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FAULT LOCATION IN EXTRA LONG HVDC TRANSMISSION LINES USING DISCRETE WAVELET TRANSFORM
O.M.K.K. NANAYAKKARA1, A.D. RAJAPAKSE1, RANDY WACHAL2 University of Manitoba1 (CAN), Manitoba HVDC Research Centre 2(CAN)
SUMMARY
In this paper, the accuracy of the two-terminal travelling wave based transmission line fault
location using wavelet transform technique is investigated for a 2400km long overhead
HVDC transmission line. The feasible of using the measured DC voltages and the surge
capacitor currents to detect travelling wave arrival was studied. Simulations were carried out
with PSCAD/EMTDC and the fault location algorithm was implemented in MATLAB.
Results show that the wavelet based edge detection can be used in the fault identification in
HVDC systems with extra long overhead lines. The influence of noise on the fault location
accuracy is presented. The results also show that either DC terminal voltages or the surge
capacitor currents can be used in line fault location.
KEYWORDS Fault location, HVDC, Long transmission line, Travelling wave, Wavelet, DWT
CIGRÉ Canada
21, rue d’Artois, F-75008 PARIS (107) Conference on Power Systems
http : //www.cigre.org Vancouver, October 17- 19, 2010
1
1. INTRODUCTION The travelling wave based fault location principle, which utilizes the propagation times of the
voltage and current travelling waves generated on a transmission line when a fault occurs, is
well known [1]. Although application of this principle is challenging in the highly branched
and meshed AC networks, it has been successfully applied to transmission line fault location
[2] in the conventional HVDC systems, which have only two terminals. Depending on the
signals used, two travelling wave based fault locations methods can be identified: two-
terminal method and single terminal method. The two-terminal method is more reliable than
the single-terminal method as it only makes use of the fault generated initial surges but not the
secondary reflections. In the two-terminal method, the difference in the times of arrival of the
first fault-generated waves at the two line terminals is used to determine the fault location,
given that the propagation velocity of the surge is known.
The widely used and more accurate two-terminal measurement method requires precise
determination of wave front arrival times at both line terminals, and an easy means of
bringing the measurements from the two terminals to a common point, so that the fault
position can be determined. This method became a feasible solution with the developments of
Global Positioning System (GPS) which provides time synchronization accuracies of better
than 1 µs over the entire surface of the Earth, 24 hrs per day [3][4] and with developments in
telecommunication technology [4]. There are number of line fault locators based on this
principle [2] are installed in HVDC systems worldwide. These fault locators can achieve fault
location accuracy of less than ±0.3 km depending on the length of the transmission line.
As the demand for power grows in countries that a rapidly industrializing, many new HVDC
transmission schemes are being built. There are several HVDC transmission systems with
extra long overhead (O/H) lines such as the 2500 km long Porto Velho-São Paulo HVDC
system [5] under consideration. Accurate fault location in such extra long transmission lines is
a challenging task and when the transmission lines are longer than 1000 km, fault location has
been achieved with the help of repeater stations. Installation of extra hardware at the repeater
stations, which are required to locate line faults using the existing technology, increases the
cost of these transmission projects.
In this paper, an investigation of line fault location in a HVDC system with 2400km long O/H
line using two-terminal measurement method is presented. Discrete Wavelet Transform
(DWT) is used to detect the travelling waves arriving at the terminals. Merits of using
terminal voltage measurements and terminal surge capacitor current measurements for
detection of travelling waves is examined. Furthermore, the influence of noise in the fault
location accuracy is studied. All simulations were carried out with PSCAD/EMTDC and the
fault location algorithm was implemented in MATLAB.
2. LINE FAULT LOCATION USING SYNCHRONIZED DOUBE-ENDED MEASURMENTS
A schematic diagram showing the arrangement for line fault location (LFL) using two-end
synchronized measurements is shown in Figure 1. Arrival of the travelling waves at each end
of the line is time stamped using clock signals obtained from GPS. Distance to the fault
location from the rectifier end, xF is calculated by using the travelling wave principle as
= ( − ( − × 2 (1)
where L is the total O/H transmission line length, ti is the inverter terminal surge arrival time,
tr is the rectifier terminal surge arrival time, V is the propagation velocity of the travelling
2
surge. Synchronized two-end measurements allow for simple and accurate fault location for
conventional HVDC system with two terminals. The possibility of detecting surge arrival
time by measuring (i) the terminal voltages at two ends (VDCRp1 ,VDCIp1) and (ii) the surge
capacitor currents at two ends (SCMRp1, SCMIp1) is considered in this paper.
GPS
Calculation of LFL
xf
SCMRp1
Fault
Surge capacitor
Time stamped
inputs
Rectifier
end
Smoothing
reactor
DC filterConverter
VDCRp1
Time stamped
inputs
Inverter
end
Smoothing
reactor
DC filter Converter
VDCIp1
SCMIp1
OH line
Figure 1 - Schematic diagram of two-end synchronized LFL using GPS
Accuracy of the travelling wave based LFL depends largely on the precise identification of
the surge arrival time. For example if the precision of time measurement at a single terminal
is only up to 10µs, the approximate accuracy of fault location that can be achieved is ± 3 km
(assuming the travelling wave propagation velocity is 300000 km/s). Typically, steep wave
front is visible in terminal voltage or current of overhead line with a permanent solid fault.
However due to noise and degradation of waveform during the travel, precise detection of the
arrival of a travelling surge is harder using conventional edge detection methods such as
Short-Time Fourier Transform (STFT) and Finite Impulse Response (FIR) filtering [8][4]
etc.. However, wavelet transform can be used to identify this change in either voltage or
current. Wavelet transform is a linear transformation similar to the Fourier transform [7].
However, it is different from Fourier transform because it allows time localization of different
frequency components of a given signal [7].
In this paper, discrete wavelet transform (DWT) is used to detect incoming travelling wave as
it is used by many novel fault location algorithms [5], [2], [7]. Wavelet transform uses basis
functions that are known as mother wavelets and are defined as [4]:
,( = 1 ∗( −
(2)
where * means complex conjugate; p is a scaling factor and τ is the shifting. Performance of
the fault location by using family of Daubenchie (db) mother wavelet types was tested in this
research. According to the results ‘haar’ mother-wavelet (also called db2 mother wavelet),
was found to be the most suitable. Shape of the ‘haar’ mother-wavelet is shown in Figure 2
and it is considered the simplest mother wavelet type available. Therefore, it is expected to be
computationally less demanding and requires less resources when implementing in hardware.
Figure 2 – ‘Haar’ mother wavelet
In DWT, the scale p changes as powers of 2, i.e.: p0=20=1, p1=2
1=2, etc. and generally: pj=2
j
[4] where j is referred to as the level of details. The value of τ also changes in a discrete
0.5− 0 0.5 1 1.5
1−
1
haar t( )
t
3
manner as powers of 2: at jth
detail level, the time shifts are changes as τ0=2j×0=0, τ1=2
j×1=2
j,
etc. and generally: τn=2j×n [4]. DWT of the sampled waveform x(k) can be derived as shown
in equation (3):
= ( !∗ ("#$
%&'
(3)
!( = 2# ()2# − *+
(4)
where: and k is the sample number of x(t),M-Total number of signal samples of non zero
values of !( for the time period. Moreover, after substituting the generalized values to τ and p to the mother wavelet function shown in equation (2); the equation (4) is derived [4].
The DWT, which is also considered as multi-resolution analysis, differs from continuous
wavelet transform (CWT) with clear steps in time-frequency plane [4]. The DWT can be used
to decompose the input signal in to multiple frequency bands and this can be implemented
efficiently as a filter bank as shown in Figure 3 under DWT decomposition [4]. Only a single
level is shown in Figure 3 but this can be extended for series of levels by substituting
approximation value with the input signal of the next level.
Figure 3 - Structure of one-level DWT algorithm
This implementation is commonly known as Mallat tree algorithm and consists of series of
low-pass filters (LPF) and their dual high pass filters (HPF). The circle with downward arrow
behind 2 denotes down sampling by a factor of 2. The output xd(n) is called the detail wavelet
coefficients while the output from the last low pass filter is referred to as the approximation
wavelet coefficient.
It is possible to obtain the original signal x(t) through wavelet series reconstruction. The
reconstruction can also be carried out efficiently using a tree algorithm as shown in Figure 6
under DWT reconstruction. The filters HPF1 and LPF
1 are the inverse filters of HPF and LPF
respectively. In Figure 6, the circles with upward arrow behind 2 denotes up sampling by a
factor of 2.
3. TEST NETWORK
Modified version of the first Cigré benchmark HVDC scheme [9] is selected as the test
HVDC system. This test network has 500kV as the nominal DC voltage and it is designed to
deliver 1000MW of active power between two 50Hz AC networks.
The simplified PI model representing a cable transmission scheme in the original Cigré model
[9] was replaced with a frequency dependent distributed parameter model of a 2400km long
overhead transmission line in the modified network. Furthermore, a bipolar HVDC
configuration is used since most of the present day HVDC systems are built in bipolar
configuration, instead of the mono-polar arrangement in the original reference [9]. Original
test network does not contain a surge capacitor. Surge capacitor is used to protect converter
station equipment from surges travelling alone the overhead transmission line because when a
steep wave-front of surge travelling along the DC transmission line is first slowed down by
4
the line surge impedance and then by the surge capacitor. Since the use of surge capacitor
current to detect surge arrival as in the existing fault locator installed at the Nelson River
HVDC scheme [10] to be investigated, a 20 nF surge capacitor is added to the test network.
The presence of a series DC reactor is essential in line commutated type HVDC scheme [11].
However, original test network does not contain a separate smoothing reactor because it is
included in the simplified cable circuit. General value of the smoothing reactor is in the range
of 0.5-1H [11]. Therefore, 0.5H smoothing reactor is placed in series with the transmission
line at both ends.
The terminal voltage and surge capacitor current measurements are monitored for large
number of simulation cases with different fault locations. The input signals were conditioned
assuming 2 MHz sampling rate, 16-bit Analog to Digital (A/D) conversion resolution, and 0-
20 V range before use in the line fault location algorithm to understand the performance under
realistic conditions. These A/D parameters are selected after careful testing and considering
the availability of commercial A/D converters.
Figure 4 - Monitored input signals conditioned by A/D
A sample of simulation results is shown in Figure 4. The waveforms shown are the measured
terminal voltages and surge capacitor currents after normalization between 0-20V and
quantization with a 16-bit resolution at 2MHz sampling rate during a short circuit fault at
400km from the rectifier end. The input vector limits are taken as 0-2pu for voltage and -1 kA
to 1 kA for surge capacitor currents. Therefore values below zero are set to zero due to
normalization effect as seen in voltage waveform in Figure 4. This does not have any impact
in operation of the line fault locator since it only uses initial change in voltage. In the two-end
synchronized measurement based fault location method proposed in this paper, the transient
can be recognized by analyzing the DWT coefficients of the measured terminal voltage or
surge capacitor current signals. Magnitude values of the DWT detail coefficients were
obtained for the corresponding input signals for scale (j) values of level 2 to level 5 for each
terminal. The DWT coefficients for the above sample waveforms are shown using voltage at
the rectifier end (VDCRp1) and surge capacitor current at the rectifier end (SCMRp1) in
Figure 5. Surge arrival point is clearly visible in both input signals with a sharp wave front for
each level shown in Figure 5. If a proper threshold value is set then the initial surge arrival
point can be easily detected.
2.402 2.404 2.406 2.408 2.41 2.4120
2
4
6
8
10
12
14
16
18
20Terminal Voltage
Time (s)
Norm
aliz
ed v
oltage
Rectifier end
Inverter end
2.402 2.404 2.406 2.408 2.41 2.4120
2
4
6
8
10
12
14
16
18
20Surge Cap.Current
Time (s)
Norm
aliz
ed c
urr
ent
Rectifier end
Inverter end
5
Figure 5 - Magnitude values of DWT level details applied to terminal voltage
4. LFL ALGORITHM
Simplified fault location algorithm is presented in Figure 6. Initially either terminal voltage or
surge capacitor current measurement, which is the input data, is stored to a buffer. DWT is
applied to the input buffer and magnitude values of detail coefficients of level 2, 3, 4 and 5
are extracted.
Figure 6 - Simplified DWT based LFL algorithm
A threshold to identify the surge arrival point is set about 10% above the maximum value of
the corresponding input signal under the normal conditions. The safety margins are required
to allow for the noise. Different threshold values are found for each level of the detail DWT
coefficient considered in the algorithm. The time when the magnitude of the considered DWT
coefficient rises above the threshold is recognized as the time of arrival of a surge at the
terminal. From the measurements at the other end of the transmission line, the time of arrival
of the surge in that terminal is received via telecommunication channel. Fault location is
calculated by using the travelling wave principle according to equation (1). As different DWT
coefficients represent different frequency bands in the signal, the velocity of propagation at
each of these frequency bands could slightly differ. These velocities can be found and the
algorithm can be calibrated by using test data for a known fault.
The algorithm attempts to find an arrival of surge in the current data buffer, and if it did not
find an edge, then the buffer window is shifted and the procedure is repeated.
2.27 2.28 2.29 2.3
x 104
0
0.2
0.4
Level 2 details
samples
Deta
il coef.
mag.
Using VDCRp1
Using SCMRp1
2.27 2.28 2.29 2.3
x 104
0
0.2
0.4
0.6
0.8
Level 3 details
Samples
Deta
il coef.
mag.
Using VDCRp1
Using SCMRp1
2.27 2.28 2.29 2.3 2.31
x 104
0
0.5
1
1.5
Level 4 details
Samples
Deta
il coef.
mag.
Using VDCRp1
Using SCMRp1
2.27 2.28 2.29 2.3
x 104
0
0.5
1
Level 5 details
Samples
Deta
il coef.
mag.
Using VDCRp1
Using SCMRp1
6
5. SIMULATION RESULTS
PSCAD/EMTDC is used to carry out the simulations with 0.1µs simulation time step. Voltage
at the pole 1 rectifier end (VDCRp1) and the inverter end (VDCIp1) together with surge
capacitor currents at both ends (SCMRp1 and SCMIp1) were recorded for many different fault
locations at a 2 MHz sampling frequency (0.5µs sampling time step). For each case,
permanent ground fault was applied between pole 1 and the ground with 0.01Ω fault
resistance. Voltages are represented in per unit value based on 500kV voltage and the surge
capacitor currents are represented in kilo amperes.
PSCAD/EMTDC output data are imported to MATLAB environment and the fault location
algorithm was implemented using MATLAB functions. The respective input signals were
scaled and quantized before using in the fault location algorithm to simulate the actual signal
acquisition steps. A/D conversion limits are assumed as 0-20 V and for scaling, the input
vector limits are taken as 0-2pu for voltage and -1 kA to 1 kA for surge capacitor currents.
After careful analysis, 16-bit resolution is selected as the A/D bit resolution.
6. FAULT LOCATION ACCURACIES
Prediction accuracies were obtained for different fault locations using voltage and surge
capacitor current inputs. Some selected results are shown in Table 1 using terminal voltage
and Table 2 using surge capacitor current. Predicted fault locations were measured from the
rectifier end is presented in kilometers. Fault locations were estimated using detail DWT
coefficients of different levels (level 2, 3, 4 and 5 coefficients). In most cases, the accuracy is
varying in the order of level 2, level 3, level 4 and level 5.
Lower detail levels give higher prediction accuracy compared with higher levels. Overall
accuracy of the system is within ±500m limit. According to the results, surge capacitor
current can also be used in fault location prediction. These results are also lie within ±500 m
accuracy limit.
Table 1 - LFL accuracies for different fault locations using terminal voltage without noise as the measurement
FL (km) 10.00 100.00 850.00 1323.00 2040.00 2240.00
LF
L u
sin
g
DW
T
lev
els
Level 2 10.01 99.96 850.06 1323.12 2040.04 2239.97
Level 3 9.71 99.36 850.06 1323.42 2040.34 2240.27
Level 4 10.60 100.19 850.32 1323.33 2040.01 2238.90
Level 5 12.37 101.83 852.03 1324.34 2039.96 2238.54
Table 2 - LFL accuracies for different fault locations using surge capacitor current without noise as the measurement
FL (km) 10.00 100.00 850.00 1323.00 2040.00 2240.00
LF
L u
sin
g
DW
T
lev
els
Level 2 11.51 99.96 850.06 1323.12 2040.04 2239.97
Level 3 9.71 99.96 850.06 1322.82 2040.34 2240.27
Level 4 10.60 101.38 850.32 1322.14 2040.01 2238.90
Level 5 12.37 101.83 852.03 1321.95 2039.96 2238.54
7. FAULT LOCATION WITH NOISY SIGNALS
Performance of the fault location algorithm is tested with input signals contaminated with
white noise. As an example, Figure 7 shows surge capacitor current contaminated with
0.001kA noise and terminal voltage contaminated with 0.01pu noise respectively.
7
Figure 7 – Surge capacitor current and terminal voltage with added white noise
LFL accuracies for some test cases using terminal voltage measurement with 0.001pu white
noise are listed in Table 3. LFL accuracy is sensitive to noise level in the input signal.
Table 3 - LFL accuracies for different fault locations using terminal voltage with 0.001pu noise as the measurement
FL (km) 10.00 100.00 850.00 1323.00 2040.00 2240.00
LF
L u
sin
g
DW
T
lev
els
Level 2 10.00 99.89 849.72 1323.03 2040.31 2240.09
Level 3 10.30 100.19 849.72 1323.03 2040.31 2240.09
Level 4 10.60 100.19 850.32 1323.33 2040.01 2240.09
Level 5 12.37 101.83 852.03 1324.34 2039.96 2238.54
Similarly, LFL accuracies using surge capacitor current with 0.001kA white noise are listed in
Table 4. In general, surge capacitor current is more sensitive to noise level than the terminal
voltage. Performance of this method is poor for very close faults. In general, a better accuracy
is achieved with lower levels DWT coefficients.
Table 4- LFL accuracies for different fault locations using surge capacitor current with 0.001kA noise as the measurement
FL (km) 10.00 100.00 850.00 1323.00 2040.00 2240.00
LF
L u
sin
g
DW
T
lev
els
Level 2 11.21 99.96 850.06 1322.82 2040.04 2239.97
Level 3 9.71 99.96 850.06 1322.82 2040.34 2240.27
Level 4 10.60 101.38 850.32 1323.33 2040.01 2238.90
Level 5 12.37 101.83 852.03 1324.34 2039.96 2238.54
8. CONCLUSION
This paper has investigated the performance of two-ended travelling wave based line fault
location algorithm with DWT based surge detection for a 2400km long HVDC transmission
line. The applicability of both the terminal voltages and the surge capacitor currents as input
signals was examined. The simulation result shows that both inputs signals would produce
similar accuracy levels: in the range of ±500m under normal conditions for permanent line to
ground faults. The analysis considered the scaling and quantization effects of the A/D
conversion. Increasing levels of noise degrades the fault location accuracy, especially in the
case of faults very close to one of the ends. Generally, higher fault location accuracy is
obtained with lower levels DWT coefficients (Levels 2 and 3) of the input signals. However,
when the noise is present, use of higher levels (Levels 4 and 5) DWT coefficients may be
desirable to achieve robust results.
2.401 2.402 2.403 2.404 2.405 2.406 2.407 2.408 2.409
-0.025
-0.02
-0.015
-0.01
-0.005
0
Time(s)
Curr
ent
(kA
)
Overhead line surge cap. currents
0.001kA noise SCMRp1
Original SCMRp1
2.404 2.4045 2.405 2.4055 2.406 2.4065 2.407
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
Time(s)
Voltag
e (
pu
)
Overhead line voltages
0.01pu noise VDCRp1
Original VDCRp1
8
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