Comparing Wave Propagation Characteristics of Various
Smart Electricity Distribution Networks
Murtaza Hashmi, Ruslan Papazyan, Matti Lehtonen
ABSTRACT
In Nordic countries, electricity distribution networks are consisted of underground cables
or overhead insulated conductors or mix of both. However, each alternative has its own
pros and cons. This chapter concentrates on determining the wave propagation
characteristics of single-phase medium voltage (MV) cross-linked polyethylene (XLPE)
cable and covered-conductor (CC) overhead electricity distribution networks. For this
purpose, time domain reflectometry (TDR) measurement technique is applied. TDR
delivers the complex propagation constant (attenuation and phase constants) of lossy
transmission lines as a function of frequency. The frequency-dependent propagation
velocity is also determined from the TDR measurements through the parameters
extraction procedure. The calibration of the measuring systems is carried out to avoid the
effect of multiple reflections on the accuracy of measurements. The wave propagation
characteristics of XLPE cable and CC line are compared and it is proved that CC line has
lower attenuation and higher propagation velocity than power cables. The measured wave
propagation characteristics can be used as a design aid to develop an intelligent fault
diagnosis and management system for distribution networks that may improve the safety
and result in reduced maintenance costs and visual inspection work. In addition, the
reliability of the distribution system will improve which is considered one of the
significant characteristics of the future smart distribution networks.
INTRODUCTION
The use of solid dielectric power cables for underground transmission/distribution and
covered-conductor (CC) lines for overhead distribution has been increasing over the past
twenty years. This trend is likely to continue since the conductor (cable or CC) material,
insulation, and manufacturing process are steadily improving. While the primary purpose
of these transmission/distribution lines is to deliver power at 50 or 60 Hz, they are also
capable of carrying high frequency signals reasonably well; i.e., their high frequency
performance is comparable to some commercial rf coaxial cables. Consequently, this
capability is likely to be utilized more and more in the future for applications such as
diagnostics, system protection, load management, and monitoring of falling trees on the
CC overhead distribution lines. While there is some data available on the wave
propagation characteristics in these conductors, there has been limited number of
systematic study to date.
There is a growing interest in the study of high frequency properties of distribution lines.
One major reason is the potential to use widely distributed cable networks for high
capacity data communications. Another relatively new application is conducting on-line
high frequency partial discharge (PD) measurements for the monitoring of falling/leaning
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trees on the CC lines. The measurements of such studies are generally carried out at high
frequencies, up to about 100 MHz, by sending pulses or signals from a point, which then
travel through the conductor that essentially acts as a transmission medium. The incident
and the reflected signals are analyzed. These signals are distorted or changed in one way
or the other by the transmission medium, and the reconstruction techniques are applied to
get the desired wave propagation characteristics (propagation constant; attenuation and
phase constants, and propagation velocity) from the measurements. Frequency and time
domain techniques are used, hence, the need for understanding basic electromagnetic
theories and their practical applications is prerequisite.
Any signal will loose some of its energy or signal strength as it propagates down the
conductor. This loss is attenuation, which is frequency-dependent. Propagation velocity is
a specification of the conductor indicating the speed at which a signal travels down
through it. Different conductors have different propagation velocities. Typically,
propagation velocity of a communication cable under test is listed in the cable
manufacturer’s catalogue. However, this figure for MV power cables or CC lines is not
specified. In this case, a required procedure is to take TDR measurements on a known
length of the conductor. An even more accurate way to estimate propagation velocity is
to make measurements from both ends of the conductor. Propagation velocity depends
upon the phase constant and the frequency of the impressed signal.
POWER CABLES VS COVERED-CONDUCTOR LINES
The use of XLPE cables in MV networks has been increasing rapidly since long. The
basic material used for XLPE cable is polyethylene (PE). PE has very good electrical
properties, however, its mechanical strength decreases significantly above 75 °C, thus
restricting its continuous operating temperature to a certain limit. The improved thermal
characteristics of PE are obtained by establishing a large number of cross-links by
employing suitable techniques resulting in higher continuous current carrying capacity
and short circuit temperature (250°C) than that of PE. These cables have low dielectric
losses, low environmental requirements, light in weight, and are trouble-free in
maintenance.
In the Nordic countries, the CC lines in distribution networks were originally introduced
due to their good applicability for passing through forest areas and having better
operating safety. The conductor material in CC overhead distribution lines, is aluminum
alloy and the insulation material is XLPE or high density polyethylene (HDPE), usually
having a thickness of 2.3 mm. Carbon black is mixed with plastic to reduce the effect of
ultra violet radiations. According to Finnish structure, the conductor is stranded and
compacted. In Finland, corrosion in aluminum conductors is not a problem; therefore, CC
structures are not greased. The insulators used on CC lines are normally porcelain pin or
post insulators. Epoxy resin insulators are also used. The phase-to-phase distances at
poles are one-third as compared with bare conductor lines (40-50 cm on 20 kV lines).
The cross-sectional views of the power cable and CC line are shown in Fig. 1.
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Fig.1. Typical power cable design for voltages up to 230 kV (top), the cross-sectional
view of overhead CC in distribution networks (bottom)
PRINCIPLE OF OPERATION OF TDR INSTRUMENTS
The most common method for evaluating a transmission line and its load has traditionally
involved applying a sine wave to a system and measuring waves resulting from
discontinuities on the line. From the measurements, the standing wave ratio (SWR) is
calculated and used as a figure of merit for the transmission system. When the system
includes several discontinuities, however, the SWR measurement fails to isolate them. In
addition, when the broadband quality of a transmission system is to be determined, SWR
measurements must be made at many frequencies. This method soon becomes very time
consuming and tedious.
When compared to other measurement techniques, TDR provides a more intuitive and
direct look at the characteristics of the device under test (DUT). Using a high speed
oscilloscope and a pulse generator, a fast edge is launched into the transmission line
under investigation. The incident and the reflected voltage waves are monitored by the
oscilloscope at a particular point on the line. The block diagram of a domain
reflectometer is shown in Fig. 2.
Another aspect of TDR measurements is that it demonstrates whether losses in a
transmission system are series or shunt losses. All of the information is immediately
available from the oscilloscope’s display. Additionally, TDR gives more meaningful
information concerning the broadband response of a transmission system than any other
measuring technique.
TDR instruments work on the same principle as radar, but instead of air, they work
through wires. A pulse of energy is transmitted down a line. When the launched
propagating wave reaches at the end of the line or any impedance change along the
transmission line, part or all of the pulse energy is reflected back to the instrument. This
reflected wave is energy that is not delivered to the load. The magnitude of the
impedance change can be calculated using the reflection coefficient Γ, defined in the
frequency domain as the ratio between the reflected voltage wave Vr and the incident
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voltage wave Vi. The distance to the impedance change can also be estimated knowing
the speed of the propagated wave. Γ is related to the load impedance ZL and the
characteristic impedance of the line Z0, by the following expression:

Vr Z L  Z 0

Vi Z L  Z 0
(1)
The transmission coefficient T is given as:
T  1  
2ZL
ZL  Z0
(2)
Fig.2. Functional block diagram of a time domain reflectometer
Vi
TDR EXPERIMENTAL SET-UP
TDR measurements require a special test arrangement including a high speed digitizing
signal analyzer (DSA) and a fast leading-edge pulse generator e.g. producing a pulse of 5
V amplitude with 10 ns pulse-width having rise-time of 200 ps. DUT is a single-phase 20
kV XLPE power cable having 6 m length. Although not mentioned when theoretically
introducing the concept of time domain reflectrometers, there are two more components
in the measurement set-up, which are of extreme importance for the quality of TDR
testing. These are the T-connection needed for monitoring the incident and reflected
pulses by DSA, and the connection between the measuring equipment and the DUT. The
TDR measuring set-up including DUT and MS is depicted in Fig. 3.
In practice, a narrow electric pulse is applied to the DUT and the incident and reflected
waves are measured by means of a DSA at T-connection. The measured data is
transferred to the computing system (laptop) connected to the DSA through the general
purpose interface bus (GPIB), where the analysis is done using MATLAB.
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Fig.3. Schematic drawing of the TDR measuring set-up
MV XLPE cable
T-Connection
AVX-CP-2
Pulse Generator
Coaxial cables
AV-1030-C
GPIB port
Data acquisition
2
Test connection
Open end
DEVICE UNDER TEST
Digizing Signal
Analyser DSA602
MEASURING SYSTEM
CALIBRATION AND PARAMETERS EXTRACTION
It has already been shown that if one assumes the transmission line model, the line is
characterized by its primary parameters: resistance R in Ω/m; inductance L in H/m;
conductance G in S/m; and capacitance C in F/m. All of these parameters depend more or
less on the frequency . The line is described by its propagation constant γ with its real
and imaginary parts: the attenuation constant , is the attenuation (Np/m); and the phase
constant , is the phase shift (rad/m). The following relation holds:
    j  ( R  jL)(G  jC )
(3)
The propagation constant of a wave traveling along a transmission line segment of a
length l is the complex voltage ratio between the output (reflected pulse Vout) and the
input (incident pulse Vin) of the line segment. If the cable is considered as a linear system,
this ratio represents the cable transfer function H() and the following relation holds:
H ( ) 
Vout
 e  ( )l
Vin
(4)
In the measuring system, the incident and the reflected pulses are measured in the time
domain. For a TDR measurement, Vout is the signal coming back after reflection at the
open end of the cable. Since the measurements are done at the input side of DUT (see
Fig. 2), the total traveling distance is twice the length of the DUT, i.e. 2l. These time
domain measurements are then transformed into the frequency domain by the use of the
fast Fourier transforms (FFTs) in MATLAB.
Generally, MV power cables have characteristic impedance in the range of 25 Ω. As the
power cable has an impedance different from that of the MS (50 Ω), a significant
reflection occurs at the MS / DUT interface (see Fig. 2). This reflection is recognized to
have a major influence on the precision of the cable response measurement. A calibration
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procedure has already been developed for this purpose in order to identify and remove the
influence of the different effects on the parameters extraction. The transfer function can
be modified after calibrating MS as:
H ( )  e  2l 
V3Vshort
3
V   V
m 2
3

(5)
short 2
3
where V–3m is mismatch reflection, V–3 is DUT response, and V–3short is the measured
signal reflected at the short-circuited end of cable 2 and is referred as incident pulse. It
can be deduced from (5) that:
 
1
 ln H ( )
2l
(6)
 
1
 H ( )
2l
(7)
Thus, the attenuation and phase constants are determined using the time domain
measurements obtained. The propagation velocity v (m/s) can be determined using phase
constant as:
v
 2f



(8)
XLPE POWER CABLE MEASUREMENTS AND RESULTS
The following two TDR measurements have been captured in the data acquisition system
and are processed in MATLAB for the extraction of wave propagation characteristics
from the measurements.
1.
TDR-DUT response: This measurement is captured when the DUT is opencircuited (see Fig. 3). The time domain waveform for this measurement is
shown in Fig. 4.
2.
TDR-calibration: This measurement is captured when the coaxial cable 2 is
short-circuited (see Fig. 3). The time domain waveform for this measurement is
shown in Fig. 5.
The mismatch reflection V–3m and the DUT response V–3 are extracted from the TDRDUT response measurement, while the incident pulse V–3short is extracted from the TDRcalibration measurement. These pulses are taken and padded with zeros up to the length
of N = 2n; for n = 16. The modified zero-padded waveforms are shown in Fig. 6. Using
FFTs of the modified zero-padded pulses in (5-8), the measured attenuation constant and
wave propagation velocity in the DUT can be determined, and the dependency of these
parameters on the frequency of the propagated signals is shown in Fig. 7. A time step of
0.2 ns is used in the Fourier analysis.
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It is revealed from Fig. 7 that the attenuation and propagation velocity of the signals in
the cable under investigation are fairly constant at lower frequencies (0.02 dB/m and 154
m/µs). At higher frequencies (beyond 10 MHz), these parameters begin to increase with
an increase in the frequency of the propagated signals.
Fig.4. TDR response when the DUT is open-circuited
0.8
Amplitude (V)
0.6
0.4
0.2
0
0
0.1
0.2
0.3
Time (s)
0.4
0.5
Fig.5. TDR response when the coaxial cable 2 is short-circuited
0.8
Amplitude (V)
0.6
0.4
0.2
0
-0.2
-0.4
0
0.1
0.2
0.3
Time (s)
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0.4
0.5
151
Fig.6. Modified zero-padded waveforms; (a) mismatch reflection, (b) DUT response, and
(c) incident pulse
(a)
Amplitude (V)
0
-0.05
-0.1
-0.15
0.02
0.04
0.06
0.08
0.1
Time (s)
(b)
0.12
0.14
0.16
0.18
0.3
Amplitude (V)
0.25
0.2
0.15
0.1
0.05
0
0.1
152
0.12
0.14
0.16
0.18
0.2
Time (s)
0.22
0.24
0.26
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(c)
0
-0.05
Amplitude (V)
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
-0.4
0.02
0.04
0.06
0.08
0.1
0.12
Time (s)
0.14
0.16
0.18
The significant signal attenuation is attributed to the highly dispersive materials of the
conductor insulation/shields and concentric neutral beds. The latter is used for improved
potential distribution and mechanical properties at the interface between concentric
neutral and the insulation shield.
The resolution of the measured wave propagation characteristics (see Fig. 7) is good up
to 81 MHz, beyond which it is lost in the certain repetitive disturbances or noise level.
One possible way to explain the disturbances in the measurements is to have a look at the
FFTs of the incident pulse and DUT response as shown in Fig. 8.
Fig. 7. Measured wave propagation characteristics of single-phase MV XLPE power
cable; (a) attenuation constant, (b) and propagation velocity
(a)
5
0.12
0.1
Attentuation (dB/m)
4
0.08
0.06
3
0.04
0.02
2
6
7
10
10
Zoom in
1
0
-1
5
10
6
10
7
10
Frequency (Hz)
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8
10
9
10
153
(b)
Propagation velocity (m/s)
154
152
150
148
146
144
142
5
6
10
10
7
10
Frequency (Hz)
8
10
9
10
The magnitude of these FFTs remains constant up to 10 MHz, therefore, the attenuation
is also constant up to this range of frequency. Beyond this frequency, FFT of the DUT
response starts to decrease at a higher rate, resulting in linear increase in the attenuation.
Beyond 81 MHz, FFTs suffer in noise that has different values than the actual functions.
The noise level has some peaks, which are taken into account instead the actual functions,
resulting in the noisy peaks in the attenuation.
Another mathematical interpretation is on the basis of the Fourier transform function. For
an ideal square pulse as:
1, t  a
f (t )  
0, t  a
(9)
The analytical Fourier transform function is in the form:
F  f (t ) 
154
2 sin a
,  0

(10)
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Fig.8. FFTs of the incident pulse and the DUT response
Incident pulse
DUT response
1
10
Amplitude |FFT|
0
10
-1
10
-2
10
-3
10
5
10
6
7
10
10
Frequency (Hz)
8
9
10
10
It can be concluded that the Fourier transform function would periodically equal to zero
and the zero crossings can be defined as:
f0 
k
2a
(11)
where k=1,2,….,N and f0 is the frequency at which the Fourier function equals to zero. In
the presented case the pulse width for the incident signal is 2a=12 ns (see Fig. 4), so it
could be expected that zero crossings and the respective numerical artefacts to be in the
vicinity of f0 = 81 k MHz.
COMPARING WAVE PROPAGATION CHARACTERISTICS
The wave propagation characteristics of CC overhead distribution line have already been
determined using TDR measurements. Fig. 9 shows a comparison of measured wave
propagation characteristics of single-phase MV XLPE power cable and CC overhead
distribution line. It is revealed from Fig. 9 (a) that CC line has much lower attenuation as
compared to XLPE power cable. In MV power cables, the semi-conducting layers have
significant contribution to the wave propagation characteristics and the attenuation is
higher due to the presence of these layers. High frequency attenuation in shielded cables
is generally considered as a negative attribute, but can be used positively in certain
situations. In the CC overhead distribution lines used in Finland, semi-conductive layers
are absent; therefore, attenuation is lower than in power cables.
It is clear from Fig. 9 (b) that the measured propagation velocity in the CC line seems to
be lower than propagation velocity in power cables, however, the practical CC lines
(placed at a height of 10 m or more above the ground level) have comparatively higher
propagation velocities. The lower value of the measured propagation velocity is due to
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the location of the CC line (laying near the ground level at a height of 7 cm) in the TDR
experimental set-up.
The measured wave propagation characteristics of CC line suffer in repetitive
disturbances or noise at lower frequency as compared to the characteristics of XLPE
power cable (see Fig. 9). The measurement limitation at varying frequencies for different
conductors is due to the different sampling rates for XLPE cable and CC line TDR
measurements. XLPE cable measurements ate sampled at 0.2 ns, while CC line
measurements are sampled at 0.5 ns. Therefore, the resolutions of wave propagation
characteristics of XLPE cable and CC line are good up to 81 MHz and 25 MHz,
respectively.
The theoretical model of the CC line has already been developed and experimentally
verified for determining its line characteristics. The results drawn from the model show
that attenuation and propagation velocity in the CC line is strongly influenced by its
location i.e., the height D of the conductor-core above the ground level. The attenuation
decreases and propagation velocity increases by increasing the height of the practical CC
line above ground level. However, the location of the power cable does not have any
effect on the propagation velocity as the distance between the conductor-core and
grounding wire remains constant anywhere (for coaxial mode only). Fig. 10 shows a
comparison of measured attenuation of single-phase MV XLPE power cable (using TDR)
and calculated attenuation (using the theoretical model) of the practical CC lines at
different heights. It is revealed from Fig. 10 that practical CC lines have lower
attenuation than in power cables. The practical CC lines have higher propagation
velocities than power cables and this fact is revealed from Fig. 11.
Fig. 9. Measured wave propagation characteristics of single-phase MV XLPE cable and
CC overhead distribution line; (a) attenuation constant, (b) and propagation velocity
(a)
5
XLPE cable
CC line
0.025
0.02
4
0.015
0.01
Attentuation (dB/m)
0.005
3
0
-0.005
5
10
2
Zoom in
1
0
-1
5
10
156
6
10
7
10
Frequency (Hz)
8
10
9
10
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(b)
XLPE cable
CC line
Propagation velocity (m/s)
170
160
150
140
130
120
110
100
5
6
10
7
10
10
Frequency (Hz)
8
10
9
10
Fig. 10. Measured attenuation for single-phase MV XLPE power cable (for coaxial
mode) and calculated attenuation for practical CC lines at different heights above ground
level
0.05
XLPE cable
CC line at D=10 m
CC line at D=12 m
CC line at D=15 m
Attenuation (dB/m)
0.04
0.03
0.02
0.01
0
5
10
6
10
7
Frequency (Hz)
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10
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Fig. 11. Measured propagation velocity of single-phase MV XLPE cable and calculated
propagation velocities of the practical CC lines at different heights above ground level
Propagation velocity (m/m)
300
250
200
150
XLPE cable
CC line at D=10 m
CC line at D=12 m
CC line at D=15 m
100
5
10
6
10
7
10
Frequency (Hz)
8
10
9
10
The effect of snow on the wave propagation characteristics of the bare conductor has
already been investigated. It is revealed that the admittance is increased by the snow. The
difference from the case of no-snow becomes smaller as the frequency becomes higher,
because the permittivity of the snow reaches unity as the frequency increases. The
increase of the admittance is roughly proportional to the depth, density, and temperature
of the snow. The effect of snow on the attenuation constant increases and that on the
propagation velocity and characteristic impedance decreases, as the frequency increases.
The difference from the no-snow case in the attenuation constant, the velocity, and the
step response of wave deformation increases as the snow depth, the density, and the
temperature increase. The characteristic impedance depends on the snow depth but not on
the density and temperature. The effect of snow on the wave propagation characteristics
of a CC line or power cable has not been included in this research work, however, the
similar effects of snow are expected as mentioned for bare conductor.
CONCLUSIONS
The TDR measurement technique has been used to extract the frequency-dependent wave
propagation characteristics of single-phase MV XLPE power cables. The wave
propagation characteristics of XLPE power cable and CC overhead distribution line are
also compared. It is revealed that the signal attenuation and propagation velocity in
power cable or CC line are fairly constant at lower frequencies, but these parameters are
frequency-dependent at higher frequencies i.e. their values increase by increasing the
frequency of the propagated signals. Attenuation in a CC line is much lower than that of
power cables; conversely, it is true for propagation velocity i.e. signals propagate faster in
CC line.
The TDR measurement results on XLPE power cable can be used to localize the
discontinuities as well as the design of communication through smart distribution power
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cables. On the other hand, TDR measurement results on the CC line can be used to decide
the number and positioning of PD sensors for the monitoring of falling trees over a
specific length of the CC overhead smart distribution network. Therefore, the measured
wave propagation characteristics can be used as a design aid to develop an intelligent
fault diagnosis and management system for distribution networks that may improve the
safety and result in reduced maintenance costs and visual inspection work. In addition,
the reliability of the distribution system will improve which is considered one of the
significant characteristics of the future smart distribution networks.
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