OF5-01
TEMPERATURE DEPENDENCY OF WAVE PROPAGATION VELOCITY
IN MV POWER CABLE
1*
1
2
2
Yan LI , Peter A. A. F. Wouters , Paul Wagenaars , Peter C. J. M. van der Wielen and
1,2
E. Fred Steennis
1
Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
2
DNV KEMA Energy & Sustainability, P.O. Box 9035, Arnhem 6800 ET, Netherlands
*Email: <y.li.4@tue.nl>
Abstract: Propagation velocity of high frequency signals, e.g. from partial discharge, is a
vital parameter for time domain power cable diagnostic techniques. The propagation
velocity is mainly dependent on the permittivity of the insulation material, which can be
affected by external parameters like temperature or water ingress. This paper focuses on
the influence of temperature on the propagation velocity in medium voltage (MV) cables.
Laboratory scale tests are performed for both PILC and XLPE cable. Test results show
that the high frequency signal propagation velocity for XLPE will increase with the
temperature rise while PILC has opposite behaviour. The variation of propagation velocity
of XLPE is confirmed by data of a power cable subjected to strong load cycling monitored
over eight months.
1
power cable via 50 Ω coaxial cable. The injected
pulse and its reflections are recorded by an
oscilloscope. Heating is accomplished by a 10 kW
DC current source, capable of generating 600 A at
a maximum voltage of 16 V. It is connected to the
conductor from the second segment to the last
cable segment.
INTRODUCTION
In time domain reflectometry measurements, e.g.
in partial discharge diagnostic techniques for
power cable [1-3], propagation velocity should be
accurately known for precise defect location. On
one hand, the propagation velocity can be affected
by temperature. On the other hand, information on
variability in propagation velocity informs on
changing conditions as temperature variation by
e.g. cable loading or insulation ageing.
Two sets of laboratory scale test are presented to
evaluate the temperature effect on wave
propagation velocity in both XLPE (Section 2) and
PILC cables (Section 3). The effect is compared
after translating measured temperature to
temperature inside the insulation (Section 4). In
addition, propagation time data are extracted from
Smart Cable Guard systems [4] installed on live
cable connections with XLPE insulation (Section
5). The field data, with variation recorded over a
year is then compared with the load profile. The
observed temperature effect on propagation
velocity will be briefly further discussed in Section
6.
2
Figure 1: Test circuit for TDR on heated XLPE
cable; the connector numbers correspond to the
connector types illustrated in Figure 2.
LABORATORY TEST ON XLPE CABLE
2.1 Test circuit
Six segments of 12/20kV XLPE single core
(aluminium) cable are connected to form the test
circuit. Each piece is about 12 m resulting in a
cable circuit of about 72 m. The test circuit is open
at both sides. Pulse signals are injected into the
cable via one open end and reflections are
recorded at the same end (time domain
reflectometry, TDR). Due to space limitation, the
test circuit is half inside the test room and half
outside in open air. Figure 1 illustrates the test
circuit. An 8 ns wide pulse is injected into the
(1)
(2)
(3)
Figure 2: Connector types applied for combining
XLPE cable segments; numbers correspond with
the connectors indicated in Figure 1
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OF5-01
Temperature sensors are attached on the surface
of the cable outer jacket to measure the outer
sheath temperatures of indoor and outdoor cables.
These sensors are shown in Figure 1 as dots and
labeled as T1 and T2. Letters A-G indicate the
reflection points of TDR measurements shown
later in Figure 3. Figure 2 shows the connector
types. Connector type 3 was improvised for the
present measurements. The cable earth screen
connections were realized with short wires parallel
to the connectors for all types.
14.4C,12.0C
20.4C,17.0C
27.6C,21.9C
37.3C,27.0C
48.7C,31.8C
Amplitude [V]
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
0.95
1
2.2 Test results
Amplitude [V]
After heating for about 3 hours, the cable outer
jacket temperature has increased from 9 °C to
48 °C (indoor) and from 8 °C to 30 °C (outdoor).
TDR signals are recorded continuously. Results at
different temperatures are shown in Figure 3. All
reflected signals are labelled with symbols to
identify the reflections coming from the transition
between coaxial cable and power cable (A), the 5
cable connectors (B-F) and the open far end (G).
Reflection C (from connector type 1), E (from
connector type 2) and G (from open end) are
zoomed in and shown in Figure 4. It is qualitatively
observed that with the increase of temperature, the
propagation time decreases, indicating that the
propagation velocity has increased.
10
10.8C,9.0C
8
20.8C,17.4C

Amplitude [V]
0.6
B
2
DE
A
1
Time [s]
1.5
2
14.4C,12.0C
20.4C,17.0C
27.6C,21.9C
37.3C,27.0C
48.7C,31.8C
Amplitude [V]
0.6
0.4
0.2
-0.2
0.76
0.77 0.78
Time [s]
0.79
1.5
Insulation temperature conversion: A thermal
ladder network can be used to model the
temperature distribution in radial direction of the
cable [6]. Each layer of cable can be modelled by a
thermal resistor and a thermal capacitor. The heat
source can be represented as a current source.
According to the thermal ladder network,
logarithmic temperature distribution across the
dielectric material is assumed. Based on this
model, the time response of the temperature in the
middle of dielectric material is shown in Figure 5.
The measured temperature of the outdoor cable
jacket is then converted to outdoor temperature at
0
0.75
1.4
1.45
Time [s]
In order to analyse the measured result, two issues
have to be addressed. The first issue is the
temperature correction, since the temperature
sensors are attached on the outer jacket of the
XLPE cable. The propagation velocity is mainly
determined by permittivity of the insulation.
Therefore, the measured jacket temperature will be
converted to the temperature at the midpoint of the
insulation. The second issue concerns the
quantitative calculation of the pattern shift at
different temperatures.
Figure 3: Reflection patterns at different
temperatures; the legend indicates first the indoor
temperature, next the outdoor temperature, letters
A-G correspond to the ones in Figure 1
0.8
1.35
2.3 Analysis
F
G
0.5
0
Figure 4: (a) depicts reflection C from connector 1;
(b) shows reflection E from connector 2 and (c)
illustrates reflection G from open end

0
-2
0
14.4C,12.0C
20.4C,17.0C
27.6C,21.9C
37.3C,27.0C
48.7C,31.8C
0.2
(c)
48.8C,32.1C
C
0.4
-0.2
1.3
40.8C,28.8C
4
1.1
(b)
30.9 C,23.4 C
6
1.05
Time [s]
0.8
(a)
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OF5-01
midpoint of the insulation, Table 1. The outdoor
temperature is used since the propagation time
between the connector 1 and open far end will be
used for analysis in order to exclude the indoor
and outdoor temperature difference. Tjx is the
jacket temperature of the XLPE cable, and Tdx is
the temperature at the middle of insulation of the
XLPE cable; t is the heating time according to
Figure 5.
0
-6
12
1
2 10
3
8
4
6
-8
4
-10
2
-12
0
-14
-2
-2
15
time delay [ns]
-4
T [C]
10
5
0
0
-16
0
0.5
1
1.5
t [h]
2
2.5
0.5
3
3
Table 1: Insulation temperature for XLPE; the
outer jacket temperature Tjx is converted to the
midpoint value Tdx of the insulation reached at time
t (see Figure 5)
1
2
3
4
Tjx (°C)
12.0
17.0
21.9
27.0
31.8
t (h)
0.27
0.60
1.15
2.24
5.47
Tdx (°C)
23.6
30.3
35.3
40.4
45.2
1.5
2
time [s]
2.5
3
-4
3.5
Figure 6: Time shift of reflection patterns of XLPE
cable at different temperatures
Figure 5: Derived temperature difference between
the midpoint of XLPE insulation and the outer
jacket surface for single core XLPE cable
Ref.
1
amplitude [V]
reflection from the far end. This might be caused
by the indoor and outdoor temperature difference
and lower signal to noise ratio. Directly past this
peak, structures arise which travelled additional
length along a not heated part. Later also the
heated part is included resulting in a steeper time
shift again.
LABORATORY TEST ON PILC CABLE
3.1 Test circuit
The laboratory scale cable setup at DNV KEMA is
utilized for PILC cable test. The setup consists of
50 m three core XLPE cable and 70 m three core
PILC cable (outdoor). 100 ns wide pulse is injected
into the cable. Due to the setup limitation, the
current source for heating (same as for XLPE test)
is connected to the earth screen of cables, which is
lead for PILC and copper for XLPE. Figure 7
shows the test setup. Since the resistivity of lead is
much higher than copper, heating power
distributes mainly along the PILC cable. Due to
power source limitation, about 130 A current could
be loaded to the cable. Two temperature sensors
are attached on the surface of the PILC and the
XLPE cable separately.
Quantitative time shift: The minimum square
error (MSE) [5] detection with time window is
applied to get the time shift between two patterns.
When time shift between pattern P (reference) and
Q (at elevated temperature) is calculated, a time
window (length t) taken from the complete record
will be shifted along pattern Q back and forth to
find the best match in pattern P, i.e. where the
minimum error occurs. The time window length is
chosen to be 1500 ns to get a reasonable flat
result excluding error from noise. Figure 6 shows
the calculated time shift along the pattern between
heated cable and reference cable. The numbers in
the legend correspond to the patterns in Table 1.
The pattern shifts more as the temperature
difference increases. The shift becomes most
nd
rd
apparent as from the 2 – 3 reflection (at 700 ns,
B-C in Figure 3). This is where the heated part of
the cable begins. The time delay increases after
each clear reflection from joint due to longer
propagation distance. After the steep part the time
delay slowly increases around and just after the
Figure 7: Test setup for TDR on heated PILC
cable
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OF5-01
3.2 Test results
1
Approximately 3 hours heating increased the
temperature of the PILC cable with about 25 °C
and the XLPE with about 5 °C. The measured
result is shown in Figure 8. In the pattern, the
injected pulse is located around 2.1 μs. The first
reflection near 2.6 μs is from the coaxial cable
connection to the power cable; the reflection
around 4.1 μs arises from the transition joint, and
the reflection around 5 μs from the open end. The
later reflections are secondary or higher order
reflections. The transition joint reflection and the far
end reflection are depicted enlarged in Figure 9. It
is observed that with the increase of temperature,
the propagation time increases, indicating a lower
propagation velocity, which is opposite to the
observations for XLPE insulation.
Amplitude [V]
0
-2
4
Time [s]
6
8
T [C]
1.5
1
Amplitude [V]
0.5
PILC:33.1C XLPE:25.8C
PILC:38.2C XLPE:26.1C
0
0
PILC:43.0C XLPE:27.3C
-0.2
PILC:48.1C XLPE:28.8C
5
5.05
5.1
5.15
Time [s]

PILC:28.1 C XLPE:24.9 C
-0.1
4.95
2
PILC:23.5C XLPE:24.0C
0
4.9
2.5
10
Figure 8: Reflection patterns at different
temperatures; the legend indicates first the indoor
temperature, next the outdoor temperature

PILC:43.0C XLPE:27.3C
Insulation temperature conversion: Applying a
similar approach as for the XLPE cable heating
test, the temperature difference between the
insulation midpoint and jacket of PILC cable is
shown in Figure 10. The measured outer jacket
temperature for PILC cable is converted to
temperature at the midpoint of the paper insulation
as shown in Table 2.
PILC:48.1C XLPE:28.8C
2
PILC:38.2C XLPE:26.1C
0.2
3.3 Analysis

PILC:43.0C XLPE:27.3C
-4
0
PILC:33.1C XLPE:25.8C
Figure 9: (a) enlargement of reflection from PILC
to XLPE transition joint; (b) enlargement of
reflection from open end
PILC:38.2C XLPE:26.1C
2
PILC:28.1C XLPE:24.9C
0.4
(b)
PILC:33.1 C XLPE:25.8 C
4
PILC:23.5C XLPE:24.0C
4.85
PILC:28.1C XLPE:24.9C

0.6
0
PILC:23.5C XLPE:24.0C
6
Amplitude [V]
0.8
PILC:48.1C XLPE:28.8C
-0.3
0.5
1
1.5
t [h]
2
2.5
3
Figure 10: Derived temperature difference
between the midpoint of paper insulation and the
outer jacket surface for the three-core PILC cable
-0.4
-0.5
4.05
4.1
4.15
4.2
Time [s]
4.25
Table 2: Middle of insulation temperature for PILC
(a)
Ref.
1
2
3
4
5
Tjp (°C)
23.5
28.1
33.1
38.2
43.0
48.1
t(h)
0.08
0.35
0.60
1.05
1.83
3.13
Tdp (°C)
25.0
30.1
35.3
40.4
45.2
50.3
Quantitative time shift: The previously described
MSE method is applied to the PILC cable patterns
to find the time shift. The results are shown in
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OF5-01
of the PILC cable is affected more by temperature.
Also this figure suggests that the variation is not
linear and becomes more pronounced at higher
temperatures.
Figure 11 for five measurements. The time shift
increases with propagation time and temperature
difference. The steep rise observed directly after
the reflection from the injection cable is caused by
the time window beginning to cover the reflection
from the PILC to XLPE transition point, which gives
a clear shift. The increase in time delay directly
after the first reflection is where the heated cable
starts.
50
2
time shift [%]
1
2
3
4
5
-XLPE
PILC
10
0
1.5
1
0.5
amplitude [V]
time delay [ns]
100
2.5
0
0
5
10
15
20
25

temperature difference [ C]
Figure 12: Propagation time variation comparison;
the absolute values are indicated
-10
10
5
Propagation time data from installed Smart Cable
Guard system recorded over a year is compared
with load profile data over the same time period.
The propagation time and load of a XLPE cable
st
section (4.8 km long with 6 RMUs) from May 1 ,
th
2010 to January 14 2011 is shown in Figure 13. It
shows that though the load does not have a clear
summer winter cycle, the propagation time is lower
at summer time and higher at winter time. This
indicates a clear ambient temperature variation. On
top of the ambient temperature effect, the load also
influences the propagation time. The peak load
th
around July 9 , 2010 corresponds to a lower
propagation time at that period. A weekly trend is
observed. The propagation time variation is
opposite compared to the load current variation.
Besides, the variation within each day is observed.
The relatively high load on Thursday and Monday
correlates with the relatively large drop in
propagation time. Further, there is a delay between
the increase in current and the thermal response.
2010
31.8
31.7
31.6
705
-0
10
703
-0
31.4
10
16: 35
10: 40
2010
28-11-
701
2010
-0
01-10-
10
05:44
629
-2010
01-08
-0
02: 43
-0
2010
10
31.4
628
31.6
31.5
30-05-
0
705
30-12-
-0
1
10
2010
703
21-10-
-0
0
00:40
0
10
2010
0
5: 35:0
628
13-08-
0
6: 10:0
-0
1
0
5: 05:0
Saturday
10
2010
0
8: 25:0
Propagation time [s] Load [A]
Load [A]
Propagation time [
 s]
0
04-06-
12:40
500
500
701
Test results show that the XLPE and PILC cable
have an opposite temperature effect on
propagation velocity. With the conversion from
measured jacket temperature to conductor
temperature, it is possible to compare both cables.
For XLPE, the time shift is calculated from
reflection C (from connector 1 in Figure 1) to G
(from open end) utilizing the outdoor part
(consistent with the temperature data in Table 1).
For PILC, the time shift is derived from the
reflections at both ends of the PILC cable. The
comparison between the XLPE and PILC cable’s
propagation time variation is shown in Figure 12.
The deviations caused by different time window
lengths are indicated in the error bar. The velocity
-0
COMPARISON OF THE TEMPERATURE
EFFECT OF PILC AND XLPE CABLE
10
Figure 11: Time shift of reflection patterns of PILC
cable at different temperatures
4
FIELD DATA
629
8
-0
4
6
time [s]
10
2
10
0
0
Figure 13: Propagation time and load of XLPE cable for year and week cycle
1865
OF5-01
This thermal response time of typically 3 hours is
more apparent when the cable load starts
compared to when the load is switched off
probably because the temperature rise due to
higher load is faster than the temperature
decrease caused by lighter load. It should be noted
that the load profile is not the same over the
complete cable section. The measured current
represents the highest loaded part of the section.
9
[1] G. M. Hashmi, R. Papazyan, M. Lehtonen:
“Comparing Wave Propagation Characteristics
of MV XLPE Cable and Covered-Conductor
Overhead
Line
using
Time
Domain
Reflectometry Technique,” 2007 International
Conference on Electrical Engineering (ICEE
'07), pp.1-6, 11-12 April 2007
[2] G. M. Hashmi, R. Papazyan, M. Lehtonen:
“Determining wave propagation characteristics
of MV XLPE power cable using time domain
reflectometry technique,” 2009 International
Conference on Electrical and Electronics
Engineering (ELECO 2009), pp.I-159-I-163, 58 Nov. 2009
[3] S. Markalous, T. Strehl, C. Herold, T. Leibfried:
“Enhanced signal processing for conventional
and unconventional PD measuring methods:
Wavelet de-noising, automatic detection
algorithms and averaging for arrival time-based
PD location in transformers and power cables,”
2008 International Conference on Condition
Monitoring and Diagnosis (CMD 2008),
pp.1115-1118, 21-24 April 2008
[4] Peter C.J.M. van der Wielen and E. Fred
Steennis: “Risk-controlled application of current
MV cable feeders in the future by intelligent
continuous diagnostics,” in 2011 IEEE Power
and Energy Society General Meeting, pp.1-6,
24-29 July 2011
[5] F. Censi, G.Calcagnini, M. D’ Alessandro, M.
Triventi, P. Bartolini: “Comparison of alignment
algorithms for P-Wave coherent averaging,”
Computers in Cardiology, 2006 , pp.921-924,
17-20 Sept. 2006
[6] George J. Anders: “Rating of Electric Power
Cables in Unfavorable Thermal Environment,”
pp.1-75, May 2005, Wiley-IEEE Press
[7] V. Dubickas, H. Edin: “On-line time domain
reflectometry measurements of temperature
variations of an XLPE power cable,” 2006 IEEE
Conference on Electrical Insulation and
Dielectric Phenomena, pp.47-50, 15-18 Oct.
2006
[8] C. Fanggao, G. A. Saunders, R. N. Hampton,
S. M. Moody and A. M. Clark: “The effect of
hydrostatic pressure and temperature on the
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[9] I. Mladenovic, C. Weindl, C. Freitag:
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PILC cables,” Conference Record of the 2012
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Unfortunately, at present there is no correlated
PILC data available for propagation time and load
current. From the laboratory tests a clearer effect is
expected here.
6
DISCUSSION
The velocity change of the XLPE cable with
temperature can be attributed to the real part of the
permittivity ε of the XLPE. The decrease of velocity
in percentage is in agreement with the ε decrease
in the measured temperature range [7,8], which is
about 0.7-3% in the temperature range of 20 °C to
60 °C. For PILC, ε increases with temperature [9];
however quantitative analyses on the temperature
dependence of ε in high frequency range is scarce
in literature. Furthermore, it is acknowledged that
the insulation parameters of paper insulation can
vary a lot depending on manufacturer, production
year, country and even from cable to cable. Further
study is needed to demonstrate the velocity
dependence of ε for PILC cable in live circuits.
Another factor that may affect the velocity is the
change in dimension of the cable. This may have
an effect on the pressure on the dielectrics.
7
CONCLUSION
Experiments show that high frequency signals
propagates faster with higher temperatures for
XLPE cable and slower for PILC.
It is observed that the temperature effect on
propagation velocity is more significant for PILC
than for XLPE.
The temperature dependence of the real part of
permittivity (ε) dominates the velocity change for
XLPE cables. For PILC, further work is needed to
explain the origin of the velocity dependency with
temperature.
8
REFERENCES
ACKNOWLEDGMENTS
The authors would like to thank DNV KEMA
Energy and Sustainability, Enexis, Alliander and
Locamation for their financial support.
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