ERK'2021, Portorož, 238-241 238
Power Cable Wave Propagation Velocity Estimation Based on 
Travelling-Waves 
Marko Hudomalj
1,2
 
1
 Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia 
2
 ComSensus d.o.o., Brezje pri Dobu 8a, 1233 Dob, Slovenia 
E-pošta: marko.hudomalj@ijs.si 
 
 
Abstract. This paper presents a method for estimation of 
power cable wave propagation velocity transfer 
function. The method determines signal propagation 
velocity based on the measurements of travelling-wave 
signals at each frequency. Travelling-waves are caused 
by different events on power cables such as partial 
discharges, faults and lightning strikes. The method will 
be used for improving localization of events on power 
cables. Method uses wavelet transform to analyze the 
signals in the frequency domain. 
 The method is tested with the use of 
frequency-dependent transmission line model in 
Simulink. Propagation velocity calculated based on 
wavelet transform is compared to propagation velocity 
calculated from analytic transmission line parameters. 
 
1 Introduction 
The electrical power system (EPS) is migrating to 
renewable energy in order to lower pollution. With the 
introduction of renewable energy sources new control 
and protection challenges are emerging in EPS. There is 
also a constantly increasing demand of electrical energy 
especially with the transition to electric mobility and 
introduction of new advanced HVAC systems to the 
grid. With this increasing demand, EPS is being pushed 
to its limits during peak demand hours. The upgrades in 
EPS are expensive and take a lot of time, so great effort 
is being put into how to exploit existing EPS 
infrastructure. EPS must provide continuous and 
reliable electrical energy and must operate safely. To 
enable optimal control, protection and quick fault repair 
of the EPS, a good observability of the EPS operation 
must be provided. In recent times, many new Intelligent 
Electronic Devices (IEDs) were developed to provide a 
better insight into the operation of EPS. This was 
enabled with the development of processing units, new 
algorithms, measurement devices, and communication 
devices. However, in the field of IED there is still a lot 
of research opportunities. IEDs help EPS to become 
even more digitalized. In recent years IEDs with high 
sampling frequencies are being developed [1] that 
monitor transformers, generators, switching equipment, 
and power cables. 
Our research focuses on devices that monitor events 
on the EPS at frequencies much higher than system 
frequency. Sampling frequency is in the range of 10 
MHz and above. The main field of our research is event 
detection, localization on power cables and 
characterization of power cables. The events analyzed 
are faults, partial discharges (PD) and lightning strikes. 
Faults are meant as short circuits on the power cables 
between phases or between phase and ground. In the 
case of a fault, the rest of the EPS must be protected 
which is done with relays. Similarly, in the case of 
lightning strikes, the rest of the system must be 
protected against overvoltage. Faults and short circuits 
are one-time events on the cable, but the PD activity is 
constantly present on the cables with isolation. PDs 
happen in the cable isolation where voids occur because 
of cable isolation degradation. Because of the high 
voltages on the power cables breakthroughs happen in 
the voids. 
The described events cause travelling-waves (TW) 
on the power cables. TW are short-time high-frequency 
transient signals. In the instance of power cables, signals 
propagate in both directions along the cables from the 
location of the event towards the cable ends. TW events 
and the signals are represented in Figure 1. When TW 
reaches an end of the cable, where medium changes, it 
is reflected back. Additionally, the propagating TW 
signal is attenuated and because the propagation 
velocity depends on the frequency the transient signal is 
elongated in time. This is the effect of dispersion. In our 
research, we want to exploit dispersion effects of the 
TW signal propagation to improve event detection and 
localization on power cables. 
 
 
2 State of the art 
TW detection and localization methods on power cables 
can be either single- [2], [3] or double-ended [3], [4]. In 
a single-ended approach, TW is detected just on one 
side of power cables, using reflected waves for 
localization. In a double-ended approach, detection of 
the original signal at both sides is used for localization. 
Another approach is detection of TW with multiple 
devices on a single cable, where the methods are similar 
to double-ended approach. 
To improve TW localization on power cables, recent 
developed methods consider cables transfer function 
Figure 1: Representation of traveling-wave on power 
cables 

239
 
(TF). TFs are determined based on different approaches. 
The first approach is to determine the TF based on 
power cable parameters (electrical cable characteristics, 
geometry, isolation characteristics, etc.) [5]. Another 
approach is to use TF determined based on 
measurements when the power line was deployed [6] or 
measurements during maintenance. These two 
approaches for TF estimation do not consider the 
changing of the TF because of environmental changes 
of temperature and humidity, and ageing of cables, 
especially isolation degradation. To include the 
changing of TF for more accurate representation, some 
researchers have worked on determining the TF based 
on online measurements. One such approach is to use a 
reference signal generator at one end of the power cable 
[7]. With a known reference signal, TF can be 
accurately determined by measuring the signal at the 
other cable end, where the reference signal was induced 
and comparing the reference and measured signal. 
Different algorithms for the detection of TW were 
proposed [6], [7]. Some algorithms use specific point on 
the TW which is then used for location. This approach 
requires good synchronization of the measurement 
equipment and stable sampling frequency. Another 
approach is to use the slopes of the detected TW or 
transform the time-based signal to the frequency domain 
and look at TW at different frequency components [8]. 
Another method is so called “propagation distance” that 
was proposed in the ref. [6]. The algorithm does not 
need to determine a specific point on TW which reduces 
the need for high sampling accuracy. Some proposed 
methods also do not need synchronization between 
measurement equipment, as in the case of ref. [7]. 
An interesting research field is also the ageing 
estimation of EPS equipment, which is generally based 
on PD measurements [9]. With an ageing estimation, 
preventive repair of equipment can be scheduled and 
potential future faults avoided. 
In praxis today, TW is used for fault detection, such 
as the TW87 scheme (travelling-wave differential 
protection scheme). In recent years, analysis of different 
parameters of TW87 were carried out and commercial 
products are emerging. But there is still work being 
done on improving detection and localization algorithms 
that consider online cable TF estimation and how 
junctions or other network equipment affects the 
propagation of TW. 
The presented paper focuses on developing an 
algorithm for online TF estimation based on TW to 
improve event detection and localization on power 
cables. 
 The frequency-dependent propagation of 
electromagnetic waves is exploited in our method to 
determine the fault location and simultaneously 
determine the dispersion function, which is dependent 
on the cable characteristics and the surrounding 
medium. In this paper, we focus on propagation velocity 
transfer function estimation. 
 
3 Methods 
To analyze TW on power cables, we prepared a 
simulation in MATLAB Simulink. For the simulation of 
the power cables we used the Simulink model of 
frequency-dependent transmission line [10]. The used 
transmission line model is an implementation of the 
Universal Line Model (ULM). It uses frequency-
dependent series resistance, reactance and susceptance 
per unit length as the line parameters. The model is 
packaged to be used as a four terminal electric 
component. The transmission line is executed with 
ULM equivalent circuit in Laplace domain. 
For the simulation of a power cable, we used three 
transient line components. For the event generation, an 
impulse signal generator was used. The used simulation 
model is presented in Figure 2. 
Three transient line components were used to enable 
voltage measurements and impulse signal generation at 
different positions along the cable. In the simulations, 
we assigned same line parameters to all three sections to 
simulate a single power cable. Line parameters are 
shown on Figure 3. 
For the impulse signal generator, we used voltage 
generator with a parallel resistor and a switch which 
Figure 2: Simulation power cable model 

240
applies the voltage to the frequency dependent 
transmission line. The circuit is represented on the left 
of Figure 2. Voltage measurement were done along the 
cable: between sections of the transmission line 
components and at both ends of the cable.  
 
 
The simulation results were further analyzed in 
MATLAB. 
We determine the TF of the transmission line from 
the voltage measurements, in particular we were 
interested in propagation velocity. Generated pulse is a 
short time high-frequency bandwidth signal that 
propagates across the transmission line. We used 
wavelet transform to transform the time domain signal 
to the frequency domain and determined the peak 
amplitude at each frequency. The propagation velocity 
is then calculated based on the time of peak magnitude 
at different measurement locations on the transient line 
and the known length of the line in between. 
 
4 Results 
For the results presented in this paper we generated 
an impulse at the middle of a simulated 16 km long 
power cable. The cable was divided into three sections. 
Two series cable sections were 4 km in length and the 
third section was 8 km in length. We used a sampling 
frequency of 60 MHz for all of the signals. The impulse 
was generated at 0.1 ms from the start of the simulation 
and had raise time of one sampling step and one 
sampling step of fall time. The maximal value was 100 
V which also persisted for one sampling step. 
The time-series graph measured at the end of the 
8 km section is shown in the lower graph in Figure 4. 
From the graph, the first incident wave can be observed. 
The reflected waves can also be observed, especially the 
first reflected wave. 
To better observe the frequency behavior of the 
signal, we used continuous wavelet transform on the 
time-series. We used symmetrical Morse wavelet with 
MATLAB's continuous wavelet function cwt(). The 
upper graph of Figure 4 presents the wavelet transform 
magnitude in time and at different frequencies. 
On the upper graph of the Figure 4, we also marked 
the maximal magnitude at each frequency level for the 
incident wave and the first reflected wave. From the 
graph, we can observe the dispersion effect: the 
magnitudes are attenuated and the lower frequency 
components propagate slower than the higher frequency 
components. 
Later we used discrete wavelet transform on the 
time-series signal. Discrete wavelet transform needs less 
processing power and is better suited to be implemented 
in an IED. We used MATLAB's maximal overlap 
discrete wavelet transform function modwt(). In our 
calculations we used Symlets wavelets with 20 
vanishing moments. The result of the function are 
values in time as coefficients at different wavelet scales. 
Wavelet scales represent the signal in the frequency 
band around the scale central frequency. For our 
calculations, we treated the coefficients as if they would 
represent the signal at the wavelet scale central 
frequency. 
Similarly to the process presented before with the 
continuous wavelet transform, we determined the 
maximal magnitudes of the transformed signal at 
different central frequencies in time. From the 
timestamps of the maximal values at both ends of the 
simulated power cable, we calculated the signal 
propagation velocity along the cable. The velocity is 
calculated from the time the wave travels from the 
source to both of the cable ends and with the known 
cable length. 
We then compared the calculated signal propagation 
velocity at each central frequency with the propagation 
Figure 3: Transmission line parameters 
Figure 4: Time-series signal and signal wavelet transform at cable end V2. 

241
 
velocity calculated from the transmission line 
parameters which are given as inputs to the simulation. 
This is shown on the graph represented in Figure 5. The 
graph shows the calculated transient line propagation 
velocity from the line parameters (represented with the 
solid line). For this case, the velocity is determined for 
each frequency point. The calculated propagation 
velocity after simulation and with the use of discrete 
wavelet transform is represented at discrete frequencies. 
From Figure 5, it can be observed that the 
propagation velocity acquired with the use of discrete 
wavelet transform is well determined in the range above 
10 kHz and up to 1 MHz which is the limit of our 
model. Velocity values at lower frequencies start to 
diverge more since the signal's wavelength is too high 
compared to the section distance, thus are not well 
defined in time. 
 
 
5 Discussion 
From the results presented in this paper, we can 
determine that the calculation of power cable 
propagation velocity can be acquired by analyzing the 
travelling-waves caused by the events on the cable. In 
the paper, we used wavelet transform on the time-series 
signal measurements obtained by simulation to analyze 
the signal at different frequencies. Results show that the 
wavelet transform technique is an appropriate tool for 
determining the propagation velocity of the power 
cables. 
In the future, the concepts shown in this paper will 
be improved to automatically determine the propagation 
velocity from the time-series signal measurements, thus 
improving the localization of the events on the power 
cable. Different event types have different 
characteristics not only related to time but also to 
power. Therefore the presented method would have to 
be adjusted accordingly. Here different timescales and 
measuring setups would have to be considered. 
Additionally, different types of wavelets could be more 
suitable for a different configuration. We are planning 
to test the methods in different electrical power grid 
settings. 
The method is also usable for continuous online 
power cable observability. With the constant cable 
characteristic observation, also other innovative services 
can be developed, such as long-term aging estimation, 
scheduling of preemptive repairs and scheduling of 
maintenance. 
 
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Figure 5: Comparison of propagation velocity