DEVELOPMENT UNDER
VOLTAGE POLARITY REVERSAL
3.1.1 SPACE CHARGE ACCUMULATION WITH
POSITIVE VOLTAGE AT CENTRAL CONDUCTOR
Figure 3a illustrates the space charge evolution in the
insulation of cable A when a positive voltage of +80 kV was
applied to the central conductor. It was found that
heterocharge gradually accumulated in the vicinities of the
inner and outer electrodes and approached an apparently
stable distribution within 90 minutes.
3.1.2 SPACE CHARGE EVOLUTION FOLLOWING
POLARITY REVERSAL AT THE INNER
CONDUCTOR
Following the measurements with positive voltage at the
central conductor the external voltage polarity was switched to
a negative polarity and space charge measurements again
carried out. The results obtained during the polarity reversal
(e.g. ramping up of the negative voltage on the inner
conductor) are presented in Figure 3b. The heterocharge
previously accumulated remains almost the same during the
voltage ramp. See, for example, the positive charge labelled
by b adjacent to the outer electrode. The continued existence
of this positive charge in the bulk insulation contributes a
negative image charge on the outer electrode (peak a) in
addition to the positive capacitive charge from the applied
voltage. Consequently the net electrode charge only has a
small positive magnitude at this stage, albeit one that increases
linearly with the applied voltage.
After the applied voltage reached its assigned reversal value
of –80 kV, the bulk space charge regions were first reduced in
magnitude and then reversed polarity to become heterocharge
again, as shown in Figure 3c. The polarity reversal occurs by
the penetration of space charge of opposite polarity to the
retained charge, which first reduces the magnitude of the
retained charge and then cancels it out to form the reversed
polarity peak in essentially the same position. This can be
seen clearly in the space charge distribution in Figure 3c
corresponding to 30 minutes at -80 kV, which exhibits
successive positive and negative peaks as one moves away
from the outer electrode towards the inner conductor (anode).
The final result of the cancellation is the formation of a new
negative heterocharge peak, and a corresponding increase of
the capacitive charge at the outer electrode/insulation
interface. The time required for the space charge distribution
to approach a new steady state is about 90 minutes just as was
the case when the applied voltage had a positive polarity. The
interesting point here is that this time is the same even though
the negative heterocharge now accumulates in a region where
positive space charge had been present as a result of the
previous poling, whereas the data in Figure 3a was obtained
for a sample that initially contained no space charge.
The steady state heterocharge distributions under reversed
voltage polarity have almost the same shapes but the opposite
polarities to those obtained initially. They even have the same
charge accumulation rate. This phenomenon had been
reported in [16, 25] and was termed the “mirror image effect”
charge in [25]. Such “mirror image” charge distributions are
clearly displayed in Figure 3d where the capacitive charge on
both electrodes due to the external voltage has been removed.
-1.5
-1
-0.5
0
0.5
1
1.5
01234567
Position (mm)
Charge density (C/m
3
)
Outer electrode
Inner electrode
0 time
30 min
60 min
90 min
(a) Space charge accumulation with ageing time (+80kV at central conductor)
-1.5
-1
-0.5
0
0.5
1
1.5
01234567
Position (mm)
Charge density (C/m
3
)
Outer electrode
Inner electrod
e
b
a
+80kV for 90 min
Voltage increase
(b) Space charge during the polarity reversal ramp-up
854
M. Fu et al.: Space Charge Formation and its Modified Electric Field under Applied Voltage Reversal
-1.5
-1
-0.5
0
0.5
1
1.5
01234567
Position (mm)
Charge density (C/m3)
+ 80kV for 90min
- 80kV for 0 time
- 80kV for 30min
- 80kV for 60min
- 80kV for 90min
Outer electrode Inner electrode
with ageing time
(c) Space charge accumulation with reversed voltage application time
-1.5
-1
-0.5
0
0.5
1
1.5
01234567
Position (mm)
Charge density (C/m
3
)
Outer electrode
Inner electrode
Positive voltage
Negative voltage
(d) “Mirror image” space charge distribution with capacitive charge removed
from the electrode signal
Figure 3. Space charge development over the voltage polarity reversal
3.2 SPACE CHARGE ACCUMULATION IN XLPE
CABLES WITH A TEMPERATURE GRADIENT
Cable B (prototype HVDC power cable with 5.7mm thick
insulation) was used to investigate the influence of a
temperature gradient on space charge behaviour. First
however, the space charge behaviour was measured for a
uniform temperature (room temperature T~25
o
C) under the
application of an external voltage of + 80kV to the inner
conductor. This cable exhibited homocharge at the inner
electrode and heterocharge at the outer electrode, and so all
the measurements were carried out both with the external
voltage applied and also with the external voltage temporarily
switched off during the measurement. This procedure allowed
a clear separation of the homocharge from the capacitive
charge on the inner electrode.
Figure 4a shows the space charge accumulation obtained
with temporary removal of the external voltage. The strongest
feature is a heterocharge peak next to the outer electrode. A
barely noticeable homocharge peak was also generated
adjacent to the inner electrode (anode). After reaching a
steady state distribution the external voltage was removed and
the electrodes short-circuited, and measurements made of the
space charge over a period of de-polarization. It was found
that there was hardly any detectable change in the space
charge distribution over 48 hours of de-polarization, see
Figure 4.
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0246810
Position (mm)
Charge density (C/m
3
)
0 time
1 hr
8 hr
24 hr
Outer electrode
(cathode)
Inner electrode
(anode)
(a) Space charge accumulation under applied voltage (measurement with
external voltage temporarily removed)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0246810
Position (mm)
Charge density (C/m3)
0 time
1 hr
8 hr
24 hr
48 hr
Inner electrodeOuter electrode
(b) Space charge profiles in decay after short-circuiting
Figure 4. Space charge behaviour in prototype HVDC cable B at room
temperature
Measurements of space charge accumulation and decay in
Cable B under a temperature gradient were carried out on a
new piece of HVDC prototype cable. A temperature
difference of 13
o
C between conductor and outer sheath was
obtained with the central conductor heated up to 70
o
C while
leaving outer semiconductor sheath in a natural convection
condition. The space charge accumulation during polarization
is shown in Figure 5a, and its subsequent behaviour during
depolarization in Figure 5b. Because the space charge density
in the bulk insulation is very small in comparison with that at
a uniform room temperature its presence could only be
discerned from the two induced image charge peaks at the
outer and inner electrodes, obtained when the applied voltage
was removed for measurement (i.e. the capacitive charge
present during polarization was temporarily removed) . A very
small positive charge peak (homocharge) was observed next
to inner conductor (high temperature side), similar to that
found at a uniform room temperature. In this case however,
there is no measurable heterocharge near the outer conductor.
A further difference is that the space charge accumulation
IEEE Transactions on Dielectrics and Electrical Insulation Vol. 15, No. 3; June 2008
855
![Figure 8. Space charge distributions in a third type of XLPE cables with opposite voltages applied at central conductor. Taken from [29].](/figures/figure-8-space-charge-distributions-in-a-third-type-of-xlpe-22u8topa.webp)
