Fault Location on Transmission Lines Based on

Travelling Waves
F. V. Lopes, Student Member, IEEE, D. Fernandes Jr., Member, IEEE, W. L. A. Neves, Member, IEEE

Abstract—Automatic and accurate fault location methods for instants at both transmission line ends. Then, fault location
transmission lines may reduce the search time technicians would may be determined using expressions proposed in [3] in which
take to find out where the fault is, leading to a quick recovery of the input data are the propagation velocity of travelling waves,
the system. Usually, transient detection techniques use more than
the line length and the initial transient instants in monitored
one sample of voltage or current to make possible the required
transient analysis. This paper presents a very simple method for terminals.
fault location on transmission lines based on travelling waves In [4], the Discrete Wavelet Transform (DWT) and the
using Park’s Transformation to perform the transient detection. Redundant Discrete Wavelet Transform (RDWT) are
An advantage of the proposed method is that only one voltage presented as efficient techniques for transient detection. In [5]
sample at each phase is used and transients in all three phases are is proposed a fault location method based on the analysis of
monitored simultaneously by the analysis of only one signal: the correlation coefficients which are calculated from the voltage
direct axis voltage. The method is implemented in the Alternative
oscillographic records in both line ends.
Transients Program (ATP) using the MODELS language and
simulations were carried out for a 230 kV transmission line with a The accuracy of travelling wave methods is a function of
digital fault recorder (DFR) at each terminal to evaluate the the sampling frequency of DFRs, i.e., it depends on the
applicability of the proposed technique. The results show the hardware used for data acquisition. In fact, it is rather refer to
effectiveness of the algorithm which can be used as an additional reliability than accuracy and define a maximum expected error
routine for digital protective relays. as a function of the sampling frequency.
It is important to know that the transient detection is a
Keywords: Fault location, Park’s Transformation, transient critical step for fault location procedure and, thus, the
detection, transmission lines.
reliability of the fault point estimation by any algorithm
depends directly on the reliability of the method used to
I. INTRODUCTION
estimate the initial transient instants. In this paper, a very

T HE exact fault location on transmission lines is a problem

that has been studied for decades. The theory of travelling
waves has been recently used for this purpose. Such methods
simple method for transient detection is proposed.
Conventional methods usually need a window with more than
one sample of current or voltage waveforms to perform the
are based on the transient detection at specific points of the required transient analysis. Here, the window has only one
electrical system in question and are classified according to the sample, i.e., no previous voltage samples are needed. All three
number of monitored points. Several methods for transient phases are monitored by the direct axis voltage signal Vd
detection have been proposed in order to enable an accurate obtained through Park’s transformation (Tdq0) and the method
and reliable fault location for transmission lines [1]. automatically determines the fault location point immediately
Methods based on travelling wave’s theory utilize voltage after the fault occurrence.
and/or current data captured by DFRs (Digital Fault
Recorders) installed in monitored line terminals. According to II. DOUBLE ENDED FAULT LOCATION METHODS
[2], for double ended fault location methods, it is necessary to
The main difference among travelling wave methods is the
use GPS (Global Positioning System) in order to synchronize
number of monitored terminals and the technique to detect the
oscillographic records at both monitored ends. So, digital
transients. In [3] are presented expressions for determination
signal processing techniques are applied to synchronized data
of fault location considering one and two transmission line
from DFRs, making possible the detection of initial transient
monitored ends. In [6] is proposed a three-terminal method
that avoids the utilization of the propagation velocity of the
This work was supported by Brazilian Coordination for the Improvement of travelling waves in the fault location procedure. In order to
Higher Education Personnel (CAPES).
eliminate the propagation velocity variable, three terminals of
F. V. Lopes is M. Sc. candidate at the Federal University of Campina Grande
(UFCG), Av. Aprígio Veloso, 882, Bodocongó, 58.429-140, Campina two neighbor transmission lines are monitored and a unique
Grande-PB, Brazil (e-mail: felipe.lopes@ee.ufcg.edu.br). value of propagation velocity is utilized for both lines. The
D. Fernandes Jr. and W. L. A. Neves are with Department of Electrical problem of such method is that the waves present different
Engineering of UFCG. (e-mail: damasio@dee.ufcg.edu.br,
propagation velocities depending on the ground resistivity and
waneves@dee.ufcg.edu.br).
line parameters and, consequently, the utilization of the same
Paper submitted to the International Conference on Power Systems propagation velocity for both lines can be considered as a
Transients (IPST2011) in Delft, the Netherlands June 14-17, 2011 source of error. Other works, as [7] and [8], present single
ended fault location methods. Such method use incident and it is necessary to detect the first incident waves at buses 1 and
reflected waves to perform the fault location. 2 to compute the time instants t11 and t21. Secondly, the fault
Basically, the key idea of all mentioned methods is the point location is obtained from an expression proposed in [3]:
l + (t11 − t 21 ) ⋅ v ,
determination of initial transient instants in monitored
terminals. Here, the fault location method is based on the d = (1)
2
analysis of voltage waveforms recorded by DFRs in two
where v is the propagation velocity of travelling waves and l is
transmission line terminals and, so, it is considered to be a
the line length. The procedure to perform the transient
double ended method. In this way, only incident travelling
detection is explained next.
waves are used to perform the fault location, avoiding the
utilization of reflected waves at the fault point and,
III. TRANSIENT DETECTION USING PARK’S TRANSFORMATION
consequently, making the method more reliable. A GPS must
be used in order to synchronize the DFRs measurements to The proposed method for transient detection is based on the
bring voltage samples to the same timebase and to ensure that work presented by R. H. Park in the United States in 1929 [9].
the initial transient instants will be correctly obtained. Park’s transformation (Tdq0) has been used in the whole area
Regarding the GPS usage, it is important to know that, in of electrical engineering, especially on researches regarding to
practice, it can present synchronization errors in the order of salient pole synchronous machines where variable inductances
±1µs. In spite of such limitation, it is possible to use an in a static reference frame are seen as constant inductances
independent clock on the fault location device that initiates the when the reference frame rotates at synchronous speed. Here,
counter at the moment of the first transient detection and stop the rotating reference system is used to remove power
the counter at the second transient detection at the opposite frequency signals from voltage waveforms allowing transient
bus. In this way, synchronization errors are minimized. To time detection. An analogy between the Tdq0’s application in
understand the principles of travelling wave methods, consider electrical machines research and in transient detection is
Fig. 1 in which is shown DFRs placed at Buses 1 and 2. A time shown in Fig. 2.
space diagram (Lattice diagram) is shown in the middle of the
figure. A scheme of the DFRs and GPS application in the
proposed double ended method is also presented in Fig. 1.

(a)

Fig. 1. Double ended fault location method scheme.

Where:
t11 is the initial transient instant at Bus 1;
(b)
t21 is the initial transient instant at Bus 2; Fig. 2. Park’s Transformation (Tdq0) application: (a) Electrical machine
t12 is the arrival instant of the reflected wave at Bus 1; researches; (b) Transient detection and fault location.
t22, t23 are the arrival instants of reflected waves at Bus 2;
For power system operating at normal conditions, zero
t22r is the arrival instant of the refracted wave at Bus 1;
frequency signals are calculated and, if transients occur,
l is the line length;
oscillatory signals are obtained. Such signals are called direct
d is the distance to the fault point.
and quadrature axes components which will be represented
The t21r instant was left off in Fig. 1 to simplify the diagram. from now on as Vd and Vq. Both components may be used for
It is important to know that fault location algorithms consist on transient detection but, here, only Vd will be considered.
two main steps – the transient detection and the fault point For high impedance fault cases, Vd coefficients presents
location. For the first step, considering double ended methods, high attenuation. Thus, to increase the sensitivity of the
proposed algorithm, difference coefficients (cdif) are calculated reference frame, (c) calculation of an orthogonal voltage
using Taylor´s approximation: phasor in a rotating reference frame, (d) determination of the
V d (i ) − V d (i − 1) .
initial transient instants and (e) fault location.
c dif (i ) = (2)
∆t A. Data Acquisition Using DFRs in Both Line Ends
Where: Here, only voltage signals are used. An important
Vd is the direct axis component; characteristic of data acquisition is related to the sampling
i is the sample number; frequency utilized by DFRs. The low sampling rates of
∆t is the time step. commercially available DFRs (usually in between 15 kHz and
20 kHz) is a limitation for fault location methods based on
In the literature, difference quantities are widely used in travelling waves. A 50 µs time step was used in ATP
protective relaying algorithms [10]. In this work, [cdif]2 will be simulations to simulate DFRs with 20 kHz sampling frequency
used to detect de initial transient instants in monitored (333 samples/cycle). Keeping the number of samples/cycle the
terminals. [cdif]2 makes the transient detection more robust same, smaller time steps would be even more appropriate to
because coefficient related to transient signals are amplified reduce errors produced by numerical integration methods.
and coefficients related to normal conditions of the system are Anyway, even with this limitation, algorithms based on
kept with low magnitude. An example of transient detection travelling waves are more reliable than those based on
using Tdq0 is shown in Fig. 3. fundamental frequency components.
5
x 10
2 B. Orthogonal Voltage Phasors (Static Reference Frame)
PhaseA
Voltage Signal (V)

1 The Tdq0’s input variables are orthogonal phasors obtained

Three-phase

PhaseB
through Clarke’s transformation which calculates the aerial
(a)

0 PhaseC

-1 modes (Vα, Vβ) and the ground mode (V0):

-2
 1 1 1 
0.8 0.9 1 1.1 1.2 1.3 1.4
Sample Number
1.5 1.6 1.7 1.8
V 0   2 2 2  V A 
 
4

− 1  ⋅ V B 
2  . (3)
Direct Axis Componente - V d (p.u.)

x 10
Vα  = ⋅
3 
1 −1
2 2 
V β   0  
− 3  V C 
0.5
  3
 2 2
(b)

0
Here, only aerial modes are used because their propagation
velocity is higher than those of ground mode waves. Vα and Vβ
-0.5
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 are used as Tdq0’s inputs variables in order to obtain the
Sample Number 4
x 10 orthogonal voltage phasors in a rotating reference frame. Note
4
that Clarke’s transformation is used here only as an operator to
x 10
obtain the orthogonal voltage phasors in a static reference
Difference Coefficients

3
2
system, differently from other applications where it is used to
c dif (p.u.)

1 decouple the three-phase voltage system [11]. Then, the

(c)

0 application of the method does not depend on the transmission

-1 line transposition scheme, i.e., it may be applicable to
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 untransposed lines as well.
Sample Number 4
Square of the Difference Coefficients

x 10
x 10
8 C. Orthogonal Voltage Phasors (Rotating Reference Frame)
10 This is the most important step in the proposed algorithm
because it makes possible the analysis of the aerial modes (Vα,
[c dif ]2

Vβ) using a rotating reference frame, allowing the correct

(d)

transient detection. Park’s transformation is applied to the

0 output voltage signals of Clarke’s transformation to obtain the
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
Sample Number 4
voltage Vd, used to determine the fault location:
x 10

Fig. 3. Transient detection from a double phase to ground fault using Tdq0: V d   cos (ω ⋅ t + θ ) − sin (ω ⋅ t + θ ) Vα  .
V  =  ⋅ 
(4)
 q   sin (ω ⋅ t + θ ) cos (ω ⋅ t + θ )  V β 
(a) Three-phase voltage signal; (b) Direct axis component Vd; (c) Difference
coefficients cdif; (d) Square of the difference coefficients [cdif]2.
Where:
IV. METHOD IMPLEMENTATION ω is the angular power frequency;
The proposed method implementation is divided into five t is the DFRs clock synchronized by GPS;
steps: (a) voltage data acquisition using DFRs in both line θ is the angle between Vd and the voltage phasor at phase A
ends, (b) calculation of an orthogonal voltage phasor in a static (see Fig. 2b).
 Apparently, the non alignment of Vd with the voltage phasor E. Fault Location Estimation
of the phase A may pose a problem. As illustrated in Fig. 2, if Voltage signals from both transmission line ends are used
θ is greater than zero, a constant non-zero Vd signal is obtained to detect the first transient instants t11 and t21 at buses 1 and 2
when the system is operating at normal conditions and, so, (as shown in Fig. 1). The identification of t11 and t21 is shown
transients may be wrongly detected. Here, the cdif coefficients in Fig. 5.
overcome that problem because, even getting constant non- Once t11 and t21 (in seconds), the line length and the
zero Vd signals, each cdif coefficient would be nearly zero. propagation velocity of aerial modes are known, (1) is used to
Therefore, the proposed method does not require alignment calculate the fault point location.
between Vd component and the voltage phasor of the phase A 5
x 10

Voltage Signal - Bus 1 (V)

to detect transients correctly. Another good characteristic of 2
PhaseA
the method is that only current voltage samples are used in the 1

Three-phase
PhaseB
calculation of Vd coefficients, simplifying the implementation PhaseC

(a)
0
and making possible the fault location almost immediately -1
after its occurrence. Other techniques as DWT and RDWT,
-2
utilize more than one voltage or current sample of each phase 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4
to calculate coefficients for the transient analysis of the Sample Number 4
x 10
5
x 10
system, making fault location a more complex procedure.

Voltage Signal - Bus 2 (V)

2
PhaseA
D. Detection of the Initial Transient Instants 1

Three-phase
PhaseB
In a two-terminals fault location method, [cdif]2 from both PhaseC
(b)
0

line ends must be calculated. The analysis of the [cdif]2 -1

coefficients allows the identification of the sample number in -2
which occur initial transients. So, to use (1) to estimate de fault 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4
Sample Number 4
point, it is necessary to obtain the initial transient instants in x 10

seconds. [cdif]2 with magnitude below a given preset threshold

7
x 10
[cdif ] 2 coefficients - Bus 1

6 t11 Initial transient

are eliminated and, so, coefficients related to noise and low
frequency oscillation are ignored. Consequently, only [cdif]2 4 instants detection
(c)

coefficients related to transients by the fault occurrence are 2

considered.
0
As shown in Fig. 4, first non-zero [cdif]2 occurs one sample
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4
after the transient beginning. Finally, considering the sampling Sample Number 4
x 10
frequency Fs used by DFRs, the initial transient instants ttransient 7
x 10
t21
[cdif ] 2 coefficients - Bus 2

(in seconds) may be determined according to (5a) and (5b).

8
6
4
(d)

2
0

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4
Sample Number 4
x 10
Fig. 5. Example of the initial transient instants detection in both terminals of
the transmission line through the [cdif]2 analysis: (a) Three-phase voltage
signals at Bus 1; (b) Three-phase voltage signals at Bus 2; (c) [cdif]2
coefficients related to Bus 1; (d) [cdif]2 coefficients related to Bus 2.

V. SIMULATION STUDIES

A. Simulation Model
ATP [12] simulations of the 230 kV system presented in
Fig. 6 were performed to evaluate the proposed method. The
Fig. 4. Detection of the initial transient instants through the [cdif]2 analysis.
system parameters are shown in Table I. A constant
If [c dif ( i ) ]2 = 0 ⇒ t transient = {} ; (5a) distributed-parameter transmission line model with a 50 µs
[
If c dif (i ) ]
2
> 0 ⇒ t transient = (i − 1) F s ; (5b)
time step was used. The line length is 500 km and the distance
d from bus 1 to the fault point is to be calculated. All
Where: algorithm steps were implemented using the MODELS
ttransient is the initial transient instant in seconds; language [13] and performed directly in the ATP one sample
cdif is the difference coefficients calculated from Vd; at a time similar to what occurs in real time protection system,
i is the sample number. with no need to analyze off line oscillographic records.
 TABLE II
FAULT LOCATION SIMULATIONS FOR TRANSPOSED TRANSMISSION LINE
Fault No of simulated No of reliable Reliable
type cases simulations simulations (%)
AG 960 949 98.85%
BG 960 949 98.85%
CG 960 949 98.85%
Fig. 6. Three-phase system considered in ATP simulations. AB 960 960 100.00%
TABLE I BC 960 960 100.00%
SYSTEM PARAMETERS CA 960 960 100.00%
SOURCE A SOURCE B TRANSMISSION LINE ABG 960 960 100.00%
VG1 = 1,014∠10o pu VG 2 = 1,000∠0o pu l = 500 km BCG 960 960 100.00%
Z0 = 0,236 + j1,035Ω km
R0 = 1,445 Ω = 1,445 Ω
G1 G2 CAG 960 960 100.00%
R0
= 2,49 µmho / km
shunt
L0
G1
= 13,996 mH L0
G2
= 13,996 mH Y0 ABC 960 960 100.00%
Z + = 0,054 + j0,527 Ω km Total: 9600 9567 99.66%
= 1,963Ω = 1,963Ω
G1 G2
R+ R+
= 3,144 µmho / km
shunt
L+
G1
= 14,982 mH L+
G2
= 14,982 mH Y+
TABLE III
B. Applied Disturbances FAULT LOCATION SIMULATIONS FOR UNTRANSPOSED TRANSMISSION LINE
Fault No of simulated No of reliable Reliable
For validation purposes, situations where the transmission
type cases simulations simulations (%)
line is transposed and untransposed were analyzed. For each
AG 960 944 98.33%
type of transposition scheme, 9600 different cases were run, BG 960 947 98.65%
totaling 19200 different cases in which fault parameters were CG 960 950 98.96%
changed: the fault resistance (5 Ω to 95 Ω with steps of 30 Ω), AB 960 954 99.38%
the fault inception angle (0° to 180° with steps of 20°) and the BC 960 960 100.00%
distance from fault point to Bus 1 (20 km to 480 km with steps CA 960 954 99.38%
of 20 km). Digital simulations were performed for phase to ABG 960 955 99.48%
ground, double phase, double phase to ground and three-phase BCG 960 960 100.00%
faults. The most adverse cases were considered, as high fault CAG 960 959 99.90%
resistance cases, fault inception angle near to zero (or at zero ABC 960 960 100.00%
crossing) and faults very close to the substations. Total: 9600 9543 99.41%
To perform such a high quantity of simulations, batch files
were created with Matlab® to allow the automatic run of the In Table IV is shown a general analysis of the simulations
ATP files. in which transposed line and untransposed line cases are
considered.
C. Simulation Results and Analysis In Table V, unreliable simulations cases are analyzed. As
As shown in Table II and Table III, all results show the expected, in most of unreliable simulations the errors are
reliability of the fault location method. It is important to point related to high impedance fault cases and situations in which
out that the maximum expected error is a function of the fault inception angle is nearly to zero.
sampling rates, i.e., it is a hardware limitation. The travel time According to the results, less than 0.5% of 19200
of waves is not interpolated and, thus, the initial transient performed cases diverged. Approximately 70% of unreliable
instants are approximated to the nearly multiple of the time results are related to high impedance fault cases and only
step ∆t used by DFRs. In this way, errors in the order of a half about 6% are related to fault inception angle nearly to zero
time step can be introduced in the calculated initial transient crossing cases. So, the proposed method for fault location
instants and are considered to be admissible errors. So, the presents low sensitivity in front of adverse cases related to
module of such admissible errors is calculated using (6). fault resistance and fault inception angle.
e ≈ (∆ t ⋅ c ) 2 (6) TABLE IV
Where: GENERAL RESULTS OF FAULT LOCATION SIMULATIONS
c is the speed of light (≈ 3.105 km/s). Considered No of No of No of Reliable
system simulated unreliable reliable simulations
For the used 20 kHz sampling frequency, the admissible cases simulations simulations (%)
error is approximately 7.5 km in absolute value. This value is Transposed 9600 33 9567 99.66%
used as the error threshold throughout the analysis of the Untransposed 9600 57 9543 99.41%
results. So, cases in which the fault location estimation Total: 19200 90 19110 99.53%

presents error above such threshold are classified as unreliable

cases.
 TABLE V The proposed method was applied to transmission lines
ANALYSIS OF UNRELIABLE SIMULATION RESULTS
taking into account the influence of fault resistance, voltage
Considered system Transp. Untransp. Total: inception angle and the transmission line transposition scheme.
Case analysis
An analysis of the effect of the sampling frequency on the
No of unreliable 33 57 90 method’s accuracy was performed. The algorithm was
simulations (100.00%) (100.00%) (100.00%) implemented in ATP using the MODELS language. Batch files
No of cases related to 22 41 63 were created with Matlab® to allow the automatic run of the
high impedance fault (66.67%) (71.93%) (70.00%) ATP files. A total of 19200 EMTP simulations for a 230 kV
(>60 Ω)
transmission line were performed. In more than 99% of the
No of cases related to fault 0 6 6
inception angle nearly to (0.00%) (10.53%) (6.67%) simulated cases, the proposed algorithm presented errors
zero crossing (< 10°) below the admissible value.
No of cases related to 11 10 21 Finally, the proposed method is very simple, fairly accurate,
unknown reasons (33.33%) (17.54%) (23.33%) do not require phasor estimation and may be used as an
The sampling frequency used by DFRs is a limitation of additional routine in transmission lines protective relays.
fault location methods based on the theory of travelling waves.
VII. ACKNOWLEDGMENT
In fact, increasing the sampling frequency Fs, the maximum
expected error decreases and a greater accuracy is obtained. In The authors would like to thank the reviewers for
order to address such considerations, some faults in the system invaluable suggestions.
shown in Fig. 6 were performed using a transposed
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