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1
Abstract-- Single-ended unsynchronized traveling wave fault
location algorithms have been around for several years. They
avoid the costs and complexities associated with remote end
synchronization. Nevertheless, there is a corresponding increase
in required signal processing as each reflection must be identified
and then related in time to the signal wave front.
The current signal processing techniques include a
combination of modal and wavelet analysis, where the resulting
vectors are often squared. However, the performance of this
process degrades dramatically with the filtering associated with
the substation transducers and secondary circuits. Furthermore,
the variation in observed reflection patterns demonstrates that
these methods cannot adequately distinguish between faults on
the near, or far half of the transmission line.
This paper considers the traveling wave data observed on a
330kV transmission system and presents a new signal processing
methodology to cater for the observations. This is based on the
continuous wavelet transform that is calculated at a suitably
large scale. The polarities of the resulting coefficients are used to
confirm the nature of the fault, and to infer the true fault
location.
Index Terms-- Current transformers, Fault location, Traveling
wave devices, Transmission lines, Wavelet transforms
I. INTRODUCTION
he use of fault location systems on transmission circuits
can aid by improving the system availability and
performance, as well as reducing the operating costs and
losses in deregulated electricity markets.
Traveling wave fault location techniques are recognized as
some of the most accurate methods currently in use. Several
types have been documented in [1] although these can
generally be categorized as synchronized or unsynchronized.
The synchronized algorithm is the most predominant on
overhead transmission lines, and calculates the fault location
based on the relative arrival times of the traveling wave
transients at each terminal using a synchronizing clock.
Unsynchronized algorithms identify the location of the
fault by observing the time delay between successive
reflections in the traveling wave signal observed at one
location. This is similar to the off-line approach of time
domain reflectometry, which has been used very successfully
on de-energized cables and transmission lines with the aid of
D. J. Spoor was with Transgrid, Sydney, New South Wales, Australia
during the development of this paper. He is now with Integral Energy,
Sydney, New South Wales, Australia (e-mail: darren.spoor@integral.com.au).
J. Zhu is with the Department of Electrical Engineering, University of
Technology, Sydney, Australia (e-mail: joe@eng.uts.edu.au).
accurate transducers.
These single-ended traveling wave algorithms avoid the
costs and complexities associated with remote end
synchronization. Nevertheless, there is a corresponding
increase in the required signal processing as each reflection
must be identified and then related in time to the signal wave
front.
Such algorithms have been noted as being too complex and
erroneous for operations personnel to accurately locate faults
[2], due to the problems with distinguishing between traveling
waves reflected from the fault and from the remote end of the
line [3]. In some situations, it may also be difficult to identify
the true wave front of the recorded signal as the transient can
become lost in the disturbances created by a previous event.
As a result, many implementations incorporate other
technologies. For instance, the single ended, unsynchronized
algorithm has been combined with a one-terminal impedance
based fault location algorithm [4,5]. However, many other
single ended implementations still require the operator to
manually identify the forefront of the initial transient.
The approaches adopted in [6] and [7] are indicative of the
signal processing methods that have recently been proposed.
Here, the traveling wave transients are decoupled into their
modal components, and are then further decomposed into their
wavelet coefficients using the discrete wavelet transform
(DWT). This gives simulated accuracies better than 3 miles on
a 200 mile circuit.
Abur [3] has also proposed an algorithm for single ended
fault location that distinguishes between grounded and
ungrounded faults from the ground mode signals. These are
applied to a threshold on the DWT
2
vector. If the fault is
grounded, and the wavelet transform of the ground mode
signal is small, the fault is in the remote half of the line, and
vice versa.
The techniques presented in [3] and [8] also conclude that
the traveling wave signals can be adequately identified using
discrete wavelet analysis with a scale of 1, where the resulting
coefficients are squared (DWT
2
).
However, the combined effect of the sampling rate, the
poor frequency response of many substation transducers, and
the variation in reflection patterns appear to give erroneous
results when applying these techniques to observed data. This
paper presents an alternate wavelet approach that provides a
reliable fault location estimate under these conditions.
Improved Single Ended Traveling Wave Fault
Location Algorithm Based On Experience
With Conventional Substation Transducers
D. J. Spoor, and J. Zhu, Senior Member, IEEE
T
2
II. SIGNAL PROCESSING TECHNIQUES
This section describes the common traveling wave signal
processing methods required for three-phase lines. A good
overview of the Fourier, windowed Fourier and wavelet
transforms is provided in [8,9]. However, several authors have
recognized the benefits of applying modal analysis in
conjunction with the wavelet transform. Reference [3]
specifically presents the discrete wavelet transform as one of
the best for identifying traveling wave transients on power
systems.
A. Modal Analysis
Using a modal transformation, the phase signals can be
decoupled into several independent modes of propagation. For
a three-phase system, the transformed quantities will contain
one ground mode and two independent aerial modes, which
travel close to the speed of light on overhead circuits.
Conversely, the earth mode signals travel at a somewhat
slower velocity with a higher attenuation. This earth mode, as
with the transmission line zero sequence impedance, is
frequency dependant due to the non-uniform distribution of
the earth current. On the other hand, the aerial modes can be
assumed to be frequency independent.
Clarke’s matrix is one of several commonly used
transformation matrices: [10]
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−−=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
)(
)(
)(
330
112
111
3
1
)(
)(
)(
)2(
)1(
)0(
tI
tI
tI
tI
tI
tI
C
B
A
(1)
where I
A,
I
B
and I
C
are the phase currents, I
0,
is the ground
mode current and I
1
and I
2
are the decoupled aerial modes.
Such simple transformations are real and assume a
transposed circuit. Untransposed circuits require an
eigenvalue based transformation matrix that is frequency
dependent [11]. However, most untransposed lines may be
assumed as transposed for the purposes of identifying the
modal parameters.
B. Continuous Wavelet Transform
Wavelet techniques maintain the correlation between time
and frequency for the observed signal. This proves to be
advantageous in determining the wave front of the traveling
wave and the subsequent reflections.
The continuous wavelet transform (CWT) is defined as the
sum over time of the input signal f(t) multiplied by scaled,
shifted versions of the wavelet function
Ψ
:
∫
∞
∞−
⎟
⎠
⎞
⎜
⎝
⎛
−
= dt
a
bt
tf
a
baCWT
*
)(
1
),(
ψ
(2)
The coefficients a and b are the scaling and translation
constants respectively. These can be used to alter the
characteristics of the ‘mother’ wavelet function, which may be
either real or complex [8,3]. The wavelet function itself can
be of any particular form as long as it complies with the
admissibility conditions presented in [10].
Using a continuous scale of a and b results in many
wavelet coefficients, some of which are redundant due to the
similarity to those produced at other close scales. The pseudo-
frequency which corresponds to each coefficient is
proportional to the scale factor a, the sampling period T
S
of
the input signal, and the centre frequency for the particular
wavelet function F
C
, as the following: [12]
aFTfrequency
CS
/
=
(3)
The first (and lowest) scales have the highest time
resolution, and cover a broad frequency range at the high end
of the spectrum. The frequency resolutions of these scales are
only limited by the sampling rate of the input signal.
Conversely, higher scales cover an increasingly longer time
interval and correspond to the lower end of the frequency
spectrum.
C. Discrete Wavelet Transform
The Discrete Wavelet Transform overcomes some of the
problems associated with obtaining redundant coefficients.
The DWT algorithm is not continuously scaleable and
translatable. Instead it can only be adjusted in discrete steps,
resulting in a piecewise continuous function:
∑
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
k
m
m
m
a
kan
kf
a
nmDWT
0
0
0
*)(
1
),(
ψ
(4)
Here, the scaling and translation parameters are replaced
with a
0
m
and ka
0
m
, where k and m are integers, and a
0
>1 is the
fixed dilation step. The DWT determines the coefficients on a
dyadic basis rather than a continuous shifting and scaling as
with the CWT.
When implementing the DWT, the signal f(k) is applied to
a multi-stage filter bank [9] where a
0
=2 and m is the level of
decomposition. Downsampling is performed at the output of
each low-pass filter within the filter bank in preparation for
the next stage. Consequently, the scale has an inverse
relationship to the frequency [10], and the resulting series of
wavelet coefficients is referred to as the wavelet series
decomposition [8]. The pseudo-frequency corresponding to a
particular level of decomposition m, or scale a
0
m
can be
determined from:
m
CS
aFTfrequency
0
/=
(5)
In principle, any admissible wavelet can be used in wavelet
analysis [12]. Similar to the observations made in [13], the
differences between the results obtained from many well-
known wavelets in the following analysis were small, and so
the sym2 wavelet has been used in all cases.
III. T
RANSDUCER SELECTION AND FREQUENCY RESPONSE
On-line traveling wave fault location techniques require
transducers capable of withstanding power system voltages.
High voltage transducers with a large dynamic range are
available for these applications, such as optical current
3
transducers and Rogowski-Chattock coils. However, the
additional installation costs and the requirement to take high
voltage equipment out of service during installation is often a
major limitation in their use. The overall commissioning costs
are a significant factor, as traveling wave techniques must
compete with cheaper impedance-based algorithms
incorporated in most protection relays and fault recorders.
As a result, conventional substation transducers are often
the only economic means of monitoring the voltage or current
transients during normal operation. In most cases this means
that the traveling wave recorder is connected via split-core
inductive couplers to the secondary protection circuits from
the substation current transformers. Unfortunately, this
approach can constrain the accuracy in the fault location due
to the band-pass nature of the secondary circuit [14].
The transfer function response of the substation current
transformer and secondary cabling can be calculated using the
approach presented in [15].
The analysis considered in this paper is based on the
observations from a particular 330kV double circuit line,
186km in length and with traveling wave recorders
permanently installed at each end. A similar system was
described in [2,16,17]. These recorders sample the line
currents at 1.25MHz with an 8-bit resolution via inductive
couplers on the substation protection secondary circuits. The
traveling wave systems are designed to use a synchronized
algorithm, and so have a common GPS time base with a 1μs
resolution [13]. GPS is a worldwide satellite system
incorporating 24 satellites which orbit the earth twice a day.
Each of the GPS receivers provide 1PPS (pulse per second)
signal synchronized 1MHz clock.
Fig.1 shows the correlation between scale and pseudo-
frequency for the ‘sym2’ wavelet function where the sampling
rate is 1.25MHz. Similarly, the frequency response of the
aerial mode currents in this installation is shown in Fig. 2,
where the current in the substation secondary circuit is
calculated relative to the primary line current for a traveling
wave installation on Transgrid’s 330kV network. The
response is highly dependant on the length and type of
secondary cabling, the current transformer parameters and the
resistance and inductance of the relay burden. Noting that the
traveling wave recorder samples at 1.25MHz, the current
transformer and secondary circuit clearly impacts the higher
frequency components and the corresponding smaller wavelet
scales.
Fig. 1. Calculated pseudo-frequency at various scales for the sym2 wavelet
with a sampling rate of 1.25MHz
Fig. 2. Frequency response of current transformer, secondary cabling and
relay burden compared to various CWT scales and DWT levels
IV. THE UNSYNCHRONIZED TRAVELING WAVE ALGORITHM
Single ended traveling wave algorithms have primarily
been implemented by recording the time difference between
successive reflections observed at one end of the line. Here,
Δ
T is the time between these reflections, and T
L
is the line
reflection travel time
2
v
Tm ×Δ=
(6)
v
l
T
L
2
=
(7)
where, l is the line length and v is the average velocity of the
aerial modes.
This technique has shown a high level of accuracy in
simulation. However several limitations exist when applied to
the data obtained from conventional transducers.
A. Discrete and Continuous Wavelet Applications
Single ended wavelet calculations performed on observed
data indicate that the performance of the DWT technique
degrades dramatically due to the filtering associated with the
substation transducers and secondary cabling.
The coupling between the modes in the secondary cabling
of the substation current transformers can result in ‘apparent’
ground mode oscillations, whether the fault was grounded or
not. Similarly, the resonant nature of the secondary cabling
can produce several decaying peaks in the DWT
2
vector
where only one reflection previously existed. Moreover, the
DWT has poor noise rejection when applied to digitized data
with significant quantization errors.
Figs. 3 to 6 compare the DWT and CWT techniques for an
observed fault, 71.6km from the recorder. This is compared to
a simulation of an identical fault on this particular circuit
using the Alternative Transients Program (ATP) where a
simulation frequency of 1.25MHz was also used and ideal
coupling transducers have been assumed.
As shown in Figs. 3 and 5, Both the DWT and CWT
4
algorithms appear to have a high degree of accuracy when
applied to simulated data. However, the observed traveling
wave signals are less recognizable in the scale 1 and scale 2
DWT vectors due to the filtering imposed by the secondary
cabling.
Fig. 3. DWT coefficients for a simulated incipient fault at 71.6km
Fig. 4. DWT coefficients for an observed incipient fault at 71.6km
Fig. 5. CWT coefficients for the simulated incipient fault at 71.6km
Fig. 6. CWT coefficients for the observed incipient fault at 71.6km
A similar loss of resolution at high frequencies is seen in
the CWT calculations, although the CWT technique appears
to maintain a good resolution when using a large scale for the
correlation. Consequently, it appears that the DWT cannot be
adequately applied to a noisy, filtered signal, as is commonly
observed using conventional substation current transformers.
B. Solid and Incipient Faults
One of the difficulties with single ended techniques is in
distinguishing between faults on the near and remote half of
the transmission line. This is particularly relevant for high
impedance faults that can create reflection patterns similar to
both a solid and incipient fault.
Incipient faults are discharges that are short in duration,
resulting in few (if any) reflections from the fault itself,
whereas solid faults are characterized by long fault durations
and strong repetitive reflections from the fault.
Since the CWT algorithm appears to provide a consistent
and reliable analysis of observed traveling wave transients at a
large scale, the CWT
2
vectors for simulated incipient and solid
faults have been shown in Figs. 7 and 8. Each simulation
incorporated a fault that was located at 30% of the line length
from the monitored busbar. It is clear that the conventional
unsynchronised traveling wave algorithm will give an
erroneous location estimate for the incipient fault.
Fig. 7. CWT
2
for a simulated solid fault at 56km
Fig. 8. CWT
2
for a simulated incipient fault at 56km
